Satellite Geodesy - Foundations, Methods and Applications

Seeber Satellite Geodesy Günter Seeber Satellite Geodesy 2nd completely revised and extended edition Walter de Gruyter Berlin New York 2003 Author Günter Seeber Univ Prof DrIng Institut für Erdmessung Universität Hannover Schneiderberg 50 30167 Hannover Germany 1st edition 1993 This book contains 281 figures and 64 tables Printed on acidfree paper which falls within the guidelines of the ANSI to ensure permanence and durability Library of Congress CataloginginPublication Data Seeber Günter 1941 Satellitegeodaesie English Satellite geodesy foundations methods and applications Günter Seeber 2nd completely rev and extended ed p cm Includes bibliographical references and index ISBN 3110175495 alk paper QB343 S3431 2003 5261dc21 2003053126 ISBN 3110175495 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie detailed bibliographic data is available in the Internet at httpdnbddbde Copyright 2003 by Walter de Gruyter GmbH Co KG 10785 Berlin All rights reserved including those of translation into foreign languages No part of this book may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying recording or any information storage and retrieval system without permission in writing from the publisher Printed in Germany Cover design Rudolf Hübler Berlin Typeset using the authors TeX files I Zimmermann Freiburg Printing and binding Hubert Co GmbH Co Kg Göttingen To the memory of my grandson Johannes Preface Methods of satellite geodesy are increasingly used in geodesy surveying engineering and related disciplines In particular the modern development of precise and opera tional satellite based positioning and navigation techniques have entered all fields of geosciences and engineering A growing demand is also evident for finestructured gravity field models from new and forthcoming satellite missions and for the monitor ing of Earths rotation in space For many years I have had the feeling that there is a definite need for a systematic textbook covering the whole subject including both its foundations and its applications It is my intention that this book should at least in part help to fulfill this requirement The material presented here is partly based on courses taught at the University of Hannover since 1973 and on guest lectures given abroad It is my hope that this mate rial can be used at other universities for similar courses This book is intended to serve as a text for advanced undergraduates and for graduates mainly in geodesy survey ing engineering photogrammetry cartography and geomatics It is also intended as a source of information for professionals who have an interest in the methods and results of satellite geodesy and who need to acquaint themselves with new developments In addition this book is aimed at students teachers professionals and scientists from related fields of engineering and geosciences such as terrestrial and space navigation hydrography civil engineering traffic control GIS technology geography geology geophysics and oceanography In line with this objective the character of the book falls somewhere between that of a textbook and that of a handbook The background required is an undergraduate level of mathematics and elementary mathematical statis tics Because of rapid and continuous developments in this field it has been necessary to be selective and to give greater weight to some topics than to others Particular importance has been attached to the fundamentals and to the applications especially to the use of artificial satellites for the determination of precise positions A compre hensive list of references has been added for further reading to facilitate deeper and advanced studies The first edition of this book was published in 1993 as an English translation and update of the book Satellitengeodäsie that was printed in the German language in 1989 The present edition has been completely revised and significantly extended The fundamental structure of the first edition has been maintained to facilitate continuity of teaching however outdated material has been removed and new material has been included All chapters have been updated and some have been rewritten The overall status is autumn 2002 but some of the most recent technological developments to March 2003 have been included Extensions and updates mainly pertain to reference coordinate systems and refer ence frames 22 signal propagation 23 directions with CCD technology 52 the Global Positioning System GPS and GNSS 7 satellite laser ranging 8 satellite viii Preface altimetry 9 gravity field missions 10 and applications 12 In particular the chap ter on GPS and GNSS 7 has been almost completely rewritten and now covers about 200 pages Together with chapters 2 3 and 12 it forms a comprehensive GPS manual on its own New technological developments of the space and user segment are included as is the current state of data analysis and error budget Differential GPS and permanent reference networks are now treated in a comprehensive section of their own 75 GLONASS and the forthcoming GALILEO are included in a new section on GNSS 77 Gravity field missions like CHAMP GRACE and GOCE because of their increas ing importance are dealt with in a new chapter 10 VLBI together with the new inclusion of interferometric SAR form another new chapter 11 Coverage of histor ical techniques like photographic camera observations 5 and Transit Doppler 6 has been considerably reduced The basic principles however are still included because of their historical importance and because they are shared by new technologies like CCD cameras 52 and DORIS 67 The geodetic history of Transit Doppler tech niques in addition is an excellent source for understanding the evolution and basic concepts of the GPS The chapter on applications now renumbered 12 has been updated to include modern developments and a new section on the combination of geodetic space techniques 125 International services of interest to satellite geodesy have been included namely the IGS 781 the ILRS 851 the IVS 1113 and the IERS 124 The bibliography has been updated and expanded considerably by adding an in creased number of English language references The total number of references is now reaching 760 about half of which are new in this edition Many of the examples within this book are based on field projects and research work carried out in collaboration with my graduate students doctorate candidates and scientific colleagues at the University of Hannover over more than 20 years I would like to thank all these individuals for their long standing cooperation and the many fruitful discussions I have had with them In addition the help of the staff at the Institut für Erdmessung is gratefully acknowledged Most figures have been redrawn by cand geod Anke Daubner and DiplIng Wolfgang Paech My sincere thanks for checking and correcting the English language go to Dr Graeme Eagles of the Alfred Wegener Institut für Polar und Meeresforschung Bremerhaven I should also like to thank the many colleagues from all over the world who helped to improve the book through their comments on the first edition and the individuals and organizations who provided illustrations Finally my gratitude goes to my wife Gisela for her never ending support and under standing The publisher remained excellently cooperative throughout the preparation of this book My cordial thanks go to Dr Manfred Karbe Dr Irene Zimmermann and the staff at Walter de Gruyter Hannover May 2003 Günter Seeber Contents Preface vii Abbreviations xvii 1 Introduction 1 11 Subject of Satellite Geodesy 1 12 Classification and Basic Concepts of Satellite Geodesy 3 13 Historical Development of Satellite Geodesy 5 14 Applications of Satellite Geodesy 7 15 Structure and Objective of the Book 9 2 Fundamentals 10 21 Reference Coordinate Systems 10 211 Cartesian Coordinate Systems and Coordinate Transformations 10 212 Reference Coordinate Systems and Frames in Satellite Geodesy 12 2121 Conventional Inertial Systems and Frames 13 2122 Conventional Terrestrial Systems and Frames 15 2123 Relationship between CIS and CTS 17 213 Reference Coordinate Systems in the Gravity Field of Earth 21 214 Ellipsoidal Reference Coordinate Systems 23 215 Ellipsoid Geoid and Geodetic Datum 25 216 World Geodetic System 1984 WGS 84 28 217 Threedimensional Eccentricity Computation 30 22 Time 31 221 Basic Considerations 31 222 Sidereal Time and Universal Time 32 223 Atomic Time 35 224 Ephemeris Time Dynamical Time Terrestrial Time 37 225 Clocks and Frequency Standards 39 23 Signal Propagation 42 231 Some Fundamentals of Wave Propagation 43 2311 Basic Relations and Definitions 43 2312 Dispersion Phase Velocity and Group Velocity 45 2313 Frequency Domains 46 232 Structure and Subdivision of the Atmosphere 48 233 Signal Propagation through the Ionosphere and the Troposphere 52 2331 Ionospheric Refraction 54 2332 Tropospheric Refraction 56 x Contents 3 Satellite Orbital Motion 62 31 Fundamentals of Celestial Mechanics TwoBody Problem 62 311 Keplerian Motion 63 312 Newtonian Mechanics TwoBody Problem 66 3121 Equation of Motion 66 3122 Elementary Integration 69 3123 Vectorial Integration 74 313 Orbit Geometry and Orbital Motion 77 32 Perturbed Satellite Motion 82 321 Representation of the Perturbed Orbital Motion 84 3211 Osculating and Mean Orbital Elements 84 3212 Lagranges Perturbation Equations 85 3213 Gaussian Form of Perturbation Equation 87 322 Disturbed Motion due to Earths Anomalous Gravity Field 88 3221 Perturbation Equation and Geopotential 89 3222 Perturbations of the Elements 94 3223 Perturbations Caused by the Zonal Coefficients Jn 96 323 Other Perturbations 98 3231 Perturbing Forces Caused by the Sun and Moon 98 3232 Solid Earth Tides and Ocean Tides 101 3233 Atmospheric Drag 102 3234 Direct and Indirect Solar Radiation Pressure 104 3235 Further Perturbations 105 3236 Resonances 107 324 Implications of Perturbations on Selected Satellite Orbits 108 33 Orbit Determination 109 331 Integration of the Undisturbed Orbit 110 332 Integration of the Perturbed Orbit 114 3321 Analytical Methods of Orbit Integration 114 3322 Numerical Methods of Orbit Integration 116 3323 Precise Orbit Determination with Spaceborne GPS 119 333 Orbit Representation 120 3331 Ephemeris Representation for Navigation Satellites 121 3332 Polynomial Approximation 122 3333 Simplified Short Arc Representation 124 34 Satellite Orbits and Constellations 126 341 Basic Aspects 126 342 Orbits and Constellations 128 343 Sunsynchronous Geostationary and Transfer Orbits 131 Contents xi 4 Basic Observation Concepts and Satellites Used in Geodesy 135 41 Satellite Geodesy as a Parameter Estimation Problem 135 42 Observables and Basic Concepts 139 421 Determination of Directions 139 422 Determination of Ranges 141 423 Determination of Range Differences Doppler method 143 424 Satellite Altimetry 144 425 Determination of Ranges and RangeRates SatellitetoSatellite Tracking 144 426 Interferometric Measurements 145 427 Further Observation Techniques 147 43 Satellites Used in Geodesy 147 431 Basic Considerations 147 432 Some Selected Satellites 149 433 Satellite Subsystems 152 4331 Drag Free Systems 152 4332 Attitude Control 153 4333 Navigation Payload PRARE 154 434 Planned Satellites and Missions 156 44 Some Early Observation Techniques Classical Methods 158 441 Electronic Ranging SECOR 159 442 Other Early Observation Techniques 160 5 Optical Methods for the Determination of Directions 161 51 Photographic Determination of Directions 161 511 Satellites used for Camera Observations 162 512 Satellite Cameras 163 513 Observation and Plate Reduction 164 514 Spatial Triangulation 169 515 Results 170 52 Directions with CCD Technology 172 521 Image Coordinates from CCD Observations 172 522 Star Catalogs Star Identification and Plate Reduction 174 523 Applications Results and Prospects 176 53 Directions from Space Platforms 176 531 Star Tracker 177 532 Astrometric Satellites HIPPARCOS 177 533 Planned Missions 178 6 Doppler Techniques 181 61 Doppler Effect and Basic Positioning Concept 183 62 One Successful Example The Navy Navigation Satellite System 186 621 System Architecture 187 622 Broadcast and Precise Ephemerides 188 xii Contents 63 Doppler Receivers 190 631 Basic concept 190 632 Examples of Doppler Survey Sets 192 64 Error Budget and Corrections 193 641 Satellite Orbits 194 642 Ionospheric and Tropospheric Refraction 195 643 Receiver System 196 644 Earth Rotation and Relativistic Effects 197 645 Motion of the Receiver Antenna 198 65 Observation Strategies and Adjustment Models 199 651 Extended Observation Equation 199 652 Single Station Positioning 201 653 MultiStation Positioning 202 66 Applications 203 661 Applications for Geodetic Control 204 662 Further Applications 205 67 DORIS 207 7 The Global Positioning System GPS 211 71 Fundamentals 211 711 Introduction 211 712 Space Segment 213 713 Control Segment 217 714 Observation Principle and Signal Structure 218 715 Orbit Determination and Orbit Representation 222 7151 Determination of the Broadcast Ephemerides 222 7152 Orbit Representation 223 7153 Computation of Satellite Time and Satellite Coordinates 225 7154 Structure of the GPS Navigation Data 227 716 Intentional Limitation of the System Accuracy 229 717 System Development 230 72 GPS Receivers User Segment 234 721 Receiver Concepts and Main Receiver Components 234 722 Code Dependent Signal Processing 239 723 Codeless and Semicodeless Signal Processing 240 724 Examples of GPS receivers 243 7241 Classical Receivers 243 7242 Examples of Currently Available Geodetic Receivers 245 7243 Navigation and Handheld Receivers 248 725 Future Developments and Trends 250 73 GPS Observables and Data Processing 252 Contents xiii 731 Observables 252 7311 Classical View 252 7312 Code and Carrier Phases 255 732 Parameter Estimation 258 7321 Linear Combinations and Derived Observables 258 7322 Concepts of Parametrization 265 7323 Resolution of Ambiguities 269 733 Data Handling 277 7331 Cycle Slips 277 7332 The Receiver Independent Data Format RINEX 281 734 Adjustment Strategies and Software Concepts 283 735 Concepts of Rapid Methods with GPS 289 7351 Basic Considerations 289 7352 Rapid Static Methods 290 7353 Semi Kinematic Methods 292 7354 Pure Kinematic Method 294 736 Navigation with GPS 295 74 Error Budget and Corrections 297 741 Basic Considerations 297 742 Satellite Geometry and Accuracy Measures 300 743 Orbits and Clocks 304 7431 Broadcast Ephemerides and Clocks 304 7432 Precise Ephemerides and Clocks IGS 307 744 Signal Propagation 309 7441 Ionospheric Effects on GPS Signals 309 7442 Tropospheric Propagation Effects 314 7443 Multipath 316 7444 Further Propagation Effects Diffraction and Signal Interference 319 745 Receiving System 320 7451 Antenna Phase Center Variation 320 7452 Other Error Sources Related to the Receiving System 323 746 Further Influences Summary the Issue of Integrity 323 75 Differential GPS and Permanent Reference Networks 325 751 Differential GPS DGPS 326 7511 DGPS Concepts 326 7512 Data Formats and Data Transmission 329 7513 Examples of Services 332 752 Real Time Kinematic GPS 336 753 Multiple Reference Stations 338 7531 Wide Area Differential GPS 339 7532 High Precision Networked Reference Stations 341 xiv Contents 76 Applications 345 761 Planning and Realization of GPS Observation 345 7611 Setting Up an Observation Plan 346 7612 Practical Aspects in Field Observations 348 7613 Observation Strategies and Network Design 350 762 Possible Applications and Examples of GPS Observations 356 7621 Geodetic Control Surveys 357 7622 Geodynamics 362 7623 Height Determination 366 7624 Cadastral Surveying Geographic Information Systems 368 7625 Fleet Management Telematics Location Based Services 371 7626 Engineering and Monitoring 372 7627 Precise Marine Navigation Marine Geodesy and Hydrography 375 7628 Photogrammetry Remote Sensing Airborne GPS 378 7629 Special Applications of GPS 380 77 GNSS Global Navigation Satellite System 383 771 GLONASS 384 772 GPSGLONASS Augmentations 392 773 GALILEO 393 78 Services and Organizations Related to GPS 397 781 The International GPS Service IGS 397 782 Other Services 401 8 Laser Ranging 404 81 Introduction 404 82 Satellites Equipped with Laser Reflectors 406 83 Laser Ranging Systems and Components 411 831 Laser Oscillators 411 832 Other System Components 412 833 Currently Available Fixed and Transportable Laser Systems 414 834 Trends in SLR System Developments 416 84 Corrections Data Processing and Accuracy 418 841 Extended Ranging Equation 418 842 Data Control Data Compression and Normal Points 422 85 Applications of Satellite Laser Ranging 424 851 Realization of Observation Programs International Laser Ranging Service ILRS 424 852 Parameter Estimation 427 853 Earth Gravity Field Precise Orbit Determination POD 428 854 Positions and Position Changes 431 Contents xv 855 Earth Rotation Polar Motion 432 856 Other applications 435 86 Lunar Laser Ranging 436 87 Spaceborne Laser 441 9 Satellite Altimetry 443 91 Basic Concept 443 92 Satellites and Missions 444 93 Measurements Corrections Accuracy 451 931 Geometry of Altimeter Observations 451 932 Data Generation 452 933 Corrections and Error Budget 454 94 Determination of the Mean Sea Surface 460 95 Applications of Satellite Altimetry 461 951 Geoid and Gravity Field Determination 462 952 Geophysical Interpretation 464 953 Oceanography and Glaciology 465 10 Gravity Field Missions 469 101 Basic Considerations 469 102 SatellitetoSatellite Tracking SST 473 1021 Concepts 473 1022 HighLow Mode CHAMP 476 1023 LowLow Mode GRACE 477 103 Satellite Gravity Gradiometry 480 1031 Concepts 480 1032 GOCE mission 482 11 Related Space Techniques 485 111 Very Long Baseline Interferometry 485 1111 Basic Concept Observation Equations and Error Budget 485 1112 Applications 491 1113 International Cooperation International VLBI Service IVS 496 1114 VLBI with Satellites 498 112 Interferometric Synthetic Aperture Radar InSAR 500 1121 Basic Concepts Synthetic Aperture Radar SAR 500 1122 Interferometric SAR 502 1123 Differential Radar Interferometry 505 12 Overview and Applications 506 121 Positioning 506 1211 Concepts Absolute and Relative Positioning 506 1212 Global and Regional Networks 510 1213 Operational Positioning 511 xvi Contents 122 Gravity Field and Earth Models 514 1221 Fundamentals 514 1222 Earth Models 519 123 Navigation and Marine Geodesy 523 1231 Possible Applications and Accuracy Requirements in Marine Positioning 523 1232 Marine Positioning Techniques 524 124 Geodynamics 527 1241 Recent Crustal Movements 527 1242 Earth Rotation Reference Frames IERS 529 125 Combination of Geodetic Space Techniques 534 1251 Basic Considerations 534 1252 Fundamental Stations 535 1253 Integrated Global Geodetic Observing System IGGOS 537 References 539 Index 575 Abbreviations ACP Area Correction Parameter ADOS African Doppler Survey AI I Accuracy Improvement Initiative APL Applied Physics Laboratory ARP Antenna Reference Point AS Anti Spoofing ASIC ApplicationSpecific Integrated Circuit BCRS Barycentric Celestial Reference System BIH Bureau International de lHeure BIPM Bureau International des poids et Mésures BKG Bundesamt für Kartographie und Geodäsie BPS Bits Per Second BPSK Binary Phase Shift Keying CACS Canadian Active Control System CAD Computer Assisted Design CBIS Central Bureau IGS Information System CCD Charge Coupled Device CDP Crustal Dynamics Program CEP Celestial Ephemeris Pole CEP Circular Error Probable CIO Conventional International Origin CIP Celestial Intermediate Pole CIS Conventional Inertial Reference System CNES Centre National dÉtudes Spatiales CONUS Continental US CORS Continuously Operating Reference Station CPU Central Processing Unit CRF Celestial Reference Frame CRS Celestial Reference System CTP Conventional Terrestrial Pole CTS Conventional Terrestrial Refer ence System DÖDOC German Austrian Doppler Campaign DD Double Difference DEM Digital Elevation Model DGFI Deutsches Geodätisches Forschungsinstitut DGPS Differential GPS DOD Department of Defence DOP Dilution of Precision DOY Day Of the Year DRMS Distance Root Mean Square EDOC European Doppler Campaign EGM96 Earth Gravitational Model 1996 EGNOS European Geostationary Naviga tion Overlay System EOP Earth Orientation Parameter EOS Earth Observing System EPS RealTime Positioning Service SAPOS ERM Exact Repeat Mission ERP Earth Rotation Parameter ESA European Space Agency ESNP European Satellite Navigation Program EU European Union FAA Federal Aviation Administration FAGS Federation of Astronomical and Geophysical Data Analysis Services FIG Fédération Internationale des Géomètres FK5 Fifth Fundamental Catalogue FOC Full Operational Capability FRNP Federal Radio Navigation Plan xviii Abbreviations GAST Greenwich Apparent Sidereal Time GCRS Geocentric Celestial Reference System GDR Geophysical Data Record GEM Goddard Earth Model GEO Geostationary Orbit GFO GEOSAT Follow On GFZ GeoForschungsZentrum Potsdam GIC GPS Integrity Channel GIS Geo Information System GLAS Geoscience Laser Altimeter System GM Geodetic Mission GMST Greenwich Mean Sidereal Time GNSS Global Navigation Satellite System GRGS Groupe de Recherche de Géodésie Spatiale GRS80 Geodetic Reference System 1980 GSFC Goddard Space Flight Center HEPS High Precision RealTime Posi tioning Service SAPOS IAU InternationalAstronomical Union ICD Interface Control Document ICO Intermediate Circular Orbit ICRF International Celestial Reference Frame ICRS International Celestial Reference System IDS International DORIS Service IERS International Earth Rotation and Reference Systems Service IF Intermediate Frequency IGEB Interagency GPS Executive Board IGN Institut Géographique National IGS International GPS Service IGSO Inclined Geosynchronous Orbit ILRS International Laser Ranging Service ILS International Latitude Service INSAR Interferometric SAR ION Institute of Navigation IPMS International Polar Motion Service IRIS International Radio Interferomet ric Surveying IRM IERS Reference Meridian IRP IERS Reference Pole IRV InterRange Vector ITRF International Terrestrial Reference Frame IUGG International Union of Geodesy and Geophysics IVS International VLBI Service JD Julian Date JGM Joint Gravity Model JGR Journal of Geophysical Research JPL Jet Propulsion Laboratory LADGPS Local Area Differential GPS LAN Longitude of Ascending Node LBS Location Based Service LEO Low Earth Orbiter LLR Lunar Laser Ranging LOD Length of Day MAS Milli Arc Second MEO Medium Earth Orbit MERIT Monitoring Earth Rotation and Intercomparison of Techniques MJD Modified Julian Date MSAS Multifunctional Satellitebased Augmentation System NAD North American Datum NASA National Aeronautics and Space Administration NdYAG Neodymium Yttrium Aluminium Garnet NDGPS Nationwide Differential Global Positioning System NEOS National Earth Orientation Service NGS National Geodetic Survey NIMA National Imagery and Mapping Agency Abbreviations xix NIST National Institute of Standards NOAA National Oceanic and Atmo spheric Administration OCS Operational Control Segment PCV Phase Center Variation PDA Personal Digital Assistant PDGPS Precise Differential GPS PDOP Position Dilution of Precision PE Precise Ephemerides POD Precise Orbit Determination PPP Precise Point Positioning PPS Precise Positioning Service PRN Pseudo Random Noise PTB Physikalisch Technische Bundesanstalt RA Radar Altimeter RDS Radio Data System RF Radio Frequency RMS Root Mean Square Error RNAAC Regional Network Associate Analysis Center RTCM Radio Technical Commission for Marine Sciences RTK Real Time Kinematic SA Selective Availability SAD South American Datum SAO Smithsonian Astrophysical Observatory SAPOS Satellite Positioning Service SAR Search And Rescue SAR Synthetic Aperture Radar SBAS Satellite Based Augmentation System SEP Spherical Error Probable SGG Satellite Gravity Gradiometry SI International System of Units SIR Shuttle Imaging Radar SIS Signal in Space SISRE Signal in Space Range Error SLR Satellite Laser Ranging SNR SignaltoNoise Ratio SPAD Single Photon Avalanche Diode SPS Standard Positioning Service SST SatellitetoSatellite Tracking SST Sea Surface Topography SV Space Vehicle SVN Space Vehicle Number SWH Significant Wave Height TP TOPEXPOSEIDON TAI International Atomic Time TCB Barycentric Coordinate Time TCG Geocentric Coordinate Time TDB Barycentric Dynamical Time TDT Terrestrial Dynamical Time TEC Total Electron Content TECU Total Electron Content Unit TID Travelling Ionospheric Disturbances TIGO Transportable Integrated Geodetic Observatory TRF Terrestrial Reference Frame TT Terrestrial Time TTFA Time To Fix Ambiguities UEE User Equipment Error UERE User Equivalent Range Error URE User Range Error USCG US Coast Guard USNO US Naval Observatory UT Universal Time UTC Universal Time Coordinated VLBA Very Long Baseline Array VLBI Very Long Baseline Interferometry VRS Virtual Reference Station VSOP VLBI Space Observatory Program VTEC Vertical Electron Content WAAS Wide Area Augmentation System WADGPS Wide Area Differential GPS Following the classical definition of Helmert 18801884 geodesy is the science of the measurement and mapping of the Earths surface This definition includes the determination of the terrestrial external gravity field as well as the surface of the ocean floor cf Torge 2001 Satellite Geodesy comprises the observational and computational techniques which allow the solution of geodetic problems by the use of precise measurements to from or between artificial mostly nearEarth satellites Further to Helmerts definition which is basically still valid the objectives of satellite geodesy are today mainly considered in a functional way They also include because of the increasing observational accuracy timedependent variations The basic problems are 1 determination of precise global regional and local threedimensional positions eg the establishment of geodetic control 2 determination of Earths gravity field and linear functions of this field eg a precise geoid 3 measurement and modeling of geodynamical phenomena eg polar motion Earth rotation crustal deformation The use of artificial satellites in geodesy has some prerequisites these are basically a comprehensive knowledge of the satellite motion under the influence of all acting forces as well as the description of the positions of satellites and ground stations in suitable reference frames Consequently satellite geodesy belongs to the domain of basic sciences On the other hand when satellite observations are used for solving various problems satellite geodesy can be assigned to the field of applied sciences Considering the nature of the problems satellite geodesy belongs equally to geosciences and to engineering sciences By virtue of their increasing accuracy and speed the methods and results of satellite geodesy are used more and more in other disciplines like eg geophysics oceanography and navigation and they form an integral part of geoinformatics Since the launch of the first artificial satellite SPUTNIK1 on October 4 1957 satellite geodesy has developed into a selfcontained field in geodetic teaching and research with close relations and interactions with adjacent fields Fig 11 The assignments and contents are due to historical development In Geodetic Astronomy based on the rules of Spherical Astronomy the orientation of the local gravity vector geographical longitude λ geographical latitude Φ and the astronomical azimuth A of a terrestrial mark are determined from the observation of natural celestial bodies particularly fixed stars By Gravity we mean the measure of gravity gravity intensity g which is the magnitude of the gravity acceleration vector g Torge 1989 With Terrestrial Geodetic Measurements horizontal angles 2 1 Introduction Figure 11 Main relations between geodetic fields of teaching and research distances zenith angles and levelled height differences are provided and serve for the determination of surface point locations Satellite Geodesy finally is based on the observation of artificial celestial bodies Directions ranges and rangerates are determined between Earth surface locations and satellites or between satellites Some measurements for instance accelerations are taken within the satellites themselves The results of geodeticastronomic or gravimetric observations are used within the field of Astronomical and Physical Geodesy for the determination of the figure and gravity field of Earth Torge 2001 In German this classical domain is called Erdmessung Torge 2003 and corresponds to the concept of Global Geodesy in the English language The main problems are the determination of a mean Earth ellipsoid and a precise geoid cf 215 The determination of coordinates in ellipsoidal or threedimensional coordinate systems mainly based on terrestrial geodetic measurements is treated within the field of Mathematical Geodesy Alternate expressions for this domain are Geometrical Geodesy or in German Landesvermessung eg Großmann 1976 The separate classification of observation and computation techniques as developed within the classical fields of geodetic teaching and practice has not occured to the same extent in satellite geodesy Here observation computation and analysis are usually treated to gether As far as global problems are concerned satellite geodesy contributes to global geodesy for example to the establishment of a global reference frame In regional and local problems satellite geodesy forms part of surveying and geoinformatics Conversely the fields of mathematical geodesy and geodetic astronomy provide important foundations in satellite geodesy with respect to reference systems The same is true for the field of astronomical and physical geodesy which provides infor mation on Earths gravity field Due to these close interactions a sharp separation of the different fields in geodesy becomes more and more difficult and it is no longer significant A combined consideration of all geodetic observables in a unified concept was developed rather early within the field of Integrated Geodesy eg Hein 1983 It 12 Classification and Basic Concepts of Satellite Geodesy 3 finds a modern realization in the establishment of integrated geodeticgeodynamic observatories see 125 Rummel et al 2000 The term Satellite Geodesy is more restrictive than the French denomination Géodésie Spatiale or the more general expression Geodetic Space Techniques The latter term includes the geodetic observation of the Moon as well as the use of planets and objects outside the solar system for instance in radio interferometry Occasionally the term Global Geodesy is used where global stands for both global measurement techniques and for global applications In this book the term Satellite Geodesy is employed because it is in common usage and because artificial nearEarth satellites are almost exclusively utilized for the observations which are of interest in applied geodesy Where necessary other space techniques are dealt with 12 Classification and Basic Concepts of Satellite Geodesy The importance of artificial satellites in geodesy becomes evident from the following basic considerations 1 Satellites can be used as high orbiting targets which are visible over large distances FollowingtheclassicalconceptsofEarthboundtrigonometricnetworks the satellites may be regarded as fixed control points within largescale or global three dimensional networks If the satellites are observed simultaneously from different New Station P1 P2 P3 N Figure 12 Geometrical method the satellite is a high target ground stations it is of no importance that the orbits of artificial satellites are governed by gravitational forces Only the property that they are targets at high altitudes is used This purely geometric consideration leads to the geometrical method of satellite geodesy The con cept is illustrated in Fig 12 It has been realized in its purest form through the BC4 World Network see 515 Compared with classical techniques the main advantage of the satellite meth ods is that they can bridge large dis tances and thus establish geodetic ties between continents and islands All ground stations belonging to the network can be determined within a uniform threedimensional global coordinate reference frame They form a polyhedron which goes around Earth As early as 1878 H Bruns proposed such a concept later known as the Cage of Bruns Bruns regarded this objective to be one of the basic problems of scientific geodesy The idea however could not be realized with classical methods and was forgotten The geometrical method of satellite geodesy is also called the direct method 4 1 Introduction because the particular position of the satellite enters directly into the solution 2 Satellites can be considered to be a probe or a sensor in the gravity field of Earth The orbital motion and the variation of the parameters describing the orbit are observed in order to draw conclusions about the forces acting Of particular interest is the relation between the features of the terrestrial gravity field and the resulting deviations of the true satellite orbit from an undisturbed Keplerian motion 311 The essential value of the satellite is that it is a moving body within Earths gravity field This view leads to the dynamical method of satellite geodesy The main advantage of satellite observations when compared with classical tech niques is that the results refer to the planet Earth as a whole and that they have a global character by nature Data gaps play a minor role Among the first spectacular results were a reasonably accurate value of Earths flattening and the proof that the figure of Earth is nonsymmetrical with respect to the equatorial plane ie the pearshape of Earth cf 122 Fig 125 p 517 In dynamical satellite geodesy orbital arcs of different lengths are considered When arc lengths between a few minutes and up to several revolutions around Earth are used we speak of short arc techniques the term for the use of longer arcs up to around 30 days and more is long arc techniques The orbits are described in suitable geocentric reference frames The satellite can thus be considered to be the bearer of New Station P1 P2 P3 P4 N Figure 13 Orbital method the satellite is a sensor in Earths gravity field its own coordinates The geocentric co ordinates of the observing ground sta tions can be derived from the known satellite orbits This socalled orbital method of coordinate determination is illustrated in Fig 13 The combined determination of gravity field parameters and geocentric coordinates within the domain of dy namical satellite geodesy leads to the general problem of parameter determi nation or parameter estimation This may include the determination of the ro tational parameters of Earth Earth rota tion polar motion as well as other geo dynamical phenomena cf 41 The dynamical method of satellite geodesy is also characterized as the indirect method because the required parameters are deter mined implicitly from the orbital behavior of the satellites The distinction geometricdynamic has for many years characterized the develop ment of satellite geodesy Today most of the current techniques have to be considered as combinations of both viewpoints A further classification of the observation techniques refers to the relation between the observation platform and the target platform We distinguish the following groups 13 Historical Development of Satellite Geodesy 5 1 Earth to Space methods directions from camera observations satellite laser ranging SLR Doppler positioning TRANSIT DORIS and geodetic use of the Global Positioning System GPS GLONASS future GNSS 2 Space to Earth methods radar altimetry spaceborne laser and satellite gradiometry 3 Space to Space methods satellitetosatellite tracking SST Earthbound methods are the most advanced because the observation process is better under control With the exception of radar altimetry the methods mentioned in 2 and 3 are still under development or in their initial operational phase 13 Historical Development of Satellite Geodesy The proper development of satellite geodesy started with the launch of the first ar tificial satellite SPUTNIK1 on October 4 1957 The roots of this development can however be identified much earlier If we include the use of the natural Earth satellite the Moon then dynamical satellite geodesy has existed since the early 19th century In 1802 Laplace used lunar nodal motion to determine the flattening of Earth to be f 1303 Other solutions came for example from Hansen 1864 with f 1296 Helmert 1884 with f 12978 and Hill 1884 with f 12972 see Wolf 1985 Torge 2001 The geometrical approach in satellite geodesy also has some forerunners in the lu nar methods These methods have undergone comprehensive developments since the beginningofthelastcentury Inthiscontext theMoonisregardedasageometrictarget where the geocentric coordinates are known from orbital theory The directions be tween the observer and the Moon are determined from relative measurements of nearby stars or from occultation of stars by the Moon Geocentric coordinates are thereby received Within the framework of the International Geophysical Year 195758 a first outcome from a global program was obtained with the Dual Rate Moon Camera developed by Markovitz 1954 The methods of this socalled Cosmic Geodesy were treated comprehensively in 1960 by Berroth Hofmann They also form a considerable part of the classical book of Mueller 1964 Introduction to Satellite Geodesy Further foundations to satellite geodesy before the year 1957 were given by the work of Väisälä 1946 Brouwer 1959 KingHele 1958 and OKeefe 1958 Therefore it was possible to obtain important geodetic results very soon after the launch of the first rockets and satellites One of the first outstanding results was the de termination of Earths flattening as f 12983 from observations of EXPLORER1 and SPUTNIK2 by OKeefe 1958 KingHele Merson 1958 Some significant 6 1 Introduction events during the years following 1957 are 1957 Launch of SPUTNIK1 1958 Earths Flattening from Satellite Data f 12983 1958 Launch of EXPLORER1 1959 Third Zonal Harmonic Pear Shape of Earth 1959 Theory of the Motion of Artificial Satellites Brouwer 1960 Launch of TRANSIT1B 1960 Launch of ECHO1 1960 Theory of Satellite Orbits Kaula 1962 Launch of ANNA1B and 1962 Geodetic Connection between France and Algeria IGN By the year 1964 many basic geodetic problems had been successfully tackled namely the determination of a precise numerical value of Earths flattening determination of the general shape of the global geoid determination of connections between the most important geodetic datums to 50 m With hindsight the development of satellite geodesy can be divided into several phases of about one decade each 1 1958 to around 1970 Development of basic methods for satellite observations and for the computation and analysis of satellite orbits This phase is characterized by the opticalphotographic determination of directions with cameras The main results were the determination of the leading harmonic coefficients of the geopotential and the publication of the first Earth models for instance the Standard Earth models of the Smithsonian Astrophysical Observatory SAO SE I to SAO SE III and the Goddard Earth Models GEM of the NASA Goddard Space Flight Center The only purely geometrical and worldwide satellite network was established by observations with BC4 cameras of the satellite PAGEOS 2 1970 to around 1980 Phase of the scientific projects New observation techniques were developed and refined in particular laser ranging to satellites and to the Moon as well as satellite altimetry The TRANSIT system was used for geodetic Doppler positioning Refined global geoid and coordinate determinations were carried out and led to improved Earth models eg GEM 10 GRIM The increased accuracy of the observations made possible the measurement of geodynamical phenomena Earth ro tation polar motion crustal deformation Doppler surveying was used worldwide for the installation and maintenance of geodetic control networks eg EDOC DÖDOC ADOS 3 1980 to around 1990 Phase of the operational use of satellite techniques in geodesy geodynamics and surveying Two aspects in particular are remarkable Satellite methods were increasingly used by the surveying community replacing conventional methods This process started with the first results obtained with the NAVSTAR Global Positioning System GPS and resulted in completely new perspectives in surveying 14 Applications of Satellite Geodesy 7 and mapping The second aspect concerned the increased observation accuracy One outcome was the nearly complete replacement of the classical astrometric techniques for monitoring polar motion and Earth rotation by satellite methods Projects for the measurement of crustal deformation gave remarkable results worldwide 4 1990 to around 2000 Phase of the international and national permanent services In particular two large international services have evolved The International Earth Rotation Service IERS initiated in 1987 and exclusively based on space techniques provides highly accurate Earth orientation parameters with high temporal resolution and maintains and constantly refines two basic reference frames These are the Inter national Celestial Reference Frame ICRF based on interferometric radio observations and the International Terrestrial Reference Frame ITRF based on different space tech niques The International GPS Service IGS started in 1994 and evolved to be the main source for precise GPS orbits as well as for coordinates and observations from a global set of more than 300 permanently observing reference stations At the national level permanent services for GPS reference data have been established and are still growing eg CORS in the USA CACS in Canada and SAPOS in Germany 5 2000 onwards After more than 40 years of satellite geodesy the development of geodeticspacetechniquesiscontinuing Wehavesignificantimprovementsinaccuracy as well as in temporal and spatial resolution New fields of application evolve in science and practice For the first decade of the new millennium development will focus on several aspects launch of dedicated gravity field probes like CHAMP GRACE and GOCE for the determination of a high resolution terrestrial gravity field establishment of a next generation Global Navigation Satellite System GNSS with GPS Block IIR and Block IIF satellites and new components like the Eu ropean Galileo refinement in Earth observation eg with high resolution radar sensors like interferometric SAR on various platforms further establishment of permanent arrays for disaster prevention and environ mental monitoring and unification of different geodetic space techniques in mobile integrated geodetic geodynamic monitoring systems 14 Applications of Satellite Geodesy The applications of geodetic satellite methods are determined by the achievable accu racy the necessary effort and expense of equipment and computation and finally by the observation time and the ease of equipment handling A very extensive catalogue of applications can be compiled given the current developments in precise methods with realtime or near realtime capabilities Starting with the three basic tasks in satellite geodesy introduced in 11 we can give a short summary of possible applications 8 1 Introduction Global Geodesy general shape of Earths figure and gravity field dimensions of a mean Earth ellipsoid establishment of a global terrestrial reference frame detailed geoid as a reference surface on land and at sea connection between different existing geodetic datums and connection of national datums with a global geodetic datum Geodetic Control establishment of geodetic control for national networks installation of threedimensional homogeneous networks analysis and improvement of existing terrestrial networks establishment of geodetic connections between islands or with the mainland densification of existing networks up to short interstation distances Geodynamics control points for crustal motion permanent arrays for 3Dcontrol in active areas polar motion Earth rotation and solid Earth tides Applied and Plane Geodesy detailed plane surveying land register urban and rural surveying geographic information systems GIS town planning boundary demarcation etc installation of special networks and control for engineering tasks terrestrial control points in photogrammetry and remote sensing position and orientation of airborne sensors like photogrammetric cameras control and position information at different accuracy levels in forestry agricul ture archaeology expedition cartography etc Navigation and Marine Geodesy precise navigation of land sea and airvehicles precise positioning for marine mapping exploration hydrography oceanogra phy marine geology and geophysics connection and control of tide gauges unification of height systems Related Fields position and velocity determination for geophysical observations gravimetric magnetic seismic surveys also at sea and in the air determination of ice motion in glaciology Antarctic research oceanography determination of satellite orbits and tomography of the atmosphere ionosphere troposphere With more satellite systems becoming operational there is almost no limit to the possi ble applications This aspect will be discussed together with the respective techniques A summarizing discussion of possible applications is given in chapter 12 15 Structure and Objective of the Book 9 15 Structure and Objective of the Book Satellite geodesy belongs equally to fundamental and applied sciences Both aspects are dealt with however the main emphasis of this book is on the observation methods and on the applications Geodetic fundamentals are addressed in chapter 2 in order to help readers from neighboring disciplines In addition some useful information is provided concerning fundamental astronomy and signal propagation The motion of nearEarth satellites including the main perturbations and the basic methods of orbit determination are discussed in chapter 3 as far as they are required for an understanding of modern observation techniques and applications The increasing observational accuracy requires a corresponding higher accuracy in the determination of orbits In practice particularly for todays applications the user must be capable to assess in each case the required orbital accuracy and the influence of disturbing effects This is only possible with a sufficient knowledge of the basic relations in celestial mechanics and perturbation theory For further studies fundamental textbooks eg Schneider 1981 Taff 1985 or Montenbruck Gill 2000 are recommended Special references are given in the relevant sections The different observation methods of satellite geodesy are discussed in chapters 411 The grouping into currently important observation methods is not without problems because common aspects have to be taken up in different sections and be cause the topical methods develop very quickly This classification is nevertheless preferred because the user is in general working with a particular observation tech nique and is looking for all related information Also a student prefers this type of grouping because strategies for solving problems can be best studied together with the individual technique Crossreferences are given to avoid unnecessary repetitions The possible applications are presented together with the particular observation technique and illustrated with examples In chapter 12 a problemorientated sum mary of applications is given The implications of satellite geodesy affect nearly all parts of geodesy and survey ing Considering the immense amount of related information it is often only possible to explain the basic principle and to give the main guidelines Recommendations for further reading are given where relevant For example an exhaustive treatment of satellite motion chapter 3 or of the Global Positioning System GPS chapter 7 could fill several volumes of textbooks on their own As far as possible references are selected from easily accessible literature in the English language In addition some basic references are taken from German and French literature 2 Fundamentals 21 Reference Coordinate Systems Appropriate well defined and reproducible reference coordinate systems are essential for the description of satellite motion the modeling of observables and the representa tion and interpretation of results The increasing accuracy of many satellite observation techniques requires a corresponding increase in the accuracy of the reference systems Reference coordinate systems in satellite geodesy are global and geocentric by nature because the satellite motion refers to the center of mass of Earth 3 Terres trial measurements are by nature local in character and are usually described in local reference coordinate systems The relationship between all systems in use must be known with sufficient accuracy Since the relative position and orientation changes with time the recording and modeling of the observation time also plays an important role It should be noted that the results of different observation methods in satellite geodesy refer to particular reference coordinate systems which are related to the indi vidual methods These particular systems are not necessarily identical because they may be based on different data and different definitions Often the relationship be tween these particular systems is known with an accuracy lower than the accuracy of the individual observation techniques The establishment of precise transformation formulas between systems is one of the most important tasks in satellite geodesy 211 Cartesian Coordinate Systems and Coordinate Transformations z z γ xP 0 α x x yP P zP γ γ y y β xP Figure 21 Cartesian coordinate system InaCartesiancoordinatesystemwiththe axes x y z the position of a point P is determined by its position vector xP xP yP zP 21 where xP yP zP are real numbers Fig 21 The transformation to a second Cartesian coordinate system with identi cal origin and the axes x y z which is generated from the first one by a rotation around the zaxis by the angle γ can be realized through the matrix operation x P R3γ xP 22 21 Reference Coordinate Systems 11 with R3γ cos γ sin γ 0 sin γ cos γ 0 0 0 1 23 Equivalent rotations R1 around the xaxis and R2 around the yaxis are R1α 1 0 0 0 cos α sin α 0 sin α cos α R2β cos β 0 sin β 0 1 0 sin β 0 cos β The representation is valid for a righthanded coordinate system When viewed towards the origin a counterclockwise rotation is positive Any coordinate transformation can be realized through a combination of rotations The complete transformation is x P R1αR2βR3γ xP 24 The mathematical properties of rotation matrices are described using linear algebra The following rules are of importance 1 Rotation does not change the length of a position vector 2 Matrix multiplication is not commutative RiµRjν RjνRiµ 25 3 Matrix multiplication is associative RiRjRk RiRjRk 26 4 Rotations around the same axis are additive RiµRiν Riµ ν 27 5 Inverse and transpose are related by R1 i µ RT i µ Riµ 28 6 The following relationship also holds RiRj1 R1 j R1 i 29 The polarity of coordinate axes can be changed with reflectionmatrices S1 1 0 0 0 1 0 0 0 1 S2 1 0 0 0 1 0 0 0 1 S3 1 0 0 0 1 0 0 0 1 210 Finally the matrix for a general rotation by the angles α β γ is R cos β cos γ cos β sin γ sin β sin α sin β cos γ cos α cos γ sin β sin γ cos α sin γ cos α sin β sin γ sin α cos γ sin α cos β The relation between the position vectors in two arbitrarily rotated coordinate systems is then xp Rx p x p Rᵀxp In satellite geodesy the rotation angles are often very small thus allowing the use of the linearized form for R With cos α 1 and sin α α in radians neglecting higher order terms it follows that Rα β γ 1 γ β γ 1 α β α 1 Although matrix multiplication does not commute cf 25 the infinitesimal rotation matrix 213 does 21 Reference Coordinate Systems 13 2121 Conventional Inertial Systems and Frames Newtons laws of motion 312 are only valid in an inertial reference system ie a coordinate system at rest or in a state of uniform rectilinear motion without any acceleration The theory of motion for artificial satellites is developed with respect to such a system 3 Space fixed inertial system are usually related to extraterrestrial objects like stars quasars extragalactic radio sources planets or the Moon They are therefore also named celestial reference systems CRS The definition of a CRS can be based on kinematic or dynamic considerations A kinematic CRS is defined by stars or quasars with well known positions and if measurable proper motions A dynamical CRS is based on the motion of planets the Moon or artificial satellites The establishment of conventional celestial reference systems is under the respon sibility of the International Astronomical Union IAU From January 1 1988 until December 31 1997 the conventional celestial reference system was based on the ori entation of the equator and the equinox for the standard epoch J20000 cf 222 determined from observations of planetary motions in agreement with the IAU 1976 system of astronomical constants as well as related algorithms cf Seidelmann ed 1992 The corresponding reference frame was the Fifth Fundamental Catalogue FK5 Fricke et al 1988 ecliptic equator pole Z r M X α δ S Y Figure 22 Equatorial system in spherical as tronomy The equatorial system at a given epoch T0 which has been used in spheri cal astronomy Fig 22 for many years yields a rather good approximation to a conventional inertial reference system The origin of the system is supposed to coincide with the geocenter M The pos itive Zaxis is oriented towards the north pole and the positive Xaxis to the First Point of Aries The Yaxis completes a righthanded system Since Earths center of mass undergoes small accel erations because of the annual motion around the Sun the term quasiinertial system is also used The traditional materialization of the above definition for practical purposes is through a catalogue of the positions and proper motions of a given number of fundamental stars The FK5 is a catalogue of 1535 bright stars compiled from a large number of meridian observations The formal uncertainties of the FK5 star positions were about 20 to 30 milliarcseconds at the time of publication 1988 The quality of the FK5 frame is time dependent and is continuously getting worse de Vegt 1999 Walter Sovers 2000 Star positions are usually given as spherical coordinates right ascension α and declination δ The transformation of spherical coordinates α δ r into Cartesian In spherical astronomy r is usually defined as the unit radius We may consider the celestial sphere in Fig 22 as the unit sphere and apply the basic formulas of spherical geometry Detailed information on spherical astronomy can be found in Green 1985 or in textbooks on geodetic astronomy eg Mackie 1985 Schödlbauer 2000 The accuracy of the celestial reference system realized through the FK5 catalogue is by far insufficient for modern needs A considerable improvement by several orders of magnitude was achieved with the astrometric satellite mission HIPPARCOS Kovaleysky et al 1997 and with extragalactic radio sources quasars via the technique of Very Long Baseline Interferometry VLBI which uses radio telescopes 111 In 1991 the IAU decided to establish a new celestial reference system based on a kinematic rather than a dynamic definition McCarthy 2000 The system is called the International Celestial Reference System ICRS and officially replaced the FK5 fundamental system on January 1 1998 The axes of the ICRS are no longer fixed to the orientation of the equator and the vernal equinox but with respect to distant matter in the universe The system is realized by a celestial reference frame defined by a set of identifiable fiducial points on the sky eg stars quasars or on Earths surface eg fundamental stations It is described by a catalogue of precise positions and motions if measurable at a specific epoch In satellite geodesy two fundamental systems are required a spacefixed conventional inertial reference system CIS for the description of satellite motion and an Earthfixed conventional terrestrial reference system CTS for the positions of the observation stations and for the description of results from satellite geodesy 21 Reference Coordinate Systems 15 Figure 23 International Celestial Reference Frame ICRF distribution of the 212 bestobserved extragalactic sources after Ma et al 1998 J 20000 typical Hipparcos star positions can be estimated in the range of 5 to 10 mas Kovalevsky et al 1997 Walter Sovers 2000 With forthcoming astrometric space missions like FAME and GAIA Walter Sovers 2000 see 533 further improvement of the optical realization of the ICRS to the level of 10 microarcseconds µas is expected Also the link between the ICRF based on radio stars and frames at optical wavelengths will be improved For more information on conventional inertial reference systems and frames see eg Moritz Mueller 1987 chap 9 Seidelmann ed 1992 chap 2 Walter Sovers 2000 Schödlbauer 2000 chap 3 Capitaine et al 2002 and 1242 2122 Conventional Terrestrial Systems and Frames A suitable Earthfixed reference system must be connected in a well defined way to Earths crust Such a Conventional Terrestrial System CTS can be realized through a set of Cartesian coordinates of fundamental stations or markers within a global network The origin of an ideal conventional terrestrial reference system should be fixed to the geocenter including the mass of the oceans and the atmosphere The zaxis should coincide with the rotational axis of Earth Since the geocenter and the rota tional axis are not directly accessible for observations the ideal system is approximated by conventions The classical convention for the orientation of axes was based on as tronomical observations and has been developed and maintained since 1895 by the International Latitude Service ILS and since 1962 by the International Polar Mo tion Service IPMS Moritz Mueller 1987 It is established through the conventional direction to the mean orientation of the polar axis over the period 19001905 Conven 16 2 Fundamentals tional Terrestrial Pole CTP also named Conventional International Origin CIO and a zero longitude on the equator Greenwich Mean Observatory GMO GMO is defined through the nominal longitudes of all observatories which contributed to the former international time service BIH Bureau International de lHeure In 1988 the responsibility for establishing and maintaining both the conventional celestial and terrestrial reference systems and frames was shifted to the International Earth Rotation Service IERS cf 1242 Although the IERS results are based on modern space techniques like SLR 8 VLBI 111 GPS 7 and Doppler 6 the traditional convention has been maintained within the accuracy range of the classical astronomical techniques in order to provide continuity The conventional terrestrial reference system established and maintained by the IERS and nearly exclusively used for todays scientific and practical purposes is the International Terrestrial Reference System ITRS its realization is the International Terrestrial Reference Frame ITRF The ITRS is defined as follows Boucher et al 1990 McCarthy 2000 it is geocentric the center of mass being defined for the whole Earth including oceans and atmosphere the length unit is the SI meter the scale is in context with the relativistic theory of gravitation the orientation of axes is given by the initial BIH orientation at epoch 19840 and the time evolution of the orientation will create no residual global rotation with regard to Earths crust nonetrotation condition These specifications correspond with the IUGG resolution no 2 adopted at the 20th IUGG General Assembly of Vienna in 1991 The orientation of axes is also called IERS Reference Pole IRP and IERS Reference Meridian IRM The realization of the ITRS the International Terrestrial Reference Frame ITRF is formed through Cartesian coordinates and linear velocities of a global set of sites equipped with various space geodetic observing systems If geographical coordi nates ellipsoidal latitude longitude and height are required instead of Cartesian coordinates X Y Z use of the GRS80 ellipsoid is recommended cf 214 The ensemble of coordinates implicitly define the CTP Zaxis and the GMO Xaxis Nearly every year a new ITRF is realized based on new observations with geodetic space techniques eg Doppler 6 GPS 7 SLR 8 VLBI 111 The result is published under the denomination ITRFxx where xx means the last digits of the year whose data were used in the formation of the frame The most recent solution is ITRF2000 Fig 24 Altamimi et al 2001 Each particular ITRF is assembled by combining sets of results from independent techniques as analyzed by a number of separate groups The use of as many different techniques as possible provides a significant decrease of systematic errors The establishment of a terrestrial reference frame is not an easy task because Earths crust continuously undergoes various deformations Since todays geodetic space techniques provide station coordinates at the 1 cm or subcentimeter level it is necessary to model the various deformations at the mmlevel The main influences are 21 Reference Coordinate Systems 17 Figure 24 International Terrestrial Reference Frame ITRF2000 symbols indicate the number of different space techniques collocated at the particular site source IERS global plate tectonics 1241 solid Earth tides 3232 ocean and atmospheric loading effects polar tides regional and local effects Detailed models and algorithms for these effects are given in the IERS Conventions McCarthy 2000 The largest effect comes from global plate tectonics cf Fig 1213 p 529 In order to maintain the orientation of the coordinate axes stable on the dynamic Earth the orientation rate of the ITRF is defined by convention so that there is no rotation of the frame with respect to Earths lithosphere In practice the ITRF orientation rate is aligned to the plate tectonic model NNRNUVEL1A Argus Gordon 1991 DeMets et al 1994 This procedure is based on the assumption that the model fulfills the condition of nonetrotation ie the integral of model velocities over the entire surface of Earth becomes zero Drewes 1999 see also 1241 Regional realizations of the ITRS are eg the ETRF89 for Europe and SIRGAS for SouthAmerica cf 121 A particular global realization of a terrestrial reference system is the World Geodetic System 1984 WGS84 216 2123 Relationship between CIS and CTS The transition from the spacefixed equatorial system CIS to the conventional terres trial system CTS is realized through a sequence of rotations that account for precession 18 2 Fundamentals nutation Earth rotation including polar motion These can be described with matrix operations For a point on the celestial sphere described through its position vector r we can write rCTS SNP rCIS 216 The elements of the rotation matrices must be known with sufficient accuracy for each observation epoch These rotations are now considered in more detail a Precession and Nutation Earths axis of rotation and its equatorial plane are not fixed in space but rotate with respect to an inertial system This results from the gravitational attraction of the Moon and the Sun on the equatorial bulge of Earth The total motion is composed of a mean secular component precession and a periodic component nutation Fig 25 a b ecliptic equator EN PN 186 years 235 PS ES EN 156 ε 235 a 921 b 686 Figure 25 Precession and nutation Earths rotation axis PSPN describes a conic about the ecliptic poles ES EN The position and orientation of the equatorial plane and the first point of Aries is called mean equator and mean equinox respectively when only the influence of precession is considered When nutation is taken into account they are called true equator and true equinox The respective star coordinates are termed mean positions or true positions Mean positions can be transformed from the reference epoch t0 J20000 to the required observation epoch t using the precession matrix P R3zR2θR3ζ 217 with three rotations 23 by the angles z θ ζ z 06406161 T 00003041 T 2 00000051 T 3 θ 05567530 T 00001185 T 2 00000116 T 3 218 ζ 06406161 T 00000839 T 2 00000050 T 3 T t t₀ is counted in Julian centuries of 36525 days The transformation from the mean equator and equinox to the instantaneous true equator and equinox for a given observation epoch is performed with the nutation matrix N R₁ε ΔεR₃ΔψR₁ε 219 where ε obliquity of the ecliptic Δε nutation in obliquity Δψ nutation in longitude counted in the ecliptic and ε 232621448 46815 T 000059 T² 0001813 T³ 220 In 1980 the International Astronomical Union IAU adopted a nutation theory Wahr 1981 based on an elastic Earth model Δψ is computed using a series expansion involving 106 coefficients and Δε using one of 64 coefficients The principal terms are Δψ 171996 sin Ω 13187 sin2F 2D 2Ω 02274 sin2F 2Ω 221 Δε 92025 cos Ω 05736 cos2F 2D 2Ω 00977 cos2F 2Ω 222 with Ω mean ecliptic longitude of the lunar ascending node D mean elongation of the Moon from the Sun F λM Ω with λM the mean ecliptic longitude of the Moon By applying the transformations 217 and 219 we obtain true coordinates rT Xₜ Yₜ Zₜ 223 in the instantaneous true equatorial system More details can be found in Seidelmann ed 1992 and McCarthy 2000 The IAU decided at its 24th General Assembly in 2000 to replace the IAU 1976 Precession Model and the IAU 1980 Theory of Nutation by the PrecessionNutation Model IAU 2000 beginning on January 1 2003 Two versions of the model exist Capitaine et al 2002 The IAU 2000A model contains 678 lunisolar terms and 687 planetary terms and provides directions of the celestial pole in the geocentric celestial reference system GCRS with an accuracy of 02 mas The abridged model IAU 2000B includes 80 20 2 Fundamentals lunisolar terms and a planetary bias The difference between both models is not greater than 1 mas after about 50 years b Earth Rotation and Polar Motion Forthetransitionfromaninstantaneousspacefixedequatorialsystemtoaconventional terrestrial reference system we need three further parameters They are called Earth Rotation Parameters ERP or Earth Orientation Parameters EOP namely GAST the Greenwich apparent sidereal time xp yp the pole coordinates GAST is also expressed as the difference UT1UTC cf 222 Unlike precession 217 and nutation 219 Earth rotation parameters cannot be described through theory but must be determined through actual observations by an international time and latitude service Since the beginning of the last century until about 1980 this service was based mainly on astronomical observations see 1242 On January 1 1988 the International Earth Rotation Service IERS Boucher et al 1988 took over this task The principle observation techniques now used are laser ranging to satellites and to the Moon 855 and Very Long Baseline Interferometry VLBI 1112 Fig 26 shows the geometric situation for the transformation The Earthfixed system is realized through the conventional orientation of a Cartesian X Y ZCT system The ZCT axis is directed toward the conventional terrestrial pole CTP and the XCT axis toward the mean Greenwich meridian The relative position of the instantaneous true pole with respect to the conventional terrestrial pole CTP is usually described through the pole coordinates xp yp eg Mueller 1969 Schödlbauer 2000 GAST true equator mean meridian Greenwich true instantaneous pole CTP conventional equator ZCT ZT yp xp M XT XCT YT YCT Figure 26 True instantaneous and mean conventional terrestrial system 21 Reference Coordinate Systems 21 The relative orientation of the XCTaxis depends directly on Earth rotation and is determined through the apparent true Greenwich SiderealTime GAST cf 222 The symbol θ is often used to denote GAST The matrix which transforms the instan taneous spacefixed system to the conventional terrestrial system is S R2xpR1ypR3GAST 224 where R3GAST cosGAST sinGAST 0 sinGAST cosGAST 0 0 0 1 225 and because of small angles R2xpR1yp 1 0 xp 0 1 0 xp 0 1 1 0 0 0 1 yp 0 yp 1 1 0 xp 0 1 yp xp yp 1 226 For most practical purposes the pole of the instantaneous true spacefixed equatorial system can be considered to be identical to the socalled Celestial Ephemeris Pole CEP The CEP is defined to be the reference pole for the computation of polar motion and nutation and is free of the quasi diurnal nutation terms with respect to Earths crust and inertial space Seidelmann ed 1992 The observed differences between the CEP and the conventional precessionnutation model are named celestial pole offsets dψ dε They reach a few milliarcseconds and are published by the IERS see 1112 The CEP will be replaced by the Celestial Intermediate Pole CIP along with the introduction of the IAU 2000 precessionnutation model Accordingly for the rigorous definition of sidereal rotation of Earth based on the early concept of the nonrotating origin Guinot 1979 the Terrestrial Ephemeris Origin TEO and the Celestial Ephemeris Origin CEO defined on the equator of the CIP will be introduced This implies that UT1 be linearly proportional to the Earth rotation angle The CIP coincides with the CEP in the lowfrequency domain periods larger than two days The reason for the adoption of the CIP is to clarify the difference between nutation and polar motion at high frequencies periods less than two days For details see eg Capitaine et al 2000 Capitaine et al 2002 The IERS will introduce the new system in 2003 The old system however will continue to be used and the IERS will continue to provide all necessary data until further notice 213 Reference Coordinate Systems in the Gravity Field of Earth Terrestrial geodetic observations with the exception of the slant ranges s are related to the local gravity vector g They can therefore easily be described in a local reference coordinate system which is tied to the direction of the plumb line n at the observation point P The orientation of the vector n is usually determined from astronomical observations and described as the astronomical latitude Φ and the astronomical longitude Λ n cos Φ cos Λ cos Φ sin Λ sin Φ 227 The relationship between the local astronomical system defined as origin at the observation point P Zaxis directed to the astronomical zenith Xaxis directed to the north astronomical meridian Yaxis directed to the east and the global conventional terrestrial system CTS is described in Fig 27 Torge 1980 2001 The location of a point Pi within the local astronomical system is derived from terrestrial observations astronomical azimuth A horizontal directions azimuth differences slant ranges s and zenith angles z and may be written as X X Y Z s cos A sin z sin A sin z cos z 228 Observed coordinate differences may be transformed from the local system into the global system CTS using ΔX AΔX 229 with A R₃180 ΛR₂90 ΦS₂ The matrix S₂ changes the orientation of the Yaxis and converts a lefthanded into a righthanded coordinate system The explicit form of A is A sin Φ cos Λ sin Λ cos Φ cos Λ sin Φ sin Λ cos Φ sin A cos Φ sin A 230 The inverse formula reads Torge 2001 ΔX A1ΔX ATΔX 231 with A1 sin Φ cos Λ sin Φ sin Λ cos Φ cos Λ sin Λ cos A cos A 0 The formulas 229 and 231 are used in the combination of results from local terrestrial observations and from satellite techniques either in the global Cartesian system or in the local astronomical system 214 Ellipsoidal Reference Coordinate Systems For most practical applications ellipsoidal coordinate systems are preferred because they closely approximate Earths surface and they facilitate a separation of horizontal position and height Usually a rotational ellipsoid is selected which is flattened at the poles and which is created by rotating the meridian ellipse about its minor axis b The geometric parameters are semimajor axis a and flattening f a ba 232 Alternatively the first numerical eccentricity e is used e² a² b²a² 233 Further suitable relations between these quantities are e² 2f f² 1 e² 1 f² 234 A best possible approximation to the figure of the whole Earth is a global ellipsoidal system Fig 28 The ellipsoidal geographic coordinates are φ ellipsoidal latitude λ ellipsoidal longitude h ellipsoidal height Figure 28 Global and local ellipsoidsystems origin at the center O of the ellipsoid Zaxis directed to the northern ellipsoidal pole along the minor axis Xaxis directed to the ellipsoidal zero meridian and Yaxis completing a righthanded system slant ranges s ellipsoidal azimuths α ellipsoidal directions or horizontal angles Δα and ellipsoidal zenith angles ζ It is evident that the geoid undulation N must be known when observations from satellite geodesy leading to ellipsoidal heights and from terrestrial geodesy leading to heights defined in the gravity field are used in a combined adjustment This aspect will be treated in more detail in chapter 7623 at least five parameters a semimajor axis of the reference ellipsoid f flattening and ΔX ΔY ΔZ coordinates of the ellipsoid origin with respect to the geocenter For ΔX ΔY ΔZ 0 the geodetic datum is called an absolute datum The Geodetic Reference System 1980 GRS80 adopted by the IUGG General Assembly in Canberra 1979 belongs to this group a 6 378 137 m 245 f 1 2982572 Further constants of the GRS80 are Moritz 2000 the geocentric gravitational constant of Earth including the atmosphere GM 398 6005 km3 s2 the dynamical form factor of Earth related to f J2 0001082863 and the mean angular velocity of Earth ω 7292115 105 rad s1 For a large number of particular local reference systems the socalled datum shift constants or datum shift parameters ΔX ΔY ΔZ can be derived from satellite observations They represent however only a mean position of the particular local system with respect to the geocentric system cf 121 28 2 Fundamentals Z2 εx X1 r0 M X2 Z1 εz 0 r2 r1 εy Y1 Y2 Figure210 Datumtransformationbetweentwo Cartesian systems For limited areas only three local or regional translation parameters may be sufficient cf 121 The number of datum parameters in creases to nine when the parameters of the ellipsoid have to be considered The number is further increased when spe cific rotations or deformations are al lowed for parts of the terrestrial network cf 7621 and when the datum in formation is derived from satellite or bits In the latter case the potential coef ficients of Earths gravity field as well as some fundamental constants like Earth rotation velocity of light and geocentric gravitational constant form parts of the datum definition One example of the latter group is the World Geodetic System WGS 84 216 World Geodetic System 1984 WGS 84 WGS has been developed by the US Department of Defense DoD since about 1960 in order to define and establish a geocentric terrestrial reference system WGS 60 was followed by WGS 66 then by WGS 72 and finally by WGS 84 Each realization of the reference system incorporated more data better computational techniques a better knowledge of Earth and improved accuracy Malys Slater 1994 Slater Malys 1997 Merrigan et al 2002 WGS 72 and WGS 84 have been used to compute the operational broadcast ephemeris of Transit Doppler 62 and GPS 715 satellites As a consequence coordinates derived from the broadcast ephemeris with Transit or GPS refer to WGS This is the main reason for the high acceptance of WGS 84 as a primary reference coordinate system The major parameters of WGS 72 and of the latest version of WGS 84 are given in Table 21 cf NIMA 2000 Table 21 Main parameters of WGS 72 and WGS 84 Parameter Name WGS 72 WGS 84 semimajor axis a 6 378 135 m 6 378 137 m flattening f 129826 1298257223563 angular velocity ω 7292115147 7292115 105 rad s1 105 rad s1 geocentric GM 398 6008 km3 s2 398 6004418 km3 s2 gravitational constant 2nd zonal harmonic C20 4841605 106 48416685 106 WGS 84 practically coincides with the Geodetic Reference System 1980 The associated gravity field is the Earth Gravitational Model 1996 EGM96 complete to degree and order 360 Lemoine et al 1998 cf 3221 1222 The WGS 84 coordinate system is a Conventional Terrestrial Reference System CTRS and follows the criteria outlined in the IERS Conventions cf 2122 McCarthy 2000 The Zaxis is in the direction of the IERS Reference Pole IRP the Xaxis is in order the intersection of the IERS Reference Meridian IRM and the plane passing through the origin and normal to the Zaxis The Yaxis completes a righthanded Earthcentered orthogonal coordinate system Fig 211 The realizations of the WGS 84 after several refinements now coincide with the ITRF at the level of 1 cm Merrigan et al 2002 Hence for most practical purposes WGS 84 and ITRF can be considered as identical with Δf 03121057 107 a 6 378 135 m Δa 20 m Δr 14 m The latitude is counted positive to the north and the longitude positive to the east Absolute geocentric coordinates of an isolated single observation station which have been derived from satellite observations with TRANSIT 661 or GPS 762 have usually standard deviations in the order of several meters or even tens of meters It is evident that a datum transformation with 247 cannot improve the coordinate accuracy The worth of a general transformation formula like 247 must not be overestimated For more details on datum transformation see 661 7621 121 and the cited document NIMA 2000 22 Time 31 22 Time 221 Basic Considerations Three basic groups of time scales are of importance in satellite geodesy 1 The timedependent orientation of Earth with respect to the inertial space is required in order to relate the Earthbased observations to a spacefixed reference frame The appropriate time scale is connected with the diurnal rotation of Earth and is called Sidereal Time or Universal Time 2 Forthedescriptionofthesatellitemotionweneedastrictlyuniformtimemeasure which can be used as the independent variable in the equations of motion An appropriate time scale can be derived from the orbital motion of celestial bodies around the Sun It is called Ephemeris Time Dynamical Time or Terrestrial Time 3 The precise measurement of signal travel times eg in satellite laser ranging requires a uniform and easily accessible time scale with high resolution The appropriate measure is related to phenomena in nuclear physics and is called Atomic Time All these time scales are based on the observation of uniform and repetitive astro nomical or physical phenomena The time interval between two consecutive phenom ena forms the scale measure of the particular time scale A certain multiple or fraction of the scale measure is called the time unit In general the second s is used as the basic time unit Larger time units such as days or years are derived from the second Within the time scale a starting point or origin has to be fixed This may be achieved through a certain astronomical event such as the particular position of a star or the meridian transit of a particular celestial object The instant of the occurrence of some phenomena or observations can be related to a certain reading of the particular time scale and gives the datation of the event In astronomy such an event is called the epoch of the observation With respect to the particular time scale the epoch determination reflects an absolute time measurement For many purposes eg for the determination of signal travel times a relative time measurement ie the determination of the time interval between two epochs is suffi cient In many cases the relative time measurement can be done much more accurately than the absolute time measurement In satellite geodesy the datation of an event is often called timetag or timetagging eg when the instant of transmission or reception of a signal is considered Strictly speaking we have to distinguish between the ideal conception of a time scale and the practical realization through observations This becomes particularly evident with the atomic time when we compare the definition of the atomic time second with its practical realization through a group of individual atomic clocks A time scale may be regarded as an approximation to the particular time concept In the following we will not use this distinction For further reading see eg Seidelmann et al 32 2 Fundamentals 1992 Guinot 1995 A useful source on time in relation to GPS is Langley 1991b the GPS World Supplement on Precise Timing December 1998 or Lombardi et al 2001 dT3 dT2 Pole B dT1 Figure 212 Effect of timing errors in satel lite geodesy In order to meet the various require ments stemming from science and technol ogy the relationship between the different time scales have to be established with the highest possible accuracy Fig 212 illus trates how timing errors in satellite geodesy are related to a position error of 1 cm 1 cm motion of a point on the equator caused by Earths rotation corre sponds to about 2 105 s 1 cm motion of a nearEarth satellite in the orbit corresponds to about 1106 s 1 cm in the satellite range derived from signal travel time eg laser ranging corresponds to about 1 1010 s The related requirements for the accuracy of time determination dTi are as follows dT1s 2 105 for Earth rotation dT2s 1 106 for orbital motion and 250 dT3s 1 1010 for signal travel time 222 Sidereal Time and Universal Time Sidereal time and universal time are directly related to the rotation of Earth and they are thus equivalent time scales Sidereal time equals the hour angle of the vernal equinox and consequently depends on the geographical longitude of the particular observation station From Fig 213 we may easily derive the following relations The Local Apparent or True Sidereal Time LAST referred to the true vernal equinox is LAST Local hour angle of the true vernal equinox For Greenwich we obtain the Greenwich Apparent Sidereal Time GAST GAST Greenwich hour angle of the true vernal equinox The vernal equinox is subject to the nutation in longitude cf 212 Removing the nutation term we obtain the Local Mean Sidereal Time LMST and the Greenwich Mean Sidereal Time GMST respectively the diurnal motion of Earth in its orbit amounts to 360365 1 The approximative relation is 22 Time 35 The half day is subtracted so that the day starts at midnight as is the case with civil time reckoning The MJD has been recommended by various international bodies such as IAU as a decimal day count which is independent of the civil calendar MJD is usually reckoned in universal time UT The modified Julian day number has to be distinguished from the Day of the year DOY DOY is counted from the beginning of the respective year Thus for 2002 MJD 52275 DOY for 2003 MJD 52640 DOY for 2004 MJD 53005 DOY for 2005 MJD 53371 DOY 223 Atomic Time The international atomic time scale TAI Temps Atomique International was intro duced to meet the requirements for an easily accessible and strictly uniform time scale The unit of the atomic time was selected in such a way that it equals the duration of the ephemeris second 224 The definition of the second of the atomic time scale has been worded by the 13th Conference of the International Committee of Weights and Measures in Paris 1967 as follows The second is the duration of 9192631770 periods of the radiation corre sponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom This is also the definition of the unit of time of the International System of Units SI The international atomic time scale is maintained by the Time Section of the Inter national Bureau of Weights and Measures Bureau International des Poids et Mesures BIPM in Paris based on the readings of a large number of the most accurate atomic clocks in various laboratories The Bureau International de lHeure BIH was respon sible for maintaining the atomic time scales until the 31st of December 1987 In practice atomic time scales are derived from groups of commercial and labora tory cesium standards 225 which generate time intervals based on the definition of the SI second The readings refer to nonmoving clocks at sea level TAI is computed as the weighted mean of individual clocks about 250 clocks in 2002 TAI is hence a statistically formed common time scale for international use Each laboratory time scale can be regarded as a particular realization of the atomic time scale The differ ences between TAI and the time scales of the participating laboratories are distributed on a monthly basis in the Circular T of the BIPM Time Section The epoch of TAI agreed with the epoch of UT1 on January 1 1958 Due to the deceleration of Earths rotation the difference between the time scales is increasing in this concept a time scale is regarded as one of the coordinate axes of a spacetime reference frame 36 2 Fundamentals The difference for some selected dates amounts to TAI UT1 6s1 on January 1 1968 16s4 on January 1 1978 23s6 on January 1 1988 30s8 on January 1 1998 31s9 on January 1 2001 32s3 on January 1 2003 The rather large size of the differences stems from the fact that the unit of the SIsecond was adopted from the length of the ephemeris second and the ephemeris second was derived from the mean duration of the solar day between 1756 and 1895 when Earths rotation was faster than today For many applications navigation in particular a time scale is required which provides both a highly uniform time unit and the best possible adaptation to UT1 and hence to Earth rotation This is why in 1972 a compromise time scale Universal Time Coordinated UTC was introduced UTC and TAI differ by an integer number n of seconds UTC TAI n 1 s 257 Depending on the prevailing situation n can be changed at given dates namely on January 1 andor July 1 Thus the epoch of UTC is adapted to UT1 by inserting or removing socalled leap seconds The unit of UTC remains the SI second The difference DUT1 between both times should not exceed 09 s in absolute value DUT1 UT1 UTC 09 s 258 DUT1 is distributed through the bulletins of the IERS and it must be taken into account with all calculations related to Earthfixed reference systems In most countries the disseminated time signals refer to UTC On January 1 2003 the difference between TAI and UTC was TAI UTC2003 32 s 259 The Global Positioning System GPS uses its own particular time scale GPS time It differs from UTC by a nearly integer number of seconds Both time scales had identical epochs on January 5 1980 Because GPS time is not incremented by leap seconds the difference between UTC and GPS time is increasing The unit of GPS time is the SI second However GPS time is only derived from atomic clocks which form part of the GPS system It is hence a free atomic time scale and may show slight differences when compared to TAI The relation between UTC and GPS time is included in time bulletins of the USNO and the BIPM and it is also disseminated within the GPS satellite message 713 In 2003 the difference was approximately GPS time UTC2003 13 s 260 22 Time 37 The exact relation is eg BIPM 2002 GPS time UTC n s C0 nisanintegernumber andthecorrectiontermC0 isintheorderofseveralnanoseconds Thus the reception of GPS signals provides realtime access to TAI and UTC with uncertainties below 1 microsecond A similar relationship holds for GLONASS time 77 and UTC Note that UTC and GPS time as well as GLONASS time are atomic time scales 224 Ephemeris Time Dynamical Time Terrestrial Time A strictly uniform time scale can be found in the independent arguments of the theories of dynamics and of the ephemerides ie the timedependent positions of celestial bodies described in adequate reference frames Time scales which are based on such concepts fulfill at best the conceptional idea of Inertial Time In 1952 the IAU introduced Ephemeris Time ET as a theoretically uniform time scale for use with ephemeris The Ephemeris Second was defined as a certain fraction of the TropicalYear 1900 and hence it was strictly uniform In practice the ephemeris timewasderivedfromlunarobservations anditdependedonatheoryoftheSunandthe system of astronomical constants Its reading accuracy was only about 01 s on yearly averages ET has never been disseminated by time signals It was made available only through the publication of differences with respect to UT1 and later to TAI Guinot 1995 In 1977 the IAU adopted the socalled Dynamical Time Scales in order to meet the arising requirements for a relativistic formulation of orbital motion Barycentric Dynamical Time TDB was defined to be the timelike argument for the barycenter of the solar system and Terrestrial Dynamic Time TDT was referred to geocentric ephemerides In the concept of General Relativity a clock moving with Earth experiences peri odic variations up to 16 milliseconds caused by the annual motion within the gravity field of the Sun This effect however must not be considered in the computation of nearEarth satellite orbits because the satellites move together with Earth This is why Terrestrial Dynamical Time TDT was the appropriate time scale for geocentric calcu lations in satellite geodesy A further advantage is that compared with the Barycentric Dynamical Time TDB TDT is independent of various forms of relativistic theories Seidelmann et al 1992 Dynamical time has been used as the argument for astronomical ephemerides since January 1 1984 The SI second was formally introduced as the fundamental time unit in the TDT scale It corresponds to the time which an atomic clock would measure on the rotating geoid For the sake of continuity TDT was set equal to ET at the beginning of January 1 1984 This is why a constant difference of 32s184 exists between the TAI time scale and the TDT or ET time scale In 1991 the IAU has defined new time scales in the framework of the general theory of relativity to clarify the relationships between spacetime coordinates In 225 Clocks and Frequency Standards In satellite geodesy precise information is required on time and frequency In many cases it is necessary to relate the epochs of some events which are observed at different stations separated by large distances with an accuracy of 1 microsecond 1µs The performance of frequency standards must reach a stability of up to 1 1015 over several hours These high demands can only be fulfilled with atomic clocks The most important component of a clock C1 is an oscillating system oscillator The periodic motion of this system has to be generated maintained and read out by suitable means In modern clocks eg in atomic clocks the conversion of the oscillator cycles to the scale unit one second is realized via electronic counters or dividers For an ideal clock C1 the relation between the cycle period T1 and the oscillator frequency f1 is defined as T1 1 f1 263 Counting N1 cycles over a given time interval tt0 yields the ideal strictly uniform time scale t t0 N1T1 N1 f1 264 Here N1 equals the integral N1 t t0 f1 dt f1t t0 265 which is the total number of cycles since the starting epoch t0 For an atomic clock C1 which exists in reality like for every other clock the frequency is not strictly constant The behavior of the frequency is usually described as eg Fell 1980 Wübbena 1991 Hahn 1999 f1t f1 f1 f1t t0 f1t 266 The individual terms are f1 constant frequency bias of the oscillator C1 f1 frequency drift and f1 random frequency error Counting the oscillations of this real clock C1 yields N1 t t0 f1t dt f1t t0 f1 f1 t t0 f1t t02 2 t t0 f1t dt 267 The related epoch is t t0 N1T1t t0 f1 f1 t t0 f1 2f1 t t02 t t0 f1t f1 dt 268 When f1t0 N0T1 269 is the synchronization error at the first epoch t0 we obtain for some later epoch t the total timing error of the clock C1 as f1t t1 t f1t0 f1 f1 t t0 f1t t02 2 t t0 f1t f1 dt 270 After renaming the expressions in 270 we get a frequentlyused description of the timing error f1t f1t Tit0 Rit t0 Di 2 t t02 t t0 yt dt 271 with Tit0 constant time bias Ri time drift Di quadratic term drift rate ageing and yt random relative frequency error For a particular clock the first three terms have to be estimated Consequently the timing of the clock depends on the uncertainty of the estimation and on the integral of the random frequency error from the start epoch of the estimation The particular estimation can be obtained through comparison with other clocks This is why time laboratories and fundamental observation stations may operate several atomic clocks which are compared against each other or with clocks at other institutions on a regular basis The relative frequency errors show a typical behavior for different types of atomic clocks These errors can be characterized either in the time domain or in the frequency domain A suitable measure for relative frequency errors in the time domain is the socalled Allan variance Allan 1987 It should be noted that because of the extremely high accuracy requirements in some parts of satellite geodesy the behavior of clocks in fundamental observation stations and in the satellites must be carefully studied This is particularly true for the clocks in navigation satellites like GPS 712 The typical frequency performance of clocks is demonstrated in Fig 215 In satellite geodesy the following classes of oscillators are in use precision quartz crystal oscillator rubidium standard cesium standard and hydrogen maser Precision quartz crystal oscillators are completely sufficient as time generators in satellite receivers when they are continuously controlled and updated by external signals for example by the time and frequency signals from satellites This is eg the case with the GPS satellites Characteristic features of the quartz oscillators are that they are quite sensitive to temperature variations and that they are prone to a rather strong ageing process In practice it is of importance that the quartz runs in stable temperature conditions and without interruptions or other disturbances The frequency stability per day may range from 109 to 1013 The characteristic feature of the rubidium frequency standard is its excellent long term stability A rubidium standard can be used as an external oscillator for GPS observations in particular to bridge periods with insufficient satellite coverage A rubidium clock can reach a stability of 1 1013 per day under the best conditions The cesium frequency standards because of their high short and longterm stability can be regarded as the atomic clocks par excellence Assembled in groups they form the core of time laboratories and they are also present in fundamental satellite observation stations in tracking stations for orbit control or in laser ranging systems The time base in the GPS satellites is realized through cesium and rubidium standards Cesium standards are transportable and commercially available Laboratory cesium beam standards can realize the second with an accuracy of 15 1014 Commercially available standards are less accurate but may equal the stability of laboratory standards for periods up to about 1 year Seidelmann et al 1992 Hydrogen masers are necessary to meet the highest accuracy demands such as those required by Very Long Baseline Interferometry VLBI 111 A frequency stability ατ of 1015 is required over time periods of 102 to 105 seconds Hydrogen 42 2 Fundamentals masers are very sensitive and to date have only been operational under laboratory conditions For a deeper treatment of the subject see the special literature such as Bauch et al 2000 PTTI 2000 or the Supplement on Precise Timing from GPS World Decem ber 1998 From modern developments for improved time and frequency standards an uncertainty of about 1 1015 or even 1016 can be expected Technology de velopments with laser cooling of atoms mercury ion chambers and cesium fountains are but some of the efforts Their optimum use would require global time comparison with uncertainties of down to 10 ps ie the time taken by a photon to travel 3 mm A correct modeling of time comparison then has to include among other effects solid Earth tides and plate tectonics Guinot 1995 Detailed information on new develop ments can be taken from publications of leading time laboratories like the National Institute of Standards NIST in the US or the Physikalisch Technische Bundesanstalt PTB in Germany A completely new development is pulsar time Fast rotating neutron stars so called pulsars can be used as stable cosmic frequency generators Pulsar PSR193721 discovered in 1982 is rotating with a period of 16 ms and emitting a beam of elec tromagnetic radiation sweeping Earth at each revolution The arrival of each pulse can be dated with uncertainty of 03 µs A number of other millisecond pulsars have subsequently be found After correction for the orbital motion of Earth and of the pulsars and for other effects like deceleration of pulsar rotation pulsars can serve as clocks at least as stable as the best atomic clocks In future the combination of pulsar data with the readings of atomic clocks may generate stable long term time scales Guinot 1995 23 Signal Propagation Signals on their path between satellites and ground stations propagate through at mospheric regions of different nature and variable state and thus experience different kinds of influences Perturbations may occur to the direction of propagation to the velocity of propagation and to the signal strength For the user who is interested in the undisturbed signal the atmosphere introduces unwanted perturbations The impacts on the observational results are in many cases much larger than the accuracy required in satellite geodesy Consequently atmospheric influences have to be determined di rectly by measurements andor by modeling and they have to be considered within the adjustment process On the other hand information on the state of the upper atmosphere can be obtained when the received satellite signals are compared with signals that would be observed under atmospheric free conditions eg Coco 1991 Wanninger 1992 Wild 1994 Schüler 2001 This latter aspect is however not discussed here In this chapter some elementary fundamentals of wave propagation are given 231 232 and the characteristics of signal propagation through the troposphere and the ionosphere are presented 233 For a full treatment of the subject see the special literature eg Maral Bousquet 1986 Davies 1990 DeMunck et al 1992 Parkinson et al 1996 Langley 1998b The explicit correction formulas for a particular observation technique for example Doppler GPS or SLR are given in the relevant chapters 642 744 841 2πΦ is called the phase angle φ With 274 it follows from 277 that y A sinωt φ0 23 Signal Propagation 45 The wavelengths of electromagnetic waves and hence their propagation velocity depend on certain properties of the medium in which the waves are propagating In a vacuum the velocity is c λvac P f λvac ω kvac 281 The numerical value c for the propagation velocity in a vacuum is adopted by inter national scientific bodies The value currently in use in satellite geodesy is McCarthy 2000 c 2997 924 58 108ms1 282 For propagation media other than a vacuum the propagation velocity is characterized by the index of refraction n n c v λvac λ k kvac 283 Instead of n which is near to 1 the refractivity N n 1 106 284 is preferred The appropriate determination of the refractivity N along the signal propagation path is essential in satellite geodesy because travel times of electromagnetic signals or phase differences between different electromagnetic waves are measured and they are scaled into distances measured in meters with the adopted or modeled propagation velocity 2312 Dispersion Phase Velocity and Group Velocity A medium in which the propagation velocity of electromagnetic waves depends on the frequency is called a dispersive medium In such a medium the refractivity depends on the frequency or the wavelength The dispersion effect is caused by electromagnetic interactions between the electrically charged field of the medium and the external field of the penetrating wave When the atomic frequency of the medium and the frequency of the penetrating wave are close together resonance occurs which generates a frequencydependent influence on the propagation velocity see eg Wells 1974 Davies 1990 Brunner 1992 Langley 1998b The expression dv dλ is called velocity dispersion 285 In a medium with velocity dispersion we observe different propagation velocities for sinusoidal waves phases and groups of waves We must distinguish the propagation velocity of the phase of a particular wave with uniform wavelength phase velocity vp and the 46 2 Fundamentals propagation velocity of a wave group generated by a superposition of different waves of different frequencies group velocity vg The relation between group velocity and phase velocity was first described by Rayleigh 1881 as vg vp λdvp dλ 286 For the derivation of 286 seeWells 1974 or textbooks on physics or electromagnetic waves Corresponding relations are valid for the refraction index ng np f dn df 287 The group velocity characterizes the velocity at which energy or information is propa gated Following the theory of Fourier such a signal can be regarded as a superposition of many particular periodic waves with different frequencies which all experience a different dispersion In satellite geodesy we have to prove carefully whether for a particular observable the group velocity or the phase velocity has to be applied In GPS technology for instance the propagation of code signals is affected by the group velocity vg and the propagation of carrier phases by the phase velocity vp The ionosphere is a dispersive medium for microwaves but the troposphere is not For frequencies in the optical domain the contrary holds The phase velocity in a dispersive medium can exceed the vacuum velocity c The group velocity however cannot in accordance with the relativity theory In nondispersive media vg vp 2313 Frequency Domains The frequency spectrum of electromagnetic waves spans nearly 20 orders of magnitude Fig 217 In satellite geodesy only two rather small domains are used namely the visible light 04081015 Hz and microwave domains 1071010 Hz Some prefixes and symbols which are commonly used for the description of frequencies are explained in Table 22 Figure 217 Spectrum of electromagnetic waves m acoustic waves are included for informa tion 23 Signal Propagation 47 Table 22 Prefixes symbols and orders of magnitude centi c 102 Hecto H 102 milli m 103 Kilo K 103 micro µ 106 Mega M 106 nano n 109 Giga G 109 pico p 1012 Tera T 1012 femto f 1015 Peta P 1015 Different kinds of subdivisions and terminology are in use for electromagnetic waves In information technology a subdivision into frequency bands is customary Table 23 In satellite geodesy the subdivision into radar bands is also in use Ta ble 24 The particular assignments to capital letters were generated in a random way during World War II Table 23 Frequency bands symbol denomination wavelength frequency VLF Very Low Frequency 10 000 m 30 KHz LF Low Frequency 100010 000 m 30300 KHz MF Medium Frequency 1001000 m 3003000 KHz HF High Frequency 10100 m 330 MHz VHF Very High Frequency 110 m 30300 MHz UHF Ultra High Frequency 10 cm1 m 3003000 MHz SHF Super High Frequency 1 cm10 cm 3 GHz30 GHz EHF Extremely High Frequency 1 mm1 cm 30300 GHz Table 24 Radar bands denomination frequency mean wavelength Pband 220300 MHz 115 cm Lband 12 GHz 20 cm Sband 24 GHz 10 cm Cband 48 GHz 5 cm Xband 8125 GHz 3 cm Kuband 12518 GHz 2 cm Kband 18265 GHz 135 cm Kaband 26540 GHz 1 cm 48 2 Fundamentals 232 Structure and Subdivision of the Atmosphere The structure of the atmosphere can be described for most practical purposes as a set of concentric spherical shells with different physical and chemical properties Various subdivisions are possible that in most cases follow the main characteristic feature of interest Fig 218 gives a simplified schematic representation With respect to signal propagation a subdivision into troposphere and ionosphere is advisable because the particular propagation conditions are quite different The troposphere is the lower part of Earths atmosphere which extends from the surface to about 40 km Signal propagation depends mainly on the water vapor content and on temperature The ionosphere is the upper part of Earths atmosphere between approximately 70 and 1000 km Signal propagation is mainly affected by free charged particles Figure 218 Possible subdivision schemes of Earths atmosphere The troposphere is the gaseous atmosphere where the daily weather takes place The temperature decreases with height by 65 Ckm Horizontal temperature gradients are only a few degrees100 km Charged particles are virtually absent The uncharged atoms and molecules are well mixed and thus the troposphere is practically a neutral gas The index of refraction is slightly greater than 1 It decreases with increasing height and becomes nearly 1 at the upper limit of the troposphere corresponding to the continuously decreasing density of the medium Nearly 90 of the atmospheric mass is below 16 km altitude and nearly 99 is below 30 km Lutgens Tarbuck 1998 For electromagnetic waves in the radiofrequency spectrum the troposphere is not a dispersive medium The index of refraction does not depend on the frequency it de pends on air pressure temperature and water vapor pressure Because of the dynamic behavior of tropospheric conditions it is difficult to model the index of refraction 23 Signal Propagation 49 The ionosphere can be defined as that part of the high atmosphere where sufficient electrons and ions are present to affect the propagation of radio waves Davies 1990 Langley 1998b The generation of ions and electrons is proportional to the radiation intensity of the sun and to the gas density A diagram indicating the number of ions produced as a function of height shows a maximum in ion production rate Such a Height Intensity of solar radiation Ion production rate Density of ionized gas hmax ne Figure 219 Chapman curve of ionization diagram is called the Chapmanprofile the general behavior of this profile is il lustrated in Fig 219 The exact shape of the curve and the related numerical val ues are not given in the graph because they depend on several parameters and they are highly variable functions see later The spatial distribution of elec trons and ions is mainly determined by two processes photochemical processes that de pend on the insolation of the sun and govern the production and de composition rate of ionized parti cles and transportation processes that cause a motion of the ionized layers Both processes create different layers of ionized gas at different heights The main layers are known as the D E F1 and F2layers In particular the F1layer located directly below the F2layer shows large variations that correlate with the relative sun spot number Geomagnetic influences also play an important role Hence signal propagation in the ionosphere is severely affected by solar activity near the geomagnetic equator and at high latitudes cf 7441 The state of the ionosphere is described by the electron density ne with the unit number of electronsm3 or number of electronscm3 The four principal layers are designated in Table 25 Table 25 Characteristic features of the main ionospheric layers layer D E F1 F2 height domain km 6090 85140 140200 2001000 electron density at day 102104 105 5 105 106 ne elcm3 at night 2 103 5 104 3 105 Due to variable insolation of the Sun the spatial distribution of the layers varies during the day The Dlayer is only generated over the daylight side of Earth The F increases with increasing zenith angle z to a satellite target Table 26 Wanninger 1994 shows that for small elevation angles TEC can reach at most three times the value of VTEC This is also true for the effect of ionospheric path delay in satellite geodesy see Table 26 23 Signal Propagation 51 Table 26 Obliquity factor F and distance d between observer and subionospheric point E z zI F d degree degree degree km 90 0 0 100 0 60 30 28 113 215 30 60 55 173 603 20 70 62 214 873 10 80 68 266 1344 5 85 70 287 1712 geographic location time of the day season of the year and solar activity Regions of highest TEC are located approximately 15 to 20 degrees each side of Earths magnetic equator cf Fig 752 p 313 The day to day variability has a standard deviation of 20 to 25 of monthly average conditions Klobuchar 1996 Short term variations are travelling ionospheric disturbances TID with a period of minutes to about 1 hour and ionospheric scintillation with a period of seconds Of particular importance is the variance of the solar UV flux The sun varies in its energy output over an approximate 11year cycle see Fig 221 The last maximum was in the year 2000 In times of solar maximum the signals of operational GNSS systems can be heavily corrupted cf 7441 1950 1960 1970 1980 1990 2000 1995 2000 1990 0 50 100 150 200 250 solar activity sunspot number 250 200 150 100 50 0 year Figure 221 11year cycles of solar activity The high variability of the ionosphere makes modeling and prediction difficult Models of the electron density fall into two types empirical models derived from existing data and physical models derived from physical principles Examples of 52 2 Fundamentals empirical models are the International Reference Ionosphere IRI the Bent model and the Klobuchar model Physical models are rather cumbersome and seldom used in satellite geodesy Within the models theVTEC is described either by twodimensional polynomials for local and regional applications or by spherical harmonic expansion for continental and global representation For details see Davies 1990 Wild 1994 Klobuchar 1996 Wanninger 2000 Since 1996 the International GPS Service IGS 781 has generated on a regu lar basis global TEC models from GPS observations at selected globally distributed stations Rapid products are available after several hours and precise products after three days The ionosphere is a dispersive medium for radio waves For an index of refraction n in ionized gas the formula of dispersion eg Davies 1990 is n2 1 ne C2e2 πf 2me 292 with e elementary mass and me electron mass Rearranging and neglecting higher order terms gives n 1 C ne f 2 293 with C 403 The coefficient C contains all constant parameters An explicit deriva tionof293canbefoundinHartmann Leitinger1984orintextbooksongeophysics Formula 293 indicates that the index of refraction and thus the time delay of signal propagation is proportional to the inverse of the squared frequency Consequently one part of the ionospheric delay can be modeled when two frequencies are used 233 Furthermore 293 shows that higher frequencies are less affected by the ionosphere 233 Signal Propagation through the Ionosphere and the Troposphere Fig 222 shows for the microwave domain the behavior of the refractivity N as a function of height For the troposphere N is positive and independent of the frequency used For the ionosphere N is negative and depends on the frequency According to 293 the refractivity decreases with increasing frequency One consequence is that higher accuracy can be obtained in propagation modeling when higher frequencies are used cf Table 27 Two considerations however limit the increase of the selected frequencies Higher frequencies are technically demanding The frequency domain above 10 GHz cannot easily be utilized with existing technology With higher frequencies the atmospheric absorption in the troposphere increases Without rainfall the absorption can be neglected for frequencies between 30 MHz and 30 GHz With precipitation however signals in the frequency domain 1 GHz experience considerable attenuation 23 Signal Propagation 53 NI h Height km 250 MHz 400 MHz 16 GHz 1000 100 10 Nth 1 N 1200 900 600 300 300 600 Figure 222 Behavior of the refractivity N for microwaves as a function of height for the troposphere Nt and the ionosphere NI Table 27 Effect of the ionospheric propagation delay on range measurements for single frequency observations and residual errors for dualfrequency observations Hieber 1983 singlefrequency 400 MHz 1600 MHz 2000 MHz 8000 MHz average effect 50 m 3 m 2 m 012 m for 90 250 m 15 m 10 m 06 m maximum effect 500 m 30 m 20 m 12 m dualfrequency 150400 4002000 12271572 20008000 MHz MHz MHz MHz average effect 06 m 09 cm 03 cm 004 cm for 90 10 m 66 cm 17 cm 021 cm maximum effect 36 m 22 cm 45 cm 043 cm The selection of frequencies for a particular satellite system is always a compro mise This was the case with the TRANSIT system 6 when 150400 MHz were selected reflecting the technological progress of the 1960s And this is true for the GPS system 7 with the selection of 1216 GHz Table 27 gives an impression of how the ionosphere affects the propagation delay at different frequencies and it indicates the residual errors when measurements on two frequencies are available It becomes clear that for the GPS system operating with two frequencies the residual errors are mostly below 1cm 54 2 Fundamentals Because of the very different behavior of signal propagation in the troposphere and ionosphere their effects are usually discussed and treated as separate topics For a review see Davies 1990 DeMunck et al 1992 Wanninger 1994 Schüler 2001 2331 Ionospheric Refraction The influence of the ionosphere on signal propagation in the radio frequency domain is mainly characterized by the dispersion The refraction coefficient describing the propagation of phases can be written as a power series np 1 c2 f 2 c3 f 3 c4 f 4 294 The coefficients ci are independent of the carrier frequency f however through the electron density ne they depend on the state of the ionosphere The coefficient c2 was estimated with 293 to be c2 403 ne Hence we find the approximate relation np 1 403 ne f 2 295 Consequently with a knowledge of the electron density an approximate correction can be computed for the delay in signal propagation Various some highly sophisticated models have been developed for estimation of the electron density For correction of GPS measurements the model of Klobuchar 1987 is usually applied 7441 This model corrects about 50 of the total ionospheric effect The model is represented through a set of variable coefficients that are valid for a few days A much better correction is possible when the coefficient c2 can be determined from simultaneous observations of satellite signals transmitted on two different frequencies These re quirements were fulfilled with the TRANSIT system 62 and by modern systems like GPS 7 GLONASS 77 PRARE 4333 DORIS 67 and most of the altimeter sensors 92 The first order term c2f 2 can be separated from higher order terms when they are sufficiently different in magnitude For the frequencies of the TRANSIT system the 3rd order term is 10 times smaller than the 1st order term the 2nd order term can be neglected Black 1980 For GPS the 1st order term is nearly three orders of magnitude larger than the other terms The remaining residual errors are discussed together with the particular observation method eg 642 7441 933 The refraction coefficient ng of the group delay follows from equation 287 and with the first derivative of 294 dn df 2c2 f 3 3c3 f 4 4c4 f 5 296 as ng np 2c2 f 2 3c3 f 3 4c4 f 4 297 and with 294 as ng 1 c2 f2 2c3 f3 3c4 f4 298 for the phase and the group delay ΔSIONp 403TEC f2 and ΔSIONg 403TEC f2 2106 N T C1 P T C2 e T C3 e T2 2107 For H 11 000 m The integration of 2111 along the curved signal path is very difficult and not possible in the closed form In practice several simplifications are used the line of sight is assumed to be a straight line Kd 1552 10⁷ P τ¹ Hd Kw 1552 10⁷ 4810 e τ² Hw When larger portions of the satellite orbit are observed for example with GPS or GLONASS 7 a tropospheric scale bias CT can be introduced into the adjustment algorithm as a parameter for the total correction term Black 1980 proposed for the adjustment of Transit observations ΔST ΔSd ΔSw CT Ia with Ia 1 cos E 1 015 H r 2 ½ 23 Signal Propagation 61 For recent developments see Nothnagel 2000 or Schüler 2001 Satellites designed for Earth observation like ERS12 ENVISAT 432 92 carry besides other sen sors also a radiometer The radiometer data can be used for the tropospheric delay correction of altimeter measurements cf 933 When the highest accuracy is required for groundbased observations eg in the use of VLBI 1112 or GPS 7622 for geodynamic modeling attempts can be made to measure the water vapor content directly along the signal propagation path with a water vapor radiometer The development of such devices began in about 1980 and has now reached a certain level of maturity Nothnagel 2000 Besides stationary instruments eg in connection with VLBI antennas Elgered Jarlemark 1998 systems are also available for field applications Bürki Kahle 1995 Fig 224 shows a portable dual frequency microwave water vapor radiometer developed for geodetic applications at the Technical University ETH Zürich Switzerland The instrument operates at 238 and 315 GHz and is capable of automatically tracking space targets like GPS satellites The accuracy estimate for the determination of the signal path delay is about 2 mm Figure 224 Portable dual frequency microwave water vapor radiometer WVR2000 courtesy ETH Zürich In stable meteorological conditions the water vapor content of the air shows a high regional correlation over horizontal distances to about 50 km In such cases the biases are nearly identical at adjacent stations and they cancel through differencing The propagation delay caused by the troposphere is nearly identical for the total spectrum of visible light and for the radio frequency domain Due to the wet compo nent however the absorption is much greater for visible light 3 Satellite Orbital Motion Precise timedependent satellite positions in a suitable reference frame are required for nearly all tasks in satellite geodesy The computation and prediction of precise satellite orbits together with appropriate observations and adjustment techniques is for example essential for the determination of geocentric coordinates of observation stations 121 field parameters for the description of the terrestrial gravity field as well as for the determination of a precise and high resolution geoid 122 trajectories of land sea air and spacevehicles in realtime navigation 123 Earths orientation parameters in space 124 Essentially the accuracy of the final results depends on the accuracy of the available satellite orbits This is increasingly true for tasks in applied geodesy such as the determination of relative coordinates with the Global Positioning System 7 The requirement for 1 cm relative accuracy in coordinates implies the requirement for the knowledge of satellite orbits on the few meter accuracy level or even better 743 Those who apply satellite methods in geodesy navigation and adjacent fields must have a basic knowledge of satellite orbital motion including the major perturbations in order to assess the appropriate requirements for orbit determinations Chapter 3 aims to provide this basic knowledge Starting with the undisturbed Keplerian motion in a central force field 31 the major perturbations as well as an elementary perturbation theory are discussed 32 The effects of perturbations on satellite orbits are also treated 324 A section on the integration and representation of orbits 33 follows because algorithms for orbit improvement are included in modern software packages for applied satellite geodesy The appropriate use of satellite ephemerides is discussed together with the corresponding observation methods eg 715 31 Fundamentals of Celestial Mechanics TwoBody Problem In celestial mechanics we are concerned with motions of celestial bodies under the influence of mutual mass attraction The simplest form is the motion of two bodies twobody problem For artificial satellites the mass of the smaller body the satellite usually can be neglected compared with the mass of the central body Earth The twobody problem can be formulated in the following way Given at any time the positions and velocities of two particles of known mass moving under their mutual gravitational force calculate their posi tions and velocities at any other time Under the assumption that the bodies are homogeneous and thus generate the grav itational field of a point mass the orbital motion in the twobody problem can be 31 Fundamentals of Celestial Mechanics TwoBody Problem 63 described empirically by Keplers laws 311 It can also be derived analytically from Newtonian mechanics 312 The twobody problem is one of the few problems in celestial mechanics that has a complete solution Other subjects of celestial mechanics are the threebody and the multibody problem ie motions of three and more celestial bodies under the influence of their mutual gravitation These problems have no general solution Orbit perturbations 32 orbit determination 33 and ephemeris computation are also treated in celestial mechanics Orbit determination refers to orbital parameters derived from observations 331 Ephemeris computation refers to geocentric or topocentric positions of celestial bodies or artificial satellites that are derived from orbital elements eg 333 715 Modern celestial mechanics has its origin in the year 1687 with the publication of Isaac Newtons Principia Philosophiae naturalis principia mathematica Herein the law of gravitation and the laws of motion are described for the first time In the subsequent 300 years there were no major revolutions in celestial mechanics Only the launch of the first artificial satellite and the development of powerful computers gave an impetus for new ideas Besides the classical observation of directions the measurements of ranges and rangerates can now be made Also the influences of Earths anomalous gravitational field and nongravitational forces have to be modeled in addition to the classical perturbations caused by the Sun the Moon and the planets Through the development of high speed computers large amounts of data can be processed and numerical integration methods can be used Comprehensive textbooks are available for a detailed study of problems and meth ods in celestial mechanics such as Stumpff 195919651974 Brouwer Clemence 1961 Kovalevsky 1971 Kovalevsky et al 1989 Schneider 1981 1993 Taff 1985 Vinti 1998 Easily readable introductions with special regard to satellite and rocket orbits are Escobal 1965 Bate et al 1971 Roy 1978 Chobotov 1991 Logsdon 1998 and Montenbruck Gill 2000 Suitable references with particular emphasis on GPS orbits are Rothacher 1992Yunck 1996 and Beutler et al 1998 311 Keplerian Motion JohannesKepler 15711630formulatedthethreelawsofplanetarymotionassociated with his name from an empirical study of observational data collected by Tycho Brahe 15461601 an astronomer who mainly worked in Denmark The three laws give a description of the planetary motion but not an explanation They provide a very good approximation to the real motion within the solar system because the planetary masses can be neglected when compared to the mass of the sun and because of the fact that the sun can be considered a point mass due to the large distances involved This is why the undisturbed gravitational motion of point masses is also called Keplerian motion From a historical point of view it may be of interest that Kepler through his three laws provided the major breakthrough for Copernicuss heliocentric hypothesis In the following Keplers laws of planetary motion are introduced and explained 1st Law The orbit of each planet is an ellipse with the Sun at one focus The orbital geometry is defined by this law The usual relations and symbols are shown in Fig 31 The major axis in the ellipse Aπ is called the line of apsides The orbital point farthest from the center of mass of the orbital system O is named the apocenter The point π on the orbit closest to the center is named pericenter When 0 is the center of the sun A and a are called aphelion and perihelion respectively When 0 is identical with Earths center of mass then A and π are named apogee and perigee The angle ν is the true anomaly The Keplerian motion refers to a plane The orbital plane can be used for the definition of a coordinate system with 0 being the origin The location of a point mass m may be described with polar coordinates r ν when 0π is selected as one axis of the orbital coordinate system With r distance of the point mass m from the center of the primary mass ν true anomaly a semimajor axis e numerical eccentricity and p parameter of the ellipse we find for the equation of the elliptical curve r p 1 e cos ν Equation 31 also gives the mathematical form of Keplers first law From the elliptical geometry other relations follow p b2 a e 1 b2 a2 a 1 1 e2 b p 1 e2 a e is the linear eccentricity and gives the distance of the focal points from the orbital center For e 0 it follows a b p ie the ellipse evolves to a circle The eccentricity angle φ may be used instead of e The following relations are then valid e sin φ p a cos2 φ 1 e2 cos φ b a cos φ p sec φ 2nd Law The line from the Sun to any planet sweeps out equal areas of space in equal lengths of time Keplers second law also called the Law of Areas describes the velocity of a planet in its orbit With this law it is possible to determine the location of a planet as a function of time with polar coordinates r and v According to Fig 32 the formula ΔF 1 2 r2ρΔν is approximately valid for the area of an infinitesimal triangle 0 P P According to the second law the area ΔF swept by is proportional to the corresponding time interval Δt thus r2Δν c Δt Equation 34 is the mathematical expression of the law of areas Kepler actually found it earlier than his first law 31 Further relations can be deduced Introducing rectangular coordinates x y into Fig 31 we get x r cos v y r sin v r x2 y2 and tan v y x The derivative of 36 with respect to time leads to dν cos2 v xy yx x2 Substituting cos v in 37 by 35 and introducing 37 into 34 gives an alternative representation of Keplers second law using rectangular coordinates xy yx c c is called the constant of areas Equation 38 will also be derived using Newtonian mechanics 312 66 3 Satellite Orbital Motion In mathematical formulation this means for different planets Pi with periods of revo lution Ui mean motions ni 2πUi 39 and semimajor axes ai a3 i U2 i C2 4π2 310 C is a constant for the planetary system Inserting 39 into 310 gives the commonly used expression a3 i n2 i C2 311 This law was found empirically by Kepler because it approximates very well the motion of the large planets However a completely different numerical value for C2 is obtained for the system of Jovian moons Therefore a more general relation is useful a3 U2 k2 4π2 M m 312 where k is a universal constant and M m are the respective masses Using 312 it is possible to determine the masses of celestial bodies Keplers laws describe the simplest form of motion of celestial bodies under the assumptionthatnoexternalperturbingforcesarepresent andthattherespectivemasses can be considered to be point masses or homogeneous bodies with spherical mass distribution For the motion of an artificial Earth satellite these assumptions are only valid in a first approximation Keplerian orbits consequently can only be used as a simple reference orbit and they give only qualitative information on the kind of motion Kepler himself was convinced that his three empirically found laws followed a more general law This more general law was formulated by Isaac Newton 16431727 in the form of the Law of Gravitation 312 Newtonian Mechanics TwoBody Problem 3121 Equation of Motion In the first book of Principia Newton introduced his three laws of motion 1 Every body continues in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by an external impressed force 2 The rate of change of momentum of the body is proportional to the force im pressed and is in the same direction in which the force acts 3 To every action there is an equal and opposite reaction The second law expressed in mathematical form is K mr 313 31 Fundamentals of Celestial Mechanics TwoBody Problem 67 where K is the vector sum of all forces acting on the mass m and r is the vectorial acceleration of the mass measured in an inertial reference frame In addition we find Newtons famous law of universal gravitation 1687 in the third book section I of the Principia Every particle of matter in the Universe attracts every other particle of matter with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them K GMm r2 314 M and m are two particles of matter and G is the universal constant of gravitation with Torge 2001 G 667259 000085 1011m3kg1s2 315 Notice that the law of gravitation in Newtons text is not written in the above closed form but it can be taken from a somewhat broader explanation α M x1 r m x2 Figure 33 Components within Newtons equa tion of motion Within a Cartesian coordinate sys tem with the axes x y z and with α β γ being the angles between the direction of force and the respective axes of the system we find from 313 for the mo tion of M with respect to m expressed in components Fig 33 M x1 Kx K cos α and after substituting 314 M x1 GMm r2 cos α GMm r3 x1 x2 After rearrangement we obtain for all three components M x1 GMm r3 x2 x1 M y1 GMm r3 y2 y1 Mz1 GMm r3 z2 z1 316 For the motion of m with respect to M mx2 GMm r3 x2 x1 my2 GMm r3 y2 y1 mz2 GMm r3 z2 z1 317 Transferring the origin of the coordinate system to the center of mass M using the substitutions x2 x1 x y2 y1 y z2 z1 z 68 3 Satellite Orbital Motion dividing 316 by M and 317 by m and then subtracting 316 from 317 x GM m x r3 y GM m y r3 z GM m z r3 where r2 x2 y2 z2 In vector form 318 becomes r d2r dt2 G M m r3 r For artificial Earth satellites the mass m can be neglected The basic equation of satellite motion is then r G M r3 r Equation 320 is the vector form of a second order differential equation with six integration constants In other words the motion of a celestial body around its central body governed by the mutual gravitation has six independent parameters Usually the six Keplerian orbital parameters Fig 34 are used The equation of motion 320 was derived under the assumption that only gravitational forces are present that the mass of the satellite can be neglected and that the central mass can be considered as a point mass This is in fact not correct in particular the inhomogeneous structure of Earth is acting on the motion of the nearEarth satellite As a consequence the Keplerian orbit 320 can only be considered to be a first approximation to the true satellite orbit The implications of the perturbing forces are treated in 32 laws of gravitation and motion in a rigorous way Some elements are presented in the sections that follow A comprehensive treatment of the subject may be found in textbooks on celestial mechanics such as Stumpff 195919651974 Brouwer Clemence 1961 Schneider 1981 1993 Taff 1985 Vinti 1998 3122 Elementary Integration Multiplication of 318 by x y z respectively and forming pairs of differences yields xy xi zy 0 yz xy 0 xi xz 0 321 Integration of 321 gives xy yi C1 yz xy C2 xi xz C3 322 where C1 C2 C3 are arbitrary constants Multiplying the equations one after the other with x y and forming the total sum cancels out the left hand terms to give C1 C2X C3Y 0 323 This is the equation of a plane containing the origin of the coordinate system We can state that the satellite or planet is moving in a plane which contains the center of the central body The orientation of the orbital plane in space can be specified using two parameters for instance i and Ω as defined in Fig 34 The relation between i Ω and C1 C2 C3 is given by Roy 1978 p 103 f Montenbruck Gill 2000 p 28 C1N cos i C2N sin Ω sin i and C3N cos Ω sin i 324 with N C1² C2² C3² being the normal to the orbital plane Since the motion occurs in a plane a rectangular plane coordinate system ξ η can be introduced with the origin at the mass center of the central body Fig 35 The equations of motion corresponding to 320 and described in components hold ξ GM ξ r³ η GM η r³ 325 with r² ξ² η² The equivalent of 321 follows ξ ηs 0 326 Figure 35 Illustration of the law of areas 70 3 Satellite Orbital Motion which after integration becomes ξ η ηξ p1 327 Substituting 327 with polar coordinates ξ r cos χ and η r sin χ 328 gives r2 χ p1 329 Considering an infinitesimal small area dF being swept by r during the infinitesimal time interval dt Fig 35 we find for the area of the infinitesimal triangle dF 1 2r2 χdt dF dt 1 2r2 χ 1 2p1 330 hence F 1 2p1t p2 331 The equations 330 and 331 contain in essence Keplers second law Hence it can be stated the motion takes place within a plane and the motion is governed by the law of areas What is missing is a statement about the shape of the orbit Multiplying equations 325 by 2 ξ and 2 η respectively gives ξ 2 ξ GM ξ r3 2 ξ η 2 η GM η r3 2 η 332 and summing 332 gives d dt ξ2 η2 2 GM r3 ξ ξ η η 333 With r2 ξ2 η2 2 r r 2 ξ ξ 2 η η it follows that d dt ξ2 η2 2 GM r2 r 2GM 1 r 334 which after integration becomes ξ2 η2 2GM r p3 335 With polar coordinates 328 and after differentiation we get i² r²χ² 2GMr p3 336 One solution of this differential equation is Brouwer Clemence 1961 r p 1 e cosχ ω 337 where p e ω are constants Equation 337 is the polar form of a conic section For χ ω the satellite distance r becomes a minimum ie the satellite passes through the perigee Since the angular distance of a satellite from the perigee was introduced as the true anomaly ν 34 the identity χ ω ν is valid If ν 90 then r p Further we know from ellipsoidal geometry 32 p a1 e² Now the integration constants p e ω can be expressed geometrically and 337 can be rewritten as r p 1 e cos ν 338 If the argument of the latitude u is measured from the ascending node of the satellite orbit the origin of the angular measurement can be fixed An alternative formulation of 338 is r p 1 e cosu ω 339 where ω is known as the argument of the perigee 34 With these substitutions we have dealt with five of the six integration constants namely Ω i ω e a The last free constant is the quantity p2 in equation 331 Keplers law of areas which specifies the timedependent position of the satellite in its orbit Several equivalent parameters are in use among others the time of transit through the perigee t0 or the true anomaly ν The following relations can be established between Keplers orbital elements and the integration constants eg Arnold 1970 Brouwer Clemence 1961 p p1² GM e² 1 p1² p3 G²M² p1 GM p3 GM a 340 With 331 and the use of 340 Keplers third law can be deduced The period of one satellite revolution is T t2 t1 and thus we obtain for the area swept after one revolution F2 F1 12 p1t2 t1 πab 341 ie the area of an ellipse With p1 GM b² a²1 e² p a1 e² we obtain after some rearrangement T 2π GM a32 342 With the mean angular motion n 2π T we obtain the mathematical expression for Keplers third law n² a³ GM 343 With this we have derived Keplers three laws using only Newtons basic equations 313 and 314 Using equation 335 another important relation can be deduced Substituting 340 for p3 gives the velocity of a satellite in its orbit v² ξ² η² 2GMr GM a 344 Equation 336 with χ x gives the following equation in polar coordinates v² i² r²χ² GM 2r 1a 345 Equation 345 is well known as the energy integral and demonstrates that the velocity of a celestial body depends on the distance r and the semimajor axis a but not on the eccentricity and thus not on the form of the orbit cf 361 Furthermore equation 329 substituting 340 for p1 leads to another form of Keplers second law r²ν GMa1 e² 346 By replacing ν in 345 with 346 we obtain i² r² GM a1 e² r⁴ GM 2r 1a 347 Substituting 343 into 347 and rearranging gives Brouwer Clemence 1961 ndt r a dr a²e² r a² 348 The geometrical relation from Fig 36 r a1 e cos E 349 is put into 348 ndt 1 e cos EdE 350 Integration gives nt t0 E e sin E 351 The variable E is called the eccentric anomaly The integration constant t0 can be considered to be the epoch of transit through the perigee The lefthand side of 351 increases linearly with time Instead of t a new variable M the mean anomaly can be defined as M nt t0 352 The form M E e sin E 353 is called Keplers equation The relationship with the true anomaly ν is given by tan ν2 1 e² sin E cos E e 354 All three anomalies E M ν are zero when the satellite passes through the perigee They can be used to determine the satellite position within the orbit and hence each is suitable as a sixth orbital parameter In satellite geodesy the mean anomaly M is usually given preference because it can be interpolated linearly with time In order to compute E from M equation 353 has to be transformed into an elliptical series expansion Many solutions can be found in the literature One example is Brouwer Clemence 1961 p 76 Taff 1985 p 61 E M e 18 e³ 1192 e⁷ 19216 e⁹ sin M 12 e² 16 e⁴ 148 e⁶ sin 2M 38 e³ 27128 e⁵ 2435120 e⁷ sin 3M 132 e⁴ 415 e⁶ sin 4M 125384 e⁵ 31259216 e⁷ sin 5M 2780 e⁶ sin 6M 1680746080 e⁷ sin 7M 355 For small eccentricities the following iteration yields a very fast solution E0 M Ei M e sin Ei1 i 1 356 3123 Vectorial Integration Starting with the equation of motion 320 it is possible to derive the basic theorem of the twobody motion in an explicit and elementary way On the other hand the use of vector operations gives a rather transparent and closed representation eg Bate et al 1971 Taff 1985 Basic equations for energy angular momentum and orbital characteristics can be easily derived Dot multiplication of equation 320 with the velocity vector r v yields r r r r GMr³ 0 357 or v v GMr³ r r 0 358 Since in general a a a a we find vi GMr³ r 0 359 Substituting ddt v²2 vi and ddt GMr GMr² r into 359 it follows that ddt v²2 ddt GMr 0 or ddt v²2 GMr 0 360 Integration of 360 results in a constant EM the energy integral EM v²2 GMr 361 which we know already from equation 345 in a different notation The first term on the righthand side is the kinetic energy of the satellite with unit mass m 1 and the second term its potential energy GMr Hence the total mechanical energy of the satellite motion is constant which is to be expected when no external forces are present The negative sign for the potential energy comes from choosing its zero reference at infinity Through this procedure a free integration constant inherent in equation 360 is fixed Cross multiplication of equation 320 with r leads to r r r GMr³ r 0 362 The cross product of a vector with itself is zero hence r r 0 363 With ddt r r r r r r it follows that ddt r r 0 and after integration h r r r v 364 h is a constant vector perpendicular to the plane containing r and v The physical interpretation of equation 364 is that the angular momentum of a satellite with unit mass m 1 remains constant along its trajectory With h constant the satellite motion must occur within a spacefixed plane The orientation of this orbital plane can be described through the elements Ω and i which have been introduced before The relation is given by h₀ sin i sin Ω sin i cos Ω cos i h₀ h h 365 At the same time h₀ defines the direction of motion of the satellite From the definition of the cross product we find for the magnitude of h according to Fig 37 h rν cos Φ 366 The flightpath angle Φ indicates the direction of the orbital motion A further vector multiplication of 320 with h leads to the form of the satellite orbit r h GMr³ h r 367 It can be easily proved that the lefthand side of 367 equals ddtr h For the righthand side we find with 365 and r ṗ r ṙ GMr³h r GMr³r v r Furthermore GM ddtr h GMr υ GMṙr² r Thus 367 can be reformulated as ddtr h GM ddt1r The integration of both sides gives ṙ h GMr ṗ B The vector integration constant B is a linear combination of ṗ h and r and consequently it lies in the orbital plane B is directed toward the perigee as can easily be verified eg Batt et al 1971 Dot multiplication of both sides of 370 creates a scalartype equation because a b c a b c and a a a² h² GM r r B cos υ υ is the angle between the constant vector B and the radius vector r Solving for r gives r h²GM B cos υ Introducing p h²GM and e BGM it follows the already known equation of a conic section r p1 e cos υ With the three basic integrals Integral of energy 361 Integral of momentum 364 Integral of the orbit 372 we can summarize our knowledge concerning orbital motion 31 Fundamentals of Celestial Mechanics TwoBody Problem 77 1 The family of curves called conic sections circle ellipse parabola hyperbola represent the only possible paths for an orbiting object in the twobody problem 2 The focus of the conic orbit must be located at the center of the central body 3 The sum of kinetic and potential energy does not change as the satellite moves along its conic orbit which means that the satellite must slow down as it gains altitude and speed up as r decreases in such a manner that the energy sum remains constant 4 The orbital motion takes place in a plane which is fixed in inertial space 5 The angular momentum of a satellite about the central body remains constant The reader should note that in the literature the basic integrals listed above are also called constants of the motion 313 Orbit Geometry and Orbital Motion Some fundamentals of orbit geometry have already been introduced Table 31 summa rizes the most important properties of the four conic sections which serve as possible orbits One characteristic quantity is the parameter p which is also called the semi latus rectum Table 31 Characteristic properties of conic sections circle ellipse parabola hyperbola eccentricity e 0 0 e 1 1 e 1 parameter p a a 1 e2 p a e2 1 semimajor axis a a a a 0 semiminor axis b a a 1 e2 a e2 1 pericenter distance rp a a 1 e p2 a e 1 apocenter distance ra a a 1 e Comparing 372 with 338 demonstrates that the parameter p only depends on the angular momentum h p h2 GM 374 This is clarified in Fig 38 Bate et al 1971 where it is supposed that a cannonball is fired horizontally from a cannon in an atmospherefree environment From equation 366 we obtain h rv because the flight path angle equals zero Therefore progressively increasing the muzzle velocity υ is equivalent to increasing the angular momentum h generating a family of curves as is shown in the figure Each of the curves represents a conic section with the focal point located at the Earths center of mass Furthermore it is illustrated that the velocity vector at perigee vp is horizontal ie perpendicular to the radius vector rp as follows from 366 The same is valid at apogee EM v²2 GMr h²2r²p GMrp With rp a1 e and p a1 e² from Table 31 and with 374 it follows that h² GM a1 e² and EM GM a1 e²2a²1 e² GMa1 e This can be reduced to EM GM2a This simple equation 378 is valid for all conic sections and demonstrates that the semimajor axis of a satellite orbit only depends on the total energy In other words the energy of the orbital motion is characterized by the size of the semimajor axis Since on the other hand the orbital angular momentum h only depends on p following 374 it can easily be shown that the shape of the orbit which is characterized through e e 1 2EMh²GM² is determined both by the orbital energy and the angular momentum With substitutions from Table 31 equation 378 develops to EM GM2a for the ellipse EM 0 for the parabola and EM GM2a for the hyperbola For a closed curve circle and ellipse a 0 the total energy is negative it has to be considered that the zero reference is at infinity by convention All along the orbit the magnitude of the potential energy exceeds the kinetic energy thus m remains tied to M With a positive energy balance there is kinetic energy left even at infinity thus the orbiting body will leave the gravity field of the central body For escape to just take place the velocity must be changed until the total energy is zero Inserting the expressions of 380 into the energy equation 361 and solving for the velocity v we get v²E GM2r 1a for the ellipse v²P 2GMr for the parabola and v²H GM2r 1a for the hyperbola These equations known as visvivaequations allow the computation of velocities for every point of the orbit when a is known For circular orbits we obtain the simple equation vC GMr For an elliptic orbit cf Table 31 the satellites velocity varies between a maximum vPE GMa1 e1 e and a minimum at apogee vAP GMa1 e1 e According to 380 Earths gravity field can be left on a parabolic orbit The required minimum velocity at the surface escape velocity is using 381 ve 2GMr0 With r0 6370 km and GM 398 600 km³s² it follows that ve 112 kms The period of a satellite revolution in an elliptic orbit was found to be T 2πa³GM Evidently the period only depends on a but not on the eccentricity e The description of a satellite orbit with the six Keplerian elements a e i Ω ω ν is demonstrated in Fig 34 This list is not exhaustive many other parameters are in use Instead of the true anomaly ν often the mean anomaly M or the time of perigee passage is used The parameter p can be utilized instead of the semimajor axis a Instead of the argument of perigee ω the following arguments are used Fig 39 π Ω ω longitude of perigee u ω ν argument of latitude l Ω ω ν π ν Ω u true longitude The right ascension Ω is an angle in the equatorial plane ω and ν are angles in the orbital plane ω and derived quantities containing ω are not defined for circular orbits The relationship to Keplers elements of orientation is given via simple vector operations Fig 310 cos i h Z h h z h cos Ω n X n n x n cos ω n e n e cos ν e r e r Also p h2 GM and e e We can compute a from p using 32 and M from ν using 353 and 354 because the inversion of 354 gives cos E e cos ν 1 e cos ν G is here a variable and not the gravitational constant The relationships between Keplerian elements and Hills variables are given by the equations 394 In order to avoid misunderstanding we introduce here the symbol μ for the product of Earths mass M and the gravitational constant G so that G μa1 e232 u ν ω r G2 1 1 e cos ν H G cos i described by the basic equation 320 32 Perturbed Satellite Motion slowy Because the acceleration of the central body exceeds the remaining perturbing accelerations at least by a factor 10³ cf 324 122 It is therefore possible to approximate for the use of orbit predictions the orbital elements by a power series in time differences t t₀ with t₀ being a mean epoch This form will be used later in 3223 With Lagranges perturbation equations a relationship between the disturbing potential R and the variation of the orbital elements is established eg Brouwer Clemence 1961 p 284 Kaula 1966 p 29 da dt 2 R na dM de dt 1e2 na2 e R M 1e2 na2 e R ω dω dt cos i na2 e R i 1e2 na2 e R e di dt 1 cos i R i na2 1e2 sin i R S dS dt 1 R R i dM dt n 1e2 na2 e 2 R R a In order to avoid singularities alternative forms of perturbation equations are available eg Brouwer Clemence 1961 p 287 Taff 1985 p 308ff In particular for orbits with small eccentricity indeterminate or with small inclination Ω indeterminate other forms are preferable For the entrust set of Hills elements 394 the following relations hold with the geocentric gravitational constant GM μ dr dt μ r2 G2 r3 R r dr dt r R r dG dt R u du dt G r2 dr dt G G sin i i di dt cos i R i 1 G sin i R The analytical integration of the perturbation equations 396 or 3106 requires that the disturbing potential R is written as a function of the orbital elements With the derivatives at hand the integration can then be executed cf 3322 So long as R only depends on Earths anomalous gravity field the relation between the coefficients of the potential expansion and the orbit perturbations can be formulated This aspect is Figure 315 Relation between orbit inclination height and nodal regression left relation between orbit inclination height and perigee rotation right cf Bate et al 1971 V GM r 1 n1 n0 ae r η Cnm cos mλ Snm sin mλPnmcos ϕ 3109 m0 Cnm nm2ts c n ms ptc 1c 3113 Pnpqk h r0h r left frac2p 2nh r left fracn 2p q1 sqrt1e22 right right fracry1yr fracdSnmpqdt GMaefracFnmpGnqpna3sqrt1 e2 sin i cdots fracdlambdanmpqdt GMaeFnmpGnqp left n 2p cos i m right Snmpq ldots Delta nmpq GMaeFnmpGnqpCnmpq cdots Delta lambdat sumnmpq Delta inmpqt ldots ψ n 2p ω n 2p q M mΩ Θ 3121 equals zero Hence only secular perturbations are generated by such nmpqcombinations Again from the condition m 0 it is evident that only the zonal coefficients Cn0 can cause secular perturbations Consequently the influence of the tesseral and sectorial harmonic must be smaller than the influence of the zonal harmonics C20 does not produce secular perturbations in the elements i a e However C20 does give rise to secular variations of the elements Ω ω M because the numerical value of C20 exceeds all other potential coefficients by a factor of 103 These variations can be used as reference elements they represent a secularly preceding Keplerellipse with the elements a e i Ω ω M The remaining perturbations are then described as deviations from the reference values This type of procedure is particularly suitable when very small perturbations have to be analyzed like those produced by geodynamical effects such as solid Earth tides Table 32 Characteristics of perturbations in the elements Parameter secular perturbations longperiod perturbations shortperiod perturbations a e i Ω ω M J3 frac38 left fracaer right5 left 35 fraczr 210 fracz3r3 231 fracz5r5 right J6 left fracaer right6 left 35 945 fracz2r2 3465 fracz4r4 3003 fracz6r6 cdots right ddoty fracpartial Vpartial y dotx 3130 ddotz fracGMzr3 J2 fracaer23 5fracz2r2 J3 left fracaer right2 left 10fracz2r3 35 fracz3r3 r right J5 left fracaer right4 left 15 70 fracz2r2 63 fracz4r4 right J5 frac18 left fracaer right5 left 315fraczr3 945 fracz3r3 693fracz5r5 15fraczr right J6 left fracaer right6 left 315 2205 fracz2r2 4851 fracz4r4 3003 fracz6r6 cdots right 3131 ddotr0 G left fracmEr3 hatr fracmmrm3 hatrm right 3132 Furthermore the acceleration of mE caused by mm ddotrE G fracmm mErr3 hatrm 3133 The relative acceleration of the satellite with respect to Earth is ddotr0 ddotrE ddotr G left fracmmmM3 hatr fracmmrm3 hatrm fracmEr3 right 3134 ddotr fracGMr3 hatr G mm left fracrm rrm3 fracrmrm3 hatrm right 3135 The corresponding influence ddotrs due to the Sun is ddotrs G ms left fracrs rrs3 fracrsrs3 right 3136 The masses of the disturbing bodies and their locations within a geocentric reference frame have to be known for numerical computations Useful constants are for the mass of the Sun GMs approx 1325 cdot 108 ext km3 exts2 and for the mass of the Moon GMm approx 49 cdot 102 ext km3 exts2 3137 Furthermore there are periodic perturbations in the elements Ω ω a e i They are related to the annual and monthly orbital motions of the Sun and the Moon Explicit derivations of the formulas are given by Giacaglia 1973 and Taff 1985 p 348ff Orbital perturbations caused by the Sun and the Moon may be significant see Table 34 They have to be taken into account for orbit computation The acceleration acting on a GPS satellite at a height of 20 000 km is about 5 106 ms2 for the Moon and 2 106 ms2 for the Sun The influence of the planets is only about 3 1010 ms2 It should be noted that 3135 gives the basic equation of the Nbody problem in celestial mechanics 3232 Solid Earth Tides and Ocean Tides Solid Earth tides and ocean tides change Earths gravitational potential and thus cause additional accelerations acting on the satellite which can be considered as an indirect gravitational effect of the Sun and the Moon The acceleration of the satellite caused by solid Earth tides is Rizos Stolz 1985 re k2 2 Gm d r3 d r4 d 3 15 cos2 θ r r 6 cos θ rd rd 3139 where md mass of the disturbing body Sun Moon θ angle between the geocentric position vector r of the satellite and rd and k2 Love number describing the elasticity of Earths body The acceleration of a GPS satellite is rather small being 2 109ms2 For loworbiting satellites such as STARLETTE it is much greater This is why STARLETTE is used for the determination and modeling of solid body tides The tidally induced variations in Earths external potential can be expressed as variations in the spherical harmonic geopotential coefficients For explicit formulas see eg Balmino 1973 Eanes et al 1983 Dow 1988 Kang 1998 Rim Schutz 1999 The effects of ocean tides on satellites are rather difficult to model because of the irregular coast lines Using a global tide model eg from Schwiderski 1984 Eanes Bettadpur 1996 LeProvost et al 1998 it is possible to compute for each point P on the ocean surface the tidal heights and the resulting tidalinduced mass variations dmp ρ0hP t dσ 3140 ρ0 is the average density of water t the time and dσ a surface element The potential variation caused by this mass variation is Rizos Stolz 1985 ΔU Gdmp ae n 1 knPn0 cos Ψy 3141 which can be related to the orbit perturbations via the perturbation equation 3110 In 3141 kn relates the deformation coefficients Pn0 the Legendre polynomials and ψ the geocentric angle between the initial point A and the surface point P The effect of ocean tides on satellite orbits is very small The largest influences are sensed in the inclination angle i and in the nodal longitude Ω The effects have periods between 10 days and 100 days and they are mostly below 07 1 Goad 1977 For GPS satellites the acceleration is of the order of 5 1010ms2 corresponding to less than 1 meter after 2 days For the orbital analysis of nearEarth satellites a detailed modeling of tidal influences is essential Explicit derivations and discussions can be found in Lambeck et al 1975 Goad 1977 Dow 1988 Kang 1998 Rim Schutz 1999 Detailed formulas for the practical computation of solid Earth and ocean tides are described in McCarthy 2000 3233 Atmospheric Drag For loworbiting satellites the most important nongravitational perturbation is caused by a drag due to the interaction between the satellite and particles of the atmosphere The aerodynamic forces acting on the surface of the spacecraft depend on the geometry of the satellite the velocity of the satellite the orientation of the satellite with respect to the flow and the density temperature and composition of the atmospheric gas Hence the appropriate mathematical modeling of the resulting forces turns out to be a rather complicated problem Based on many years of empirical investigation the following formula proves to give useful results Here the acceleration rD is in a direction opposite to the force of the atmospheric resistance rD 1 2 CDρr t A ms r rar ra 3142 where ms mass of the satellite A effective crosssectional area of the satellite CD drag coefficient satellite specific ρr t density of the atmosphere near the satellite r r position and velocity vector of the satellite and ra velocity of the atmosphere near the satellite Assuming that the atmosphere rotates rigidly with Earth we obtain in a geocentric equatorial coordinate system the relative velocity of the satellite with respect to the atmosphere r ra y θ y x y θ x z θ Earth rotation rate 3143 32 Perturbed Satellite Motion 103 Typical values of the coefficient CD range from 15 to 30 and are usually estimated as parameters along with the orbit determination process Montenbruck Gill 2000 For a spherical satellite CD is approximated as 2 For more complicated surfaces like a cylinder a cone or a plane CD becomes larger For the areatomass ratio the spacecraft attitude must be known The density of the atmosphere depends not only on the height but also on other parameters like geographic location season time of the day Sun activity and geo magnetism and it can be computed with suitable models Jacchias 1971 models were derived from satellite orbit perturbations and they form part of the CIRA 72 atmosphere Conventional International Reference Atmosphere For recent model developments see eg Montenbruck Gill 2000 The influence of atmospheric drag decreases rather rapidly with increasing height Table 33 gives an idea of the mean atmospheric density for different heights Cappelari et al 1976 Montenbruck Gill 2000 Table 33 Density of the upper atmosphere Height Density Height Density km gkm3 km gkm3 100 497 400 600 0081 0639 200 255 316 700 0020 0218 300 17 35 800 0007 0081 400 22 75 900 0003 0036 500 04 20 1000 0001 0018 The perturbing forces on the satellite may cause accelerations varying between 103 and 109ms2 see Fig 320 The atmospheric drag for higher regions strongly varies with the solar and geomagnetic activity This is why predictions are required for spacecraft operations eg for remote sensing satellites The mean anomaly M will be the most disturbed by the drag effect because the influence of the atmospheric friction is directed toward the orbital motion of the satellite Because of the energy balance the total energy of the satellite motion will decrease together with the kinetic energy and thus the semimajor axis a will reduce According to Keplers third law the angular velocity of the satellite will increase through the friction force of the atmospheric drag For satellites with an orbital height of about 1000 km or less for example Earth observation satellites or satellites of the former TRANSIT system cf 43 the drag effects can be rather large For TOPEXPOSEIDON with an orbital height of 1340 km the atmospheric acceleration is of the order 41010ms2 For satellites in higher orbits like GPS the atmospheric drag has no effect 104 3 Satellite Orbital Motion 3234 Direct and Indirect Solar Radiation Pressure The particle radiation continuously emitted by the Sun has two effects on a satellite These are the direct radiation pressure resulting from the interaction of the solar radiation with the spacecraft and the indirect Earthreflected portion albedo The force acting directly on the satellite is proportional to the effective satellite surface area to the reflectivity of the surface and to the solar flux it is inversely proportional to the velocity of light and to the square of the distance between the satellite and the Sun The resulting perturbing acceleration is thus Cappelari et al 1976 Montenbruck Gill 2000 rSP νPS CrO m AU2 r rS r rS3 3144 with PS Sunconstant quotient of solar flux and velocity of light in the Astronomical Unit AU Astronomical Unit 15 108 km Om crosssection area of the satellite as seen from the Sun divided by its mass r rS geocentric position vector of the satellite and of the Sun in the spacefixed equatorial system Cr factor of reflectivity for the satellite surface Cr 195 for aluminium and ν shadow function ν 0 satellite in Earths shadow ν 1 satellite in sunlight and 0 ν 1 satellite in halfshadow shadow boundary δ r Sc r S satellite ae Sun Figure 318 Cylindric shadow model A simple cylindric shadowmodel is suf ficient for the decision whether the satel liteisinEarthsshadowornotCappelari et al 1976 According to Fig 318 the satellite is in sunlight when D rr S 0 3145 and in shadow when D 0 Sc r DrS ae ae is the semiaxis of the shadow gen erating body Earth and r S is the unit vector to the Sun This simple model is not sufficient for higher accuracy demands In order to avoid discontinuities in the numerical orbit computation near the shadow transits it is possible to use a suitable smoothing shadowtransferfunction for ν Also 32 Perturbed Satellite Motion 105 the Sunconstant PS can be introduced as a variable in order to model variable Sun activity The solar radiation pressure shows an annual variation of about 3 due to the elliptic Earth orbit Finally detailed models for complicated satellite surfaces can be used to account for the effect of the satellites orientation with respect to the Sun Commonly Cr is estimated as a free parameter in orbit determination programs and thus absorbs the effect of unknown details of the satellite orientation and reflectivity The radiation pressure on GPS satellites is rather complicated to model accurately due to the complex structure of the spacecraft Usually a bodyfixed spacecraft coor dinate system is introduced The Yaxis is along the solar panel beam Fig 319 In the tailored ROCK4 and ROCK42 models the GPS satellite is subdivided into several Z X Y Figure 319 The satellitefixed coordinate sys tem surfaces which are modeled either as a plane or a cylinder with particular re flectivity characteristics Landau 1988 Fliegel Gallini 1989 Fliegel et al 1992 Rothacher 1992 The influence of the direct radiation pressure is mainly effective in the direction of the orbital motion along track and can reach 10 m and more after a few hours The ac celeration is in the order of 1107ms2 An excellent introduction into the prob lem is given by Ziebart et al 2002 Part of the solar radiation is reflected by Earth The ratio between the reflected radiation and the incoming flux is called albedo The albedo part of the radiation pressure is very difficult to model because of the varying distribution of land sea and clouds but in most cases it is less than 10 of the direct radiation The estimate for GPS satellites lies between 1 and 2 King et al 1987 This is why the albedo effect is usually neglected for GPS orbit computations except for very long orbital arcs The magnitude of the perturbing acceleration is approximately 4 1010ms2 A very detailed discussion of the direct and indirect solar radiation effect as well as other nongravitational perturbations can be found in Milani et al 1987 For recent models in GPS orbit computation see McCarthy 2000 3235 Further Perturbations For very precise orbital analysis other perturbations may be considered whose indi vidual contributions to the acceleration of the satellite are usually far below 109ms2 These are for example friction caused by charged particles in the upper atmosphere thermal radiation of the satellite heating effects at shadow boundaries electromagnetic interaction in the geomagnetic field and The centrifugal force Z m d2l dr d r 3146 gyro force T m d2l dr r 3147 Coriolis force C 2md r t 3148 which an observer in a spacefixed system would not notice From the equation of motion in the stationary system m d2r dt2 Kt r r 3149 follows the equation of motion in the moving system Schneider 1981 m 2r t2 K m d d r m d r 2md r t 3149 with K for the force in the rotating system r the position vector in the rotating system and d the rotation vector For an explicit computation of the apparent accelerating forces using the expression for the rotational vector d and the derivatives thereof in the moving system see for example Reigber 1981 Relativistic effects are for most applications in satellite geodesy smaller than the observation accuracy In many cases they are cancelled by the observation technique or they are modeled through other parameters Insofar as relativistic effects are of importance they will be discussed together with the particular satellite methods eg 741 With respect to orbital dynamics it follows from general relativity that the orbital elements are subject to additional secular perturbations These influences are much greater for the orbits of nearEarth satellites than for planets cf the relativistic perihelion rotation of Mercury Cugusi Proverbio 1978 give the appropriate formulas and they find as mean values for satellites of geodetic interest 10year for ω 02year for Ω and 02year for M The correction to the acceleration of an artificial satellite based on general relativity is McCarthy 2000 rrel GM c2r3 4 GM r i2 r 4 r r r 3149 32 Perturbed Satellite Motion 107 with c speed of light r satellite position vector r satellite velocity vector and GM geocentric constant of gravitation The relativistic correction of the accelerations is in the order of 3 1010 ms2 for GPS satellites and 1 108 ms2 for TOPEXPOSEIDON For some satellite systems particular nongravitational accelerations are generated from thrust or attitude control maneuvers They have to be considered in orbital analyses Thrust forces appear in connection with maneuvers for orbit corrections Attitude control systems change the satellites orientation in space Cappellari et al 1976 or Montenbruck Gill 2000 p 104f give formulas for the consideration of such effects In dynamical Orbit determination it is not possible to model all perturbations perfectly This holds in particular for the nonconservative force models which are limited by uncertainties in the knowledge of platform orientation material properties and surface temperatures Montenbruck Gill 2000 This is why empirical accelerations are employed to take account of this effect In general the empirical forces are described by an equation of the following type rem Ea0 a1 sin v a2 cos v 3150 where a0 is a constant acceleration term and a1 and a2 are coefficients related to the frequency eg one cycle per orbital revolution and E is a matrix to transform the acceleration biases from the local orbital frame radial crosstrack and alongtrack into the inertial system For details see eg Montenbruck Gill 2000 p 112 3236 Resonances Resonances occur when the period of a satellite revolution is an integer multiple of Earths rotation period This leads to an amplification of certain nonzonal harmonics Smn Cmn resulting in much higher amplitudes in the element perturbation than normal In geometric terms resonances appear when consecutive revolutions of a satellite are separated exactly by an interval which corresponds to the wavelength of the particular harmonic coefficient After a given number of revolutions the subsatellite orbit repeats ie the satellite crosses the same regions and is subject to the same perturbations This causes an amplification of the initial perturbation and generates the resonance effect Consequently a satellite with m revolutionsday will be sensitive to resonant influences from the tesseral coefficients Cmn Smn From a mathematical point of view resonances develop when the denominator in the perturbation equation 3119 becomes very small ψinmpq n 2p ω n 2p q ßM mΩ Θ 0 3151 108 3 Satellite Orbital Motion Satellite orbits can be explicitly selected to determine particular tesseral harmonics with high accuracy using the resonance effect and equation 3118 The corollary is that in orbit computation it is essential to know whether specific high order potential coefficients can give rise to large perturbations caused by resonances Low orbiting satellites because of their frequent revolutions are particularly affected by short wave structures of the geopotential Resonances may be present also for Earth observation and remote sensing satellites because of their dedicated orbital design with partic ular repetition rates GPS satellites experience resonance effects caused by Earths ellipticity Delikaraoglou 1989 Insofar as different coefficients generate resonances of identical phase and ampli tude they cannot be separated and only derived jointly from orbital analyses The determinationofsuchsocalledlumpedcoefficients istreatedforexamplebyKlokoˇcník 1982 For a detailed discussion of resonances in high satellite orbits GPS geosyn chronous see eg Hugentobler 1998 324 Implications of Perturbations on Selected Satellite Orbits The effect of perturbations on the motion of satellites which are used in geodesy is demonstrated for some typical orbits in Fig 320 Figure 320 Relation between the orbital height and the magnitude of different perturbing forces Ataheightofabout1000km aboveEarthssurfacewefindtheTRANSITnavigation satellites satellites for remote sensing eg SPOT LANDSAT the altimeter satellites GEOS3 SEASAT1 ERS12 and many other satellites with corner cube reflectors which are used in the determination of Earth models At a height of about 6000 km 116 3 Satellite Orbital Motion Main advantages The relations and dependencies between disturbing forces and variations of elements can be explicitly formulated and studied The characteristic behavior of the orbital motion can be identified and predictions of the longterm stability and the development of orbits can be made The numerical value of an individual orbital element at a particular epoch can be determined with a single evaluation of equation 3166 Main disadvantages NearEarth satellites are very sensitive to perturbations so the algebraic expres sions rapidly become rather complex and bulky Perturbations caused by nonconservative forces like the solar radiation pressure are discontinuous functions and thus difficult to model with analytical expressions Analytical solutions are approximations because they depend on truncated series expansions Singularities occur for elliptical elements when e i 0 The efficiency of computation is rather low because of the many trigonometric functions in the algebraic expressions 3322 Numerical Methods of Orbit Integration The numerical methods are distinguished by their simplicity and universal applicability when compared with analytical methods With the use of the modern computer tech niques the numerical effort only plays a minor role This is why numerical methods are now used almost exclusively for orbit computations in satellite geodesy One basic requirement for the numerical integration is a suitable orbit determina tion method for example a procedure named after Cowell or Encke Noton 1998 The method of Cowell 1910 was developed at the beginning of the last century and has been applied to the orbit determination of Halleys comet and the moons of Jupiter With the availability of fast and efficient computers the method is now particularly suitable The basic idea is that the equation of motion 397 r GM r3 r ks including all perturbations is integrated stepwise Equation 397 can be rewritten in the form of two first order differential equations r v v ks GM r3 r 3167 33 Orbit Determination 119 Many alternative orbit determination methods have been developed in celestial mechanics see eg Stumpff 195919651974 Roy 1978 Battin et al 1978 none have particular advantages when compared with the two abovementioned methods The numerical integration itself is realized with methods taken from approximation theory Basically a polynomial has to be fitted to a limited series of consecutive points in order to generate an additional point through extrapolation of the polynomial This process is repeated at will The polynomial coefficients are derived from the given points and their derivatives based on the equation of motion Different methods are used depending on the number of points required on the extrapolated values on the smoothing process and so on They are generally subdivided into singlestep and multistep methods A wellknown member of the family of singlestep methods is the RungeKutta method Here a Taylor series of a certain order is used as an extrapolation function A special feature of the singlestep method is that only the last integration step is used so the knowledge of the history of the function to be integrated is neglected To avoid this multistep solutions are usually applied in satellite geodesy They are also called predictorcorrector methods The basic idea is to first predict a satellite position with a certain algorithm and then to correct that position As a first step a predicted value Xn1 is calculated from Xn It is then substituted in the differential equation of the process in order to obtain with Xn1 a corrected value of Xn1 The process can be iterated until the result does not change Many predictorcorrector formulas may be found in the literature The formulas of AdamMoulton or GaussJackson are frequently used In principle these are filter techniques this is also why the Kalman filter is now used more and more Battin et al 1978 Here r and v are state vectors with a relevant variancecovariance matrix see eg Egge 1985 Two main error sources have to be considered when numerical integration methods are applied These are roundoff errors and truncation errors The roundoff errors depend on the numerical representation accuracy in the computer being used In order to limit these influences rather large stepsizes are an advantage in the integration Truncation errors develop when the last terms of a series expansion which is used for the integration are cut off The errors can be minimized with small stepsizes These two conflicting requirements have to be fulfilled with appropriate compromises Except for these deficiencies the numerical integration methods can be considered as rigorous orbit integration methods without approximations The only disadvantage is that many unwanted intermediate satellite positions have to be calculated before the final solution is obtained For a detailed treatment of current numerical integration solutions including exer cises see Montenbruck Gill 2000 A short review is given by Beutler et al 1998 3323 Precise Orbit Determination with Spaceborne GPS A new technique of orbit determination evolved with the placement of GPS receivers into space vehicles to determine directly the position and velocity vector of the space 120 3 Satellite Orbital Motion craft A first experiment was flown on TOPEXPOSEIDON Melbourne et al 1994b cf 92 Since then GPS receivers have been positioned on a number of satellites in particular on Low Earth Orbiters LEO like CHAMP or GRACE 102 Three basic strategies are distinguished for Precision Orbit Determination POD They are the dynamic strategy the kinematic strategy and reduceddynamic strategy The dynamic strategy corresponds to the classical approach of dynamic orbit modeling as treated in the previous chapters A mathematical model of the forces acting on the satellite is used to estimate the accelerations over time and to integrate the equation of motion A final trajectory is then estimated by a best eg least squares fit to the GPS measurements In this procedure the effect of noisy measurements on the solution is reduced whereas the dynamical model remains unchanged The dynamic strategy is essential in missions where forces have to be modeled for example in gravity field missions with LEO observations In the kinematic or nondynamic strategy the high accuracy potential of the GPS position estimates is exploited This is in particular true for low eg 400 km orbits where an accurate modeling of perturbing accelerations is difficult to make The rationale for this is that the actual path of the LEO may be closer to the GPS position estimates than to the trajectory determined from a dynamic model The kinematic strategy is based on an underlying dynamic model However the dynamic modeling errors are avoided by highweighting of the precise GPS observations The reduceddynamic strategy combines the advantages and reduces the disad vantages of the two previous strategies The kinematic technique neglects any ex isting dynamic information on the platform behavior in order to eliminate dynamic mismodeling but maintains the GPS measurement noise The dynamic technique neglects the high inherent precision of GPS measurements but maintains dynamic mismodeling A combination of both techniques in a Kalman filter process with appropriate weighting counterbalances the disadvantages The basis of the strategy is again correction of the dynamic solution with continuous GPS data The key factor is a proper weighting of the Kalman filter process noise The process noise model is characterized by two parameters the process variance V and the time constant correlationlength T When the time constant is large and the variance approaches 0 the geometric information is suppressed and the model depends exclusively on the dynamic strategy When the time constant T 0 white noise and the process variance is high the solution depends mainly on the geometric data For more information see Melbourne et al 1994b Schwintzer et al 1995 Yunck 1996 333 Orbit Representation For many practical applications in satellite geodesy only a short part of the orbit is used for instance that portion which can be directly observed from the participating 34 Satellite Orbits and Constellations 129 In addition we have particular orbits such as IGSO Inclined Geosynchronous Orbit HEO Highly Elliptical Orbit and orbits without commonly used abbreviations such as the sunsynchronous orbit geosynchronous orbit and polar orbit Low Earth Orbits LEOsinsatellitegeodesyaremostlycircular Typicallytheymayaccommodategravity field missions 10 such as CHAMP GRACE or GOCE at orbital heights of about 400 km remote sensing satellites such as SPOT LANDSAT ERS at orbital heights of about 8001000 km and altimeter satellites 9 such as TOPEXPOSEIDON ENVISAT JASON at orbital heights of 10001500 km LEOs are also used for communication satellite constellations like Globalstar and Iridium The orbital period at these altitudes varies between 90 minutes and two hours The radius of the satellite footprint ie the area on the surface from where the satellite is visible above the horizon is rather small and varies between 2000 and 4000 km Advantages Low launch costs lowpower radio transmitters provide sufficient signal strength for simple receivers on the ground the rapidly varying Doppler shift can be used for high precision navigation purposes eg TRANSIT DORIS 6 Disadvantages Satellites are only in sight for 15 to 20 minutes because of the short orbital period Continuous data transfer to ground stations requires relay satellites in high orbits For communication purposes a rather large number of LEOs is required because of the small footprint eg more than 60 satellites for Iridium h 780 km Medium Earth Orbits MEOs are used for constellations of navigation satellites such as GPS GLONASS about 20 000 km or the European GALILEO about 24 000 km The laser satellites LAGEOS12 about 6000 km also belong to this group Circular MEOs are also called Intermediate Circular Orbits ICO Advantages Satellites are in view for several hours communication satellite systems require less satellite swapping The orbits are not affected by atmospheric drag and hence are quite stable Disadvantages Low Doppler shift more expensive launch costs Geostationary Earth Orbits GEOs are mainly used for communication satellites A satellite placed into a circular orbit of inclination i 0 at an altitude of 35 800 km has a 24h period and appears fixed to an Earthbound observer The footprint of a GEO satellite covers almost 13 of Earths surface from about 75 degrees N to about 75 degrees S so that near global coverage can be provided with a minimum of three satellites These favorable characteristics have led to international regulations and the assignment of individual longitude slots 01 to interested countries and agencies Montenbruck Gill 2000 Advantages The orbits are very stable and few satellites are required for global coverage 130 3 Satellite Orbital Motion Disadvantages Rather high launch costs limited slots in the geostationary belt and no coverage around the poles Inclined Geosynchronous Orbits IGSOs are circular orbits with a 24 hours period They differ from GEOs in that they are inclined with respect to the equatorial plane For an observer on Earth the satellite will move The ground track is like a large figure eight Advantages Excellent coverage of the areas close to the poles Highly Elliptical Orbits HEOs typically have a perigee at about 500 km and an apogee as high as about 50 000 km The orbits are near the critical inclination at 634 degrees cf 322 in order to avoid rotation of the line of apsides The subsatellite point beneath the apogee is at latitude 634 North or South HEOs hence provide communication services to locations in high northern or southern latitudes Polar Orbits Polar orbits have an inclination of i 90 The orbits are fixed in space and Earth rotates underneath A single satellite in a polar orbit hence provides coverage of the entire globe One example of a configuration with polar orbits is the Navy Navigation Satellite System cf 62 A good overview of particular orbits for slow moving satellites is given by Hugen tobler 1998 Constellations Constellations consist of multiple satellites mainly of the same type with similar orbits but placed into suitably shifted orbital planes or rotated trajectories One well known example is the Global Positioning System GPS 7 LEOconstellation These consist of about 48 to 65 LEO satellites at any time aug mented by a number of payloads on GEO communication satellites in order to provide global coverage Advantages small cheap easily replaceable satellites lowpower radio transmitter strong Doppler shift high signal strength for simple user equipment Disadvantages short orbital period only 15 to 20 minutes in view requires rapid intersatellite switching and a large number of ground control stations MEOconstellation These are ideal for navigation purposes It is currently used for GPS and GLONASS and will be used for the European GALILEO It provides global coverage except for polar areas The performance can be augmented by a number of GEO satellites eg EGNOS WAAS 772 MEOs are mostly distributed in several orbital planes hence each plane can contain spare satellites Advantages excellent ground coverage except for polar areas satellites remain visible for several hours Disadvantages slow moving satellites provide rather slow Doppler shift high launch costs IGSOGEOconstellation These are regional systems consisting of several GEO satel lites and several IGSO satellites A system can at first be deployed to cover a given region and later expanded to other regions Advantages good coverage over polar 134 3 Satellite Orbital Motion Earth Moon 60 Earths Orbit L3 L1 L2 L4 L5 Satellite Sun Figure 329 The five Lagrange points libration points in the SunEarth system equilateral triangle with the other two bodies they are in stable equilibrium For more details see eg Roy 1978 chap 5 41 Satellite Geodesy as a Parameter Estimation Problem 137 It is obvious that a complete solution where all parameters are determined simultane ously cannot be obtained by simple means Certain conditions or requirements have to be introduced in order to avoid a singularity of the equation system The combined determination of coordinates and gravity potential coefficients is often called a satellite solution or only a solution the product is named an Earth model 122 In general only a few particular parameters or groups of parameters are of interest and the other parameters are considered to be known values The satellite orbit is often treated as known when the coordinates of the observation stations are to be estimated For the determination of polar motion parameters and universal time the coordinates of the control stations and Earths gravity field are usually introduced from other solutions The parameters of group 3 the socalled bias parameters have a more technical meaning and are mostly treated at a preprocessing stage Instead of estimating the parameters during the adjustment process they can be eliminated through a suitable arrangement of observations They are cancelled when simultaneous observations at different stations are differenced This technique is often appliedfortheparametersofgroup3 Thesatellitecoordinatescanalsobeeliminated and need no longer be treated as unknown parameters when observations are made simultaneously at a sufficiently large number of stations The observation technique becomes more geometric in character 12 This geometrical concept of satellite geodesy was used particularly with camera observations 51 Geometrical methods are by their nature relative methods and they do not provide geocentric coordinates This is why some problems in satellite geodesy cannot be solved with the geometrical methods Dynamical methods of satellite geodesy are used when a force model is required for the description of the satellite motion The orbit must either be known from external sources for instance from an ephemeris service or the orbit must be determined within the adjustment process be it completely or partially Different concepts are in use When simultaneous observations are available from at least two stations correc tions to some particular orbital elements or degrees of freedom up to six in number can be estimated for a short portion of the orbit together with the other adjustment parameters This procedure is also called adjustment with a relaxed orbit or the semishortarc method No particular forces acting on the satellite are considered in this technique rather some of the degrees of freedom in the satellite orbit orbital parameters are eliminated via a geometric procedure A further step is that for a short portion of the orbit based on a given force field some orbital elements are estimated as parameters from the observations This proce dure is called the shortarc method For even longer orbits of several revolutions a larger number of perturbation parameters must be estimated cf Fig 42 The term for this technique is the longarc method The method is used eg for the parameter estimation of polar motion Earth rotation solid Earth tides and the anomalous gravity field of Earth 138 4 Basic Observation Concepts and Satellites Used in Geodesy Fixed orbit Short Arc Long Arc 0 6 3 6 degrees of freedom Semi Short Arc relaxed orbit Figure 42 Role of the satellite orbit in the parameter estimation process Longarc methods are mostly used for the analysis of scientific problems For operational tasks of applied satellite geodesy the orbit is either taken as known or a limited number of parameters are estimated for the orbit improvement within the adjustment process For global radio navigation systems like GPS in general no orbit improvement is necessary because very precise orbits are available through particular services like the International GPS Service IGS 781 With observations from a single station the parameter estimation process is usually restricted to the determination of the station coordinates only The number of pa rameters can be increased when simultaneous observations are available from several stations corrections to the satellite orbit and observation biases may then be estimated For the solution of a general and global parameter estimation problem observations to a large number of different satellites are required from many globally distributed stations Fig 43 contains a schematic representation concerning the process of ob servation and parameter estimation Satellite observations Preprocessing Computed values from observations Parameter estimation Estimation of accuracy and reliability Transform raw data into observations Corrections for signal propagation time relativity ambiguities normal points Numerical analysis Orbital mechanics Coordinate transformations Geodesy Station coordinates Gravity field coefficients Satellite positions Polar motion Earth rotation Ocean and solid Earth tides Geodynamic parameters Atmospheric parameters Observation biases Statistics Reliability Accuracy measures Figure 43 Functional scheme for the use of satellite observations 42 Observables and Basic Concepts 139 42 Observables and Basic Concepts The observation techniques used in satellite geodesy can be subdivided in different ways One possibility has been already introduced in 12 namely a classification determined by the location of the observation platform Earth based techniques ground station satellite satellite based techniques satellite ground station intersatellite techniques satellite satellite Another classification follows from the observables in question A summary of the most important operational techniques is given below References to the specific artificial satellites are included A graphical overview is given in Fig 44 The detailed presentation and discussion of the individual observation methods follows in later chapters R1 R2 R3 R4 e d r a0 r r r r Figure 44 Overview of observation techniques in satellite geodesy 421 Determination of Directions Photographical methods are almost exclusively used for the determination of direc tions An artificial satellite which is illuminated by sunlight by laser pulses or by some internal flashing device is photographed from the ground together with the background stars The observation station must be located in sufficient darkness on the night side of Earth The stars and the satellite trajectory form images on a pho tographic plate or film in a suitable tracking camera or on a CCD sensor 52 The photogram provides rectangular coordinates of stars and satellite positions in the image plane which can be transformed into topocentric directions between the observation station and the satellite expressed in the reference system of the star catalog equatorial system CIS 140 4 Basic Observation Concepts and Satellites Used in Geodesy Two directions measured at the same epoch from the endpoints of a given base line between observing stations define a plane in space whose orientation can be determined from the direction cosines of the rays This plane contains the two ground stations and the simultaneously observed satellite position The intersection of two or more such planes defined by different satellite positions yields the interstation vector between the two participating groundstations Fig 45 When more stations Figure 45 The use of directions with satellite cameras are involved this leads to regional con tinental or global networks 51 Note that these networks are purely geomet ric Direction measurements have also been used for orbit determination and they were introduced into early com prehensive solutions for Earth models gravity field coefficients and geocentric coordinates 122 Some satellites are equipped with laserreflectors In such cases the directions and ranges can be determined simultaneously and provide immediately the vector ρt between the ground station and the satellite Initially passive balloon satellites were used as targets such as the first ex perimental telecommunication satellites ECHO1 and ECHO2 In 1966 a dedicated geodetic balloon satellite PAGEOS PAssive GEOdetic Satellite with a diameter of 30 m was launched for the observation of the BC4 World Network 515 The satellite was placed into an orbit of about 3000 to 5000 km altitude and was used for about six years Today laser pulses can be reflected by satellites equipped with corner cube reflectors and be used for the determination of precise directions However the achievable accuracy is very low when compared with modern ranging methods This is why today the measurement of directions only plays a minor role in satellite geodesy A certain revival took place with the launch of the Japanese Geodetic Satellite AJISAI in 1986 Sasaki 1983 Komaki et al 1985 see 432 A modern application is the use of powerful CCDtechniques for the directional observation of geostationary satellites 523 Directional information can also be derived by analysis of electromagnetic signals transmitted from a satellite The related techniques which have been realized so far yield only a rather low accuracy 44 Very Long Baseline Interferometry VLBI on the other hand is one of the most accurate observation techniques in geodesy cf 111 and provides precise directions to extragalactic radio sources The application of the VLBI technique using radio signals from artificial satellites is under discussion 1114 146 4 Basic Observation Concepts and Satellites Used in Geodesy The interferometric principle can be realized through observation techniques in very different ways Equation 415 contains different quantities which can be used as derived observables namely the baseline length b between the two antennas the residual distance d between the antenna and the satellite and the angle θ between the antenna baseline and the satellite In each case it is necessary to know or to determine the integer ambiguity term N The determination is possible through a particular configuration of the ground antennas through observations at different frequencies or through well defined observation strategies One example for the determination of directions to satellites by interferometric measurements is with the classical MinitrackSystem 442 where the individual antenna elements are connected with cables The achievable accuracy however is not sufficient for modern requirements in satellite geodesy With increasing baseline lengths the antennas cannot be connected directly with cables The phase comparison between the antennas must then be supported by the use of very precise oscillators atomic frequency standards This is for instance the case with the Very Long Baseline Interferometry VLBI concept 111 When natural radio sources eg quasars are observed with the VLBI technique the range difference d is not determined through methods of phase comparison but by the correlation of the signals obtained at both antennas The signal streams are registered together with precise timing signals at both antenna positions and they are later shifted one against the other within a correlator until the maximum correlation is obtained The time delay τ corresponds to the signal travel time between P and A1 and can be scaled to a range difference d τ c 416 When artificial Earth satellites are used in the VLBI technique it cannot be assumed that the directions from the antennas to the satellites are parallel Instead the real geometry has to be introduced by geometric corrections eg the wavefronts must be treated as curved lines 1114 The interferometric principle has been widely used in the geodetic application of the GPS signals Both methods described above for the determination of the range differences d are possible aThe signals from the GPS satellites can be recorded at both antenna sites without any a priori knowledge of the signal structure and later correlated for the determination of the time delay τ A very large instrumental and computational effort is required so the method is not really suitable for operational applications It is however used to some extent in modern GPS receiver technology in order to access the full wavelength of L2 under AntiSpoofing AS conditions 723 b The phase of the carrier signal at both antenna sites can be compared and the difference formed These socalled single phase differences can be treated as the 43 Satellites Used in Geodesy 147 primary observables The method is now widely used for processing GPS observations 7321 There are different opinions in the literature on the extent to which method b ie the use of phase differences belongs to the class of interferometric observation techniques Both terms namely interferometric techniques and phase differences were often used as synonyms in the early GPS literature 427 Further Observation Techniques Besides the observables and observation techniques already mentioned other methods were proposed or are still in use or are planned for forthcoming satellite missions In many cases combinations of different observables are employed One of the concepts proposed and now under development is satellite gradiometry 103 A gravity gra diometer measures directly the second derivatives of Earths gravitational potential It is very hard to achieve the required resolution with the available instrumentation The same is true for the application of accelerometers in the satellite A first mission based on this concept will be GOCE planned for launch in 2006 103 Earth observation satellites or remote sensing satellites carry a large quantity of sensors for the optical and microwave frequency domain Of particular interest to geodetic applications is the Interferometric Radar InSAR technique which can be used to detect small deformations of Earths crust A short overview of this technique is given in chapter 112 In general remote sensing techniques are not included in this book For information see eg Leberl 1990 Cracknell Hayes 1991 Lillesand Kiefer 2000 43 Satellites Used in Geodesy 431 Basic Considerations Most of the satellites which have been used and still are used in satellite geodesy were not dedicated to the solution of geodetic problems their primary goals are various Typical examples of this group are the navigation satellites of the TRANSIT and of the GPS systems and remote sensing Earth observation satellites carrying a radar altimeter Examples of satellites which were exclusively or primarily launched for geodetic andor geodynamic purposes are PAGEOS PAssive GEOdetic Satellite USA 1966 STARLETTE STELLA France 1975 1993 GEOS1 to 3 GEOdetic Satellite 1 to 3 USA 1965 1968 1975 LAGEOS1 2LAser GEOdynamic Satellite USA 1976 1992 AJISAI EGS Experimental Geodetic Satellite Japan 1986 GFZ1 GeoForschungs Zentrum Germany 1986 CHAMP CHAllenging Mini Satellite Payload Germany 2000 148 4 Basic Observation Concepts and Satellites Used in Geodesy This group of dedicated satellites includes some which were used during the first years of the satellite era for the establishment of geodetic datum connections eg SECOR 441 ANNA1B 1962 All satellites which are dedicated to a given observation technique will be treated in detail together with this technique eg 511 62 67 712 82 92 10 In this chapter more general aspects are discussed The orbital height of a satellite is mainly determined by the purpose of the mission A satellite used for gravity field determination should have a rather low orbit about 300 to 500 km and it must carry highly sophisticated instrumentation A satellite used for precise position location should have a rather high and stable orbit and could be much simpler from the technical point of view This is why dedicated missions for the mapping of a fine structured Earth gravity field have only been realized recently or are in the final stage of realization cf 10 In order to separate gravitational and nongravitational forces the satellites must be carefully designed One possibility is to select a favorable massarea relation which minimizes the forces acting on the satellite surface In another solution the surface forces are compensated by a thrusting system This keeps the satellite centered on a proof mass which is shielded from the satellite surface forces cf DISCOS system 4331 Fig 413 A frequently used distinction for the purposes of subdivision is passive and active satellites Passive satellites are exclusively used as targets They have no active electronic elements and are independent of any power supply Their lifetime is usually extremely long Active satellites in most cases carry various subsystems like sensors transmitters receivers computers and have a rather limited lifetime Table 41 gives an overview of the most important satellites that are in use or have been used in satellite geodesy Table 41 Satellites used in geodesy Passive Satellites Active Satellites ECHO1 ETALON1 ANNA1B ERS2 ECHO2 ETALON2 GEOS3 TOPEXPOSEIDON PAGEOS GFZ1 SEASAT1 GFO Geosat Follow On STARLETTE NNSS satellites CHAMP STELLA NAVSTAR satellites JASON LAGEOS1 GLONASS satellites ENVISAT LAGEOS2 GEOSAT GRACE EGS AJISAI ERS1 Another possible subdivision is into Geodetic Satellites Earth Sensing Satellites Positioning Satellites and Experimental Satellites 43 Satellites Used in Geodesy 149 Geodetic satellites are mainly high targets like LAGEOS STARLETTE STELLA ETALON ASIJAI and GFZ which carry laser retroreflectors They are massive spheres designed solely to reflect laser light back to the ranging system The orbits can be computed very accurately because the nongravitational forces are minimized Earth sensing satellites like ERS GFO TOPEX JASON ENVISAT carry instru ments designed to sense Earth in particular to monitor environmental changes Many of these satellites carry altimeters 9 The satellites are rather large with irregular shape hence drag and solar radiation forces are also large and difficult to model Most are equipped with an orbit determination payload eg PRARE GPS andor DORIS 4333 In addition most satellites carry laser reflectors to facilitate precise orbit determination Positioning satellites are equipped with navigation payload To this class belong the former TRANSIT GPS GLONASS and future GALILEO satellites Some of the spacecraft carry laser reflectors eg GPS35 36 and all GLONASS satellites The satellites are arranged in constellations of up to 24 and more to provide global or regional coverage Experimental satellites support missions with experimental character They are used in the development of various other kinds of satellites to test their performance in real space operations A large number of experimental satellites have been launched for communication technology Experimental satellites of interest to geodesy are mostly irregularly shaped and fly in low orbits Precise orbit determination POD is supported by laser cube corner reflectors andor a navigation payload like GPS Examples include TiPs Tether Physics and Survivability and Gravity Probe B 432 Some Selected Satellites In this section some satellites and subsystems are described that are in use or have been used for different observation techniques in satellite geodesy and that are not discussed later in detail in the context of a particular method GEOS3 The third satellite of the GEOS series was launched by NASA on April 9 1975 The initial orbital elements and some physical parameters are period 102 minutes apogee height 844 km perigee height 837 km inclination 115 weight 340 kg diameter 132 cm and length 81 cm The antennas are orientated toward Earth using a 195 m gravity gradient boom and a 45 kg boom end mass Fig 411 shows the configuration of the spacecraft and its main elements The experiment package consists of the following 150 4 Basic Observation Concepts and Satellites Used in Geodesy Laser reflectors Cband antenna Radar altimeter mass Figure 411 GEOS3 spacecraft Radar Altimeter for the satellitetoocean surface height measurements 92 57 GHz precision 60 cm CBand Transponder providing for range rangerate and angle measurements in conjunction with appropriately equipped ground stations 442 SBand Transponder 21 and 22 GHz for satellitetosatellite tracking experi ments 102 Laser Retroreflector Array with 264 quartz cube corner reflectors design accuracy 10 cm 82 Doppler System dual frequency 162 and 324 MHz providing the determina tion of positions and position changes from ground stations 6 GEOS3 because of the wellequipped experiment package became the geodetic satellite par excellence Many problems from science and practice could be solved with GEOS3 data cf 122 The most important subsystem from the geodetic point of view was the radar altimeter It was in operation for more than three years until the end of 1978 without any considerable interruptions The laserreflector array can still be used SEASAT1 The oceanographic satellite SEASAT1 was launched on June 26 1978 with an orbit similar to that of GEOS3 namely a period of 109 minutes an altitude of 800 km and an inclination of 108 cf 92 The spacecraft carried several sensors for use in oceanography and a radar altimeter with a 10 cm resolution which exceeded by far the designaccuracy of the GEOS 3 altimeter Due to a breakdown in the power system SEASAT1 only delivered altimeter data for five months However because of the much higher data rate the size of the SEASAT1 data set is similar to the GEOS3 data set The results of the SEASAT mission have contributed considerably to the progress of geodesy 9 122 ERS1 ERS2 The designation ERS1 stands for the First European Space Agency ESA Remote Sensing Satellite It was launched on July 17 1991 ERS1 flies in a sunsynchronous 43 Satellites Used in Geodesy 151 orbit at an altitude of about 800 km and an inclination of 985 degrees The mission had the following main objectives cf 92 monitoring of the global oceans observing polar and sea ice monitoring regionally the land surface and supporting geodetic research From the geodetic point of view the two onboard systems of greatest interest were the radar altimeter RA and PRARE The radar altimeter is a single frequency Kuband 2 cm waves instrument of the SEASAT type with an anticipated heightresolution of 01 m over sea and 04 m over ice 92 PRARE 4333 should have been used for precise orbit determination at the 10 cm accuracy level Unfortunately the PRARE system could not be activated after launch ERS1 is also equipped with laser retro reflectors providing the primary tracking of the spacecraft The remote sensing objectives of the mission were covered by a large variety of instruments such as an Active Microwave Instrument AMI including a Synthetic Aperture Radar SAR and an Along Track Scanning Radiometer ATSR providing information on sea state winds and waves For a deeper study of techniques and objectives in remote sensing see the related literature eg Maul 1985 Cracknell Hayes 1991 Lillesand Kiefer 2000 For the use of altimeter data see 95 A very powerful tool for geodetic deformation studies developed with the interfer ometric use of the SAR antenna the Interferometric SAR InSAR see 112 ERS2 was the followon mission to ERS1 It was launched on April 21 1995 into an orbit similar to ERS1 It carries similar instruments to ERS1 as well as the Global Ozone Monitoring Experiment GOME Precision orbits were determined with PRARE and SLR For a period of time both satellites flew in the combined tandem mission see 92 ASIJAI EGS The Japanese Experimental Geodetic Satellite EGS was launched on August 12 1986 The unofficial name is AJISAI watersnake The spacecraft is well suited Laser reflectors diameter 215 cm mirror Figure 412 AJISAI EGS Japan for laser ranging and for photographic camera observations It is polyhedron shaped with an effective diameter of 215 m It carries 318 mirror elements and 120 reflector assemblies for laser light Fig 412 The total weight amounts to 685 kg The nearly circu lar orbit has an inclination of i 50 and a period of 1157 minutes The orbital height is about 1500 km The satellite initially rotated around its own axis at 40 revolutions per minute rpm The sunlight was thus reflected in such a way that an observer on the 152 4 Basic Observation Concepts and Satellites Used in Geodesy dark side of Earth could see about two short flashes per second with a duration of 5 ms and an apparent star magnitude of 1m5 to 3m5 These flashes could be photographed together with the background stars In the meanwhile the rotation rate slowed down by about 000145 rpmday and arrived at 339 rpm by March 1998 Otsubo et al 1999 The 120 reflector groups contain in total 1436 retroreflectors for laser light The design accuracy of these reflectors corresponds to a range resolution of 1 to 2 cm cf 82 TDRSS The Tracking and Data Relay Satellite System TDRSS provides tracking and data communication between low Earth orbiting LEO spacecrafts and groundbased con trol and data processing facilities The space segment consists of seven Tracking and Data Relay Satellites TDRS located in geosynchronous orbits The constellation pro vides global coverage The system is capable of transmitting to and receiving from the spacecraft over 100 of their orbit The ground segment is located near Las Cruces New Mexico The system has worked successfully since 1983 and supports a large number of scientific missions Among these are the Hubble Space Telescope Space Shuttle Landsat Ocean Topography Experiment TOPEX Earth Observing System EOS Space VLBI International Space Station ISS and JASON 433 Satellite Subsystems 4331 Drag Free Systems A dragfree satellite is built by isolating a proof mass within the satellite completely from the surrounding environmental influences The spacecraft is equipped with a socalled Disturbance Compensation System DISCOS In its basic form a massive spherical proof mass is shielded from the forces on the satellite surface within a hollow ball The ball is attached to the satellite and experiences all surface forces such as drag and radiation pressure The proof mass is only affected by gravitational forces Changes in the relative position of the proof mass and hollow ball are measured and allow separation of the gravitational forces from surface forces Fig 413 Two objectives can be achieved a Through a closed loop thrusting system the satellite can be kept centered on the proof mass and thus in a much more stable orbit This is of particular importance for loworbiting navigation satellites because otherwise the surface forces create large differences between the predicted broadcast orbit and the true satellite position DISCOS was tested in the experimental navigation satellite TRIAD launched 1972 and was later installed on the NNSS satellites of the new NOVA type 62 Eisner et al 1982 154 4 Basic Observation Concepts and Satellites Used in Geodesy A basic distinction in attitude control concepts is between passive and active attitude control Passive control requires less complicated and less expensive hardware One example is gravity gradient attitude control realized through a boom end mass see eg GEOS3 432 Fig 411 Components of an active attitude control system may be accelerometers star sensors gyros and GPS arrays Accelerometers are most suitable for sensing translations CCD star sensors are par ticularly suitable for monitoring the orientation of spacecrafts Quine 1996 Star po sitions are referred to inertial space and they can be considered as pointlike sources With these characteristics star sensors allow attitude determination with accuracies in the arcsecond range 531 The use of mechanical gyros is suboptimal because the fast rotating rotor elements produce high frequency vibrations that disturb the accelerometer readout Karslioglu 2000 The development of laser gyros may improve the situation The use of GPS receivers or GPS antenna arrays gains importance with advanced receiver technology 7629 A detailed study of system behavior for attitude control is of high importance for sensor modeling with the new gravity field satellite missions cf 10 An excellent reference for details on the subject is Sidi 1997 4333 Navigation Payload PRARE Three main systems are being used for precise orbit determination as active payload onboard spacecraft GPS DORIS and PRARE GPS is flown on an increasing number of Low Earth Orbiters Its use as navigation payload is discussed in 3323 and 7629 DORIS is based on the Doppler tech nique it forms part of several missions in particular for Earth observation satellites Several future missions are planned DORIS is therefore treated within the chapter on Doppler techniques 67 PRARE is a discontinued technology The system has been flown on several platforms but most probably will not be included in future space missions Nonetheless from the conceptual and technological point of view PRARE is a very powerful and interesting system Its main characteristics and features are therefore explained in more detail PRARE stands for Precise Range And Rangerate Equipment The original con cept was developed at the University of Stuttgart and the German Geodetic Research Institute DGFI Munich Reigber Hartl 1989 1990 PRARE was flown for the first time on the ERS1 satellite but could not be activated Successful missions were with the Russian METEOR37 satellite and with ERS2 43 Satellites Used in Geodesy 155 PRARE is an autonomous spaceborne twoway dualfrequency microwave track ing system consisting of three components the space segment a small unit containing all necessary instruments including telemetry and data storage but less the power supply in a box measuring 400 mm x 200 mm x 100 mm with a mass of 17 kg the control segment for system control and calibration time control commu nication with the space segment preprocessing distributing and archiving the data the ground segment consisting of small transportable automated ground sta tions PRARE XBand 2Way PN Coded Ranging 10 Mchips SBand 1Way PN Coded Ranging 1 Mchips user station user station user station segment space Figure 414 PRARE concept The observation principle of PRARE is demonstrated in Fig 414 Two pseudo random noise PRN coded microwave signals are transmitted si multaneously from the space segment to the ground station one signal is in the Sband 22 GHz the other in the Xband 85 GHz At the ground sta tion the time delay in the reception of both signals is measured with an accu racy better than 1 ns and transmitted to the space segment for a calculation of ionospheric correction At the same time the atmospheric parameters at the ground station are transmitted for tro pospheric modeling purposes The ranging signal in the Xband is transposed in the ground station to 72 GHz and retransmitted to the space segment The twoway signal travel time is determined in the space segment via a correlation process and provides a measure for the twoway slant range between the satellite and the ground station In addition to this the Dopplershifted carrier frequency is counted in the space segment and is used to derive the relative velocity between the spacecraft and the ground station Up to four ground stations can be tracked simultaneously All data are collected and stored in the onboard memory and can be transmitted to the ground control station whenever contact is made The overall noise of the preprocessed full range data 1 range measurement per second and the 30 seconds Doppler count integration is 25 to 65 cm for range data depending on multipath effects at the ERS2 solar panels and 01 mms for the rangerate Doppler data The normal point noise is less than 1 cm and 0015 mms respectively Flechtner1997 The main reason for the good rangerate measurement precision is the high carrier frequency about 8 GHz A PRARE ground station consists of 3 separate units easily carried by hand 156 4 Basic Observation Concepts and Satellites Used in Geodesy an antenna unit with a 60 cm parabolic dish based on an azimuthal mounting the steering commands for the antenna mount are derived from the data signal broadcast from the satellite an electronic unit with RFmodules station processor and power supply and a monitor and computer as a user interface Up to 29 ground stations can be operated in a global network Fig 415 shows a block diagram of a PRARE ground station Figure 415 Block diagram of a PRARE ground station Dornier The primary objective of the PRARE system is to provide precise orbit determi nation for satellite missions Based on a global network of ground stations a radial orbit accuracy of better than 10 cm has been achieved Further contributions support for example Reigber Hartl 1990 Bedrich 1998 Flechtner 2000 absolute and relative position determination of the ground stations studies of ice mass balance eg Antarctica determination of sea surface topography refined modeling of Earths gravity field studies of the ionosphere total electron content and precise time transfer and clock synchronisation 434 Planned Satellites and Missions The time span between the first planning of a satellite mission and its final realization usually amounts to more than 10 years During this period concepts are developed and thoroughly studied in several phases They are reevaluated adapted to new 43 Satellites Used in Geodesy 157 developments and finally approved or rejected Very few of the many proposals that are described and discussed in the literature and dedicated studies finally come to a realization Some planned missions of interest to geodesy are indicated in the following More details are given in the respective chapters on particular observation techniques Navigation GALILEO European Satellite Navigation System first launches planned for 2004 completely deployed by 2008 773 GPS IIF New generation GPS launches begin after 2005 712 717 GPS III Followup generation GPS under design 717 Altimetry ICESATIce Cloud andLandElevationSatellite carryingtheGeoscienceLaser Altimeter System GLAS launched on January 12 2003 87 CRYOSAT part of ESAs Living Planet Program in the framework of the Earth Explorer Opportunity Mission radar altimetry mission dedicated to the obser vation of polar regions anticipated launch in 2004 or 2005 92 Gravity Field GOCE first satellite with an onboard gradiometer launch planned for 2006 103 Astrometry DIVA astrometric satellite to bridge the gap between HIPPARCOS and FAME or GAIA 15 million star positions highly elliptical geosynchronous orbit Pe 500 km Ap 71 000 km launch uncertain 53 FAME astrometric satellite positions proper motions and parallaxes for 40 million stars with 50 microarcseconds launch uncertain 53 GAIA ESAs space astronomy mission position and motion of more than 1 billion stars of our galaxy 1 microarcsecondyear launch around 20102012 Remote Sensing ADEOS2 Advanced Earth Observing Satellite also named Midori II re search on global climate changes mainly water changes and ozone layer launched on December 14 2002 RapidEYE constellation of four minisatellites carrying a CCDbased imaging system resolution 65 meters anticipated launches from 2004 onward TerraSAR twosatellite system in polar sunsynchronous orbit with 12 minutes spacing dual frequency SAR Lband Xband launches after 2005 112 Experimental Satellites GRAVITY PROBE B test of relativistic theories precise orbit determination with GPS and SLR launch planned for July 2003 STEP Satellite Test of the Equivalence Principle the experiment plans to fly several pairs of masses on a dragfree satellite in low Earth orbit launch planned after 2006 158 4 Basic Observation Concepts and Satellites Used in Geodesy 44 Some Early Observation Techniques Classical Methods The satellite tracking methods of the first years after 1957 originated from before the launch of the first artificial satellites or were based on existing techniques This is true for the methods of stellar triangulation which follow from astronomy with the Moon as a target and for the visual photographic and electronic tracking of rockets Only the satellite laser ranging technique can be regarded as an original development of the early satellite era Henriksen 1977 After the launch of SPUTNIK1 on October 4 1957 the satellite signals which were continuously transmitted on frequencies of 20 MHz and 40 MHz could be re ceived all over the world with existing antennas The Doppler shift 61 of these signals was measured mostly by observing the behavior of Lissajou figures with os cilloscopes and could be used for tracking purposes More precise radiotracking systems eg Minitrack 442 were already under development for the anticipated national American space program and were used after 1958 for the observation of a large number of satellites For monitoring and tracking of passive nontransmitting satellites powerful cameras were used the socalled tracking cameras The Smithso nian Astrophysical Observatory SAO initiated within the International Geophysical Year 19571958 the development of the BakerNunn Camera which could be used for the photography of small sunilluminated satellites Pearlman 1983 The primary motivation during the first years of satellite observation was focussed on the development of improved models for the orbital motion of near Earth satellites and to the determination of substantial geometrical and physical Earth models Many observations of a large number of satellites were included in the determination of the early Earth models 122 These data from the classical period of satellite geodesy still contribute to current Earth models In this respect the classical observation methods retain their importance and are briefly discussed in this book The present practical importance of the classical observation techniques in their original form however is very small The photographic determination of directions led to a remarkable early result in satellite geodesy namely the establishment of the first worldwide geometric network 515 Directional methods are still of high significance in satellite geodesy and found a remarkable new perspective with CCD technology This is why the method is described in a particular chapter 5 The TRANSIT technology also belongs to the classical observation techniques The underlying Doppler method however is still an important observation tool in satellite geodesy and has a modern realization in the DORIS concept Furthermore the methodology developed along with TRANSIT has considerably influenced the geodetic use of GPS This is why the Doppler method is treated in a particular chap ter 6 44 Some Early Observation Techniques Classical Methods 159 441 Electronic Ranging SECOR The development of electronic ranging techniques began rather early To implement twoway ranging capability the satellite had to be equipped with dedicated receivers and transmitters socalled transponders The SECOR technique was developed par ticularly for geodetic application SECOR means SEquential COllation of Ranges One of the first SECOR transponders was flown on ANNA1B 1962 A total of sixteen satellites with SECOR equipment were launched into near polar orbits of 1000 to 4000 km altitude between 1964 and 1970 NGSP 1977 Vol1 221 among them GEOS1 and GEOS2 The basic idea of SECOR is that four ground stations and one satellite form a group the socalled Quad Three of the four ground stations are considered to be at known positions the fourth station is the new point N to be located This is the trilateration principle a purely geometric method of coordinate determination which is illustrated in Fig 12 p 3 At least three wellselected satellite positions are determined through simultaneous ranging from the three known ground stations Based on the three determined satellite positions the coordinates of the unknown station N are derived by spatial resection Further quads of groundstations can be added to form larger networks up to a worldwide girdle of stations In addition to the purely geometric simultaneous method the orbital method of SECOR was used see Fig 13 A short portion of the orbit short arc was determined from at least three known ground stations and was then extrapolated for the determination of unknown ground stations In practice combined evaluations have also been used Note that the basic principles which have been developed for the technique of point positioning with SECOR are also applicable to modern ranging methods in satellite geodesy SECOR used a phase comparison technique for the determination of ranges Mod ulated signals on a carrier frequency of 4209 MHz were transmitted from the ground station to the satellite They were transmitted back to the ground stations via satellite borne transponders on two different frequencies 449 MHz and 2245 MHz for esti mation of an ionospheric correction The ranging signal had a frequency of 585 MHz corresponding to a resolution of 25 cm Three additional modulation frequencies were used for solving the ambiguities One of the four stations was designated the mas ter station and synchronized all measurements The interrogation period for all four participating stations was 50 ms The main purpose of the SECOR system was the geodetic connection of isolated local reference frames datum connection in particular between NorthAmerica Aus tralia Japan and several islands in the Pacific Rutscheid 1972 To achieve this objective an equatorial network consisting of 37 stations was observed between 1964 and 1966 The pure SECOR solution showed a rather weak geometry and was affected by large systematic errors The standard deviation of a single range measurement in ternal accuracy was about 3 m however the systematic differences when compared with other solutions BC4 Doppler were up to 50 m external accuracy A com bined final adjustment including short arc techniques and orientation control from 5 Optical Methods for the Determination of Directions The determination of directions from the ground to satellites based on optical obser vations is one of the early methods of satellite geodesy that led to remarkable results In addition optical tracking of satellites is of fundamental importance because it is the only technique in satellite geodesy which directly establishes access to the inertial reference frame cf 2121 All other methods like GPS 7 or SLR 8 only indirectly provide a link to the frame through the equation of motion Unfortunately the optical era in satellite geodesy came to a sudden end with the development of satellite laser ranging SLR and the use of the Doppler technique for positioning soon after about 1975 The reason is well understood A directional accuracy of 01 corresponds to 3 m for a satellite at 6000 km eg LAGEOS The optical method was not competitive compared with the cm accuracy available with laser ranging Recent progress made in the development of Charge Coupled Device CCD tech nology has led to a revival of optical satellite observations This development is promising and interesting because directional observations besides the direct link to the inertial frame still provide important contributions to satellite geodesy and satellite tracking eg Hugentobler 1998 optical observations are the most reliable and accurate source of information for small passive and remote objects like inactive satellites or space debris in particular in the geostationary belt geostationary or GPS satellites show characteristic resonances with Earths ro tation which can be accurately determined with optical observations other than VLBI or SLR only optical observations from single stations can provide important information and optical observations are an independent tool to control and calibrate other ob servation techniques The classical photographic determination of directions contributed significantly to the early development of satellite geodesy The basic methodological foundations of this method in particular the technique of plate reduction are still of value and can also be applied to the analysis of CCD images This is why a review of the photographic method is given first 51 Photographic Determination of Directions The principle of the method is based on taking photographs of illuminated or flashing satellites together with the star background 421 Satellite directions are obtained when the individual images of the chopped satellite trail are interpolated into the framework of the background stars that serves as a field 162 5 Optical Methods for the Determination of Directions of fiducial points The necessary tools are appropriate satellites appropriate tracking cameras precise star positions and appropriate methods of plate measurement and plate reduction Furthermore the observation epochs must be related with sufficient accuracy to a common time scale eg UTC in order to satisfy the geometric condition of simultaneity between stations 511 Satellites used for Camera Observations Satellites are required that are illuminated by the sunlight illuminated by a laser from the ground station or that are capable of emitting a sequence of selfgenerated flashes of light Observations can only be made at night when the ground station is located within Earths shadow Targets must be bright enough to create images in the emulsion of the photographic plate or film Initially passive balloon satellites were used for example the early experimental communication satellites ECHO1 19601968 d 30 m h 1600 km magnitude 1m0 and ECHO2 19641969 d 40 m h 1200 km magnitude 1m5 For observations of the BC4 World Network of the US Coast and Geodetic Survey now National Geodetic Survey NGS 515 a dedicated PAssive GEOdetic Balloon Satellite was launched on June 24 1966 PAGEOS 19661972 d 30 m h 2800 5600 km i 87 e 01356 magnitude 1m6 at 3000 km Also minor balloon satellites were used such as EXPLORER19 1963 d 30 m h 1300 km and EXPLORER39 1968 d 36 m h 700 2500 km Active satellites were able to emit a series of 6 to 8 flashes of about 1 millisecond length ANNA1B 1962 h 1100 km i 51 GEOS1 1965 h 1100 2300 km i 295 and GEOS2 1968 h 1100 1600 km i 106 After around 1975 very few camera observations were used in satellite geodesy in most cases images of laser echos from satellites equipped with retroreflectors were taken Well defined targets were STARLETTE 1975 d 24 cm h 810 1100 km i 498 and LAGEOS 1976 d 60 cm h 5900 km i 110 The Japanese satellite AJISAI EGS 432 AJISAI 1986 d 215 m h 1500 km i 50 is particularly suitable for camera observations because it generates flashes by sun light reflected off its rotating spherical polyhedron In addition laser ranging can be performed simultaneously because the satellite carries retroreflectors With the launch of AJISAI a certain revival of camera observations came about in particular in Japan to establish geodetic datum connections between islands 51 Photographic Determination of Directions 163 512 Satellite Cameras Dedicated cameras are required to photograph artificial satellites A special shutter is needed to divide the trails of stars and satellites into small separated images which can be measured on a comparator The optical elements must be of high quality with respect to geometry distortion and luminous intensity The following concepts have been realized cf Fig 51 satellite satellite satellite stars 1 2 3 4 Figure 51 Concepts of satellite cameras 1 Azimuthal mounting The camera is fixed with respect to the ground and follows neither the stars nor the satellites The stars like the satellites form trails on the photographic plate and have to be chopped with a shutter forming small individual images One characteristic example is the BC4 Camera Fig 52 This camera was developed by the manufacturer Wild Heerbrugg Switzerland based on existing photogrammetric cameras The objectivelensesAstrotar f 305mm andCosmotar f 450mmwereespecially developed the plate format 18 cm 18 cm corresponds to a field of 24 24 for the Cosmotar The directional accuracy of a single camera observation is 02 to 05 The BC4 cameras have been used worldwide in particular for the PAGEOS observations within the US NGS geometric satellite world network Schmid 1974 1977 Böhler 1972 515 2 Equatorial mounting This mounting permits rotation of the instrument about one axis parallel to Earths axis of rotation and thus allows for a compensation of the diurnal rotation The star images are formed as points but the satellite track has to be chopped into particular images by a rotating shutter as in case 1 One characteristic example is the Ballistic Camera BMK produced by Carl Zeiss Company Oberkochen Germany with focal lengths of 45 cm or 75 cm The high quality objective lens AstroTopar especially designed for this camera has a nominal distortion of less than 5 µm The plate format 18 cm 18 cm corresponds to a field angle 22 22 for the BMK 45 The directional accuracy of a single camera observation was found to be 01 to 02 Seeber 1972 3 Threeaxis mounting The camera can follow satellites tracking camera Also fainter satellites can be tracked The camera is however not suitable for active satellites laser echos and AJISAI echos The characteristic example is the BakerNunn Camera Fig 52 This 164 5 Optical Methods for the Determination of Directions camera was primarily operated by the Smithsonian Astrophysical Observatory SAO in its equatorial network 12 stations The optical system was designed by JG Baker the mounting and mechanical system by J Nunn The mirror optics combines a focal length of 50 cm with a relative aperture of 11 The field of view is 5 30 The direction accuracy is about 2 Many of the observations have been used in the early SAO Standard Earth models 122 For further reading see eg Pearlman 1977 Pearlman 1983 4 Combined solution The camera follows either the satellites or the stars Faint satellites can be identified within a field of faint stars The characteristic example is the Satellite Observation Instrument SBG developed by the Carl Zeiss Company Jena former German Demo cratic Republic The camera can track either the stars or the satellites The 4axis mount supports a Schmidt reflector The focal length is 76 cm and the field of view 113 The photographic plate moves in the focal plane either with star or satellite velocity Satellites up to a magnitude of 10m can be recorded with 1s exposure time The direction accuracy is about 1 to 2 Note that many of these cameras are still available around the world and can be used with CCD technology 52 Figure 52 Satellite cameras BC4 left BakerNunn right 513 Observation and Plate Reduction The organization realization and reduction of photographic satellite observations with cameras is extremely time consuming and requires much effort Only some basic considerations and the fundamental steps are explained in this chapter For a full treatment of this subject see eg Schmid 1977 or Seeber 1972 The basic principles and algorithms in particular of the plate reduction process are also valid for the reduction of CCD images 52 51 Photographic Determination of Directions 165 Camera observation satellite orbit Earth equator E shadow cylinder Sun δ A Earth shadow in the orbital plane Figure 53 Visibility conditions for passive satellites An appropriate observation epoch has to be determined based on predictions of the satellite orbits and on a computa tion of the satellite visibility for all par ticipating stations At least two stations have to observe simultaneously in order to contribute to the geometric solution 12 in satellite geodesy The amount of valuable data increases with more than two participating stations When pas sive sunlight reflecting satellites are used like AJISAI the satellite must be outside of the Earths shadow Fig 53 and the Sun must be more than 18 be low the horizon of the observation sta tion astronomical darkness The re lated areas of satellite intervisibility are a function of the geographical locations of the observation stations and of the respec tive orbital height Fig 54 shows for three stations B1 B2 B3 the visibility areas zenith angles z 60 togetherwiththesubsatellitetrackcf Fig325 p127 Itbecomesevident that only a small portion of the satellite orbit SA to SE is simultaneously visible from all three stations The visibility conditions become more favorable with increasing orbital height and decreasing station separation The best intersection conditions are B3 B1 SA SE B2 satellite orbit visibility area for station B2 Figure 54 Visibility areas for three ground stations present from geometrical considerations when the distance between the ground sta tionsequalsapproximatelytheorbitalheight of the satellite used 514 A successful ob servation from at least two stations is called an event The abovementioned conditions ex plain the difficulties that arise with the real ization of an observation project in partic ular because fine weather conditions must be present simultaneously at all participat ing stations These are the reasons for the long duration several years of all large projects which have been conducted in the past Coordinate measurements and corrections The exposed and developed plates or films photograms are measured on a comparator The results are the rectangular coordinates x y of the stars and of the satellite images defined in the plane of the photographic plate thus the analogous information of the 51 Photographic Determination of Directions 167 where ρ the geocentric distance of the observation station s constant value 000125 and d observer satellite distance A new discussion of satellite refraction after the advent of CCD astrometry is given by Bretterbauer 2001 The correction for aberration reduces the observation epochs for all participating stations to a common epoch defined at the satellite The phase correction reduces the reflected images of the sun to the center of the satellite Explicit formulas can be taken from Schmid 1977 Note that the last two geometrical corrections are also important for laser ranging to satellites 84 Plate reduction pole η 90 δ ξS S S α δ ηS C α0 δ0 ξ Figure 56 Tangential coordinates ξ η The photograph of the star field is noth ing else but the projection of the astro nomical sphere into a plane If we as sume ideal conditions ie a rigorous central perspective projection without distortion refraction etc we can com pute plane tangential coordinates ξ η from the equatorial star coordinates α δ with respect to a known camera orienta tion α0 δ0 Fig 56 The ideal tangen tial coordinates ξ η differ from the mea sured coordinates x y on the photogram only by random observation residuals vx vy In practice such ideal conditions do not exist Within the plate reduction process we try to find an adequate model for the relation between tangential star coordinates ξ η and measured coordinates x y Once the parameters of this model are identified they can be used to transform the measured satellite coordinates xS yS via the tangential coordinates ξS ηS into equatorial satellite directions αS δS Usually the plate reduction models are subdivided into astrometric methods and photogrammetric methods because they are based on developments from both fields The differences are however more in the formulation than in the results Within the astrometric plate reduction model the tangential coordinates ξ η and the plate coordinates x y are related through polynomials The tangential coordinates ξ η are determined with the formulas of the gnomonic projection Green 1985 Smart 1977 Following Fig 56 we introduce a quantity q with q cot δ cosα α0 and obtain ξ tanα α0 cos q cosq δ0 and η tanq δ0 53 170 5 Optical Methods for the Determination of Directions z M x S1 e11 P1 e21 g12 δ12 α12 e22 P2 e12 S2 y Figure 58 Spatial triangulation withdirections For a second satellite position S2 the same satellite at another position or a different satellite a second plane is de fined in space n2 e12 e22 511 With g12 n1 n2 n1 n2 512 we obtain the unity vector and hence the direction in space between the two ground stations P1 and P2 The vector g12 gives the orientation be tween two distant stations Addi tional ground stations can be included for the construction of larger networks Fig 59 or even global networks Fig 510 Several events are observed from each pair of ground stations in order to increase the accuracy S1 S2 Figure 59 Satellite triangulation A network which consists only of di rections or angles has a socalled da tum defect the scale and the origin are not fixed At least one baseline has to be measured for the determination of the scale This can for example be a laser range measurement between a ground station and a satellite position or a distance determination with terres trial techniques between two ground sta tions Usually the latter solution has been adopted in satellite geodesy In order to fix the origin of the coor dinate system either the coordinates of one station have to be defined arbitrarily or geocentric coordinates of one or sev eral network stations are determined with alternative techniques eg through Doppler measurements with known orbits 66 121 In other words the purely geometric techniques require additional dynamical information for the determination of a datum 41 For a full treatment of the subject see Schmid 1977 515 Results The method of satellite photography was used frequently between 1964 and 1975 for the establishment of regional continental and global geometrical networks within national and international projects Of historic importance is the geometric worldwide 172 5 Optical Methods for the Determination of Directions The historical importance of the worldwide BC4 network lies in the fact that for the first time a solution was obtained for the fundamental scientific problem of geometric geodesy ie the determination of a global polyhedron Cage of Bruns 12 Today photographic camera observations to artificial satellites are no longer used because of the great effort required to make and adjust the observations and the rather low accuracy Instead CCD technology is replacing this traditional method The basic methodological foundations in particular the plate reduction techniques however are of continuing importance 52 Directions with CCD Technology In the last decade of the 20th century the fast development of electronic position sensors in particular the Charge Coupled Device CCD initiated a revival of optical methods in astrometry and also satellite geodesy The key factors when compared with traditional photographic or even visual methods are higher sensitivity improved accuracy shorter observation time the image information is available in digital form fully automatic data flow no time consuming coordinate measurement neces sary and availability of new star catalogs with sufficient and accurate reference stars As a consequence in todays astrometry CCD technology is nearly universally applied eg for the construction of ground based star catalogs Ashford 2001 In geodetic astronomy many classical observation techniques have been supplanted by new tech nology based on the use of CCD Bretterbauer 1997 Fosu 1998 Gerstbach 1999 Hirt 2001 In the last decade various new applications have arisen in satellite geodesy Schildknecht 1994 Hugentobler 1998 Ploner Jackson 1999 Satellites are fast moving objects and hence generate particular problems however much experience and many solution concepts can be taken from astrometry and classical photographic satellite tracking The use of CCD technology in satellite geodesy will certainly grow and deliver significant results The basic objective is to determine the orientation of a camera with respect to the inertial frame The camera may be either fixed to the ground Earth based observatory or to a space vehicle satellite rocket platform cf Fig 511 In both cases the orientation angles declination δ0 right ascension α0 or hour angle t0 and the swing angle κ0 around the camera axis have to be determined see Fig 57 The process widely follows the procedure that has been developed in the photographic technique 51 The main steps are depicted in Fig 512 521 Image Coordinates from CCD Observations A digital image is composed of so called pixels picture elements that are arranged in the form of a matrix with r rows and c columns The image information is represented by intensities grey values usually varying between 0 and 255 The position of a 52 Directions with CCD Technology 173 Earth Satellite orbit Earth rotation axis Satellite Equator S N Bodyfixed zaxis α0 δ0 Figure 511 Orientation of a satellite in space Exposure Image extraction stars satellites Star identification Plate reduction Transformation parameters Star catalogue Orientation Camera Platform Directions to stars satellites other objects Figure 512 Process of CCD observations pixel within the picture is defined by two dimensional coordinates r c indicating the particular row and column These are naturally discrete values The origin of the image coordinate system is often transferred to the center of the sensor Fig 513 The measured coordinates are hence x y and correspond with the plate coordinates defined in 513 The coordinates xSi ySi of a star or satellite image covering several pixels can be determined with subpixel accuracy see later These coordinates hence are nondiscrete continuous numbers 0 1 2 2 1 0 c r y x Figure 513 Image coordinate system Figure 514 CCD camera Apogee KX2E A CCD camera Fig 514 uses a CCD sensor instead of the photographic plate or film to store the image information The technique was invented by 1970 in the USA The CCD sensor makes use of the photoelectric effect in silicon to convert photons into charges The sensor or chip consists of a certain number of lines and columns 174 5 Optical Methods for the Determination of Directions forming an array of pixels To give an example the CCDchip Kodak KAF1602E that is often used in small astrometric cameras has 1530 1020 pixels and measures 138 92 mm The pixel size is 9µm 9µm The corresponding field of view depends on focal length and is in most cases far below 11 Arrays of about 1000 1000 pixels are standard Larger arrays are available but are still rather expensive The market however is developing very fast For detailed information on CCD technology see the literature on digital photography Photoelectricity in astrometry is discussed in detail by Kovalevsky 1995 A good overview with respect to requirements for taking fast moving objects satellites is given by Schildknecht 1994 In order to obtain image coordinates for objects of interest the images of stars and satellites have to be recognized and the coordinates of the image centers xi yi have to be determined This is the process of image extraction The images are consid ered to be a group of pixels with similar properties they differ from the background through significantly higher grey values There exist a number of techniques of image extraction developed in the field of digital image processing With proper weighting centering algorithms may lead to accuracies of 01 to 02 pixels for the image centers Depending on the cameras focal length this may correspond to 01 arcseconds or bet ter Significant improvements can be expected with progress in CCD technology For details on algorithms see eg Schildknecht 1994 Hirt 2001 For fast moving objects like satellites precise epoch registration is of particular im portance For solution concepts see eg Schildknecht 1994 Ploner Jackson 1999 522 Star Catalogs Star Identification and Plate Reduction In the next step star images in the digital photogram have to be identified and related to the equatorial positions given by a star catalog Because of the small field of view and high sensitivity of CCD sensors star catalogs with a very high number of precise star positions down to apparent magnitudes of 15m or fainter are required Such catalogs have only recently become available or are still under construction Traditional catalogs are by far insufficient Table 51 gives an overview Table 51 Recent star catalogs and aptitude for CCD astrometry catalogue stars magn stars µ σpos aptitude HIPPARCOS 118 000 124 3 yes 001 very low TYCHO2 2 500 000 145 60 yes 006 high GSC 19 000 000 155 460 no 0510 low UCAC 80 000 000 160 2000 yes 002007 very high The HIPPARCOS Catalog is the main result of the HIPPARCOS mission see 532 one of the most important astrometric endeavors of the last century HIP PARCOS delivered positions proper motions and parallaxes of about 118 000 stars 52 Directions with CCD Technology 175 with an accuracy of milliarcseconds The catalog is today the most important and most accurate realization of the Celestial Reference System ICRS at optical wave lengths Walter Sovers 2000 It is however not suited for CCD astrometry because of the low density of only 3 stars per square degree On most CCD images for the determination of directions to satellites no HIPPARCOS star would be available The Tycho2 Catalog Hog et al 2000 was observed together with the Hipparcos mission but with lower accuracy It contains 25 million stars over the complete sky The proper motions were determined by comparison with old groundbased observations The star density varies between 25 stars per square degree near the galactic poles and 150 stars per square degree near the galactic equator The average position accuracy is 006 and for proper motions 0025year Tycho2 hence will be the most appropriate catalog for CCD astrometry until the complete publication of the UCAC The Guide Star Catalog GSC was compiled for the orientation of the Hubble Space Telescope HST The catalog contains a large number of star positions but no proper motions The position accuracy is rather low the mean epoch of the ground based observations is 1983 hence the accuracy is rapidly decreasing GSC positions are not suited for high precision work with CCD sensors The US Naval Observatory CCD Astrograph Catalog UCAC Zacharias et al 2000 Sinnott 2001 is under construction with the objective to provide a catalog of highest density for both hemispheres The catalog contains positions and proper motions of stars between magnitudes 75 and 16 with a mean accuracy of 002 to 005 The results are related to the HIPPARCOS reference frame The observations are ground based The USNO twin astrograph has been equipped with a CCD chip of 4096 4096 pixels covering about one square degree of the sky The observations started in the southern hemisphere A preliminary data set is already released The observations of the northern sky will last until 2003 With about 2000 stars per square degree the UCAC will be the most appropriate catalog for the reduction of CCD images in astrometry and satellite geodesy For the process of star identification the approximate region of the photogram is delineated in the star catalog and the equatorial star positions αi δi are converted to plane tangential coordinates ξi ηi using 53 and the approximate camera orientation α0 δ0 The two point ensembles xi yi and ξi ηi are matched against one another with a suitable algorithm using translation rotation and scale until highest correlation is achieved To start with some arbitrary points from both ensembles are set to be identical To accelerate the process the search algorithm can be restricted to the brightest stars of the field eg Quine 1996 The plate reduction itself follows the procedure as described in 513 Because of the narrow field of view the astrometric model is appropriate Schildknecht 1994 Ploner 1996 Hirt 2001 Emphasis may be given to corrections for astronomical refraction satellite refraction dispersion and aberration 176 5 Optical Methods for the Determination of Directions For details see 513 and Seeber 1993 Schildknecht 1994 Ploner 1996 As a result the orientation of the camera axis in inertial space cf 4332 andor the directions from the camera position to space objects like satellites are obtained 523 Applications Results and Prospects For CCD observation of fast moving objects like satellites two particular aspects are of importance namely the angular velocity of the object with respect to the stars or to the camera and the intensity of light crossing the pixels Table 52 gives an idea Depending on the telescope and the pixel size the pixel crossing time ranges between a few and several hundred milliseconds For details see eg Schildknecht 1994 Table 52 Observational characteristics for fast moving objects GEO GPS LAGEOS ERS Altitude km 36 000 20 000 6 000 780 Max motion arcss 15 30 240 2000 Magnitude mv 11 8 14 14 6 Telescopes can either follow the stars or the satellites or be held fixed Successful observations have been performed since about 1990 with existing satellite telescopes eg with the ballistic camera Zeiss BMK 75 512 inAustria Ploner 1996 or with the 05 m SLR telescope 83 in Zimmerwald Switzerland Schildknecht 1994 In 1996 a combined Laser Ranging and Astrometric Telescope ZIMLAT was established in the fundamental station at Zimmerwald Hugentobler 1998 The mapping scale of the latter camera is about 08 pixel Successful observations have been reported for a large number of geostationary satellites as well as for GPS LAGEOS and GFZ1 The accuracy in orientation to GEO satellites was found to be about 05 and for GPS satellites 01 to 02 Ploner Jackson 1999 Important results are for example Hugentobler 1998 determination of the resonant geopotential terms C22 and S22 from precise geo stationary orbits controlofspacedebrisinhighorbitsandthecalibrationofalternativeobservation techniques and determination of the complete position vector to satellites of interest in geodesy With further developments in CCD technology eg larger arrays smaller pixel size and improved time tagging the optical determination of directions to satellites will again play a significant role in satellite geodesy 53 Directions from Space Platforms We distinguish two different tasks a the determination of the orientation of a space platform and b the determination of directions to objects eg stars from a space 53 Directions from Space Platforms 177 platform both with respect to the inertial frame The first problem can be solved with startrackers the second is related to space astrometry using astrometric satellites Both subjects have received tremendous support from the recent developments in CCD technology 531 Star Tracker The purpose of a star tracker or star sensor is to measure the direction to a star within the reference frame fixed to the sensor body Star sensors are mainly used for orientation and attitude control of space vehicles 4332 The basic concept closely follows the procedure of CCD astrometry as explained in 52 The star tracker is basically a digital camera which takes photographs of stars or sets of stars in the direction of its optical axis The first step is to identify a star or set of stars with reference to the onboard star catalog Other than in space astrometry the approximate initial orientation of the star tracker cannot be taken as known This is why powerful algorithms are required for matching the pattern of image stars against the catalog positions without any a priori knowledge of the sensor orientation Quine 1996 This type of sensor is also called autonomous star tracker The second step is to track the stars and to control the orientation of the platform The last step is to refine the orientation with respect to the required frame Star sensors have excellent longterm stability and provide accuracy in attitude control of down to 1 arcsecond For details on instruments and algorithms see eg Quine 1996 Sidi 1997 Renken 1999 532 Astrometric Satellites HIPPARCOS Astrometric satellites have opened a new era in astrometry The unique features of a satellite as observation platform if compared with ground based astrometry are the satellite is able to observe the entire sphere from its location in space the absence of atmospheric disturbances and high instrumental stability brought about by the absence of gravitational instru mental flexure These features initiated a dramatic improvement in the accuracy of star positions over three orders of magnitude from 1 arcsecond to below 1 milliarcsecond mas Further improvement down to 1 microarcsecond µas is expected The first astrometric satellite was HIPPARCOS The acronym stands for HIgh Precision PARallax COllecting Satellite The principle of HIPPARCOS was invented by Lacroute a French astronomer in 1966 Kovalevsky 1995 After several mod ifications it was accepted as an ESA mission in 1980 and eventually launched on August 8 1989 into a highly elliptical orbit instead of the planned geostationary one This was due to a failure in the apogee booster As a consequence the perigee is about 500 km and the apogee close to 36 500 km Nevertheless the satellite after a complete modification of the observation program worked successfully for about 35 years until March 1993 53 Directions from Space Platforms 179 Orbit of spacecraft Earth Sun Rotation axis Path of rotation axis γ Figure 516 HIPPARCOS scanning the sky with a 20 day period Fig 517 due to solar radiation pressure The orbital motion of Earth around the sun along with the spacecraft rotation and precession will result in complete sky coverage after 3 months The telescope will includes 24 large format CCDs The images of stars will continuously traverse the CCD array and be time Rotation period 40 min 355 Scanned spiral Telescope fields of view SunSpacecraft line Precession period 20 days Basic angle 843 Figure 517 FAME observing concept tagged as the spacecraft rotates For technical details see publications of the USNO or eg Seidelmann et al 1998 The objective is to measure the positions parallaxes and magnitudes of 40 million stars brighter than 15m with an accuracy of 50 µas for 180 5 Optical Methods for the Determination of Directions the brighter stars and up to 300 µas for the fainter stars The realization of the mission is now questionable DIVA To bridge the gap until the launch of GAIA a small astrometric satellite DIVA Double Interferometer for Visual Astrometry has been proposed eg Bastian 1998 It is aimed to measure positions proper motions and parallaxes of at least 30 million stars with an accuracy about five times better than HIPPARCOS The basic principle is similar to that of HIPPARCOS but realized with advanced technology at much lower cost The satellite shall be launched into a highly eccentric geosynchronous orbit apogee 71 000 km perigee 500 km It will scan the sky and measure an angle of 100 degrees using the interferometric principle and CCD sensors The mission is however not yet approved GAIA The European Space Agency ESA has designed a next generation mission named GAIA GAIA stands for Global Astrometric Interferometer for Astrophysics It com bines the basic principle of HIPPARCOS with some new features GAIA will not be orbiting Earth but operate at the Lagrangian point L2 which is located some 15 mil lion kilometers from Earth in the direction away from the sun see Fig 329 p 134 Here the satellite will be free from eclipses and be in a stable thermal environment GAIA will be 2 to 3 orders of magnitude more accurate than HIPPARCOS and will provide positions distances and proper motions of about 1 billion stars at the 10 microarcseconds accuracy level The spacecraft should be launched around 2010 to 2012 and will be operated for five years Perryman Pace 2000 186 6 Doppler Techniques Substituting 68 into 67 and solving yields the observation equation Njk fg fstk tj fg c rik rij 69 The geometric interpretation of this equation is depicted in Fig 47 Equation 69 can be written in terms of coordinates cf Fig 65 By substituting in r2 ik Xk Xi2 Yk Yi2 Zk Zi2 610 r2 ij Xj Xi2 Yj Yi2 Zj Zi2 611 we have the basic observation equation of Doppler positioning Njk fg c Xk Xi2 Yk Yi2 Zk Zi2 1 2 Xj Xi2 Yj Yi2 Zj Zi2 1 2 fg fstk tj 612 with four parameters only namely Xi Yi Zi unknown station coordinates fg fs unknown frequency difference A more detailed observation equation is discussed later in 64 and 65 62 One Successful Example The Navy Navigation Satellite System TRANSIT A very successful system based on the Doppler principle and used for geodetic pur poses was the TRANSIT system Other acronyms for the system are NAVSAT An derle 1986 or Navy Navigation Satellite System NNSS It was developed in cooper ation between the Applied Physics Laboratory APL of the Johns Hopkins University and the US Department of Defence DOD The first operational TRANSIT satellite was launched in 1962 Released for civilian service in 1967 TRANSIT has provided reliable positioning and navigation information for nearly 30 years The TRANSIT program terminated navigation service on December 31 1996 The former Soviet Union has developed a similar system named TSIKADA however very little informa tion is available For three decades the use of TRANSIT considerably influenced geodetic position ing techniques With hindsight TRANSIT can be regarded as the forerunner of GPS Most of the observation and adjustment techniques used in the geodetic GPS are based on early developments during the TRANSIT era The development of GPS technology for geodetic positioning is much better understood with a knowledge of the TRANSIT history For this reason a short overview of the TRANSIT architecture and its use in geodetic positioning is given For a detailed treatment see eg the first editions of this book Seeber 1989b 1993 An excellent overview of all aspects of the system was published by the APL Pisacane ed 1998 188 6 Doppler Techniques Figure 67 Functional diagram of OSCAR satellites satellites should be replaced completely by the NOVA type spacecraft in order to achieve an overall improvement of the TRANSIT system Due to the concurrent development of the GPS system and the decision to replace TRANSIT completely by GPS after 1994 only three NOVA satellites were built One of the main new features of the NOVA satellites was the disturbance compensation system DISCOS 4331 which compensates for the effects of atmospheric drag and radiation pressure Predicted ephemerides are thus valid much longer As of January 1 1997 after termination of the navigation service several TRAN SIT satellites remained operational and could be used for ionospheric tomography The satellite system has been known since then as the Navy Ionospheric Monitoring System NIMS The message modulation however does not carry time and position information The satellites are being used as dualfrequency beacons by ground data collection sites to determine the free electron profile of the ionosphere Tucker 1998 622 Broadcast and Precise Ephemerides Two kinds of orbital information have to be distinguished the predetermined ex trapolated broadcast ephemeris derived from observations made at four US tracking stations and the postprocessed interpolated precise ephemeris derived from obser vations made at about 20 globally distributed stations The broadcast ephemerides are communicated to the user as the navigation mes sage For a detailed explication see eg Seeber 1993 p 167ff An appropriately equipped observer is able to decode the orbit information to convert the elements into Earthfixed satellite coordinates and to solve the observation equation 612 for the user position Smoothing algorithms 3332 can be used to interpolate orbit positions between the given epochs The broadcast ephemerides are generated from an orbit integration process 3322 based on observations at the tracking stations of the OPerational NETwork 62 One Successful Example The Navy Navigation Satellite System 189 OPNET In the case of TRANSIT these were the four stations at Maine Minnesota California and Hawaii Fig 68 Figure 68 Control stations of the OPNET triangles and the TRANET solid circles Precise orbit determination requires knowledge of the gravity field The gravity field parameters were determined alongside the development of the TRANSIT system and are partly based on observations with the early experimental TRANSIT satellites Fig 69 shows the evolution of the orbit prediction accuracy over more than twenty years A significant advance was achieved with the introduction of the gravity field Figure 69 Evolution of the accuracy of the TRANSIT system 190 6 Doppler Techniques APL 45 up to degree and order 15 in 1969 The gravity field of the World Geodetic System 1972 WGS 72 with potential coefficients up to 2020 was introduced 1975 and the transition to the WGS 84 occurred in 1988 216 Note that early GPS orbits were also based on WGS 72 and only since 1987 on WGS 84 Themainsourcesoferror inherentinthepredictedephemeridesofLEOspacecrafts like the TRANSIT satellites are not introduced by the gravity field model but by unmodeled alongtrack forces atmospheric drag and solar radiation pressure In particular during periods of high solar activity the predicted orbit and the real orbit may show large differences In order to improve the positioning accuracy about 30 to 50 satellite passes had to be observed at each station The accuracy of the geocentric coordinates obtained with a broadcast ephemeris was not better than 2 to 5 m because the reference system at that time could not be realized to a better level of accuracy cf 1211 through observations over a limited time span Precise ephemerides were computed for some of the TRANSIT satellites based on observations at about 20 globally distributed stations The accuracy was much higher than for the broadcast ephemerides because the orbits were not predicted but derived from measurements The network of the participating tracking stations was operated by the Defence Mapping Agency DMA however civil organizations also participated in the observations The network was calledTRANET TRAnsit NETwork seeFig68 WithTRANETmuchexperiencewasgainedwhichwaslaterincorporated into the organization and operation of a civil network for precise GPS orbits namely CIGNET Scheneweck et al 1990 and then IGS 781 Since January 1987 the precise ephemerides have been based on the WGS 84 Earth model The accuracy of the precise ephemerides was about 12 meters The ephemerides were delivered to the user as a set of 3D coordinates and velocities for each full minute Coordinates for epochs in between could be determined with appropriate smoothing algorithms 333 Geocentric coordinates based on several days of observations and precise ephemerides could be determined with an absolute accuracy of 05 to 10 m Many geodetic control points all over the world which are still in use today have been determined with point positioning techniques and precise ephemerides 652 661 63 Doppler Receivers 631 Basic concept The equipment consists of the antenna with preamplifier and the receiver with data processor data logger power supply and optionally sensors for obtaining meteo rological data Builtin microprocessors control the whole system support the field planning and provide a navigation solution or even the complete data reduction in the field Doppler receivers can be roughly subdivided into single channel and dual channel receivers Single channel sets only track one frequency eg 400 MHz For applica 63 Doppler Receivers 191 tions in geodesy only dual frequency receivers are of interest because of the need to correct for ionospheric refraction Fig 610 shows the functional diagram of a generic geodetic Doppler survey set as used for TRANSIT observations The satellite signal is received at the antenna Figure 610 Functional diagram of a geodetic doppler receiver and amplified in the preamplifier which is usually integrated within the antenna body For dual frequency receivers the incoming signal is then separated into the two eg 150 MHz and the 400 MHz signals in the deplexerpreselector module Each signal is transferred to the receiver module and mixed with the reference oscillator frequency generating the Doppler shifted beat frequency fbt 65 which reaches 32 KHz Both beat frequencies are passed to the time frame tracker Here the satellite information message is decoded and the satellite time frame is generated from the satellite time signals The beat frequencies are digitized and transferred to the Doppler counter The Doppler count can either be obtained with respect to the satellite time frame given by the timing signals from the satellite or with respect to the receiver time frame generated by the internal 5 MHz oscillator All internal functions and signal processing are controlled by the builtin microprocessor central processing unit CPU The central module of the receiver is the 5 MHz precision oscillator The ultimate accuracy depends essentially on the quality of the oscillator because instabilities during the satellite pass 1618 minutes affect directly the Doppler count 643 Usually a precise quartz oscillator is used In most cases an external oscillator rubidium cesium can be connected to the receiver For postprocessing purposes all data Doppler counts message results meteoro logical data station identification data are recorded with data logging devices The basic observable is the integrated Doppler count Njk 65 The counting interval defined by the satellite timing signals eg two minutes for TRANSIT satel lites may be too long for geodetic applications A higher resolution can be obtained from the signal structure of the broadcast message eg 46 second word length in the TRANSIT message short Doppler count The improved resolution of a single wavelength of the Doppler frequency fb is called the fractional Doppler count 192 6 Doppler Techniques Two different modes are used to count the Doppler frequency fbt during the satellite pass Fig 611 In the first mode the counter is set to zero by each satellite t0 t1 t2 t3 t4 t5 t6 t7 t8 N01 N12 N23 N34 N45 N56 N67 N78 N01 N02 N03 N04 N08 Figure 611 IID and CID Dopplercounts timing signal The procedure is named intermittently integrated Doppler count IID In the second mode the counter runs continuously and is read out with each incoming timing signal This is the continuously integrated Doppler count CID The two versions correspond to the differences between the terrestrial measurements of angles and directions One advantage of the Doppler method over range measurements is that it is far less sensitive to errors in the determination of time It is the velocity of the transmitter in the satellite and not the velocity of the signals that counts This results for the TRANSIT system in a reduction of the effect of timing errors by a factor of 5 104 Hatch 1982a 632 Examples of Doppler Survey Sets In 1967 Magnavox initiated the geodetic use of Doppler techniques with the launch of the GEOCEIVER ANPRR14 Since then the name Geoceiver has been synonymous with precise geodetic Doppler equipment The instrument was mainly used by US military and governmental agencies Only precise ephemerides 622 were used because the receiver was not equipped for decoding and recording the satellite message with broadcast ephemerides Later Magnavox developed some commercial versions of the Geoceiver finish ing in 1977 with the MX 1502 Satellite Surveyor Fig 612 Stansell 1979 The instrument is quite compact very rugged battery operated and has a weight of 19 kg The satellites were tracked automatically Realtime and accumulated single station solutions were displayed on the front panel With additional boards the data from two simultaneously observing receivers could be processed in the field translocation solution cf 653 64 Error Budget and Corrections 193 Figure 612 Magnavox MX 1502 Figure 613 Marconi CMA 751 In 1977 Canadian Marconi delivered the microprocessorbased Doppler receiver set CMA 751 A preselection of satellite passes was possible and also data reduction in the field The tracking data were recorded on digital cassettes with a separate digital cassette unit The atmospheric data could also be recorded on digital tape cassettes by the environmental sensor unit ESU Fig 613 shows a typical field survey configuration Several other manufacturers built geodetic Doppler receivers between about 1973 and 1985 All receiver systems came with powerful software for coordinate trans formation prediction of satellite passes alerts single or multistation solution All these instruments had about the same accuracy and capacity and they were able to meet all requirements until the TRANSITprogram was phased out in 1996 For DORIS receivers see 67 64 Error Budget and Corrections The basic observation equations 69 and 612 from section 61 are valid under ideal conditions The real observation situation is different mainly for the following reasons the predicted ephemerides differ from the true satellite positions 641 the signal propagation is not in vacuum 642 and the signal processing in the receiver electronics is not stable 643 Furthermore we have to consider that Earth together with the receiver antenna rotates while the signal is propagating aberration and that the transmitter and the receiver are moving relative to each other in differing gravity fields relativistic effects 644 Finally for nonstationary observers the proper motion of the user antenna plays a role 645 194 6 Doppler Techniques Some of these influences can be compensated through corrections to the obser vations Some of the remaining influences can be modeled as parameters in the ad justment process The residual unmodeled influences are regarded as observational or system noise they contribute to the error budget of the individual satellite pass 641 Satellite Orbits Orbital accuracy is of importance when Doppler beacons on satellites are used in an operational satellitebased navigation system like TRANSIT The situation is different for a system like DORIS 67 where the Doppler technique is primarily used for the orbit determination of spacecrafts The predicted orbital positions of TRANSITtype satellites broadcast ephemerides differ from the true satellite positions for three main reasons cf 622 uncertainty in the gravitational model limited accuracy of the orbit representation and inadequately modeled surface forces The relation between the degree and order of the Earth gravity field model used and the position error of a satellite at 1000 km orbital height is illustrated in Fig 614 Kaulas rule of thumb shows that the position uncertainty amounts to 46 m for a Figure 614 Kaulas rule of thumb for 1000 km orbital height potential development up to degree and order of 20 This corresponds to the ef fect of the inaccuracies of the WGS 72 Earth model on positions of a TRANSIT or typical Earth observation satellite as is illustrated in Fig 69 With the intro duction of the WGS 84 gravity field the effect has been reduced By far the largest portion of the or bit prediction error comes from unmod eled surface forces on the satellite like solar radiation pressure 3234 and at mospheric drag 3233 The latter ef fect is particularly important for naviga tion and Earth observation satellites in low Earth orbits and with an unfavor able surfacemass ratio The perturba tions are greatest in the along track di rection and may reach several tens of meters The effects can be much higher with high solar activity The situation is considerably better for satellites which have a compensation system for surface forces DISCOS 4331 621 The remaining discrepancies from the predicted orbit caused by unmodeled drag and radiation pressure was only about 65 Observation Strategies and Adjustment Models 199 When insufficient information on the antenna motion during a satellite pass is available the observed integrated Doppler count contains systematic effects that lead to systematic position errors Fig 615 demonstrates for TRANSIT satellites how an error of 1 mminute in the observers velocity propagates into the position It becomes clear that without velocity information considerable position errors may be present in the navigation solution 10 20 15 5 0 20 15 10 5 0 60 120 180 240 300 360 Azimuth of velocity error Error in east west direction Error in horizontal coordinates m Error in north south direction Figure 615 Effect of a velocity error 1mmin on the single pass position fix TRANSIT 65 Observation Strategies and Adjustment Models 651 Extended Observation Equation A simplified observation equation has been already introduced in 69 according to Fig 65 p 185 Njk fg fstk tj fg c rik rij This basic equation is mostly used in navigation It is very suitable for application to simple receivers because the timing interval tk tj for the Doppler count is provided from the space segment and no time measurement in the receiver is necessary The geodetic form of the observation equation requires some refinement and extension based on the discussions in sections 64 and 65 In particular a much more stable time measurement is required of the internal oscillator used in a geodetic receiver The transition to the receiver time frame is imperative and a variable receiverdelay has to be assumed for the beginning and the 202 6 Doppler Techniques Sj Sk r0 ik rij r0 ij rik approximate position dx adjusted position x x0 Figure 616 Single station determination point positioning ephemeris Starting with the approx imate position x0 a correction vector dx is derived from the adjustment of all observations Fig 616 A certain number of satellite passes depending on the particular satellite system has to be observed in order to achieve a reason ableaccuracy ForTRANSITandbroad cast ephemerides about 30 to 50 passes were required for an absolute accuracy of 23 m with respect to WGS 84 For DORIS see 67 With precise ephemerides the point positioning result may reach an accuracy of 1 m or better In several countries the coordinates from TRANSIT point positioning with precise ephemerides still form the basis of the national net work of control points 653 MultiStation Positioning Some of the biases are identical for nearby stations and cancel when differences are formed between the observations This is why simultaneous observations at two or morestationsisthestandardprocedureinDopplersurveying Inthecaseoftwostations the technique is named translocation Note that experiences with the translocation and multistation techniques in TRANSIT data analysis have considerably influenced the DGPS technology 75 dr dr dr dr dr true orbit broadcast orbit B drB B A drA A Figure 617 Translocation technique orbit er rors are cancelled in the difference In principle in the translocation technique some of the parameters are eliminated instead of being estimated cf Fig 617 This is true for the sys tematic orbit errors and to some extent for the propagation errors The increase in accuracy obviously only applies to the relative coordinates between stations A and B not to the absolute coordinates of both stations This is why translocation techniques are suitable when a new sta tion B is connected to an existing point A The same principle is valid for GPS 75 The parameters for orbit errors and propagation delay can also be estimated 204 6 Doppler Techniques 661 Applications for Geodetic Control Several objectives can be distinguished 1 establishment of fundamental geodetic control 2 densification of existing geodetic control 3 analysis and improvement of existing geodetic control and 4 contribution to geoid determination 1 The first objective included the establishment and realization of a geodetic datum and the installation of a basic control network Usually the World Geodetic System WGS 84 was selected as the geodetic datum The accuracy of the realization was 05 m with precise ephemerides and 1 to 2 m with broadcast ephemerides The relative accuracy between datum points was however much better and reached 02 m with 50 to 100 accepted satellite passes 2 The densification and expansion of an existing network was achieved with different procedures The easiest method from the logistical point of view was the establishment of single stations each with a precise ephemeris This procedure was widely used in the geodetic development of vast areas like Brazilian Amazonia Fig 619 The coordinates were first determined in the satellite datum and then Figure 619 Doppler control points in Brazil source IBGE 1987 66 Applications 205 converted with conventional transformation formulas to the particular national datum eg the SouthNorth American Datum SAD 69 or NAD 83 Accuracy was 05 m to 10 m Those coordinates define and realize the geodetic datum in the newly developed region 3 Doppler observations were also used to control analyze and improve existing geodetic networks Examples in Europe from the TRANSIT era are the EDOC12 European Doppler Campaign Boucher et al 1979 DÖDOC GermanAustrian Doppler Campaign Rinner et al 1982 RETDOC European Triang Network Doppler Campaign Wolf 1984 In Africa ADOS African Doppler Survey was organized in international cooperation Chodota 1987 1990 More than 300 stations in 46 African countries were included in the final computation Examples from smaller areas are the German Fundamental Network DHDN Seeber Seeger 1984 one part of theVenezuelan network Hoyer 1982 and the fundamental network in Southern Brazil Campos 1987 The GermanAustrian Doppler Campaign DÖDOC resulted in positions with standard deviations of about 15 cm and showed discrepancies to the existing classical network at the order of about 1 m This example demonstrated that Doppler observa tions over distances of several 100 km are able to meet or even exceed the accuracy standard of classical triangulation networks 4 Doppler satellite observations provide threedimensional Cartesian coordinates that can be converted to ellipsoidal latitude ellipsoidal longitude and ellipsoidal height h WithknownlevelledorthometricheightH thegeoidundulationN canbedetermined for the observation point using the simple relation cf Fig 782 p 366 N h H 640 This procedure has been used in many countries for the determination of regional geoids One example is the project ALGEDOP 19801983 for the European Alps Seeger 1984 Comparisons with existing geoid computations showed differences of less than 1 to 2 m Another example is the Doppler geoid in Africa based on ADOS results Fashir Abdalla 1991 The same relationship however with much higher accuracy is used in GPS geodesy for regional and local geoid determination 7623 662 Further Applications Satellite Doppler surveying has been widely used to determine control points in various applications besides navigation In the following some typical examples from the TRANSIT era are presented The same types of application are possible with the DORIS system 67 although in most cases today the GPS technology is preferred Control and fiducial points Fiducial points in small scale photogrammetry or for geophysical surveys eg for the determination of seismic shot points have been frequently established in the single 206 6 Doppler Techniques station or the translocation mode with few satellite passes The translocation technique could be used to reduce the necessary observation time For hydrographic surveys with conventional shortrange radio navigation eg Syledis Hifix Trisponder Miniranger the coordinates of the shorebased antennas often were determined with Doppler translocation techniques An accuracy of 1 m to 3 m was usually sufficient Another important application was inertial surveying Seeber 1979 Schwarz 1980 1983 In a first step control points with interstation distances of 100 to 150 km were determined with Doppler techniques The densification was done in the second step with inertial surveys This technique has been widely used in Canada for the determination of control points in unsurveyed areas Webb Penney 1981 Multi station Doppler techniques were required because inertial surveying determines the coordinates with a relative accuracy of 01 m to 02 m Marine and polar geodesy The increasing economic importance of the seas and the sea floor caused increasing accuracy demands The demarcation of marine boundaries and the location of drilling positions for the exploitation of marine hydrocarbons and ocean mining require a position accuracy of as high as 1 m with respect to a global datum Fixed structures in the marine environment like oil production platforms can be surveyed with the same geodetic methods used for landbased objects This is why Doppler techniques were extensively used since about 1970 for positioning marine platforms eg in the North Sea Leppard 1980 cf Fig 129 p 523 The situation is more difficult for moving objects ships buoys because the relative motion of the object during the satellite pass decreases the achievable accuracy Egge 1982 Seeber Egge 1981 cf 645 With translocation measurements to a fixed reference station the best possible accuracy was found to be 10 m Seeber 1983 TRANSIT Doppler receivers were an essential component of all integrated navigation systems Doppler observations were applied successfully to determination the velocity of ice sheets in the Arctic or Antarctic Drew 1983 Seeber Hinze 1984 In the Antarctic the rates of shelfice motion are between about 3 mday near the coast to about 01 mday for the inland ice Hinze 1990 Polar motion Satellite orbits are computed with respect to an inertial reference frame the Doppler observations are related to an Earthfixed reference frame The difference between the two systems contains among other effects the influence of polar motion 2123 In order to use the satellite observations in orbit computation they must either be corrected for polar motion or the components x y of polar motion have to be estimated as additional parameters in the orbit adjustment program This second solution has been used successfully since 1969 Anderle 1973 1986 with the computation of the precise ephemeris of the TRANSIT satellites based on the observations within the global TRANET network 622 67 DORIS 207 Dopplerderived polar motion data have been published weekly by the US Naval Observatory and were used in the regular polar motion service of the former Bureau International de lHeure BIH until 1987 Comparisons over many years demon strated a good agreement with other techniques 855 1242 The Doppler results were two to four times more accurate than classical astrometric methods Because of the even better accuracy with SLR and VLBI techniques the Doppler polar motion data derived from TRANSIT observations were not used by the IERS service 1242 that superseded BIH on January 1 1988 Since 1994 however DORIS observations have been included in the computation of Earth orientation parameters and other IERS products 67 67 DORIS DORIS Doppler Orbitography and Radio Positioning Integrated by Satellite is a French development which like TRANSIT uses the Doppler concept but in a reverse mode a stable frequency is emitted by ground beacons and the measurement of the Doppler count is made in the satellite The DORIS system was developed by the French Space Agency CNES Centre National dÉtudes Spatiales in cooperation with IGN Institut Géographique National and GRGS Groupe de Recherches de Géodésie Spatiale with the objective to support precise orbit determination for lowaltitude Earth satellites A first realization of the system was in 1990 on the remote sensing satellite mission SPOT2 The system is based on the measurement of Doppler shifts in radio signals trans mitted by ground beacons and received by the DORIS onboard package as the satellite passes overhead The ground beacons broadcast continuously and omnidirectionally at frequencies of 203625 MHz and 40125 MHz cf Fu et al 2001 p 75f A re ceiver onboard the satellite receives the signal and measures the Doppler shift over a short count interval eg 10 seconds The data are time tagged with respect to an ultrastable onboard crystal oscillator The precise Doppler measurement is made on the 2 GHz signal the use of the second frequency allows for the removal of the effects of ionospheric refraction 642 The ground beacons are also equipped with stable oscillators and sensors to provide in situ meteorological data The average precision of the range rate observations is about 03 to 05 mms The DORIS system comprises the onboard package consisting of a receiver for both frequencies total mass 17 kg an ultrastable crystal oscillator stability class 5 1013 and an omni directional antenna a global network of permanent ground beacons Fig 620 at about 50 sites each consisting of two transmitters an ultrastable oscillator microprocessor power supply meteorological sensors and an antenna dedicated location beacons functionally identical to the permanent beacons and a control segment master beacon and control center in Toulouse France 208 6 Doppler Techniques Figure 620 DORIS orbitography beacon network status 2002 The network of beacons is distributed evenly around the globe This is a key factor in the high quality of DORIS products The network also provides very good coverage of the oceans since nearly half of the stations are on islands All data are collected by the onboard receiver on a timesharing basis stored in the onboard memory and downloaded via suitable data links at regular intervals to the mission control center in Toulouse The DORIS onboard package so far has been installed on seven satellites and it will certainly be flown on more Table 61 Satellites carrying DORIS payload Satellite Launch date End of mission SPOT2 January 22 1990 TOPEXPOSEIDON August 10 1992 SPOT3 September 26 1993 November 14 1996 SPOT4 May 26 1998 JASON December 7 2001 ENVISAT March 1 2002 SPOT5 May 5 2002 DORIS is primarily an orbit determination system however it also contributes to studies of other geodetic and geodynamic problems Lefebvre et al 1995 In the following a short overview on DORIS applications is given 67 DORIS 209 Master Beacon BM System time and frequency Instruments control mission upload Orbitography Beacon BO Permanent network Precisely positioned Quartz oscillator Meteo data and beacon status transmission Customer Beacon to be positioned BC DORIS Ground Segment User Beacons Network DORIS Mission and System Center Satellite with DORIS instrument Time reference and Orbitography Beacon BOT Figure 621 DORIS System Overview Orbit determination The original design accuracy for orbit determination was about 10 cm for the radial component in postprocessing mode after about 1 month With improved network configuration better theory and error modeling the current accuracy is about 25 cm for postprocessed data For JASON the aim is to measure the satellites altitude to within 1 cm This high performance will contribute considerably to the use of altimetry in geodesy and oceanography 95 Fu et al 2001 With SPOT4 in 1998 the realtime autonomous onboard orbit determination ca pability DIODE was established providing realtime orbits with an accuracy within a few meters DIODE stands for Détermination Immédiate dOrbite par Doris Em barqué immediate onboard orbit determination by DORIS One important objective of the DIODE navigator is to deliver in realtime to SPOT image users all necessary information for a rectification of the SPOT scenes A further improvement is expected with a second generation receiver onboard JASON ENVISAT and SPOT5 that has reduced size and weight and is capable of communicating with two beacons at the same time For more information see eg Agnieray 1997 Costes 1997 Jayles et al 2000 DORIS offers three different orbit products Realtime with an accuracy of several meters and submeter accuracy in the future with the new generation system Operational with submeter accuracy after 48 hours 20 cm on the radial component and Precise withsubdecimeteraccuracyafteronemonthcmforradialcomponent 210 6 Doppler Techniques The continuous evolution of the system promises improved products in the future Positioning Once the satellite trajectory is known the exact position of a DORIS station anywhere in the world can be calculated In practice the more satellite passes are used the better is the positioning accuracy There are two services In operational geodesy with dedicated location beacons any point on Earth at any time can be determined with about 20 cm accuracy after a oneday measurement time and 10 cm after 5 days This commercial service offered by a CNES subsidiary in Toulouse may be of interest for geophysical exploration or similar work The beacons have their own power supply and only transmit when a satellite is within view They operate unattended for several months The automatic monitoring of the beacons make the system well suited for use in high risk areas eg land slide volcanic activity The permanent beacon network delivers high precision 3D coordinates for geode tic and geodynamic applications Positions and motions are available to better than 1 cm and 1 mmyear respectively Due to the dense and homogeneous global beacon network DORIS significantly contributes to the realization and maintenance of the ITRS 2122 Around 30 of the more than 50 beacons are collocated with other space techniques SLR VLBI GPS Fagard Orsoni 2000 ie they can be included in combined ITRF computations and provide important information on the stabil ity of the individual solutions Tectonic plate deformations derived from permanent DORIS observations correspond very well with the geological NUVEL1 model cf 1241 Geodesy Geodynamics and related fields Further contributions to geodesy and geodynamics are only mentioned Gravity field improvement Motion of the geocenter Vertical displacement near tide gauges Polar motion Earth rotation Ionospheric studies TEC models and Atmospheric drag For more information see the proceedings of the regularly organized DORIS Days eg CNES 2000 or documents of the future status 2002 International DORIS Ser vice IDS Because of the increasing importance of DORIS data and products for the geodetic community and related disciplines the IUGG in 1999 decided to start the DORIS Pilot Experiment with the objective to assess the need and feasibility of an International DORIS Service The IDS will be an international scientific service under the auspices of the IUGG similar the IGS International GPS Service ILRS Interna tional Laser Ranging Service and IVS International VLBI Service Tavernier et al 2000 After more than 10 years of operation DORIS has developed into one of the key technologies in geodetic space techniques 7 The Global Positioning System GPS 71 Fundamentals 711 Introduction The NAVSTAR GPS NAVigation System with Time And Ranging Global Positioning System is a satellitebased radio navigation system providing precise three dimensional position navigation and time information to suitably equipped users The system is continuously available on a worldwide basis and is independent of me teorological conditions GPS has been under development in the USA since 1973 and is primarily a military system with limited access to civil users 716 It has been used for the solution of geodetic problems since about 1983 In its final configuration available since 1995 the system nominally consists of 24 satellites placed in orbits of about 20 200 km altitude above the Earths surface Fig 71 The arrangement of satellites has been planned in such a way that at least four satellites are simultaneously visible above the horizon anywhere on Earth 24 hours a day Figure 71 The Global Positioning Sys tem GPS 24 satellites configuration Satellite 1 Satellite 4 Satellite 3 Satellite 2 GPSAntenna R 1 R 2 R 3 R 4 Figure 72 Basic principle of positioning with GPS GPS is primarily a navigation system The fundamental navigation principle is based on the measurement of socalled pseudoranges 714 731 between the user and four satellites Fig 72 Starting from the known satellite coordinates in a suitable reference frame the coordinates of the user antenna can be determined From the geo metrical point of view three range measurements are sufficient A fourth observation is necessary because GPS uses the oneway ranging technique 422 714 and the receiver clock is not synchronized with the satellite clock This synchronization error is the reason for the term pseudorange 212 7 The Global Positioning System GPS Unlike the NNSS TRANSIT system 62 GPS continuously provides navigation data in realtime on a global basis Technological advances over about twenty years also mean that a much higher accuracy is achieved than that for TRANSIT Some characteristic features of NNSS and GPS are compared in Table 71 Table 71 Characteristics of GPS and TRANSIT Features GPS NNSS TRANSIT orbital height 20 200 km 1000 km period 12 h 105 min frequencies 1575 MHz 150 MHz 1228 MHz 400 MHz navigation data 4D X Y Z t velocity 2D ϕ λ availability continuously 1520 min per pass accuracy 15 m 3040 m depending on 01 ms velocity error constellation 2124 SV 46 SV geometry repeating variable satellite clocks rubidium cesium quartz GPS has been designed to provide at best and for authorized users a realtime navigation accuracy of 10 m to 15 m It was recognized early on however Relative Range Accuracy cm Distance between stations km Distance between stations km Figure 73 Accuracy in geodetic positioning techniques status about 1985 that GPS can also support geodetic po sitioning with great accuracy Anderle 1979 predicted during a symposium on satellite geodesy inAthens that a rel ative accuracy of 10 cm over a dis tance of 2000 km would be attainable The experience to date has proved that a broad variety of problems in geodesy and geodynamics find their solution with GPS with even higher accuracy Fig 73 from the early eighties demonstrates that the advent of GPS filled a gap in ca pabilities between the terrestrial survey ing tools and the existing satellite tech niques The description of the GPS system follows the division that is customary for navigation satellites 214 7 The Global Positioning System GPS A B C D E F Plane 3 4 2 1 1 2 3 4 2 3 1 180 150 120 90 60 30 0 180 150 120 90 60 30 4 2 4 3 1 3 4 1 2 1 2 3 4 Argument of latitude deg Equator Figure 74 GPS 24 satellites baseline constellation includes 24 satellites the number of active satellites on orbit may vary due to failures launches or maintenance requirements and since 1995 has exceeded 24 On January 1 2003 the constellation comprised 28 satellites With the augmented constellation most users will have six to eight or at times even more satellites in view instead of the minimum of four satellites Three generations of satellites have been launched Block I development satellites Block IIIIa production satellites and Block IIR replenishment satellites Eleven Block I satellites NAVSTAR 1 to 11 were launched between 1978 and 1985 into two orbital planes of 63 inclination The design life of these prototype test vehicles was only five years but has been exceeded in most cases One advantage of the prototype satellites was that the navigation signals were not subject to deliberate corruption cf 716 The fundamental software concepts for the geodetic use of the GPS signals have been developed based on data from these satellites The first Block II production satellite was launched in February 1989 A total of 28 Block II operational vehicles have been built and launched to support the 24 satellite configuration The launching vehicle was the McDonnell Douglas Delta 2 booster Beginning in November 1989 a slightly modified version the upgraded advanced Block IIa carrying more capable and reliable systems was introduced The design lifetime of the operational Block II satellites is 75 years but after more than 10 years of operation the real lifetime in orbit has turned out to be much longer Fig 75 gives a schematic view of a Block IIIIa satellite Electrical power is supplied by two solar energy collector plates with a surface area of 72 m2 each The large panels and momentum reaction wheels help stabilize the satellite There is additional battery backup to provide energy when the satellite moves into Earths shadow eclipse period Each satellite weighs 845 kg and has a propulsion system for positional stabilization and orbit maneuvers As the supply of fuel is rather limited 71 Fundamentals 215 Figure 75 Schematic view of a Block IIIIa GPS satellite Figure 76 Schematic view of a Block IIR GPS satellite orbit changes usually last several weeks or months Each satellite carries high performance frequency standards with an accuracy of between 11012 and 11013 forming a precise time base The prototype satellites were partly equipped only with quartz oscillators All Block IIIIa production satellites however have two cesium frequency standards and two rubidium frequency standards 225 Van Melle 1990 The development and deployment of the next generation is underway Twenty replenishment satellites to be known as Block IIR satellites will replace the current Block II satellites as necessary Fig 76 The satellites have an inorbit mass of 1100 kg and carry Cesium and Rubidium clocks Two of the new design features are the ability to measure distances between the satellites crosslink ranges and to compute ephemeris onboard Kaplan 1996 This autonav capability enables the satellites to generate their own navigation message for a period of 180 days The signal and data transmission is identical to the Block IIIIa satellites After a launch failure the first Block IIR satellite was successfully launched in July 1997 Probably from 2004 onwards a modified version of satellites Block IIRM will include a new civil signal on L2 see 717 The Block IIR satellites will sustain the constellation at least until 2005 For details see eg Kaplan 1996 Parkinson et al 1996 Vol I chap 6 or Misra Enge 2001 A new generation of GPS satellites the FollowOn Block IIF satellites with im proved facilities is under construction The first six satellites are ready for delivery in 2003 and will be launched on need LON probably after 2005 One important feature for civil use will be the inclusion of a third civil signal L5 Plans for a new series of satellites called GPS III are underway see 717 Two carrier frequencies in the Lband are coherently derived from the fundamental 71 Fundamentals 217 713 Control Segment The tasks of the Control Segment are to eg Russel Schaibly 1980 Misra Enge 2001 continuously monitor and control the satellite system determine the GPS system time predict the satellite ephemerides and the behavior of the satellite clocks periodically update the navigation message for each particular satellite and command small maneuvers to maintain orbit or relocate to substitute an un healthy satellite Within the Control Segment are the Master Control Station MCS several unmanned monitor stations MS located around the world and ground antennas GA for upload ing data to the satellites The Operational Control Segment OCS for GPS consists of the MCS near Colorado Springs USA four monitor stations and colocated ground antennas in Ascension Island Cape Canaveral Diego Garcia and Kwajalein and two more monitor stations in Colorado Springs and Hawaii Fig 78 The monitor stations and ground antennas are operated remotely from the Master Control Station NIMA Monitor Station Air Force Monitor Station Figure 78 Control segment with observation stations The monitor stations receive all satellite signals from which they determine the pseudoranges to all visible satellites and transmit the range data along with local meteorological data via data link to the Master Control Station From these data the MCS precomputes satellite ephemerides and the behavior of the satellite clocks and formulates the navigation data message The message data are transmitted to the ground antennas and uplinked via Sband to the satellites in view Fig 79 shows this process schematically Because of the global distribution of the upload antennas at least three contacts per day can be realized between the control segment and each particular satellite Signals transmitted by GPS satellites are based on GPS System Time Until June 1990 this was the time given by the cesium oscillator at one of the monitor stations 218 7 The Global Positioning System GPS Figure 79 Data flow in the determination of the broadcast ephemeris Since then the practice has been to obtain GPS time as the weighted mean paper clock of all operational monitor station and satellite clocks GPS time is controlled over the long term to remain within one microsecond of the international time standard UTC 223 7153 Langley 1999a without considering leap seconds The requirements of an operational navigation system are completely met by the geographical distribution of the monitor stations The coverage however does not in all cases satisfy precise orbit determination requirements for geodetic and in particular geodynamic applications Much denser networks of monitor stations mostly under civil national and international responsibilities have been built up and are operational One eminent example is the International GPS Service IGS cf 743 781 The National Imagery and Mapping Agency NIMA runs its own network of monitor stations Along with the DoDs GPSAccuracy Improvement Initiative AII 717 it is planned to include data from a subset of the NIMA monitor stations into the prediction of the broadcast ephemerides see Fig 78 The upload of navigation data consisting of predicted orbits and clock corrections is made to each satellite about once daily The crosslink ranging capability of the Block IIR and IIF satellites will allow the satellites to update their broadcast ephemeris autonomously and operate over some period without contact from the control segment For further details on GPS orbit computation and orbit representation see 715 743 714 Observation Principle and Signal Structure NAVSTAR GPS is a oneway ranging system ie signals are only transmitted by the satellite 422 The fundamental observable is the signal travel time between the satellite antenna and the receiver antenna The signal travel time is scaled into a range measurement using the signal propagation velocity Oneway ranging means that a clock reading at the transmitter antenna is com pared with a clock reading at the receiver antenna In general it cannot be assumed that the two clocks are strictly synchronized The observed signal travel time thus 71 Fundamentals 219 contains a systematic synchronization error time bias Biased ranges are also called pseudoranges Hence the basic observation principle of GPS can be regarded as the determination of pseudoranges Fig 72 demonstrates that the simultaneous observa tion of four pseudoranges is required to derive the three coordinates of the user antenna and the clock synchronization error As an additional requirement it is also necessary to know the satellite position and the satellite time cf 731 GPS signals must provide a means for determining positions in realtime This is achieved by modulating the carriers with pseudorandom noise PRN codes These are sequences of binary values zeros and ones or 1 and 1 which appear to have random character but which can be identified unequivocally Their most important property is a low autocorrelation value for all delays except those that coincide exactly The pseudoranges are derived from the travel time of an identified coded PRN signal Two different codes are in use the Pcode and the CAcode P means precision or protected and CA means clearacquisition The Pcode has a frequency of 1023 MHz ie a sequence of 1023 million binary digits or chips per second This frequency is also referred to as the chipping rate of the Pcode The corresponding wavelength of one chip is about 30 m The Pcode sequence is extremely long it only repeats after 266 days 38 weeks Portions of seven days each are assigned to the various satellites As a result all satellites can transmit on the same frequency and can be identified by their unique oneweek PRN segment This technique is also called code division multiple access CDMA The code segments are set back to zero each week at midnight 0h UT from Saturday to Sunday The Pcode is the principle code for navigation and available on both carrier frequencies L1 and L2 Note that with the implementation of AntiSpoofing the Pcode has been encrypted for nonauthorized users see 716 The CAcode has a length of only one millisecond and is generated at a chipping rate of 1023 MHz The corresponding wavelength is about 300 m The CAcode is currently only transmitted on the L1 carrier The epochs of both codes are synchro nized For detailed information on the structure and the generation of the codes see eg Spilker 1980 Forsell 1991 Kaplan 1996 or Parkinson et al 1996 Note that a complete alteration in the signal structure for civil use is expected with the launch of the modified Block IIR satellites Block IIRM after 2003 and the launch of the Block IIF satellites after 2005 For details see 717 and eg Van Dierendonck Hegarty 2000 Fontana et al 2001 To determine the signal propagation time the user needs a copy of the code se quence in the receiver This code sequence is phaseshifted in time step by step and correlated with the received code signal until maximum correlation is achieved The necessary phase shift in the two sequences of codes is a measure of the signal travel time between the satellite and receiver antennas cf 7312 This technique can be described as code phase observation For precise geodetic applications the pseudoranges have to be derived from phase measurements on the carrier signals because of the much better resolution This technique requires however a solution to the problem of ambiguity determination 220 7 The Global Positioning System GPS and is discussed in more detail in section 7323 The third type of signal transmitted from a GPS satellite is the broadcast message cf 7154 The message is sent at a rather slow rate of 50 bits per second bps and repeats every 30 seconds Both code chip sequences are separately combined with the stream of message bits by binary addition ie the same value for code and message chip gives 0 and different values result in 1 The main features of all three signal types used in GPS observations namely carrier code and data signals are given in Table 73 The signal structure permits both the phase and the phase shift Doppler effect cf 61 to be measured as well as the direct signal propagation The necessary bandwidth is achieved by phase modulation 0 and 180 of the PRNcode Fig 710 and 711 Table 73 GPS satellite signals bps bits per second Atomic clock Cs Rb fundamental frequency 1023 MHz L1 carrier signal 154 1023 MHz L1 frequency 157542 MHz L1 wavelength 190 cm L2 carrier signal 120 1023 MHz L2 frequency 122760 MHz L2 wavelength 244 cm Pcode frequency chipping rate 1023 MHz Mbps Pcode wavelength 2931 m Pcode period 266 days 7 dayssatellite CAcode frequency chipping rate 1023 MHz Mbps CAcode wavelength 2931 m CAcode period 1 millisecond data signal frequency 50 bps data signal cycle length 30 seconds As a whole the L1 signal has the following structure Spilker 1980 Wübbena 1991 SL1t ApPitDit sinω1t AcCitDit cosω1t 71 where Ap amplitude of the Pcode Pit Pcode sequence with state 1 Dit data stream with state 1 Ac amplitude of the CAcode Cit CAcode sequence with state 1 and A sinω1t carrier signal The index i stands for the ith satellite 71 Fundamentals 221 The L2 signal has a much simpler structure because it does not contain the CA code SL2t BpPitDit sinω2t 72 Here Pit is again the Pcode sequence for the ith satellite and Bp is the Pcode amplitude The epochs of both codes and carriers are synchronized Fig 710 shows how code and carrier are combined The technique is called binary biphase modulation also known as binary phase shift keying BPSK see 721 Because the PRNcodes and the message are binary data streams only two states of phase modulation are possible The state 1 or 1 leaves the carrier unchanged a code transition from 1 to 1 or from 1 to 1 involves a phase shift of 180 Time Signal Carrier PRNCode 1 1 Figure 710 Structure of GPS satellite signals The L1 channel has to carry both codes This is accomplished by a technique named phase quadrature The unmodulated L1 carrier is split off and shifted in phase by 90 before it is mixed with the CAcode signal and is then added to the modulated Pcode signal This procedure is implied in equation 71 and is demonstrated in Fig 711 cf Wells ed 1986 Langley 1990 The binary biphase modulation with a PRNcode sequence produces a rather broad bandwidth for the navigation signals This technique is referred to as spread spectrum technique 721 and limits the interference from other signals Spilker 1980 Forsell 1991Parkinsonetal1996Misra Enge2001 ThePcodespectrumhasabandwidth of 20 MHz corresponding to a resolution of 1 nanosecond ˆ 30 cm for conditions with a good signaltonoise ratio The bandwidth of the CAcode is 2 MHz corresponding to a tenfold reduction in signal resolution Direct access to the Pcode is only possible for receivers that are precisely synchro nized with the GPS system time and located at a site with exactly known coordinates This is why access to the Pcode is in general achieved with the aid of the much shorter CAcode via the Hand Over Word HOW The HOW contains the socalled Zcount and appears in every subframe of the data signal cf 715 The Zcount is defined as the integer number of 15second periods since the beginning of the GPS week 7153 and thus identifies the epoch of a data record in GPS time If one knows the Zcount one can acquire the Pcode within the next six seconds 71 Fundamentals 223 For this purpose codepseudorange and carrier observations are made of all visible satellitesatallmonitorstations Thedataarecorrectedforionosphericandtropospheric delays for Earth rotation and for relativistic effects The corrected measurements and carrieraided smoothed observations are input into the Kalman filter process and are used to estimate the following states Parkinson et al 1996 chap 10 satellite position at epoch satellite velocity at epoch three clock parameters per satellite solar radiation pressure coefficients per satellite yaxis acceleration bias two clock parameters per monitor station and one tropospheric scale factor per monitor station The estimated perturbations in the elements are used to correct the satellite reference ephemeris and to generate the broadcast ephemerides In a similar way the satellite clock behavior is predicted and included in the data signal in the form of a second order polynomial Computation of the satellite trajectories is based on the gravity field parameters and the station coordinates of the World Geodetic System 1984 WGS 84 In order to improve the accuracy of the ephemeris the WGS 84 station coordinates were replaced by ITRF 91 coordinates in 1994 and by ITRF 94 coordinates in 1996 cf 216 Earth orientation parameters are taken from the IERS Rapid Service 1242 The process of orbit determination is still based on the technology of the 1980s Russel Schaibly 1980Swift1985butwillbeupgradedalongwiththeAccuracyImprovementInitiative AI I 717 7152 Orbit Representation The satellite positions estimated in the Kalman filter process are next represented in the form of Keplerian elements with additional perturbation parameters Table 74 summarizes all parameters that describe the satellite orbit and the state of the satellite clock The parameters refer to a given reference epoch t0e for the ephemeris and t0c for the clock and they are based on a four hours curve fit ICD 1993 Hence the representation of the satellite trajectory is achieved through a sequence of different disturbed Keplerian orbits At present a fresh data set is broadcasted every two hours causing small steps be tweenthedifferentoverlappingrepresentations Thesestepscanreachafewdecimeters but may be smoothed by suitable approximation techniques eg Chebyshev polyno mials 3332 The parameter set of Table 74 is used to compute the satellite time and the satellite coordinates The unit semicircles can be converted to degrees multiplication by 180 or to radians multiplication by π The first group of parameters is used to 228 7 The Global Positioning System GPS receiver manufacturers provide decoding software for postprocessing purposes in many cases combined with the socalled download software for reading data from the receiver to a computer 7332 With a bitrate of 50 bps and a cycle time of 30 seconds the total information content of a navigation data set is 1500 bits The complete data frame is subdivided into five subframes of six seconds duration corresponding to 300 bits each Each subframe contains ten data words of 30 bits each six of them being control bits The first two words of each subframe are the telemetry word TLM and the CA to Pcode hand over word HOW The TLM word contains a synchronization pattern which facilitates the access to the navigation data Figure 713 Structure of the GPS navigation data The navigation data record is divided into three data blocks Data Block I appears in the first subframe and contains the GPS week number the satellite clock correction terms and the SV accuracy and health Data Block II appears in the second and third subframes and contains all necessary ephemeris parameters for computation of the satellite coordinates Data Block III appears in the fourth and fifth subframes and contains the almanac data 7151 with clock and ephemeris parameters for all available satellites of the GPS system The data block includes also ionospheric correction parameters 7441 UTC data and particular alphanumeric information for authorized users Unlike the first two data blocks subframes four and five are not repeated every 30 seconds The two subframes consist of 25 pages that appear subsequently such that the total information content is available after 125 minutes Each page covers the almanac data of one satellite from the total constellation These are parameters representing the ephemeris of the particular space vehicle corrections to the satellite clock identification number and satellite health status The less accurate almanac data can be used for a computation of satellite predictions alerts and also for a faster lockon to satellite navigation signals Subframe 5 includes almanac and health status data for satellites numbered 124 and subframe 4 those for satellites numbered 25 and higher 71 Fundamentals 229 For a detailed description of the data format in the GPS navigation message see eg Van Dierendonck et al 1980 Parkinson et al 1996 chap 4 and the current version of the official Interface Control Document eg ICDGPS200C These sources are essential for the development of decoding software and for a deeper understanding of GPS data signals A very instructive text is also given by Tsui 2000 Note that the forthcoming L5 signal on the Block IIF satellites will have a different message format Van Dierendonck Hegarty 2000 716 Intentional Limitation of the System Accuracy GPS is a military navigation system a responsibility of the US Department of Defense DoD and has hence to meet the national security interests of the United States Accordingly it has been stated from the beginning of the systems development that only limited access to the total system accuracy would be available to the national and international civil user community The interests of the civil user community enter through the Department of Transportation DOT within the Interagency GPS Executive Board IGEB The IGEB is the coordinating body for GPS policy and it is cochaired by representatives of DoD and DOT The service available to the civil community is called Standard Positioning Service SPS while the service available to authorized mainly military users is called the Precise Positioning Service PPS Throughout the 1990s the accuracy available to SPS users was 100 m 2DRMS cf 742 This figure means that a horizontal two dimensional position accuracy of 100 m or better can be expected by a standalone user 95 of the time PPS provides the full system accuracy of 10 to 20 meters in three dimensions Two modes of limitation were introduced These are AntiSpoofing AS and Selective Availability SA AntiSpoofing entails the encryption of the Pcode ie use of a protected code named Ycode Only authorized users will have the means to get access to the Pcode while AS is activated Selective Availability means an intentional degradation of the GPS signals by adding controlled errors in the measurement data SA uses two effects These are ephemeris data manipulation ε technique and dithering or systematic destabilizing of the satellite clock δ technique Both effects corrupt the measured pseudoranges Apparently mainly the dithering technique was used resulting in a roughly fivefold increase in positioning error see Fig 714 SA was implemented for the first time on March 23 1990 but was disabled again on August 2 1990 due to the Gulf crisis SA became effective again in July 1991 and was implemented to the Standard Positioning Service level in November 1991 PPS authorized users were able to remove SA After a long discussion of the pros and cons SA was permanently deactivated on May 2 2000 based on a Presidential decision AntiSpoofing AS has the aim to prevent an adversery from generating a copy of the GPS signal and to spoof or mislead a receiver The encrypted Pcode is referred to as a Ycode AS has been active on all Block II satellites nearly continuously since 230 7 The Global Positioning System GPS Selective Availability ON May 1 2000 Selective Availability OFF May 2 2000 Longitude m Longitude m 0 50 75 50 50 50 50 50 0 0 0 0 0 75 75 75 75 75 75 75 75 75 75 75 50 50 50 50 50 50 Latitude m Latitude m Figure 714 The effect of Selective Availability on positioning results with a single receiver left SA active right after deactivation February 1994 As a consequence SPS users only have clear access to the L1 carrier signal because L2 exclusively carries the encrypted Pcode Receiver manufacturers therefore have developed proprietary techniques to gain access to L2 signals underAS however with decreased quality see 723 With disabled SA the accuracy available to SPS users is similar to that for PPS users The global average positioning accuracy is defined as 13 meters horizontal error and 22 meters vertical error 95 DOD 2001 The main advantage of PPS over SPS is its robustness against jamming and spoofing and the higher quality of the L2 signals The situation will further improve under the GPS Improvement Initiative 717 717 System Development All satellites launched before the end of 1985 were prototype or development satellites Block I for test purposes The spacecraft were launched into two orbital planes with an inclination of 63 degrees and semimajor axis of 26 600 km The constellation was optimized for maximizing coverage in the vicinity of theYumaArizona Test Range but also provided good coverage for tests in other parts of the world The ground track of the optimized constellation repeated every day and provided an identical configuration from day to day at a particular geographical location only four minutes earlier with respect to Universal Time Four of the ten successfully launched Block I satellites were still functioning in May 1993 The data of the prototype satellites were ideal for the development of software and observation concepts because no signal encryption was existent Originally it was planned to carry all Block II satellites in the Space Shuttle and to complete the configuration by 1988 Due to the tragedy of the Shuttle Challenger 71 Fundamentals 231 in January 1986 the launch schedule was considerably delayed and not resumed until February 1989 with the launch of the first Block II satellite on a Delta 2 booster A total of 28 Block II spacecraft have been built 712 and launched to support the socalled baseline constellation of 24 satellite positions with four satellites in each of the 55 degrees inclined equallyspaced orbit planes cf Fig 74 page 214 The system was declared operational in April 1995 Full Operational Capability FOC The start of the Block IIR replenishment satellites began after one launch failure in July 1997 The current constellation as of March 2003 is given in Table 75 the related satellite coverage for Washington DC is depicted in Fig 715 In total 20 Block IIR satellites will replace the current Block IIIIA satellites and will be launched Figure 715 Satellite coverage for Washington DC January 1 2003 on need to maintain the constellation at least until 2005 For the time thereafter a new generation the Block IIF satellites is under construction cf 712 and the next generation Block III is in design stages Current plans for maintaining the constellation reach until 2030 TwoinitiativeswillimproveandenhancetheGPSalsoforcivilapplications within the next years These are the GPS Modernization Program and the Accuracy Improvement Initiative Within the GPS Modernization Program besides new military capabilities Mcode two new civil signals will be added to the forthcoming Block IIR and Block IIF 232 7 The Global Positioning System GPS Table 75 Status of GPS satellites March 2003 Blk SVN PRN Orbit Launch Clock Status Seq Code Position Date Decomissioned BLOCK II II1 14 14 890214 000414 II2 13 02 B3 890610 Cs operable II3 16 16 890818 001013 II4 19 19 891021 010911 II5 17 17 D3 891211 Rb operable II6 18 18 900124 000818 II7 20 20 900326 960510 II8 21 21 900802 Cs 030127 II9 15 15 D5 901001 Cs operable BLOCK IIA II10 23 23 E5 901126 Cs operable II11 24 24 D1 910704 Cs operable II12 25 25 A2 920223 Cs operable II13 28 28 920410 920425 II14 26 26 F2 920707 Rb operable II15 27 27 A4 920909 Cs operable II16 32 01 F4 921122 Cs operable II17 29 29 F5 921218 Rb operable II18 22 22 B1 930203 Rb operable II19 31 31 C3 930330 Cs operable II20 37 07 C4 930513 Rb operable II21 39 09 A1 930626 Cs operable II22 35 05 B4 930830 Cs operable II23 34 04 D4 931026 Rb operable II24 36 06 C1 940310 Cs operable II25 33 03 C2 960328 Cs operable II26 40 10 E3 960716 Cs operable II27 30 30 B2 960912 Rb operable II28 38 08 A3 971106 Rb operable BLOCK IIR IIR1 42 12 970117 Launch failure IIR2 43 13 F3 970723 Rb operable IIR3 46 11 D2 991007 Rb operable IIR4 51 20 E1 000511 Rb operable IIR5 44 28 B5 000716 Rb operable IIR6 41 14 F1 001110 Rb operable IIR7 54 18 E4 010130 Rb operable IIR8 56 16 B1 030129 Rb operable IIR9 45 21 D3 030331 Rb operable IIR10 IIR11 71 Fundamentals 233 satellites These are a civil signal designated L2C on L2 and another civil signal L5 on a third frequency at 117645 MHz McDonald 1999 Van Dierendonck Hegarty 2000 Fontana et al 2001 see Fig 716 117645 MHz Civil code L5 12276 MHz PYCode L1 L2 157542 MHz L2CCode MCode MCode PYCode CACode 2 MHz 2 MHz Figure 716 Future GPS signals L2C will be included on modified Block IIRM satellites from 2004 onwards and L5 will be available on the Block IIF satellites probably from 2005 onwards L2C will carry two codes one without data modulation The signal will have a much better quality than it would have had as a simple addition of the CAcode on L2 as was previously planned In particular it will be possible to provide full wavelength on L2 with enhanced signal power 723 The new L5 signal falls in a band which is protected for aeronautical radionavigation and hence will not cause any interference to existing systems L5 will have four times more power than L2CThe L2C signal will be available on 24 satellites by 2010 Fontana et al 2001 The availability of three civil signals with different capabilities will support realtime ionospheric corrections and facilitate the resolution of wholecycle ambiguities in the carrierphase measurements Hatch et al 2000 7323 The high signal power will support indoor navigation and improve applications under difficult conditions such as heavy foliage Several actions are planned within the Accuracy Improvement Initiative AI I cf Hay 2000 A first step has already been realized with the use of ITRF coordinates for the monitor stations A further step includes additional monitor stations for de termination of the broadcast ephemerides Data from 6 or more NIMA stations see Fig 78 will be transmitted via powerful datalinks to the MCS The aging mainframe computer in the MCS will be replaced and the Kalman filter in the orbit software will be improved including the capability to process all satellites and ground stations simultaneously Hay 2000 Depending on necessity more frequent uploads will provide submeter broadcast orbits Based on these improvements the accuracy of a single pseudorange measurement the SignalinSpaceRangeError SISRE will be below 15 m With a PDOP of 2 742 this corresponds to a position error of about 3 m Further improvements can be expected with the inclusion of L5 and intersatellite tracking capability Information on the system status can be obtained from different public and com mercial sources The US Coast Guard USCG has the responsibility to provide GPS operational capability and status information to civil users In Germany the GPS Information Service GIBS operated by the Bundesamt für Kartographie und 234 7 The Global Positioning System GPS Geodäsie BKG delivers extensive information Current lists of information services are published regularly in GPS periodicals eg GPS World see also 782 72 GPS Receivers User Segment Appropriate satellite receivers are required to use the GPS signals for navigation pur poses andor geodetic positioning First and secondgeneration user equipment has already disappeared from the market and new models frequently appear The number of manufacturers is growing fast which makes a complete treatment of makes and models impossible and meaningless within the scope of this book Consequently only the basic aspects of GPS receivers will be discussed here A general review is given including some models for geodesy surveying and GISnavigation currently available 721 Receiver Concepts and Main Receiver Components A GPS receiver detects the signals transmitted from a GPS satellite and converts the signals into useful measurements observables The GPS signals when they arrive at the user antenna are extremely weak A particular technique named spread spectrum is used to transmit and detect the signal information The name is due to the fact that the power of the signal to be transmitted is spread over a much larger bandwidth eg 20 MHz for GPS than that of the navigation message 50 bps The bandwidth of a signal is the frequency domain in which about 99 of the signal power is transmitted For GPS the pseudorandom code sequence Pcode or CAcode is used as the spreading function This technique is also named binary phase shift keying BPSK In the receiver the spreading function is known so the signal can be despread by correlating the received signal with the locally generated signal One advantage of the technique is that the signals are quite resistent against disturbances and can be detected within a noisy environment It is through this process that rather small antennas can provide the necessary signaltonoise ratio SNR for the GPS receiver Langley 1991b For details of the technique see eg Forsell 1991 Leick 1995 Kaplan 1996 Parkinson et al 1996 Misra Enge 2001 The SNR is the ratio of the power in the received signal S to the power in the noise level N The SNR is a logarithmic measure and is given in decibel dB a dimensionless ratio between electric quantities The SNR is 1 dB if 10 log S N 1 730 The basic components of a generic GPS receiver are Fig 717 antenna with optional preamplifier radiofrequency RF and intermediatefrequency IF frontend section signal tracker and correlator section microprocessor for receiver control data sampling and data processing navi gation solution oscillator 72 GPS Receivers User Segment 235 power supply memory data storage and user interface User communication Power supply Precision oscillator Antenna Preamplifier Signal processor Microprocessor Navigation solution Data logger External communication Figure 717 Major components of a GPS receiver Theantenna detectstheelectromagneticwavesarrivingfromthesatellites converts the wave energy into an electric current amplifies the signal strength and hands the signals over to the receiver electronics The GPS signal structure requires that all GPS antennas must be righthanded circularly polarized The antenna has to be very sensitive because of the rather weak satellite signal and the gain pattern must allow signal reception from all elevations and azimuths of the visible hemisphere Further requirements for high precision geodetic applications are a high stability of the electrical phase center 7451 and protection against multipath 7443 For applications in navigation airplanes and ships signal reception below the antennas horizontal plane is required The antenna is connected to the receiver by a coaxial cable through which a voltage is sent to a preamplifier at the antenna The power of the received signal is increased and can then be sent into the receiver Several types of GPS antennas are available eg Fig 718 monopole or dipole quadrifilar helix also named volute spiral helix microstrip also named patch and choke ring Figure 718 Types of GPS antennas One of the most frequently used types is the microstrip because it is relatively easy to build The antenna has a very low profile and is ideal for airborne application It also meets the increasing demand for miniaturized GPS equipment in particular when 236 7 The Global Positioning System GPS the antenna is integrated to the receiver body It is made up of one or more patches of metal and is therefore also named a patch antenna The quadrifilar helix is often used for handheld receivers The spiral helix has nearly disappeared Geodetic antennas are usually designed for the reception of both carrier frequencies L1 and L2 They can be protected against multipath by extra ground planes or the use of choke rings A choke ring consists of strips of conductor which are concentric with the vertical axis of the antenna and connected to a ground plate For more details about GPS antennas see eg Langley 1998a The incoming GPS signals are downconverted to a lower frequency in the RFIF section front end RF stands for radio frequency and IF for intermediate frequency This step is achieved by combining the incoming RF signal with a sinusoidal signal generated by a local oscillator In general a less expensive quartz oscillator is used because precise clock information is obtained from the GPS satellites and user clock errors can be eliminated through doubledifferencing 7321 Some receiver types accept the input of an external high precision oscillator signal from atomic frequency standards with less clock noise 225 A very precise oscillator can be used to replace one satellite in the navigation solution TheIFsignalcontainsallcodeanddatasignalsfromtheoriginalRFsignal however its carrier frequency is much lower In some receivers several IF stages are used to reduce the carrier frequency in steps Langley 2000b bandpass filters are applied to reduce and suppress interference with undesired signals The IF signal then passes to the signal tracker or correlator Here the signals coming from all visible satellites are isolated identified by their codes 712 and assigned to a particular channel The receiver channel can be considered to be the primary electronic unit of a GPS receiver Signal processing within the channel is described in more detail in 722 and 723 A receiver may have one or more channels In the parallel channel concept each channel continuously tracks one particular satellite A minimum of four parallel chan nels is required to determine three coordinates and time With more channels additional satellites can be tracked Modern receivers may contain up to 12 channels for each frequency and additional channels for multisystem processing In the sequencing channel concept the channel switches from satellite to satellite at regular intervals A singlechannel receiver must switch to at least four satellites to determine a threedimensional position The sequencing rate is asynchronous to the data rate hence the full satellite message the data signal is complete only after several sequences The receiver needs at least four times 30 seconds before the first position fix can be obtained In most cases fast sequencing channels are used ie the switching rate is about one second per satellite The channels usually have no problems to recover the carrier phase when they return to the same satellite Difficulties may however arise in kinematic applications in particular at high accelerations A further variation is the multiplex technique A multiplexing channel sequences at a very high speed between different satellites and in some cases both frequencies The switching rate is mostly synchronous with the navigation message namely 50 bps or 20 milliseconds per bit 72 GPS Receivers User Segment 237 The navigation message is obtained continuously from all satellites tracked hence the first fix is achieved after about 30 seconds Carrier phase measurements are con tinuous even at high accelerations In essence a single hardware channel is used to obtain quasisimultaneous measurements to all satellites One advantage of the multi plex technique when compared with the parallel technique is that channel dependent systematic hardware delays interchannel biases do not play a role In the early years of GPS until about 1990 it was cheaper to build receivers with single channels Since then prices for building channels have dropped rapidly Current and future GPS receiver architecture will mainly be based on multichannel technology Multiplex receivers have nearly completely disappeared from the civil market The capability to track all visible satellites simultaneously is also called all inview tracking capability An overview of the different channelization concepts is Fig 719 parallel Channel 1 Channel n Channel 2 fast sequencing seconds milliseconds multiplexing Figure 719 Different channelization concepts in GPS receivers The microprocessor CPU is necessary to control the receivers operation in cluding the acquisition of signals signal processing and decoding of the broadcast message Further capabilities are the computation of online positions and velocities conversion into a given local datum or the inclusion of DGPS corrections 75 More and more user relevant software is included on integrated circuits The microproces sor also controls the input of commands from the user display of information and the data flow through a communication port if one is included The microprocessor the signal trackercorrelator and the memory form the digital part of the receiver whereas the RFIF front end forms the analog part At some point of the signal flow signals are converted from analog to digital In modern receiver development more and more functions of the receiver are performed by software rather than hardware Receivers where signal correlation and data processing are integrated in one software controlled unit are also called software receivers Pospelov Botchkovki 2000 They are still under development see 725 Fig 728 Modern tendencies are to integrate the RF and IF functions of a GPS receiver on a single applicationspecific integrated circuit ASIC and the digital signal processing functions on another ASIC This twochip GPS receiver is called a chipset Langley 2000b 238 7 The Global Positioning System GPS The power supply was a rather critical issue for firstgeneration GPS receivers because of their very high power consumption In some cases the use of generators was necessary for field operation Modern receivers use low voltage DC power and are designed to consume as little energy as possible Most have an internal rechargeable nickelcadmium or lithium battery in addition to an external power input Depending on the observation rate the internal battery may be sufficient for weeks or more of observation The modern chipset has a power consumption of less than 1 Watt For postprocessing purposes all data have to be stored on internal or external memory devices Postprocessing is essential for multistation techniques eg for some geodetic and surveying application but also for offline differential navigation Pseudoranges phase data time and navigation message data have to be recorded Depending on the sampling rate the amount of GPS data to be recorded may be very high With six satellites and 1second data a dual frequency receiver produces about 15Mbyteofdataperhour ModernreceivershaveinternalsolidstateRAMmemories or removable memory cards In general data can also be recorded onto an external microcomputer eg a laptop connected to the receiver with a RS232 or equivalent communication port or they can be transmitted to a base station via an appropriate data link Most receivers have a keypad often handheld and a display for communication between the user and the receiver The keypad is used to enter commands external data like station number or antenna height or to select a menu option The display indicates computed coordinates visible satellites data quality indices and other suit able information Current operation software packages are menu driven and very user friendly Developments in this respect are rapid GPS receivers can be divided into various groups according to different criteria One early classification was into codedependent receiver technology and codefree receiver technology This kind of division is no longer meaningful because usually different types of techniques are implemented in each receiver Hence it would be better to distinguish between codedependent signal processing codeless signal processing and semicodeless signal processing These technologies are presented in the next two chapters 722 723 Another classification criterion is the available datatype and differentiates receivers with CAcode CAcode L1 carrier phase CAcode L1 carrier phase L2 carrier phase and CAcode Pcode L1 L2 carrier phase Note that the Pcode under AS 716 is changed to the encrypted Ycode Another distinction is related to the technical realization of the channels multichannel receiver sequential receiver and 72 GPS Receivers User Segment 239 multiplexing receiver Finally a classification is possible with respect to the user community eg military receiver civilian receiver geodeticsurveying receiver navigation receiver timing receiver spaceborne receiver and handheld receiver In addition receiver units form parts of complex systems eg in modern GIS appli cations or for machine control see 762 All the above classifications appear in the literature and in technical discussions For geodetic applications it is essential to use the carrier phase data as observables 731 It is equally essential to use both frequencies L1 L2 and to have access to the full wavelength on L2 For an introductory discussion of receiver technology see eg Langley 1991a 2000b Van Dierendonck 1995 More detailed information can be obtained from the excellent handbooks by Parkinson et al 1996 Kaplan 1996 Misra Enge 2001 and from the proceedings of GPS conferences like ION GPS 722 Code Dependent Signal Processing The pseudorange from code measurements is the fundamental observable in a code dependent receiver channel The phase position of the received code sequence is compared with the phase of an identical code replica generated by the receiver via a correlation technique cf 7312 This is why the observable may be called the code phase The user must have a priori knowledge of the code ie the code must be generated within the receiver channel using the same algorithm that is utilized in the satellite The received code sequence and the generated code sequence are correlated with each other ie the two sequences are shifted stepwise in phase until maximum correlation is obtained This process happens in one of the two tracking loops namely the delay lock loop or code tracking loop The time shift that is necessary to align both code sequences with each other time delay corresponds to the signal travel time between the satellite and the receiver Essentially the code sequence is a unique function in time and hence provides us with a reading of the satellite clock at the moment a particular bit left the satellite The time delay is converted into a range using the speed of light cf 7312 The pseudorange measurements are derived from either the Pcode or the CAcode The second tracking loop is the phase lock loop or carriertracking loop Here the code and the carrier are separated to enable phase measurements to be made and the bit information of the satellite message is extracted This technique is also named reconstruction of the carrier In most cases a Costas loop that is specially designed for biphase modulated signals is used cf Forsell 1991 Kaplan 1996 Within the 240 7 The Global Positioning System GPS loop the demodulated satellite carrier phase signal is aligned with the phase signal of the receivers oscillator The observable is the carrier beat phase the relative phase between the received carrier signal and the internal reference carrier signal derived from the local oscillator cf 7312 The total process of codedependent signal processing is schematically illustrated in Fig 720 cf Wells ed 1986 Code tracking loop Correlation PRN code generator Stable oscillator Message demodulator Carrier tracking loop Message Clock counter Voltage controlled oscillator Carrier beat phase Reading of satellite clock Pseudo range code phase Figure 720 Simplified concept of a code correlation channel A complete codedependent correlation channel produces the following observ ables and information code phase carrier phase change of carrier phase Doppler frequency and satellite message The code correlation and carrier reconstruction technique only works on L2 when the Pcode is available AS not activated or for authorized users with access to theYcode 723 Codeless and Semicodeless Signal Processing Codeless GPS channels exploit satellite signals without knowledge of the codes The advantage of this concept is that the receiver systems are independent of possible restrictions on code access to civil users The main disadvantage is that neither the broadcast ephemeris nor the almanac and precise time can be extracted from the sig nals consequently alternative sources are required for mission planning and for data processing A further disadvantage is that simultaneouslyoperating pure codeless receivers have to be synchronized before observation starts Today there is no doubt that at least the CAcode will be freely available to all civil users This is why no more totally codefree receivers are built The technique 72 GPS Receivers User Segment 241 is however of much interest for L2 access in times of Pcode denial AS activated cf 716 A frequently used codeless method is the squaring technique A squaring channel multiplies the incoming satellite signal by itself and generates a second harmonic of the original carrier both the codes and the broadcast message are lost Squaring the code signal portion in equation 72 x P t sinωt 731 yields x2 P t2 sin2ωt P 21 cos 2ωt2 732 Since P t is a sequence of 1 and 1 representing the code it follows that P t2 P 2 is a sequence of 1 and thus disappears from equation 732 With x2 a pure carrier signal is obtained that is related in phase to the original carrier but with a frequency equal to twice that of the original The signaltonoise ratio SNR is also considerably decreased in the squaring process Consequently the squared phase measurements have the two disadvantages that the wavelength is cut in half and that the SNR of the phase observable is made much worse The squaring technique was developed early on Counselman Steinbrecher 1982 and used for the first time in the Macrometer 7241 Today some commercial dualfrequency receivers use this type of approach for carrier phase measurements on L2 A schematic illustration of the squaring technique is given in Fig 721 Squared output code free Bandpass filter Multiplier Oscillator Antenna Carrier with code Squaring loop Carrier with code Signal multiplication mixing Figure 721 Concept of a squaring channel Another concept uses the pure interferometric principle known from Very Long Baseline Interferometry VLBI 111 It was first proposed by Mac Doran 1979 In this method the GPS signals are recorded at two stations together with precise timing signals from an external oscillator but without knowing the code sequence From a subsequent correlation process the time difference τ in the signal reception 72 GPS Receivers User Segment 243 the Wcode is 20 times less the frequency of the Ycode ie there are Ycode portions identical to the Pcode This property is used to despread portions of the received Ycode and to enter with a much lower bandwidth into the squaring process As a result the output signal still has half the wavelength however the SNR is 13 dB better than with the unaided squaring technique PW tracking The technique also called Ztracking has been described by Ashjaee Lorenz 1992 and uses the undisturbed portions of the Pcode about 2 µs length in theYcode signal on both carriers for crosscorrelation with the Pcode replica Output signals are code ranges and full wavelength carrier signals on both L1 and L2 The SNR reduction compared with the ideal signal on L2 is just 14 dB All leading manufacturers of geodetic receivers have developed proprietary semi codeless techniques for measurements under activated AS using some of the above described or modified concepts 724 Examples of GPS receivers The receiver market is developing and growing with high speed This is why only little space is given here to describe some typical receivers The description can be regarded as a basis for the evaluation of current and future developments 7241 Classical Receivers Two examples of receivers are given that have significantly influenced the develop ment in geodetic GPS technology the codedependent TI 4100 and the codefree Macrometer Figure 722 Texas Instruments TI 4100 The Texas Instruments TI 4100 GPS Navigator Fig 722 came to the market in 1984 It was the first GPS receiver provid ing all observables of interest to the geode sist surveyor and navigator The TI 4100 is a dual frequency multiplexing receiver and can track up to four satellites simulta neously The observables are Pcode pseudoranges on L1 and L2 CAcode pseudoranges on L1 and carrier phases on L1 and L2 every three seconds The data are recorded by an external tape recorder on digital cas settes or are downloaded directly to an ex ternal microprocessor Communication be tween observer and receiver is by a hand held control display unit CDU For navi gational purposes the builtin microproces 244 7 The Global Positioning System GPS sor provides positions and velocities in real time every three seconds The equipment is rather bulky and can be packed into two transportation cases The total weight is about 30 kg and power consumption is about 100 Watts The observation noise was found to be 06 to 1 m for Pcode tracking and 2 to 3 mm for carrier phase observations The equipment has been widely used in numerous scientific and applied GPS projects Many of the results published between 1985 and 1993 are based on obser vations with the TI 4100 This is also true for some of the examples within this book Today with activated antispoofing AS the TI 4100 can only be used as a single fre quency CAcode receiver For applications and results see eg Seeber et al 1985 Seeber 1989a Gibbons Maynard 1990 Jahn et al 1991 Völksen 2000 The Macrometer V1000 Fig 723 was introduced in 1982 and was the first GPS receiver for geodetic applications The exciting results obtained with this system have Figure 723 Macrometer V1000 done much to demonstrate the potential of highly accurate GPS phase observations The complete system consists of 3 units receiverrecorder with power supply antenna with large ground plane and the P 1000 processor The processor is essential for providing the almanac data because the Macrometer cannot decode the satellite message and to preprocess the data The Macrometer V1000 is a single frequency receiver and tracks up to 6 satellites on 6 parallel channels At predetermined epochs the phase difference between the received squared carrier signal and a reference signal taken from the receiver oscillator is measured Usually 60 epochs are evenly distributed over the total observation period of several hours A typical baseline accuracy over up to 100 km was found to be 1 to 2 ppm Bock et al 1986 A dual frequency version the Macrometer II was introduced in 1985 Ladd et al 1985 The architecture is comparable to the V1000 however the weight and the power consumption are much less Both Macrometer systems require the availability of external ephemerides They were hence mainly operated by a restricted number of specialized companies Another 72 GPS Receivers User Segment 245 disadvantage is that all instruments that participate in the same observation session have to be collocated prior to observation for clock synchronization Because of these disadvantages the dualfrequency macrometer was further miniaturized and combined with a singlefrequency CAcode receiver resulting in the MINIMAC Ladd et al 1986 The Macrometer V1000 and its successors were used extensively for a number of years in particular for the establishment of geodetic control 7242 Examples of Currently Available Geodetic Receivers The currently available GPS receivers that are used in geodesy surveying and precise navigation all contain several or all of the abovementioned features Nearly all models started as single frequency CAcode receivers with the ability to track more than four satellites In a second step access to L2 was added using the squaring technique and the number of satellites that could be tracked simultaneously was increased In the third step all leading manufacturers added the Pcode on L2 and some on L1 and L2 mainly with the objective to increase the L2 data quality and to provide the full cycle length on L2 The next step was the inclusion of codeless nonsquaring L2 techniques in order to provide high quality L2 full wavelength signals under activated AS In the most recent development step all manufacturers further improved the data quality designed rugged light portable units with low power consumption and inte grated the GPS receiver into singlemodule multipurpose compact surveying equip ment In general a high precision GPS system should fulfill the following require ments track all signals from each visible satellite at any given time GPSonly system requires 12 dual frequency channels GPS GLONASS system needs 20 dual frequency channels full wavelength on L2 when AS activated low code and carrier phase noise high memory capacity for data storage high data rate 10 Hz for kinematic applications low power consumption below 4 Watts low weight below 4 kg small size track weak signals under foliage and difficult environmental conditions multipath mitigation interference suppression stable antenna phase center modular hardware easy to upgrade powerful onboard and office software and accept user commands and display results via Control Display Unit In addition some of the following features are helpful for flexible and unrestricted applications 1 pps timing output event marker ability to accept external frequencies fast data transfer to a computer 246 7 The Global Positioning System GPS few or no cable connections radio modem DGPS and RTK capability 75 operate over large temperature range and in driving rain easy interfacing to other systems also from other manufacturers ease and flexibility of use multipurpose application and flexible setup tripod pole pillar vehicle To summarize a modern GPS survey system should measure accurately and reliably anywhere under any condition and it has to be capable of being used for almost any application geodetic control geodynamics detailed GIS and topographic survey stake out engineering hydrographic survey etc cf 762 It is impossible and not meaningful to review all available GPS receivers that are currently on the market The annual Receiver Survey GPSWorld January includes currently more than 500 makes and models In the following only some of the leading products are summarized as examples The order of discussion within this text does not reflect any priority in quality or performance WildLeitz Heerbrugg Switzerland and Magnavox Torrance California devel oped in a joint venture theWildMagnavoxWM 101 geodetic receiver which appeared on the market in 1986 as a four channel L1 CAcode receiver The dual frequency WM 102 followed at the end of 1988 One key feature of the WM 102 was a modified squaring technique for receiving L2 when Pcode signals were encrypted In 1991 the company introduced a followup model the Wild GPSSystem 200 with the Magnavox SR299 dualfrequency GPS sensor tracking up to 9 satellites on L1 and L2 using codeaided squaring for L2 with activated AS In 1995 followed the Leica GPS System 300 with RTK capability The last system released by the company now named Leica Geosystems was the GPS System 500 in 1998 The System 500 family Fig 724 has a modular design and comprises three different receivers SR510 single frequency SR520 dual frequency and SR530 dual frequency RTK Various configurations are possible tripod pole mounted or backpack mounted The dual frequency sensors have 24 parallel channels A propri etary codeaided tracking technique provides fullwave L2 carrier phase measurements AS on and high accuracy L2 pseudoranges Enhanced new multipath mitigation and interference rejection techniques are reported Maenpa et al 1997 Up to 85 MB data storage is possible with a PCMCIA card The RTK sensor can be connected to a radio modem or to GSM phones 752 The software platform for postprocessing is SKI Pro For precise navigation and machine guidance the MC1000 Machine Control receiver also with 24 parallel channels has been designed Kinematic applications are supported with very little latency and 10 Hz data rate A variation of the MC1000 is known as CRS1000 continuous reference station and is operated with a choke ring antenna and special control software The product line of Leica Geosystems as for other manufacturers hence supports a broad variety of applications in geodesy and surveying 72 GPS Receivers User Segment 247 Figure 724 Leica System 500 cour tesy Leica Geosystems Figure 725 Trimble GPS Total Station 5700 courtesy Trimble Navigation Trimble Navigation SunnyvaleCalifornia has been producing its Trimble 4000 series since about 1985 The first generation was a L1 CAcode receiver with five parallel channels capable of tracking up to five satellites simultaneously Further upgrades included increasing the number of channels to twelve L2 squaring capability and Pcode capability The most advanced model of this series for geodetic purposes was the Trimble Geodetic Surveyor 4000 SSi with 12 channels dual frequency and proprietary codeless technique for full cycle carrier on L2 with activated AS This instrument has been used for many years worldwide in numerous geodetic projects for a large number of applications In 2001 Trimble now including Spectra Precision Geodimeter and Zeiss Geodetic Systems launched the GPS 5700 family The 5700 GPS receiver has 24 channels L1 CA code and L2 full cycle carrier phase The advanced GPS chip provides very low carrier phase noise and multipath mitigation The GPS Total Station 5700 a modular kinematic realtime surveying system Fig 725 includes the receiver a handheld controller GPS antenna RTK radio and processing software Its weight is 38 kg and power consumption including radio is 38 Watts the receiver alone weighs 14 kg and consumes 25 Watts Based on a newly developed receiver concept Trimble offers Continuously Operating Reference Stations CORSVirtual Reference Stations VRS and other solutions Internal data storage with compact flash card is up to 128 MB For continuous operation the 5700 GPS receiver can be linked to a choke ring antenna or the geodetic Zephir antenna designed for phase center stability enhanced multipath rejection and low elevation satellite tracking Ashtech initially Sunnyvale California was founded by Javad Ashjaee in the late 1980s He was the first to announce a receiver with 12 parallel channels and hence initiated the development of the current multichannel technology The Ashtech XII GPS receiver entered the market in 1988 and was capable of measuring pseudorange 248 7 The Global Positioning System GPS carrier phase and integrated Doppler of up to 12 satellites on L1 The L2 option added 12 physical L2 squaring type channels In 1991 the Ashtech P12 GPS receiver was launched providing 12 dedicated channels of L1 Pcode and carrier and 12 dedicated channels of L2 Pcode and carrier Together with the 12 L1 CAcode and carrier channels and the 12 codeless L2 channels the receiver contains in total up to 48 channels All observables of interest to the geodesist and from all visible satellites are available the reconstructed carrier phase data full wavelength on L2 uses the Ztracking technique 723 Ashjaee 1989 The latest version based on the P12 technology is the Ashtech ZSurveyor a light weight compact dualfrequency receiver with RTK capability The receiver tracks up to 12 satellites and provides full wavelength on both carriers Like the highend products of other manufacturers the ZSurveyor can be configured with dedicated software for a large variety of applications In 1997 Ashtech Inc was purchased by Magellan Corporation a leading manufacturer of handheld GPS equipment and later on unified with Thales Navigation a French manufacturer of navigation equipment This group now offers every type of GPS receiver In 1996 Javad Ashjaee founded Javad Positoning Corporation JPS later July 2000 bought by Topcon Positioning Systems Highend products combined GPS GLONASS receivers with up to 40 channels One example is the OdysseyE GGD launched in 2001 with 20 channels L1 CA and Pcode 20 channels L2 Pcode either for GPS or GLONASS satellites Its weight is about 2 kg and its power consump tion 4 Watts The internal memory capacity is up to 96 MB and the data recording rate up to 20 Hz Another notable development is the Rogue receiver from Allan Osborne Asso ciates originally a dedicated development for NASAs applications in geodynamics The TurboRogue SNR8100 launched in 1993 is still widely used in the scientific geodetic community The instrument has 24 channels and can track up to 8 satellites on L1 CA and Pcode and on L2 Pcode In the presence of encrypted Pcode the codeless mode produces L1L2 group and phase delay data cf 2312 Meehan et al 1992 Many such instruments are operated at IGS stations 781 7243 Navigation and Handheld Receivers A very large market is rapidly developing for navigation with handheld receivers In some cases a single CAcode sequencing or multiplexing channel is used however modules with 12 parallel channels are becoming increasingly popular Positions and velocities are derived from L1 CAcode pseudorange measurements and are dis played or can be downloaded via a RS 232 or equivalent port Usually neither raw data nor carrier phase information is available Differential navigation is possible with some advanced products also carrier smoothed code phases are used Power consumption is in the order of 1 Watt or less Weight is significantly below 1 kg and reaches in some cases only several hundred grams Most models come with a map display Some can be interfaced with map sources on CDROM Several classes of products can be distinguished 72 GPS Receivers User Segment 249 a accuracy class 10 m b accuracy class 2 to 5 m and c accuracy class below 1 m to several dm Classareceiversarethetypicallowcosthandheldreceiversforrecreationsports hiking sailing general navigation surveillance fleet management and GIS applica tions with moderate accuracy requirements Fig 726 Since SA has been switched off the accuracy range of up to 10 m or even better makes this instrument a powerful tool for many applications With the ongoing Accuracy Improvement Initiative AI I 717 the accuracy level of class b may even be reached For this receiver type a mass market with very low unit prices is developing Receivers are built on one or two chips chipset With the reduced size and very lowpower consumption they can easily be integrated into mobile phones palmtop computers or even wrist watches and they are well suited for locationbased services 7625 Figure 726 Handheld receiver Gar min eTrex GARMIN Corp 2003 Figure 727 Trimble Pathfinder ProXR cour tesy Trimble Navigation Class b receivers use L1 CA code and accept DGPS data 751 They are ideal for many realtime GIS applications forestry farming environmental monitoring and may be linked to GIS and CAD software packages They are also suited to precise car navigation fleet management and traffic control Class c receivers use in addition the L1 carrier measurements to filter the code phases without solving ambiguities 736 Depending on the observation time the DGPS carrier smoothed pseudo ranges provide submeter accuracy on a secondby second basis about 30 cm after 5 minutes and about 10 cm after 20 minutes Some models offer a data logging mode A typical example is the Trimble Pathfinder Pro XR Fig 727 Together with dedicated software the system is among others suited for GIS precision farming fleet management and mining control 250 7 The Global Positioning System GPS Several manufacturers offer GPS cards or chips for integration into other systems The developer needs to provide a power supply antenna preamplifier an application processor and user software Most of such modules deliver position and time some developments also include raw carrier phase data and hence provide a powerful basis for the configuration of a broad variety of applicationorientated systems Latest developments in the fast growing market of handheld receivers are an nounced in GPS related periodicals such as GPS World and also in the GIS literature A very profound source is the World Wide Web Current webaddresses are listed in the annual GPS World Receiver Survey 725 Future Developments and Trends The GPS market will grow further More than 1 million GPS receivers are produced each year and GPS applications are developing fast The worldwide market for GPS applications and services was estimated to have reached nearly 20 billion US Dollars by 2001 and is projected to grow to about 60 billion US Dollars by 2005 Groten et al 2001 This number will certainly further increase with the forthcoming European system GALILEO Geodesy and surveying although the most challenging part and driving force will only cover a small section of the global market The most important portions will certainly come from car navigation and traffic control together with communication services Selling and buying of companies will continue and hence the names of receiver makes and models will change rapidly Probably there will be only few manufacturers of GPS or GNSS hardware chips the great variety in makes and models comes from the configuration of sensors and the application software With respect to electronics and signal processing the trend is toward the chipset ie a complete GPS receiver on one or two chips and to software receivers ie as much digital signal processing as possible In a final step the digital data processing could start directly behind the antenna digital radio Software receivers are much more flexible and economic than the current hardwarebased data processing components Fig 728 Antenna Analog level RF Frontend Filter Amplifier IF Digital level Hardware correlator Code Carrier loops ASIC Data Control signal Micro processor Data Solutions Commands User interface User interface Data Solutions Commands Software correlator Microprocessor IF RF Frontend Antenna Figure728 ModernGPSreceiverarchitecture top currentsituation bottom softwarereceiver 72 GPS Receivers User Segment 251 Future satellites will broadcast additional signals Hence the demand for multi frequency receivers will increase Receivers will simultaneously track signals from GPS GLONASS and GALILEO Suitable signals for specific applications will be selected automatically by the receiver The new signals equally provide enhanced cross correlation properties and carrier tracking with much lower SNR Operation under foliage and other suboptimal conditions as well as indoor operation will be facilitated The semicodeless techniques however will remain an important feature as long as not enough satellites with the new signals are in orbit ie until about the year 2008 With respect to the user market we can distinguish between two different devel opment lines For the navigation receiver we will see further miniaturization and fall in prices The onechip receiver can be integrated into a wearable computer built into clothes Langley 2000b The limiting factor could be the size of the antenna How ever with improved signal processing even the antenna could be as small as 1 cm 1 cm Hence a GPS receiver could become small enough to be implemented under the skin and with a suitable data link be used to track people and transmit critical health data This concept could also be a powerful protection against criminal attacks Issues of morality and personal freedom are certainly touched by such developments For surveying receivers the development lines are different They are also likely to decrease in size however the price level most probably will remain rather high compared to the price level of lowcost navigation receivers The main reasons are the market segment is rather small the software development costs for a surveying receiver are much higher than for navigation receivers and the capacity and complexity of surveying receivers is continuously growing Receivers will become more intelligent Preprocessing of the data within the receiver already includes automatic and remotely controlled continuous operation cycle slip editing and data compression The RTK option will be a standard feature Antennas will be of improved design and increased flexibility so that one generic antenna serves for all kinds of applications The tendency of manufacturers is to provide complete and integrated sets of survey ing tools with the GPS receiver as one sensor among others and plugin solutions withnointerfacingproblems Thesurveyingtoolbox includesforexamplecf 762 GPS based products GPS reference stations GPS total station conventional instruments digital levels robotic total station data collector field computer and office and field software 252 7 The Global Positioning System GPS 73 GPS Observables and Data Processing 731 Observables 7311 Classical View Four basic observables can be identified pseudoranges from code measurements pseudorange differences from integrated Doppler counts carrier phases or carrier phase differences and differences in signal travel time from interferometric measurements A pseudorange from code measurements equals the time shift that is necessary to corre late the incoming code sequence with a code sequence generated in the GPS receiver multiplied by the velocity of light 714 7312 The fundamental observation equation for a single pseudorange is P Ri Xi XB cdtu cτi Xi XB2 Yi YB2 Zi ZB2 1 2 cdtu 735 with the notations from Fig 729 Ri geometrical distance slant range between satellite antenna Si and receiver antenna B Xi satellite position vector in the geocentric CTS 212 with the components Xi Yi Zi XB position vector of the receiver antenna B in the CTS with the components XB YB ZB τi observed signal propagation time between satellite antenna Si and observer antenna B dtu clock synchronization error between GPS system time and receiver clock and c signal propagation velocity Z X Xitj Sitj XB Xitk YB Ritj B ZB Ritk Sitk XB Y Figure 729 Geometric relations in satellite positioning 266 7 The Global Positioning System GPS a All systematic influences biases that have a stable and welldescribed struc ture are estimated together with the station parameters as socalled nuisance or bias parameters Bias parameters may be for instance corrections to the satellite orbit clock parameters ambiguity terms and tropospheric scale factors These biases can be either directly measured by additional observations eg the ionospheric delay or they are included in an extended adjustment model eg the tropospheric delay The undifferenced phase measurements 739 are used as the basic observables b Most of the biases are eliminated by taking the difference between observables It is assumed that the disturbing terms are linearly dependent with one another in the various data sets Up to a certain degree this is correct eg for clock biases orbital biases and ambiguities Single double and triple differences of the carrier phase measurements are used as derived observables 7321 The concept is primarily applied for baselines between two stations Both procedures have advantages and disadvantages The main advantage of the parameterestimationapproachaisitsflexibilityandindependenceoftherequirement for simultaneous observations at all participating stations Coordinates of a point field network are determined not derived quantities such as baselines The behavior of certain parameters like the comportment of clocks can be controlled Highly stable satellite oscillators can be used to improve the stability of the adjustment Additional biases like antenna phase center variations multipath effects or hard ware propagation delays can be modeled in a rigorous way and can be directly inte gratedintotheobservationequation ModernapproacheslikePrecisePointPositioning PPP 734 are only possible with undifferenced data In total it can be stated that carrier phase observations are physically much better represented by undifferenced ob servables than by double differences On the other hand the undifferenced approach requires that all bias and nuisance parameters have to be included explicitly in the observation equation The baseline concept b was introduced from experiences with Very Long Base line Interferometry VLBI Counselman Steinbrecher 1982 Its main advantage is that many common error effects are eliminated from the observations by differencing thus simplifying the parameter estimation This is in particular true for the satellite and receiver clock errors but also to some extent for orbit and signal propagation errors For larger station separations however the elimination process no longer works out in a rigorous manner it becomes more difficult or even impossible to fix the ambiguities to whole numbers integers Also the number of independent observations is considerably reduced by the differencing and information is lost Through the differencing process all absolute biases are eliminated and only the differences between the biases remain in the data Differenced observables are no longer single station related but vector related The error modeling of these differ ences however is much more difficult than is the error modeling for the undifferenced original bias effects see eg Wübbena et al 2001b The double difference approach introduces mathematical correlations into the resultant observables These correlations have to be modeled in the variancecovariance matrix 73 GPS Observables and Data Processing 267 S1 X1Tt1 Z X X3Tt3 S2 X2Tt2 R1 c dtu Xu S3 c dtS3 R4 c dta1 S4 Y Figure 737 Main solution parameters in posi tioning with pseudoranges The principle of positioning with GPS in the parameter estimation ap proach follows equations 744 and 751 It is illustrated in Fig 737 Here Tti is the epoch of signal transmission in the time system of the individual satel lite Si The relation to the GPS system time satellite time frame is written as Tt Tti dtsi 783 Observations are tr theepochofsignalreceptioninthe receiver time frame and Tti the epoch of signal transmission in the individual time frame of satel lite Si Known quantities are the coordinates XiTt of the satellite Si at the epoch Tt in the CTS coordinate system In their fundamental simplified formulation the observation equations 744 and 751 are solved for four unknowns These are Xu three coordinates Xu Yu Zu of the user antenna in the CTS coordinate system and dtu clock synchronization error between the users clock and GPS system time The parameter vector of the linearized observation equation is then X Xu Yu Zu dtu 784 For a more developed model of parameter estimation additional parameters can be introduced for example 3 clock biases per station 3 clock biases per satellite 6 orbital biases per satellite 1 parameter for solar radiation pressure 1 tropospheric parameter per station and satellite and 1 ambiguity parameter per station and satellite Theparameterfortroposphericpropagationdelay dtai isalreadycontainedinFig737 and in the observation equations 744 and 751 The clock behavior can be described by a polynomial model with terms for clock bias drift and ageing cf 74 225 dtu a0u a1ut t0 a2ut t02 dts a0s a1st t0 a2st t02 785 268 7 The Global Positioning System GPS The observation equation must be extended accordingly More parameters can be included if necessary for example antenna phase center variations or receiver hardware delays The singularity in equation 751 namely the linear dependency between clock parameters signal propagation delay and ambiguity term has to be treated carefully by fixing certain ambiguity parameters It is important to choose the correct number of parameters so that the singularity can just be removed and the ambiguities remain integers Wübbena et al 2001b The unknown parameters are combined into the vector of unknowns X and the observations into the vector of observations P R The linearized observation equation is then written as l P R P RX0 786 X0 is the approximation vector of the unknown parameters and l the vector of reduced observations With x X X0 787 it follows that l Ax 788 The design matrix A contains the partial derivatives of the observations with respect to the unknowns A P RX 789 The solution vector of the system is x A1l 790 With εR as the measurement noise of the pseudoranges cf 744 the error εx of the adjusted parameters is found to be εx A1εR 791 For more detailed information on adjustment techniques see eg Vaníˇcek Krakiwsky 1986 chap 12 Leick 1995 chap 4 Strang Borre 1997 chap 1 or Niemeier 2002 In the parameter elimination process b various combinations of differences are formed as described in 7321 The formulation of differences implies some con sequences that have to be considered for data processing The most important aspects are briefly discussed Algebraic correlation introduced into the differences has to be taken into account in a rigorous adjustment The covariance matrix of observations has to be updated with the increasing number of receivers and receiver types The problem is discussed eg by Beutler et al 1987 Goad Müller 1988 Goad 1998 and in most GPS textbooks like Leick 1995 HofmannWellenhof et al 2001 A preselection of differences is necessary if several stations and satellites are involved in the same session because only one part of the possible differences is 73 GPS Observables and Data Processing 269 independent One possible concept is the definition of a reference satellite and a reference station eg Goad 1985 1998 HofmannWellenhof et al 2001 that have to be introduced into all differences Difficulties arise with data gaps for the reference satellite or the reference station Differencing of observations eliminates the absolute information that is contained in the undifferenced observations A reliable absolute datum has to be introduced into the solution in order to avoid mismodeling 7613 Identical observation epochs are required for the use of differenced observations For receivers observing at different epochs within the same session the observations have to be reduced to identical epochs with appropriate interpolation models eg stochastic clock modeling eg Wübbena 1988 Because of the simple basic model and the good results in processing short base lines most commercial software packages use the baseline approach b parameter elimination with double differences as primary observables The parameter estima tion technique a with undifferenced observables is preferred in scientific software packages such as GEONAP and GIPSYOASIS II The wellknown scientific package BERNESE however is also based on the double difference concept 734 7323 Resolution of Ambiguities Carrier phase measurements are affected by the ambiguity term N 751 that is by an unknown number of complete wavelengths between the satellite and the receiver antenna This initial ambiguity has to be determined with appropriate techniques to exploit the full accuracy potential of the GPS carrier phase measurements Ambiguity determination is one of the most demanding problems in the geodetic technique of evaluating GPS observations On the other hand it is the integer nature of the phase ambiguities that guarantees the high accuracy of relative positioning with GPS in particular when the observation time is short The best and simplest possibility for determining the ambiguity would be the use of additional frequencies or signals as is the case for terrestrial electronic distance measurements eg Kahmen Feig 1988 Unfortunately for the time being GPS does not provide more than two frequencies hence other strategies were developed to solve the ambiguity problem The main approaches are see eg Han Rizos 1997 a the geometric method coordinate domain search b code and carrier phase combinations observation domain search c ambiguity search methods ambiguity domain search and d combined methods Currently the approach c is considered to be the most effective and powerful search method in particular for fast solutions and is discussed widely in the literature a Coordinate domain search The geometric method makes use of the timedependent variation in the geometric relation between receiver and satellites In general continuous phase measurements are used and the ambiguities are estimated as realnumber parameters A simple 73 GPS Observables and Data Processing 271 have been developed such as antenna swapping or reoccupation see 7353 One particular development the ambiguity function method was described for the first time by Remondi 1984 The basic idea is as follows Observables are the single differences 7321 between two stations where the coordinates of one station are taken as known Unknown parameters are only the coordinates of the second station and the difference in the receiver clock errors A search algorithm is defined that varies the baseline vector until the related computed single differences correspond best with the observed single differences Further developments of this method are described by Mader 1990 Remondi 1990 Han Rizos 1997 and HofmannWellenhof et al 2001 p 229ff The technique is from todays understanding of rather poor com putational efficiency and consequently it is of only historical interest Kim Langley 2000 Advantages and disadvantages of the geometric methods are summarized as follows Advantages basically simple and clear modeling works with few satellites usable for short long and very long distances and the ambiguity float solution rapidly provides approximate results Disadvantages long observation time necessary for sufficient geometric rigor influenced by unmodeled effects like ionosphere orbits etc no a priori use of the integer nature of ambiguities and sensitive to unrecovered cycle slips b Observation domain search Inthesecondapproachtoambiguitysolutionthe combinationofcodeandcarrierphase observations is applied The nonambiguous code phase measurements are used as an additional wavelength to resolve the carrier phase ambiguity PRCR PRCD λN dTA dε 792 This method is independent of the geometry and it is sometimes referred to as the geometryfree technique Hatch et al 2000 The difference between both observables contains however the residual errors dTA see below The basic idea is to make code measurements until the noise level of the code solution is less than half the wavelength of the carrier wave Because of the much larger mainly multipath induced noise in the code measurements determination of the cycle ambiguity requires that the code observations be smoothed over multiple epochs The idea behind this approach was discussed early by Bossler et al 1980 and Hatch 1982b but it was not considered to be operational First results were presented independently by Melbourne et al 1985 and Wübbena 1985 Today the technique is widely applied in particular for kinematic applications over short distances Hatch et al 2000 HofmannWellenhof et al 2001 It also promises good results with the forthcoming availability of three frequencies Vollath et al 1999 73 GPS Observables and Data Processing 273 long and very long baselines possible Disadvantages dual frequency Pcode receiver necessary sensitive to multipath and only wide lane ambiguities are resolved c Ambiguity domain search Ambiguity search methods have been developed with the objective of cutting down the necessary observation time for an individual observation station The more satellites that are available the better this method works The basic idea is to search for the optimum ambiguity combination of L1 L2 or derived signals The search algorithm usually starts with an initial ambiguity float solution and then restricts the solution vector to discrete integer values applying some optimization techniques The possible combinations within a predefined ambiguityspace are examined The procedure is illustrated in Fig 739 for the case of two and three satellites Each additional satellite restricts the number of possible solutions possible solutions selection final solution Figure 739 Possible solutions for the ambiguities are selected situation for two satellites left and three satellites right The basic problem with this is that the number of necessary mathematical oper ations increases rapidly beyond all limits If n is the number of cycles within the search interval and m the number of ambiguities to be determined then the number of necessary operations is as given in Table 79 It becomes evident that the problem is not solvable by the examination of all possible combinations but that appropriate selection strategies have to be applied Various proposals for selection strategies exist in the literature and have been in troduced in software packages see eg Hatch 1991 Leick 1995 Teunissen 1998 HofmannWellenhof et al 2001 Early examples are the treatment as a neural network 274 7 The Global Positioning System GPS Table 79 Number of necessary operations for fixing ambiguities in all possible combinations Wübbena 1991 nm 1 3 10 20 4 1620 48 020 39 106 56 107 8 47 105 41 108 27 1012 57 1014 20 15 1012 33 1019 11 1029 75 1034 Landau 1990 or the Fast Ambiguity Resolution Approach FARA Frei Beutler 1990 A very powerful modern technique is the LAMBDA method developed at the Delft University of Technology Teunissen et al 1995 Teunissen 1998 Joosten Tiberius 2000 LAMBDA stands for Least Squares Ambiguity Decorrelation Ad justment The basic idea is to transform the original realvalued double difference ambiguities which are highly correlated into decorrelated realvalued ambiguities As such the number of solution candidates is considerably reduced By this procedure the original highly elongated search space is transformed into a spherelike search space with the same volume which allows a much more efficient identification of the integer ambiguities see Fig 740 Float solution True integers 15 10 5 0 5 10 0 0 0 5 5 5 5 5 10 10 10 15 15 15 10 5 Figure740 Lambdamethod ambiguitysearchspacebeforeleftandafterrightdecorrelation adapted from Joosten Tiberius 2000 Other representative techniques are for example FAST Fast Ambiguity Search Filter Chen Lachapelle 1995 and OMEGA Optimal Method for Estimating Ambi guities Kim Langley 1999 Further algorithms are still under development and will improve the methods of fast ambiguity resolution in particular for surveying applica tions over short distances cf 7352 but also for longrange realtime kinematic positioning For a short review of status and trends see eg Kim Langley 2000 Advantages and disadvantages of the ambiguity search methods are summarized as follows 276 7 The Global Positioning System GPS cascade ambiguity resolution For the promises and limitations see eg Hatch et al 2000 Particular methods have been developed to rapidly determine the initial phase am biguities for kinematic surveys 735 One powerful early procedure is the antenna swapping technique ie the exchange of two antennas over a very short baseline sev eral meters before the start of the kinematic survey Remondi 1985 This procedure is described in more detail in section 7352 Today with the availability of a large number of visible satellites sometimes eight and more the ambiguity search methods are in particular a powerful means for the rapid resolution of ambiguities often based on a single epoch observation The resolution of ambiguities is a key factor for precise GPS surveying In many cases in particular if the interstation distances are small and if the data quality is good the ambiguity resolution works out satisfactorily with the routine options in the software supplied by the manufacturer In all those cases where the interstation distances are large 10 km and highest accuracy 1 cm is required the data quality is poor eg multipath cycle slips only a few satellites are visible the ionosphere is disturbed andor the observation time is short problems may arise in solving for ambiguities In such cases a careful and interactive data processing operation with multipurpose GPS adjustment software may be neces sary The proper use of the different possibilities as they have been discussed in this chapter usually requires trained and experienced personnel For precise differential GPS PDGPS in reference station networks 753 a mod eling of the error state in realtime helps to reduce the Time To Fix Ambiguities TTFA and to improve the ambiguity success rate One key question is whether the ambiguities have been fixed correctly ambiguity validation This question can be formalized in a probabilistic measure the ambiguity success rate Joosten Tiberius 2000 Since ambiguities are determined from noisy data the estimated integer ambiguities can be treated as stochastic variates similar to standard adjustment practice If the success rate is sufficiently high for example 99 it is likely that the correct integer has been found For details see Teunissen 1998 Joosten Tiberius 2000 Other procedures are to compute contrast or ratio values between the best and the second best solution namely the two smallest values of the square root sum of residuals Only when the ratio of these two values exceeds a selected threshold the solution with the smallest value is chosen as the correct solution Hatch et al 2000 With todays satellite coverage it is possible to extend the observation time at a site up to several hours or even days In such cases the ambiguity float solution already provides excellent results also for large interstation distances without the necessity to resolve the integer ambiguities For applications like the establishment of fundamental geodetic control or the monitoring of crustal deformation the problem of ambiguity fixing therefore is of minor relevance 73 GPS Observables and Data Processing 277 733 Data Handling 7331 Cycle Slips Cycle slips occur if the receiver loses phase lock of the satellite signal The reasons for cycle slips may be observation dependent eg obstructions in particular for kinematic observations signal noise in particular caused by multipath and ionospheric scintillation low satellite elevation causing low signal strength or receiver dependent eg weak signals partly caused by signal interference antenna inclination in kinematic application airplane ship caused by signal processing In a cycle slip the carrier phase shows a sudden jump by an integer number of cycles the fractional part of the phase observable remains unchanged Fig 741 The time phases Figure 741 Representation of a carrier phase cycle slip cycle slip may be as small as one or a few cycles or contain millions of cycles Cycle slips have either to be removed from the data at the preprocessing level or a new ambiguity has to be determined for the particular pseudorange A cycle slip can easily be detected if double and triple differences are formed This is demonstrated in Table 711 The notation corresponds to Fig 735 and to chapter 7321 A cycle slip SL is in troduced into the phase observation be tween station j and satellite p at epoch t All single and double differences starting with epoch t are corrupted by the cy cle slip whereas only one of the triple differences is affected It is evident that the triple difference technique of fixing cycle slips belongs to the very early and classical methods eg Remondi 1985 Two aspects have to be distinguished cycle slip detection and the elimination of cycle slips from the data the cycle slip repair also denoted as cycle slip fixing Most modern receivers have builtin algorithms that identify all or most of the cycle slips and indicate flag the slips in the data set These indications are very helpful for data preprocessing Advanced receivers also have sophisticated implementations of the phase lock loops with fewer occurrences of cycle slips Misra Enge 2001 Cycle slip repair belongs to the process of data editing either automatic or interactive Several methods are in use and have been widely discussed in the literature For a review see Gao Zuofa 1999 HofmannWellenhof et al 2001 and Bisnath et al 2001 The main differences come from the available data sets single or dual frequency codes 73 GPS Observables and Data Processing 281 2 With dual frequency receivers the ionospheric residuals method b can be used together with a Kalman filter to predict the dynamic behavior of the observation platform and to close the gaps in the observations The technique is very sensitive to high dynamics and low signalnoise ratio 3 A new ambiguity on the fly OTF is determined after loss of lock With lownoise code receivers the extrawide laning technique can be applied If a sufficient number of satellites can be tracked after the data gap 6 or more then advanced ambiguity search techniques 7323 are a powerful tool For each cycle slip a new ambiguity parameter is simply introduced into the adjustment 4 The integration of an additional sensor helps to bridge the gaps caused by cycle slips An external atomic clock rubidium oscillator replaces one satellite An inertial sensor package can be used to interpolate the GPS positions if signals to particular satellites are shaded by obstructions eg Colombo et al 1999 Böder 2002 7332 The Receiver Independent Data Format RINEX Each receiver type has its own binary data format and the observables are defined following the manufacturers individual concepts Time tags may be defined in trans mission time or in receiver time phase measurement may be expressed in whole cycles or in fractional parts of cycles code and phase may have different or identical time tags and satellites may be observed simultaneously or at different epochs As a consequence data of different receiver types cannot easily be processed simultaneously with one particular GPS data processing software package To solve this problem either all manufacturers have to use the same data output format or a common data format has to be defined that can be used as a data interface between all geodetic receiver types and the different processing software systems The first has not been realized to date However a successful solution has been found to define and accept a common data format for international data exchange Based on developments at the University of Berne Switzerland the Receiver In dependent Exchange Format RINEX was proposed by Gurtner et al 1989 at the Fifth International Geodetic Symposium on Satellite Positioning in Las Cruzes The proposal was discussed and modified during a workshop at this symposium and rec ommended for international use More discussions followed in 1989 and 1990 and brought some modifications and extensions to the data format A review of the histor ical development is given by Gurtner 1994 RINEX has indeed been accepted by the international user community and by the community of receiver manufacturers For most geodetic receivers translator software is provided by the manufacturers that converts the receiver dependent data into the RINEX format In addition all major data processing software requires RINEX data as an input RINEX hence serves as a general interface between receivers and multi purpose data processing software With RINEX one of the most serious obstacles to the routine mixing of data from different receiver types is removed It is an important precondition for large 282 7 The Global Positioning System GPS international cooperative projects like the IGS 781 and it found its first important application in the EUREF campaign in 1989 for the establishment of the European Reference Frame 7621 Since the first publication in 1989 several revisions and modifications have been introduced The current revision status is version 210 A detailed document is avail able for instance via the IGS server Gurtner 2001 The following definitions are taken from this document RINEX defines three fundamental quantities in the GPS observables Time Range and Phase The time of measurement is the receiver time of the received signals It is identical for the phase and range measurements and is identical for all satellites observed at that epoch It is expressed in GPS time not in UT The pseudorange is the distance from the receiver antenna to the satellite antenna including receiver and satellite clock offsets and other biases Pseudorange Geometrical distance c RCVR clock offset Satellite clock offset Biases 799 so that the pseudorange reflects the actual behavior of the receiver and satellite clocks The pseudorange is written in units of meters and is unambiguous ie CA code ranges add the correct number of milliseconds to obtain the definition of pseudorange given above The phase is the carrier phase measured in whole cycles at both L1 and L2 The halfcycles measured by squaringtype receivers must be converted to whole cycles and this fact is noted by the wavelength factor in the header records The phase changes in the same sense as the range negative Doppler ie range increases equal phase increases The phase observations between epochs must be connected by including the integer number of cycles The phase will not contain any systematic drifts from intentional offsets of the reference oscillator The observables are not corrected for external effects like atmospheric refraction satellite clock offsets etc The sign of the Doppler shift as additional observable is defined as usual namely positive for approaching satellites The basic RINEX format consists of three ASCII file types 1 Observation Data File 2 Meteorological Data File 3 Navigation Message File Each file type consists of a header section and a data section The observation file usually contains the data collected by one receiver at one station during one session Since RINEX version 2 it is also possible to include observation data collected in sequence by a roving receiver during rapid static or kinematic surveys From the long list of revision details only some major items are indicated inclusion of GLONASS data since 1997 continuous numbering of the GPS week no rollover 1998 inclusion of navigation data from GEO satellites 2000 and inclusion of navigation data from LEO satellites 2001 73 GPS Observables and Data Processing 283 For detailed information see the cited documents in particular Gurtner 2001 RINEX is the international exchange format for the postprocessing of GPS data For the transmission of data corrections in realtime in relative Differential GPS applications a particular data format is available the RTCM format Details of this data format are given in the section on Differential GPS DGPS 7512 734 Adjustment Strategies and Software Concepts All observations made simultaneously and continuously in the course of a particular GPS project are called a session A session may be as short as a few minutes if fast ambiguity resolution techniques are applicable in small networks or it may last several hours or even days if the highest accuracy is wanted in larger networks During the development phase with a limited number of satellites available a typical observation session lasted between one and three hours Since continuous worldwide coverage was established in 19931994 sessions can last several days For practical reasons and for analysis purposes it may be advisable to break down the complete data set into individual sessions of several hours for instance one session per day or three sessions of eight hours each per day The following observation and evaluation strategies are in use a singlestation adjustment b processing of single baselines and subsequent combination of baselines into networks c processing of all simultaneouslyobserved data of a single session in a joined adjustment multistation adjustment and d combination of several session solutions into a rigorous overall network solution multisession adjustment The singlestation adjustment a provides absolute station coordinates referred to WGS84 Because of the low accuracy 741 the results are of little interest to geode tic applications but they often meet the requirements for some tasks in geophysical prospecting GIS data acquisition or in remote sensing The typical application field is navigation cf 7627 In a rigorous geodetic adjustment relative and absolute information 743 is re quired This is why a singlestation solution is incorporated into many software pack ages for multistation postprocessing The singlestation adjustment is also used for preprocessing and editing the data eg because of cycle slips Earth rotation relativity ionosphere troposphere and formation of normal points before they enter the level of multistation adjustment More accurate absolute positions at the level of a few meters or better can be achieved if data from several days of observation are used Along with the accurate modeling of orbits and clocks 743 the concept of Precise Point Positioning PPP has been developed see below The single baseline concept b was widely used in early software development for the processing of GPS data The observations from two simultaneouslyoperating receiversareprocessedinajointadjustment mostlyindoubledifferenceform7321 73 GPS Observables and Data Processing 285 Several sessionsolutions can be combined into a multisession adjustment d or more precisely into a multistationmultisession solution This is the usual procedure if larger networks have to be broken into parts because of a limited number of available GPS receivers The basic condition is that each session is connected to at least one other session of the network through one or more identical stations where observations have been carried out in both sessions An increasing number of identical stations increases the stability and the reliability of the total network cf 7613 The multisession solution is completely rigorous and equivalent to an allinone joint adjustment if the variancecovariance matrices of the individual session solu tions are properly used The stepwise procedure starting with session solutions has the advantage of requiring less computer capacity In addition comparison of the individual session results provides an excellent insight into the networks accuracy if sufficient redundant observations at identical stations have been included Soft ware packages for GPS data processing of large networks are usually based on the multistationmultisession concept The development in the field of GPS software is fast hence only a few basic considerations are made here A first classification is possible into commercial software provided from receiver manufacturers andmultipurposescientificsoftware thatoriginatesfromdevelopments at scientific institutes Software of the first group is primarily designed for processing of data from a particular receiver type Advanced packages however also accept data from other receivers via the RINEX interface As a rule only the executable object code isavailabletotheuser andthebasicmathematicalmodelsaremostlynotdocumentedin detail Commercial software is adequate for everyday surveying work It usually offers a large variety of possible applications and can be operated easily enough by personnel with an average background in engineering and GPS technology In some cases the basic software includes baseline adjustment and additional software is necessary for network computation Usually this kind of software allows for static and kinematic 735 applications and includes extensive mission planning capabilities 7611 The RealTime Kinematic RTK capability with OTF ambiguity techniques see 7354 is today considered to be a standard option Current examples of this first group are SKIPro from Leica Geosystems TGO Trimble Geomatics Office from Trimble Navigation and Pinnacle from JavadTopcon Positioning Systems The development of a generalpurpose GPS postprocessing system second group is a major operation Beutler et al 1990 It requires several manyears of development and consists of a large number of individual programs adding up to tens of thousands of lines of code Usually these software packages are not restricted to just one receiver type but accept data from a large variety of geodetic receivers The packages serve in most cases for professional standard use in smaller networks for rapid processing professional use in high accuracy surveys also over large distances scientific use in research and education and 286 7 The Global Positioning System GPS data analysis and scientific investigations including geodynamic research and analysis of permanent arrays Besides the standard options for rapid processing these kinds of software packages offer many particular alternatives for scientific processing Interactive operation is essential Some packages include options for orbit determination or the estimation of atmospheric models Scientific processing requires a lot of experience and a deep understanding of GPS signals and error behavior Data processing is particularly difficult if the data are contaminated by ionospheric disturbances cf 7441 and when the highest accuracy over large distances is required from noisy data The mathematical models and the rationale behind the scientific generalpurpose software packages are in most cases well documented and discussed in published literature In some cases the user has access to the source code and can include modifications or new parts Current examples of this second group of GPS software are BERNESE developed at the University of Berne Switzerland eg Beutler et al 1988 Hugentobler et al 2001 GEONAP originally developed at the University of Hannover Germany eg Wübbena 1989 1991 and GIPSYOASIS II developed at the Jet Propulsion Laboratory USA eg Blewitt et al 1988 Webb Zumberge 1993 A multipurpose software package consists of several parts Three main groups can be identified the preprocessor level prepares the data for the main processing the mainprocessor level deals with the estimation of unknown parameters and the postprocessor level summarizes various information in tables or in graphical form and combines sessions to networks if required Fig 743 shows a simplified functional flow diagram of a generic software package for static multistation multisession GPS processing The structure of the GEONAP software is very similar to this diagram Starting from the raw data of all receivers involved in a single session these data must be acquired translated into a readable ASCII format and tested for rough errors blunders In most cases the RINEX format is used as a data interface between receiver and software RINEX requires additional information that is not always provided by the receivers eg antenna height approximate station coordinates meteorological data etc These data can be introduced into a database The broadcast message can be separated from the observation data checked and organized in a session dependent message file Smoothing algorithms 3332 for different portions of the message can be applied At this level external orbital infor mation eg IGS orbits 7432 781 can be introduced if required Single station solutions from code measurements or carriersmoothed pseudo ranges are usually generated at the level of the main program Necessary data correc tions can be applied at this stage these are for example corrections for ionosphere 73 GPS Observables and Data Processing 287 Figure 743 Simplified functional flow diagram of a generic GPS software package troposphere 744 antenna phase center 745 Earth rotation and relativistic effects 741 The data can be controlled for cycle slips and be condensed to normal points 3332 288 7 The Global Positioning System GPS Parameter estimation in the main program follows either the concept of parameter elimination or parameter determination or both 732 Basic observables may be the undifferenced phase data eg GEONAP GIPSYOASIS II or double differences eg BERNESE If double differences are used sophisticated decorrelation and weighting tech niques have to be applied Goad Müller 1988 Beutler et al 1990 to account for the mathematical correlations between the doubledifferences in a GPS network It may also be advisable to generate an optimum set of independent double difference observables with respect to the shortest interstation distances and minimum influences of data gaps at individual receivers Rothacher Mervart 1996 Parameters to be estimated can be station coordinates biases of satellite clock and receiver clock second degree polynomial plus stochastic clock model 225 hardware delays in the satellite and receiver electronics second degree polyno mial plus 1 stochastic parameter orbit improvement with short arc model eg up to 6 Keplerian parameters solar pressure model tropospheric scale parameter for each station constant or stochastic process local ionospheric corrections eg improved parameters in the Klobuchar model time varying parameters of a single layer ionospheric model and parameters for each nonresolved ambiguity and each unrecovered cycle slip More parameters can be included The Bernese GPS software version 42 allows among others to estimate precise orbits Earth rotation parameters precise ionospheric models and the precipitable water content of the atmosphere Hugentobler et al 2001 The adjustment process in the main program can be repeated in order to fix as many ambiguities as possible The principal results of the session solution are the coordinates of all participating stations and the variancecovariance matrix At the postprocessing level all session solutions can be rigorously combined in a network adjustment program if this is not already provided in the main program The results of the network solution can be resubstituted into the session solution with the objective of fixing remaining ambiguities External information like coordinates of fiducial stations can be introduced at this level Also improved orbits can be introduced again into the ephemeris file and a second processing run can be initiated The final results from the network solution can be transformed into a local or global datum 215 121 and compared or combined with existing terrestrial data sets 7621 A final evaluation of the results is supported by statistical tests and a series of graphical representations These may include statistics on usable simultaneous observations and the behavior of particular signals and linear combinations such as the ionospheric signal 780 A new development is Precise Point Positioning PPP This is a powerful strategy for estimating the coordinates of a single station using precise satellite orbits and satellite clocks The necessary information can be taken either from the IGS 781 or from other sources like the JPL 7432 73 GPS Observables and Data Processing 289 The idea behind PPP is as follows Precise orbits and satellite clocks are estimated based on observations from a high quality global fiducial network This information is taken to solve for station parameters of any site in the world position clock and wet troposphere Only one single station is processed at a time A disadvantage is that the method is unable to take account for correlations between stations and that orbits are assumed to be perfect which is not true The final formal errors hence have to be scaled to more realistic values If only code measurements are used the observation noise level is well above the precision of orbits and clocks The positioning accuracy hence depends mainly on the code observation and reaches several decimeters With the use of phase measurements eg with GIPSYOASIS II software the achievable accuracy is comparable to the accuracy in global networks namely 1 cm or better eg Völksen 2000 One particular advantage of the PPP strategy when compared with network adjust ment is that the processing time increases only linearly with the number of stations Note that original undifferenced observables are essential for this approach For international cooperation in the processing of global and regional networks it is necessary to exchange the results from processing centers that use different software packages with the objective to combine global and regional solutions To this end a Solution SoftwareTechnique Independent Exchange Format SINEX has been defined IGS 1996 The SINEX format contains coordinate estimates and the corresponding covariance information as well as additional information like receiver types antenna types phase center values eccentricities and a priori weights SINEX is mainly used by the IGS community 781 Information about the latest developments in the software sector can be taken from the proceedings of the series of GPS symposia such as ION GPS and IAG Symposia or from related journals eg GPS World GPS Solutions also Journal of Geodesy 735 Concepts of Rapid Methods with GPS 7351 Basic Considerations Various techniques have been developed in recent years that exploit the capability of GPStoprovideprecisecoordinatesafteraveryshortobservationtime orevenwhilethe receiver including the antenna is moving along a trajectory Sometimes misleading the related rapid methods were named kinematic GPS In addition different terms describing particular types of rapid GPS surveying procedures have been created such as semikinematic pseudokinematic true kinematic rapid kinematic pseudostatic stopandgo kinematic etc In some cases different terms were used to describe the same procedure or more confusing the same term was used to describe different procedures The related literature must therefore be read with care A clarifying overview is given by Kleusberg 1990 Rapid methods require the resolution of ambiguities in order to exploit the high accuracy potential of GPS phase measurements Otherwise the noise level of real valued solutions for the short observation times would be too high One prerequisite 290 7 The Global Positioning System GPS for the rapid solution of ambiguities is that the distantdependent errors see 743 744 be small Hence the rapid methods only work well for short distances up to severalkilometersbetweentheparticipatingstations Forlongerranges itisnecessary to model the distance dependent errors eg in active reference networks see 753 Different possibilities exist for subdividing the rapid methods of GPS The scheme used here is into rapid static methods semi kinematic stop and go methods and pure kinematic methods The rationale behind this subdivision is whether the receiver is taking measurements while it is in motion and the coordinates of the trajectory can be determined kinematic mode or whether the receiver is switched off during transportation and coordinates can only be determined when the antenna is stationary static mode A third mode is in between these possibilities in that the receiver has to maintain lock during the times of transportation but coordinates are not usually derived for the trajectory semi kinematic mode A further distinction between static and kinematic surveying can be seen with respect to accuracy issues Kleusberg 1990 In static GPS surveying most random measurement errors are absorbed in the residuals after adjustment while in kinematic surveying most random measurement errors are absorbed in the coordinates This is why the accuracy potential of static GPS cannot completely be reached with pure kinematic methods Only precise methods are considered here ie with an accuracy level of a few centimeters for kinematic surveys This implies the use of carrier phase data as the basic observables Less accurate methods for determining coordinates of a trajectory ie when code measurements are used as primary observables are discussed in 736 and 751 The dividing line between kinematic and navigational use of GPS is debatable As in nearly all geodetic applications at least two receivers are needed to determine relative coordinates In the concept of rapid methods one receiver usually remains fixed during the operation while a second receiver the roving receiver moves between stations or along a trajectory The first two methods were frequently applied after 1990 when GPS had devel oped into a powerful technique for detailed surveying cadaster GIS With improving satellite coverage after 1994 and the availability of rapid OTF algorithms currently mainly the third pure kinematic method is applied for local surveys The stopand go technique has nearly disappeared from use It is however explained in this book because of its conceptual importance and because it is still offered by a number of manufacturers 7352 Rapid Static Methods Two different modes can be distinguished Fig 744 a rapid static mode with single station occupation 73 GPS Observables and Data Processing 291 b rapid static mode with station reoccupation after about one hour appr 1 hour minutes a b static Figure 744 Modes of rapid static surveying In the first mode a fast ambiguity resolution techniques are required cf 7323 These can be for example codecarrier combination with dual frequency low codenoise re ceivers and ambiguity search methods with 6 and more satellites Basically the same techniques are used as for classical static positioning Depending on the receiver type satellite coverage and interstation distance ob servation times of several minutes up to 15 minutes are sufficient The method is particularly powerful over short distances with dualband low noise receivers a high number of visible satellites and fast ambiguity resolution algorithms The key factor is the necessary time to fix ambiguities TTFA and the ambiguity success rate The procedure is very flexible and effective and is widely used in surveying applications 7624 mostly together with near realtime data processing Rapid static applications are of particular interest with respect to reference services like SAPOS 7513 In order to augment the possible distance to the nearest reference station concepts like active networks or virtual reference stations play an increasing role The demand for surveying equipment with rapid static capability will grow further Equipment will be assessed mainly on the basis of its capability to resolve ambiguities and to provide precise position results after as short a time as possible In the second mode b each station has to be reoccupied after an interval of about 50 to 120 minutes The observation time required at each station is relatively short about four to eight minutes Tracking during the transitions is not necessary the receiver might be turned off while traveling The rationale behind this procedure is that data from a different geometric configuration are required to resolve the ambiguities geometrical method 7323 but not because there is a need for extra observations Ten minutes of data are completely sufficient to absorb most random measurement errors in the adjustment residuals Both data sets are considered as one set with one cycle slip in between The same processing software is used as in static GPS surveying the cycle slip can be fixed with triple and double difference techniques Cycle slip fixing over more than 30 minutes however only works properly if the data quality is high low noise low multipath low ionospheric effects and if the repeated station occupations are identical forced centering A further requirement is that the same satellites have to be observed for both station occupations The reoccupation method was widely used in the early years of rapid GPS meth ods Today it has nearly disappeared from the surveying market because of its rather complicated procedure and the high efficiency of method a Note that it is a static 294 7 The Global Positioning System GPS 7354 Pure Kinematic Method For many purposes precise coordinates of the trajectory of a moving GPS receiver have to be determined in particular in marine and airborne applications In these cases a loss of lock without the possibility of recovering cycle slips or ambiguities while the antenna platform is moving cannot be accepted Hence methods are required that are independent of static initialization techniques and that include the capacity to recover cycle slips andor to resolve ambiguities during motion These techniques are referred to as ambiguity solution on the way Seeber Wübbena 1989 or on the fly egAbidin Wells 1990 Cocard 1995 Only with such methods at hand can kinematic surveying be purely or truly kinematic Suitable methods for ambiguity resolution while the receiver is moving are 7323 codecarrier combination using the extra wide laning technique and ambiguity search functions for six or more satellites The efficiency of these techniques will be improved when low noise code receivers 725 or combined GPSGLONASS receivers 771 are available as well as new satellite signals 717 For the ambiguity resolution on the fly a realtime data link with sufficient capacity is required 7512 Methods for cycle slip recovery in true kinematic mode are use of redundant satellites 4 four satellites use of dual frequency data and use of codecarrier combination The inclusion of external sensors can support the recovery of cycle slips and the reso lution of ambiguities as well for example the use of eg Lachapelle 1990 Colombo et al 1999 ElSheimy 2000 Böder 2002 high quality clocks eg rubidium inertial navigation systems INS and barometric altimeters The accuracy level of pure kinematic surveying is well below 10 cm and can reach a few centimeters under favorable conditions satellite coverage low noise receivers no multipath low platform dynamics The fields of application are broad and continuously broadening 762 They include land air and ocean surveying traffic and machine control engineering surveying and GIS In many cases it is sufficient to process data afterwards Most major software packages offer options for kinematic data When the results are re quired in realtime it is essential to establish a data link between reference and user station Either the reference data are transmitted from an active network of control points like SAPOS 7513 or a particular data link between a local reference station and the roving receiver is established The latter solution is known as the RTK option Real Time Kinematic with OTF On the Fly ambiguity resolution and it is mainly used for limited ranges several km RTK systems are routinely applied for surveying tasks and they form part of every modern GPS receiver system 7242 For more details about RTK technology see 752 7624 Realtime kinematic methods over long distances are still under development 298 7 The Global Positioning System GPS Corrections to the observations are based on measurements or model assumptions If corrections are applied we are left with a certain residual error budget cf Ta ble 712 The error budget can be reduced by refined modeling and by additional observations Usually the contribution of a particular error source is analyzed in terms of its effect on the range determination The combined effect of ephemeris uncertainties propagation errors clock and timing errors and receiver noise projected onto the line connecting observer and satellite is called User Equivalent Range Error UERE or User Range Error URE Sometimes the total error is divided into SignalinSpace SIS URE also abbreviated as SISRE and the User Equipment Error UEE The rationale behind this division is that the Operational Control Segment OCS is only responsible for the SIS performance whereas the UEE depends on the particular users equipment and correction models The SIS URE includes satellite clock and ephemeris prediction errors OCS state estimate process noise and some minor residual noise SIS does not include instanta neous singlefrequency ionospheric model errors tropospheric model errors receiver noise receiver antenna phase center variations or multipath effects These influences contribute to the UEE Official statements can be taken from the document GPS SPS Performance Stan dard DOD 2001 This document contains the specific capabilities provided by the Standard Positioning Service SPS to all users on a continuous worldwide basis without any direct user charge Following the Federal Radio Navigation Plan DODDOT 2001a access to the Precise Positioning Service PPS is restricted to US Armed Forces US Federal agencies and selected allied armed forces and governments see also 716 With disabled Selective Availability SA the SIS performance for PPS and SPS is nearly identical According to the cited document the accuracy standard for the SPS SignalinSpace URE is σURE 6 m The related accuracy standards for position and height are for a global average posi tioning domain 95 SIS only 13 m horizontal and 22 m vertical For a worst site positioning domain the numbers are 95 SIS only 36 m horizontal and 77 m vertical Experiences show that in practice the achievable accuracy is much higher cf 716 The particular error sources are assigned to three main groups namely satellite position and clock errors signal propagation errors and receiver errors 74 Error Budget and Corrections 299 Table 712 includes average numerical values of the individual error sources as they are generally accepted for operational GPS Table 712 Main GPS error contributions to the single range observation Error Source RMS Range Error Satellite orbit 1 2 m clock 1 2 m Signal propagation ionosphere 2 frequencies cm dm ionosphere model best 1 2 m ionosphere model average 5 10 m ionosphere model worst 10 50 m troposphere model dm multipath 1 2 m Receiver observation noise 02 1 m hardware delays dm m antenna phase center mm cm Another separation is into distance dependent errors orbit ionosphere troposphere and station dependent errors antenna phase center variation multipath This latter grouping is used together with the error modeling in multiple reference station networks 753 The Earth rotation correction is necessary if satellite coordinates are computed in an Earthfixed reference frame at the epoch of signal transmission During signal propagation from the satellite antenna to the receiver antenna the CTS coordinate systemrotateswithrespecttothesatellite consequentlythepositionofthetransmission antenna changes in the rotated CTS system The original satellite coordinates must be rotated about the Zaxis by an angle α which is defined as the product of the propagation time τ and Earths rotational velocity ωe cf 7153 α ωeτ 7110 Let X Y Z be the original and X Y Z the corrected satellite coordinates then X X cos α Y sin α Y Y cos α X sin α Z Z 7111 The rotation angle α is smaller than 15 Hence the trigonometric functions in 7111 can be replaced by the first elements of a series expansion 74 Error Budget and Corrections 305 The baseline error db thus depends mainly on the ratio of the baseline length b to the satellite range ρ The maximum range between a GPS satellite and the observer is about 25 000 km If a baseline error of 1 cm is accepted an admissible orbit error for a specified baseline length is summarized inTable 713 The table clearly shows that for relative coordinate determination over short distances the required orbit accuracy is not a critical factor On the other hand the requirement for 1 cm accuracy over very great distances for example ingeodynamicapplicationsover1000kmandmore impliesanorbitaccuracy of better than 1 m which is not yet provided by the broadcast ephemerides Table 713 Relation between orbit errors and corresponding 1 cm baseline errors Baseline length Admissible orbit error 01 km 2500 m 10 km 250 m 10 km 25 m 100 km 25 m 1000 km 025 m In many cases the accuracy of the baseline determination is set as a ratio of the base length estimated in parts per million ppm To give an example an orbit error of 25 m propagates into a relative accuracy of 1 ppm and an orbit error of 5 m corresponds to 02 ppm ie 1 cm over 50 km The last figure is the critical limit for reference station networks see 753 The formula 7134 implies a considerable approximation and it is widely re garded as too pessimistic eg Zielinski 1989 Beutler et al 1998 p 104 Indeed the equation is derived from geometrical considerations and only reflects an instan taneous situation For a whole session the changing geometric configuration for all satellites has to be included The resulting error evolves as the sum of all individual satellite orbit errors integrated over the whole observation period Zielinski 1989 estimates the resulting baseline errors as too large by a factor of 4 to 10 The rule of thumb 7134 should therefore only be used with care and for a rough estimation More detailed equations are given in the cited literature Because of the great altitude of the GPS satellites their orbits are only slightly affected by surface forces and higherorder potential coefficients of Earths gravity field 324 For the computation of short orbit arcs a gravity field expansion up to degree and order 66 or 88 is sufficient It is necessary to include the gravitation effects of the Sun and Moon as well as the Suns radiation pressure in orbit computation models In particular the nongravitational forces on GPS satellite orbits have to be modeled carefully eg Fliegel Gallini 1989 Fliegel et al 1992 Beutler et al 1998 Ziebart et al 2002 cf 3234 The ROCK42 model is used for Block IIIIa satellites and a particular new model for Block IIR satellites Marquis Krier 2000 For precise 306 7 The Global Positioning System GPS computations a model for thermal reradiation and a particular ybias may be included eg Rothacher Mervart 1996 Experiences with the accuracy of broadcast orbits status 19982000 indicate a level of 5 to 10 meters Jefferson BarSever 2000 However there are times where significantly larger orbit errors may occur Broadcast orbits in 2002 are accurate to about 3 m following the estimation of the IGS cf Tab 731 781 p 402 Along with the Accuracy Improvement Initiative AII 717 an orbit accuracy of about 1 m can be expected According to Tab 713 this accuracy is in general sufficient for work with point distances up to several tens of kilometers When greater point distances are asso ciated with high accuracy requirements the accuracy of the operational broadcast ephemerides is usually not sufficient Hence orbit improvement techniques have to be applied along with the data adjustment in large scale networks 734 or a posteriori precise ephemerides based on observations from globally distributed tracking stations have to be used 7432 GPS time is operationally defined as the time scale used by the GPS system cf 223 Each GPS satellite carries clocks which act as the time and frequency base for the realization of the GPS system time in the particular satellite Navigation signals and carrier signals are timetagged to the particular satellite time frame GPS time is monitored by the Main Control Station MCS 713 Its relationship to the other atomic time scales is demonstrated in Fig 214 cf 223 p 38 The satellite clocks run fast by 385 µsday this correction absorbs more than 996 of the relativistic clock effect If necessary the MCS applies other corrections to synchronize the individual satellite clocks with the system time A synchronization error of 1 µs in a satellite clock will produce an error of 300 m in the pseudorange When meterlevel position accuracy is required the clock synchronization between the satellites must be controlled within a few nanoseconds This is why rubidium and cesium oscillators are used in the GPS satellites 225 These clocks have a shortterm stability of 109 to 1010 and a longterm stability of 1012 to 1013 Block IIIIa satellites carry two rubidium and two cesium atomic frequency standards and each Block IIR carries three rubidium standards The performance of each clock is observed by the Control Segment 713 and one of the clocks is selected to generate the signals The deviation of a particular clock from GPS system time is modeled as a quadratic function of time The parameters of this model are estimated uploaded to the satellite and are broadcast within the navigation message 7153 The coefficients a0 a1anda2 in equation 74 are also called the bias drift and aging parameters of the clock Typically parameter a0 is below 1 µs a1 1011 ss and a2 0 ss2 With these correction terms of the broadcast message the satellite clocks can be kept synchronized within 5 to 10 ns Misra Enge 2001 p 92 The actual behavior of each clock slightly differs from this model because of unpredictable correlated frequency errors For the highest accuracy requirements the satellite clock parameters can be estimated in the adjustment process A stochastic 74 Error Budget and Corrections 307 correlation model cf 225 Wübbena 1989 can be included for the growth of the random frequency error with time Alternatively a posteriori clock models based on observations can be used 7432 The requirements of the receiver clock are not very high The user clock in the receiver need only be stable enough to do the pseudorange measurements with code phases A quartz oscillator of medium quality usually suffices In most geodetic adjustment models receiver clock errors are eliminated by means of double differences of the carrier phase observations 7321 However the use of a more precise external clock eg a rubidium oscillator is of importance in cases where only few satellites are available The clock substitutes one satellite 7432 Precise Ephemerides and Clocks IGS A posteriori precise ephemerides PE and clock parameters are based on observations from globally distributed tracking stations At such stations dualfrequency receivers are installed that can measure both the code phases and carrier phases of all satellites in view Orbit errors can be separated from the station clockstime errors through the use of highprecision oscillators rubidium cesium atomic standard The tropospheric propagation delay can be determined with water vapor radiometers The data files usually conform to the SP3 data format Standard Product 3 fi nalized by the US National Geodetic Survey NGS Remondi 1991 Hilla 2002 This format is precise to 1 mm and 1 picosecond Several agencies provide precise ephemerides and adjusted clock parameters among them the NIMA JPL and IGS The National Imagery and Mapping Agency NIMA formerly Defense Mapping Agency DMA generates precise ephemeris PE data files and improved clock pa rameters based on observations from 20 monitor stations These are twelve NIMA and five Air Force stations see Fig 78 p 217 and three IGS stations Maspalomas Kerguelen Yakutsk The ephemerides files give position and velocity vectors for each satellite every 15 minutes Two PE data types are available one referred to the satellites center of mass and the other with respect to the satellites antenna phase center A comparison in 2001 between the IGS final orbits see below and the NIMA precise ephemerides showed differences of less than 20 cm Precise orbits and adjusted clock parameters can be used either for the post processing of data in multistation GPS networks or they can be used for the pro cessing of single receiver data in the Precise Point Positioning PPP mode 734 The NIMA precise ephemerides are freely available via Internet anonymous ftp Another resource for precise orbits are the NASA JPL Jet Propulsion Laboratory precise ephemerides and adjusted clock parameters Positions and velocities are given for every 15 minutes and clock parameters for every 5 minutes Orbits and clocks result from the same estimation process and are hence completely consistent with each other Final orbits are available after about 2 weeks Rapid orbits are given within 20 hours they agree with the final orbits at the level of about 20 cm The JPL orbits 308 7 The Global Positioning System GPS are also given as nonfiducial NF orbits ie the orbits are estimated in a free datum independent from the ITRF coordinates of the tracking stations The datum instead is derived from the orbits and clocks The adjusted network can then be transformed to any other datum without problems Precise JPL orbits and clocks are primarily required for the processing of single receiver GPS data in the Precise Point Positioning PPP mode with the software package GIPSY OASIS II 734 The necessary accuracy of the adjusted clocks is in the order of 100 picoseconds The most important source for precise ephemerides and other GPS products today is the IGS The IGS a service established by the IAG officially started its activities on January 1 1994 after a successful pilot phase of more than one year In 1999 the name was changed from International GPS Service for Geodynamics to International GPS Service Following the Terms of Reference the primary objective of the IGS is to provide a service to support through GPS data and GPS products geodetical and geophysical research activities For more details of the structure organization and the various and growing services of the IGS see 781 In the following only the main information on data orbits and clocks is given IGS collects archives and distributes GPS observation data sets from more than 300 globally distributed stations The stations have to meet certain quality criteria About 120 stations are classified as Global Stations because they are regularly analyzed by at least three Analysis Centers The IGS core products consist of weekly final products namely GPS ephemeris and clock values tabulated at 15minutes intervals for each day in SP3 format Earth Orientation Parameters EOP and Geocentric station coordinates and velocities With respect to orbits and clocks three different products are available see Table 714 status August 2002 The ultrarapid orbits predicted orbits are updated twice daily at 0300 and 1500 UT and are valid for a period of 48 hours The first 27 hours are based on actual observations and the second 21 hours are a predicted orbit Table 714 Precise IGS GPS orbits and clocks Orbits Accuracy Latency Updates Sample Interval Broadcast 260 cm 7 ns real time daily UltraRapid 25 cm5 ns real time twice daily 15 min15 min Rapid 5 cm02 ns 17 hours daily 15 min5 min Final 5 cm01 ns 13 days weekly 15 min5 min With the IGS products at hand all requirements for precise orbits are completely fulfilled Together with the precise station coordinates and the original observation data from IGS stations it is possible to connect every new station worldwide directly to the geocentric reference frame see 7621 Note that also the individual analysis 74 Error Budget and Corrections 309 centers of the IGS provide precise orbits for example the NGS in the US and CODE in Europe see 781 744 Signal Propagation The GPS signals when propagating from the satellite antenna to the user antenna are subject to the following propagation effects propagation delay in the ionosphere propagation delay in the troposphere and multipath propagation at the satellite and in the vicinity of the receiver antenna The atmospheric propagation delays are basically treated in section 23 In this chapter some of the more important properties and relationships with respect to GPS are pointed out 7441 Ionospheric Effects on GPS Signals The propagation delay in the ionosphere between about 50 km and 1000 km above the Earths surface depends on the electron content along the signal path and on the frequency used The influencing parameters are mainly solar activity and the geomagnetic field Hence ionospheric refraction varies with frequency geographic location and time The resulting range error for GPS frequencies can vary from less than 1 m to more than 100 m Wells ed 1986 Klobuchar 1991 1996 Dual frequency receivers make use of the fact that the L1 and L2 signals experience different propagation delays in the ionosphere In addition we have to note that the ionosphere is a dispersive medium 2312 and that therefore the phase velocity propagation of the carrier is not the same as the group velocity propagation of the codes To be exact we observe the combined effect from the ionosphere and the plas masphere because the GPS orbits are located far above the ionospheric layers The electron content below about 2000 km is also called the Faraday content For a de tailed study of the timevariable ionospheric behavior eg in atmospheric physics for ionospheric tomography it is hence advisable to combine measurements from Low Earth Orbiters LEO and GPS satellites or to install GPS receivers in satellites at low orbital height An observer at the surface of the Earth who uses GPS as a tool for po sitioning or navigation has no need to separate the ionospheric and the plasmaspheric propagation delay In this book as in most literature the term ionospheric delay is therefore understood as the combined effect For more information on the physics of the ionosphere with particular reference to the propagation of radio waves see eg Davies 1990 or Klobuchar 1996 For carrier phase measurements we have the refraction coefficient from equation 295 np 1 403 ne f 2 with ne electron content along the signal propagation path and 74 Error Budget and Corrections 313 of wide area augmentation or area correction parameters or virtual reference stations is treated at length in 753 At a global scale ionospheric TEC models are derived from data of the Interna tional GPS Service IGS see 781 Five socalled Ionospheric Analysis Centers IAACs deliver every 24 hours an Ionospheric Map Exchange IONEX file Schaer et al 1998 with 12 maps containing global TEC information with 2hour time reso lution For the northern hemisphere under normal conditions the different TEC maps agree with the IGS mean by about five TEC units or less At the equator and for south ern latitudes the situation is still more problematic because of poor station coverage However the use of regional networks for monitoring regional TEC behavior is being investigated eg for South America Fedrizzi et al 2001 The IGS is preparing for the establishment of an independent IGS ionospheric model and a nearrealtime service IGS 2002a Residual errors in the ionospheric modeling are cancelled out for the most part through relative observations at two stations over short distances since the satellites are observed through nearly the same atmosphere The remaining error for single frequency equipment is estimated to be 1 to 2 ppm of the interstation distance corre sponding to 1 to 2 cm over 10 km Campbell et al 1984 These numbers are valid for a quiet ionosphere and for observations in midlatitudes only The last periods of high solar activity have demonstrated that the residual error can be significantly larger It is hence advisable to use only dual frequency equipment for high precision application Irregularities in Earths ionosphere can produce shortterm signal variations in amplitude and phase egWanninger 1992 1994 Langley 2000a These scintillation effects mainlyoccurinabeltof30degreeseithersideofEarthsgeomagneticequator and in the polar auroral zones see Fig 752 A very high electron content only occurs in equatorial regions Figure 752 Regions of the world with high ionospheric activity 314 7 The Global Positioning System GPS Equatorial scintillation effects have their maximum typically from approximately one hour after local sunset until approximately midnight Klobuchar 1991 Scintil lation effects are less significant from April through August in the American African and Indian longitude regions but maximize in the Pacific region From September through March the situation is reversed Scintillation effects may cause a large number of cycle slips because the receiver cannot follow the shortterm signal variations and fading periods A very high electron content produces strong horizontal gradients and corrupts the ambiguity solution with the geometrical method even over short distances because the ionospheric signal cf 7321 overlaps even the wide lane wavelength within a few minutes of observation time Wanninger Jahn 1991 Wanninger 1994 In such situations the only reli able possibility of ambiguity resolution so far found is the codecarrier combination 7323 using data from lowcodenoise receivers Ionospheric effects are visible in double difference phase observations even over short distances Relative errors up to 30 ppm have been observed in single frequency baseline determination over 10 km in Brazil Campos et al 1989 At times ionospheric perturbations also occur in midlatitude regions Wanninger 1992 1994 In particular socalled Medium Scale Travelling Ionospheric Distur bances MSTIDs may generate serious problems for precise relative positioning in mean latitudes when the observation time is short 20 minutes In the short term the situation will improve because the current sunspot cycle is now in the declining phase with a minimum expected in 2006 As additional GPS frequencies become available as part of the GPS Modernization Program multi frequency receivers will enter the market so that the local ionospheric delay can be directly measured and eliminated 7442 Tropospheric Propagation Effects The tropospheric propagation delay is critical for precise position and baseline deter mination in particular in the height component because the tropospheric parameters are only poorly correlated over larger distances Furthermore it is difficult to separate error components stemming from the radial orbital errors signal propagation errors clock errors antenna phase center variation and errors in the station height This is one of the reasons why the height component is much worse than the horizontal components in precise GPS positioning For frequencies in the radio spectrum 23 the tropospheric delay is independent of the frequency hence it cannot be determined from dualband measurements The near surface atmospheric structure has to be adequately modeled Either mean atmospheric parameters or measured data on temperature atmospheric pressure and water vapor content along the signal propagation path must be included in the model Some of the currently accepted models are dealt with at length in 2332 For further information see also Mendes Langley 1994 1999 Spilker 1996d Langley 1998b Usually theinfluenceoftheneutralatmosphereonrangemeasurementstosatellites in the radio frequency domain is expressed by two integral terms the dry component 74 Error Budget and Corrections 315 and the wet component The wet component depends on the distribution of water vapor in the atmosphere and is therefore harder to model The wet portion however comprises only 10 of total tropospheric refraction The total delay in the zenith direction comes to about 23 m and increases near the horizon 10 elevation to about 20 m The dry component is precisely described with an accuracy of 1 by the available models The wet delay can be modeled depending on the atmospheric conditions with an accuracy no better than 1 to 2 cm Langley 1998b Most studies conclude that none of the available models has a clear priority over the others For low elevation angles the Niell model Niell 1996 is usually preferred eg Hay 2000 This is of particular relevance because the observation of low satellites down to 5 elevation is essential in precise GPS height determinations Dach 1999 7623 The Niell mapping function is of the Marini type 2116 and uses coefficients depending on latitude and season For details see also Schüler 2001 p 157ff If the stations are close together the tropospheric residual error almost completely disappears by differencing in the relative observation mode It is hence not advisable to introduce the observed meteorological data separately for each station into the ad justment of a small network in nonmountainous regions The local measurements usually do not represent the regional atmospheric situation with sufficient rigor and hence introduce biases into the solution Instead appropriate identical standard atmo spheric parameters should be used for all stations In this respect it is of interest that the Niell dry and wet functions are completely independent of surface meteorological measurements When station distances are greater say 50 km or when the height differences are larger in mountainous regions atmospheric conditions are no longer sufficiently correlated with one another Adequate modeling hence is of growing importance in particular for precise DGPS or WADGPS applications eg Collins Langley 1999 75 One way of determining the water vapor content of the atmosphere along the propagation path is direct measurement with water vapor radiometers eg Nothnagel 2000 The instruments are however very elaborate and expensive and can only be used for major tasks cf 2332 Another approach is to introduce a station dependent zenith scale factor for each satellite pass This parameter can only be estimated reliably after an observation time of 15 to 2 hours To allow for the time variable behavior of the tropospheric zenith delay stochastic modeling has been successfully applied eg Völksen 2000 Another option is elevationdependent weighting Rothacher et al 1998 In global networks the introduction of a scale factor is selfcalibrating because mismodeling in the atmospheric delay would produce a scalefactor and hence result in mismodeling of the orbits and in a violation of orbital mechanics Nothnagel 2000 A very successful approach is realtime monitoring of the tropospheric effects in active multiple reference station networks and the immediate correction of user positions 753 Along with the Accuracy Improvement Initiative 717 enhanced orbital data can be expected when new tropospheric mapping functions will be applied 318 7 The Global Positioning System GPS a Observation design Several measures and actions are possible select sites carefully avoid nearby reflectors use antenna ground plane to avoid reflections from the ground deploy absorbing material on the ground select carefully designed antennas eg choke ring antennas and use multiple antenna arrays or controlled antenna motion to average out the multipath variation near the antenna One particular procedure is to observe sidereal differences Since the satellite geom etry repeats after 24 hours of sidereal time 23h 56min UT the multipath effect for a given site also repeats By forming sidereal differences between the observables for example double differences DD at two consecutive days it is hence possible to generate multipath free observables DDSid These can for example be used for the absolute calibration of antennas 7451 and also for highly precise control measure ments Seeber et al 1997a b Receiver and software design A number of methods for reducing multipath effects use realtime signal processing in the receiver For an overview see eg Weill 1997 The basic idea is to use particular signal properties for improving the correlation process GPS signals are lefthand polarized Reflected signals change their polarization and hence can be detected in the receiver Reflected signals also arrive later at the antenna and hence can be discriminated The various techniques have been given names like narrow correlator strobe correlator correlation function Everest technology and so on Usually the details are not revealed by the manufacturers some basic concepts however are published mostly in the IONGPS Proceedings c Station calibration A rather new idea is to calibrate stations in particular reference stations for multipath effects A first step is the detection of multipath Several techniques are possible In Moving Robot Static Station Figure 755 Calibration of a reference station for multipath double differences over short baselines most errors are eliminated The remain ing residuals mainly contain the mul tipath differences However it is not possible to separate between the partic ipating stations Multipath effects are also visible in the signaltonoise ratio SNR The signal strength varies in a sinusoidal form depending on the multi path Finally the inspection of sidereal differences helps to analyze the variation of multipath effects A method for the absolute field cal ibration of multipath has recently been 74 Error Budget and Corrections 319 reported Böder et al 2001 One prerequisite is the availability of absolute calibrated antennas because otherwise the multipath cannot be separated from the antenna phase center variations 7451 The basic idea of this method is to decorrelate the multipath through controlled motion of a robot Fig 755 The robot operates near the station to be calibrated The fixed station senses the complete multipath The moving station eliminates the multipath through the controlled motion In the double differences only the multipath effects for the fixed station are present and can be described in a functional model eg with spherical harmonics Multipath effects at satellites have been reported but seem to be less critical Young et al 1985 7444 Further Propagation Effects Diffraction and Signal Interference Two main influences have to be considered signal diffraction and signal interference GPS signal diffraction comes about when the direct GPS signal is obstructed but a diffracted signal is received Fig 756 explains the geometric situation Following Obstacle Satellite B A C D Figure 756 Signal propagation near an obsta cle after Walker Kubik 1996 Walker Kubik 1996 we distinguish the regions A B C and D In A B C we have direct reception of the GPS signals In addition we may expect in A reflected signals from the ground in front of the obstacle and from the obstacle B only little or no reflection and C reflection from the ground behind the obstacle In region D from the laws of geometri cal optics we have no signal reception except for signals diffracted at the ob stacle The increased signal path of the diffracted signal may produce a phase er ror of up to several centimeters or even decimeters The effect can hence be considered as one of the dominant error sources in rapid static or kinematic GPS positioning Wanninger 2000 A powerful means for the detection of diffracted signals is inspection of the signal tonoise ratio SNRA proper weighting of the undifferenced phase observables based on the SNR values can be used for minimizing the diffraction effect on coordinate estimates Interferences with artificial signals from HFtransmitters occur for frequencies in or near the bandwidths of the GPS signals The reason is that GPS signals are not transmitted at a discrete frequency but due to the code modulation they are spread over a certain bandwidth namely 2046 MHz for the CAcode and 2046 MHz for the Pcode spread spectrum technique see 714 The effect of disturbances from signals at nearby frequencies can be minimized by adequate filter technology however 320 7 The Global Positioning System GPS it cannot completely be avoided The effects on GPS signals for strong disturbances are decreased SNR level more difficult or impossible acquisition of the GPS signal and loss of signal in phase tracking loop Interferences mainly occur for L2 L1only receivers are usually not affected Modern receivers with enhanced filter technology are better protected than older receiver types Possible sources for signal interferences are VHF UHF TV transmitters with strong radiation power within a distance of 100 to 500 m digipeater directional transmission of amateur radio in Germany just 3 MHz off L2 and radar installations of aviation control services up to 20 km distance The influence of high voltage power cables is small GPS receiver antennas should stay distant by about 10 m as from all other transmitters to avoid direct disturbances Cellular phones seem to have little influence Possible interference with the forth coming ultrawideband technology is under discussion Akos et al 2001 For more details on signal interference with GPS see Johannessen 1997 an excellent review in German is given by Kolb 1999 Aparticulareffectisfoliageattenuationforstationaryandmobileusers Depending on the type of trees and the length of foliage penetration the attenuation can vary significantly A detailed treatment of the subject is given by Spilker 1996a 745 Receiving System The main error sources in the receiving system are antenna phase center variations receiver noise interchannel bias and oscillator instability 7451 Antenna Phase Center Variation Positioning in navigation and geodesy refers to the electrical phase center of the antenna that varies with the intensity and direction of the incident signals For precise applications the phase center positions of all antennas involved in a project have to be known exactly This is of particular importance for determination of the height component because in the GPS adjustment the elevationdependent effects are highly correlated with the height and the tropospheric scale parameter The mechanical center of an antenna is usually defined to submillimeter precision It often coincides with the intersection of the vertical mechanical axis of symmetry and the ground plane Fig 757 The mean electrical phase centers for the L1 and L2 signals may be a few mm off from the mechanical center The antenna reference point ARP is also defined mechanically usually as the intersection of the vertical 74 Error Budget and Corrections 321 mechanical axis with the lowest part of the antenna housing For most antenna types the 3Dcoordinates of the offsets of the L1 and L2 mean electrical phase centers with respect to the ARP are given by the manufacturers The actual electrical phase Mechanical center Antenna reference point Antenna ground plane Phase center variations PCV Mean electrical phase center Figure 757 Antenna phase center variation and reference points center depends on the azimuth and ele vation of the observed satellites The de viations of the actual phase centers from the mean electrical phase center are the phase center variations PCVThey can reach millimeters to a few centimeters If antennas of the same type are used within one observation session over shortbaselines theremainingphasecen ter offsets and variations are eliminated in the differencing process In cases where the phase center variation is az imuth dependent all antennas have to be orientated prior to the survey For this reason some antenna types have an orientation mark directed to magnetic north If different antenna types are involved within the same project as is often the case for precise DGPS with reference stations 751 the observations have to be corrected for the PCV The same is true when identical antennas are used with very large baselines because the satellite signals are observed under different elevation angles due to Earths curvature Note that different antennas of the same type may also show differences in PCV For highest accuracy requirements only calibrated antennas should be used Three major GPS antenna calibration methods are presently available Rothacher 2000a anechoic chamber calibrations relative field calibrations and absolute field calibrations The anechoic chamber calibration Schupler 1994 Schupler Clark 2001 is a laboratorymethod anditisratherseldomappliedbecausenotmanyanechoicchambers exist A GPS antenna is tilted and dislocated with respect to an artificial GPS signal generated in the chamber Absolute PCV are determined under the assumption that they are also valid for observations in the field In relative field calibration the PCV and the mean offset of a specimen antenna is determined with respect to another antenna the reference antenna The PCV of the reference antenna often the Dorne Margolin T choke ring antenna are set to zero or taken as known Both antennas are mounted close together on pillars with very precisely known coordinates The calibration is based on single or double difference residuals The elevation and sometimes azimuthdependent PCV model uses polyno mials or spherical harmonics The method has been widely used to calibrate all major GPS antenna types eg Rothacher et al 1995 Mader 1999 Methods of absolute field calibration have only been developed recently Wübbena et al 1997 Menge Seeber 2000 Wübbena et al 2000 The basic idea is to elim 322 7 The Global Positioning System GPS inate multipath effects by either using sidereal differences between observations on two consecutive days or to use a highprecision robot Fig 758 that rotates and Figure 758 Robot for the absolute field cali bration of GPS antennas tilts at rather high speed the an tenna to be calibrated Observa tions from a nearby stationary ref erence antenna are required to elim inate distance dependent errors the results are however absolute PCVs in dependent on the type of the reference antenna Fig 759 shows one example For details of the method see the cited literature The advantages of absolute PCV val ues from field calibrations when com pared with the traditional techniques are among others they are available in realtime robot technique for L1 L2 GPS GLONASS future GNSS they are independent of a refer ence antenna and reference coor dinates they are free of multipath they cover the whole hemisphere and are independent of the northern hole 7611 they support the absolute calibration of GPS reference stations and they facilitate the separation from other error sources like troposphere and satellite antenna phase center offset 0Ê 45Ê 90Ê 135Ê 180Ê 225Ê 270Ê 315Ê Figure 759 Absolute PCV of a GPS antenna Absolute PCV of modern antennas are mostly below 10 mm but they can also reach much higher values The in fluence on height determination can be severalcentimeters Itishenceadvisable to only use absolutelycalibrated anten nas for active reference stations and for all tasks where high accuracy is required In order to facilitate the use of ref erence data a zeroantenna can be in troduced ie an antenna where all ob servations are corrected for the PCVThe rover then only has to apply its own PCV corrections AparticularRINEXformat ANTEX for the distribution of antenna PCV information has been developed IGS 2002b 74 Error Budget and Corrections 323 At some sites it is advisable to protect the antenna setup with a radome against hostile environmental influences Such radomes may change the antenna PCV charac teristics hence the antennas have to be calibrated together with the radome Kaniuth Stuber 1999 Schupler Clark 2001 Note that the azimuth dependent variation of PCV can also be used viceversa to determine the orientation of the antenna and of the related platform Tetewsky Mullen 1997 The resolution however is only in the order of several degrees With an absolutely calibrated reference antenna at hand it is also possible to calibrate satellite antennas A first result has been reported for the Block IIa satellites Mader Czopek 2002 7452 Other Error Sources Related to the Receiving System The receiver noise results from the fact that GPS phase and code observables cannot be measured perfectly but are subject to random influences For example the obser vations are affected by unwanted disturbances in the antenna amplifiers cables and the receiver itself For details see eg Langley 1997b As a rule of thumb the observation resolution for classical receivers is about 1 of the signal wavelength For the GPS signals we obtain CAcode λ 300 m noise 3 m Pcode λ 30 m noise 30 cm and carrier λ 20 cm noise 2 mm Modern receiver technology tends to bring the internal phase noise below 1 mm and to reduce the coderesolution to the 10 centimeter level 7242 Low noise code measurements are important for realtime ambiguity resolution Multichannel receivers exhibit different signal propagation delays for each hard ware channel since each satellite signal travels along a different electronic path The instrument makers try to calibrate and to compensate these interchannel biases Mul tiplexing and software receivers 721 725 are free of interchannel biases It is recommended that parameters for satellite and receiver hardware delays are included in the parameter estimation models in particular if the concept of original undifferenced phase data is used cf 7322 Oscillator instabilities play only a minor role in carefully designed receivers be cause the timing signal is taken from the satellite clock They can be modeled in the adjustment process For highest accuracy requirements and in precise navigation the use of external precision oscillators rubidium or cesium is recommended Further error sources that can be counted to the receiving system are the stability of the station ground and of the pillars as well as the quality of the station mark These items are of particular interest in geodynamic networks 746 Further Influences Summary the Issue of Integrity Several more aspects exist that influence the achievable accuracy Among them are the process noise and the tidal upload Process noise means that some liberty exists in 324 7 The Global Positioning System GPS the data analysis approach We can identify softwarenoise theagencyisfreeintheselectionofaparticularsoftwarepackage operator noise the operator is free in the selection of particular options of the software package and reference frame realization noise there exist various possibilities to select a set of fiducial stations eg from the IGS to connect a project with a given reference frame As a consequence a given data set will lead to slightly different results when different operators work with different software packages This is also true for the same package used in different laboratories An impressive example based on the analysis of a 40 dayslong data set from about 50 stations analyzed with 4 different softwarepackages at 7 laboratories is given by Dietrich et al 2001 The mean differences between solutions are 1 cm in horizontal position and 2 cm in height Tidal upload means that GPS stations show a vertical displacement due to the crustal deformation caused by oceanic and solid Earth tides Dach 1999 The effect can reach several centimeters but it is the same over large areas and hence will be cancelled by relative GPS Considering todays high accuracy potential of GPS obser vations corrections for tidal upload should be applied whenever highest accuracy of the results is attempted For details see eg Dach 1999 Zahran 2000 In summary the accuracy achievable with GPS for geodesy surveying and navi gation depends on various conditions for example single or multireceiver operation single or dualfrequency data L2 high quality access under AS available or not receiver noise level static or kinematic positioning realtime or postprocessing results accuracy of orbits used and extent of data modeling Becauseofthemanyoptionsandinfluences andtheeminentprogressinerrormodeling during the last years it is not possible and not meaningful to describe the accuracy potential of GPS with a single distance dependent formula as has frequently been done in the past eg Lichten 1990 The statement of today is that 1 cm accuracy at a global scale over all distances is achievable with appropriate instruments observation design and data analysis models For selected examples see the section on applications 762 A major issue when using GPS in navigation is the integrity of the system For navigational purposes integrity is defined as the ability of a system to provide timely warnings to users when the system should not be used Brown 1990 The timely warning is in particular required for the navigation of civil aircraft The GPS control segment does not provide sufficient warning when a component of the system fails Different solutions to the problem have been discussed With internal methods of integrity monitoring GPS integrity is achieved using information available inside the receiver such as redundant measurements to additional satellites This technique is 75 Differential GPS and Permanent Reference Networks 325 known as receiver autonomous integrity monitoring RAIM Using external methods of integrity monitoring the GPS signals are controlled in realtime through a network of ground monitoring stations The information is broadcast to users through a GPS integrity channel GIC via geostationary satellites such as INMARSAT A further approach to assuring the in tegrity of the GPS navigation solution is possible by integrating GPS data with data from other sensors These can be for example inertial navigation systems LoranC receivers GLONASS and future GALILEO receivers For more information see the discussion in the navigation literature eg the journal Navigation and also 772 A good introduction to the topic of integrity is Langley 1999b 75 Differential GPS and Permanent Reference Networks The absolute position determination with GPS is in general much less accurate than relative positioning between two stations This is due to the fact that most of the acting errors biases are highly correlated Error sources can be grouped into three categories 74 1 errors decorrelated with distance 2 errors decorrelated with time and 3 uncorrelated errors Errors of type 1 mainly ephemeris and propagation errors are nearly the same for neighboring stations as long as they are sufficiently close and hence disappear in the differences Errors of type 2 are coped with by synchronized or nearly simultaneous observations Errors of type 3 affect both participating stations and need a calibration To minimize the effect of errors of type 1 instead of absolute coordinates coor dinate differences are determined with respect to a known reference station Several concepts are in use the basic strategies are a use of the data of one or more reference stations for postprocessing b use of corrections in position or range from code observations at the reference station in realtime c use of coderange and carrier phase data from the reference station in realtime and d use of reference data from a network of reference stations in realtime The option a is often referred to as relative GPS whereas options b through d are called Differential GPS DGPS with different attributes Option b is ordinary DGPS in its proper sense whereas option c is called precise DGPS PDGPS or also RealTime Kinematic RTK GPS Option d is known as the concept of Multiple Reference Stations Networked Reference Stations or also Network RTK The wording in general is not uniform In this book the term relative GPS is used in a general sense including all concepts where data from more than one station are processed simultaneously either in postprocessing or in realtime The term Differential GPS means that processing of data from more than one station is performed in realtime or near realtime Usually 75 Differential GPS and Permanent Reference Networks 327 kilometers about the reference station Due to decorrelation of the biases with distance orbit ionospheric and tropospheric delay the accuracy decreases roughly by about 1 m per 100 km Option iii is the most flexible procedure and allows the use of DGPS over larger distances Wide Area Differential GPS WADGPS and for precise applications in surveying and geodesy networked reference stations It is explained in more detail in section 753 Whereas option ii is based on observed pseudorange corrections scalar corrections option iii is based on correction vectors Several more classifications of DGPS are in use Following the achievable accuracy we have Ordinary DGPS with code range corrections accuracy 1 to 3 m depending on the distance from the reference station Carrier smoothed DGPS at the rover station the carrier observations are used to smooth the coarse code observations with a suitable filter cf 7108 without solving for ambiguities The achievable accuracy is 05 m Precise DGPS PDGPS carrier phase observations or carrier phase corrections from the reference station are transmitted to the rover and are used to resolve ambi guities This procedure is identical to the Real Time Kinematic RTK see 752 Fig 761 shows the accuracy potential of the different options Figure 761 Accuracy potential with different modes of DGPS Another classification is into Local Area DGPS LADGPS Wide Area DGPS WADGPS and Carrier Phase DGPS CDGPS or precise DGPS PDGPS Local Area DGPS LADGPS corresponds to the procedures a and b above In option b a scalar correction to codephase measurements is applied for each satellite The corrections are used for areas up to 1000 km radius However with the de activation of SA single receiver accuracy meets the same level of accuracy as DGPS 328 7 The Global Positioning System GPS for distances larger than several hundreds of kilometers In LADGPS corrections of all the different error influences are put together in one value If more than one reference station provides corrections they can be weighted to form a mean value Wide Area DGPS WADGPS uses vector corrections for each satellite derived from observations in a continental or global network of reference stations The concept corresponds to option c The vector consists of individual corrections for the satellite clock satellite position and ionospheric delay model Compared to a scalar correction a vector correction is valid over much greater areas Parkinson Enge 1996 The concept is discussed in more detail in 7531 CarrierPhaseDGPS CDGPSisusedforsurveyingapplicationsseeRTK752 and also for attitude control of vehicles 7627 The basic model of the ordinary DGPS concept with code phases is as follows cf Misra Enge 2001 Starting from equation 744 we find expressions for the observed pseudoranges at the user station PRu and at the reference station PRr PRu Ru c dtu dT d IONu d Tropu d Eph εPRu 7150 PRr Rr c dtr dT d IONr d Tropr d Eph εPRr 7151 with dtu dtr the receiver clock errors dT the satellite clock error with respect to GPS system time d IONu d IONr the ionospheric delays d Tropu d Tropr the tropospheric delays and d Ephu d Ephr the effect of the ephemeris error at both stations The geometric range Rr xs xr 7152 is calculated from the known satellite position from broadcast ephemerides and the predetermined position of the reference station Any variation with time in the above equations has been neglected for simplicity The error in the pseudorange observation at the reference station the Differential Correction DC is given by DC Rr PRr c dtr dT d IONr d Tropr d Ephhr εPRr 7153 In addition to DC also the range rate of the correction the Differential Correction Rate DCR is being determined and transmitted DC and DCR refer to a reference epoch tk they arrive at the user station with a certain delay or latency Latency is hence defined as the elapsed time from the epoch of the measurement at the reference station until the use of the correction at the remote user site At the user station the corrections are predicted for the actual observation epoch t as DCt DCtk DCR t tk 7154 The prediction of DC was critical with activated SA because its changes with time were rather large Today a latency of up to 10 seconds would not be harmful Typical 330 7 The Global Positioning System GPS provides pseudorange and range rate corrections and is sufficient for ordinary DGPS b with an accuracy level of few meters or better All necessary information can be transmitted with a bandwidth of 1200 bps bits per second or less Depending on data rate and number of satellites the required bandwidth can be reduced to 100 bps Version RTCM 21 from January 1994 additionally includes carrier phase data and hence provides the possibility to resolve ambiguities at the rover station This version is the required standard for PDGPS and RTK The necessary data rate is at least 4800 bps Version RTCM 22 from January 1998 includes still further information in particular the option to transmit correction data from more GNSS systems eg GLONASS Version RTCM 23 from May 2001 is a further refinement allowing for example antenna phase center variation PCV data to be included A new version RTCM 30 is under discussion and will include capabilities for network RTK The RTCM message format is very similar to the format of the GPS navigation message The messages consist of 30bit words Each word consists of 24 databits and 6 parity bits Each message starts with a twoword header containing information such as the reference station identification the message type and a reference time for the parameters In total 64 message types are reserved the majority not yet defined Table 716 shows some of the message types valid in RTCM 23 For detailed information see eg Parkinson Enge 1996 Kaplan 1996 HofmannWellenhof et al 2001 or the official document of the RTCM Special Commission 104 RTCM 2001 Table 716 Selection of message types in the RTCM 23 format Message type Current Title number status 1 Fixed Differential GPS Correction 2 Fixed Delta Differential Corrections 3 Fixed Reference Station Parameters 18 Fixed RTK Uncorrected Carrier Phases 19 Fixed RTK Uncorrected Pseudoranges 20 Fixed RTK Carrier Phase Corrections 21 Fixed RTK High precision Pseudorange Corrections 31 Tentative Differential GLONASS Corrections 32 Tentative Differential GLONASS Reference Station Parameters 37 Tentative GNSS System Time Offset 59 Fixed User Defined For precise DGPS either message types 1819 or 2021 can be used One advantage of types 2021 is a higher compressibility when compared with the raw carrier data 1819 Proprietary formats have been developed to transmit compressed and possibly decoded corrections together with other information in the user defined message type 75 Differential GPS and Permanent Reference Networks 331 59 This compression allows the transfer of reference data for all satellites in view up to 12 SVs with a bandwidth of just 2400 bps Wübbena et al 1996 The possible data links for the transmission of DGPS data may be categorized as follows groundbased radio links cellular phones satellite communication and internet For groundbased radio links there exists a set of general rules the lower the frequency the larger the range the higher the frequency the higher the bandwidth and data rate and high frequency and short range installations are cheaper than low frequency and long range installations In the Low Frequency LF domain 300 KHz data can be transmitted over several hundred kilometers because the waves follow Earths curvature One example in Germany is the system ALF Accurate Positioning by Low Frequency where one transmitter near Frankfurt covers all of Germany and beyond 600 to 800 km with DGPS data at a rate of 3 seconds Medium frequency MF 300 KHz3 MHz transmitters are cheaper than LF trans mitters and also cover several hundred kilometers They are often used as marine radio beacons in coastal areas The data capacity is sufficient for ordinary DGPS services several meters accuracy Very High Frequency VHF 30300 MHz and Ultra High Frequency UHF 3003000 MHz radios can communicate over short distances limited by the line of sight The data capacity is in the range of 2400 bps and hence suffices for PDGPS with a compressed data transmission format see above A further possibility is to use a frequency modulation subcarrier in the radio data system RDS from broadcasting services The capacity is then in the order of 100 bps which is sufficient for ordinary DGPS Mobile UHF radio systems operating at 400 MHz and higher have a range of several kilometers depending on their power and can transmit 9600 bps which is sufficient for RTK applications A frequentlyused wavelength is 70 cm 428 MHz which for example at low power 025 W can be operated without permission in Germany Cellularphoneisspreadingacrossdenselypopulatedareastoprovidetelephoneand data services With decreasing user fees cellular phones are an attractive alternative to radio frequencies One disadvantage however is that with cellular phones the number of simultaneous users is limited by the number of modems at the reference station whereas the broadcast system works for an unlimited number of users Globallyoperating DGPS services use geostationary communication satellites like INMARSAT or a network of Low Earth Orbiters like Globalstar to transfer DGPS data The DGPS corrections provide accuracies at the fewmeters level Some of the services use the WADGPS concept 7531 The capacity of INMARSAT also offers PDGPS applications 332 7 The Global Positioning System GPS A very powerful technique is the distribution of DGPS data via Internet GPS data from global or regional permanent arrays like the IGS or EUREF networks are already available in the RINEX format on a routine basis de Jong 2001 Since quite recently data for realtime applications are also accessible via internet The JPL is building up an InternetBased Global Differential GPS System Muellerschoen et al 2000 Regional and local RTK services via Internet are under development Weber 2002 Table 717 gives an overview on some DGPS data channels Table 717 Frequently used data links for DGPS transmission Name User Range Capacity Type radio 2 m unlimited tens of km 2400 bps PDGPS radio 70 cm unlimited few km 9600 bps PDGPS radio LF unlimited hundreds of km 300 bps DGPS radio MF unlimited hundreds of km 100 bps DGPS radio UHFRDS unlimited tens of km 100 bps DGPS satellite unlimited global 2400 bps DGPS mobile phone 1 per channel variable 9600 bps PDGPS internet unlimited global 9600 bps PDGPS 7513 Examples of Services During the last years a large number of GPS reference station services with different architecture and performance has appeared We can distinguish between global re gional national and particular services as well as between public and commercial or postprocessing and realtime services In the following some examples are given The most important global reference network is maintained by the International GPS Service IGS 7432781 a nongovernmental scientific organization More than 300 stations worldwide are continuously operating and provide among other products information on position and observation data via regional and global data centers The IGS network Fig 7101 p 399 is closely related to the ITRF reference frame 2122 hence it is possible to connect new GPS observations everywhere in the world directly to the ITRF The IGS stations generally do not transmit DGPS data in realtime The IGS is a passive global reference network mainly used for postprocessing purposes Another global service under development is the Global Differential GPS System GDGPS of the NASA JPL Bertiger et al 1999 Muellerschoen et al 2001 Based on observations from about 60 stations in the NASA global network state parameters are modeled and provided to users via Internet The quasi realtime accuracy is esti mated to be 10 cm for the horizontal position and 20 cm in height with a latency of about 15 to 3 seconds The GDGPS approach belongs to option iii in 7511 see also 753 Examples of global commercial services are Skyfix and Omnistar Skyfix maintains a network of about 80 reference stations within the reference frame ITRF92 Correc 75 Differential GPS and Permanent Reference Networks 333 tion data in the RTCM 20 format are transmitted via INMARSAT communication satellites The achievable accuracy is about 2 m Omnistar runs about 70 reference stations covering about 95 of the world The correction data are distributed via 9 different geostationary satellites also in the RTCM 20 format and submeter accuracy is promised Both services apply some state space modeling 753 in order to obtain the indicated accuracy over large distances At the continental level the EUREF Permanent Network Fig 775 p 358 can be considered to be a densification of the IGS in Europe It consists of about 140 status July 2002 permanent stations and has a similar structure to the IGS The main purpose is maintenance and control of the European Reference Frame ETRF 89 2122 Ádám et al 2000 Similar socalled regional networks are operated in other parts of the world For example in South America in the SIRGAS project 762 a permanent network of about 30 stations related to IGS is continuously operated Seemüller Drewes 2000 National networks are being established worldwide Existing maritime radiobea cons are used to broadcast DGPS data in the standard RTCM format to marine users in the LF and MFbands 285325 kHz maritime radiobeacon band with a data rate of 100 to 200 bps Parkinson Enge 1996 Mangs et al 2001 Beacon networks are mainly located along coastlines or large navigable inland waterways but are in some regions also expanded inland In the US the beacon network is the responsibility of the Coastguard There are plans to cover the whole US with about 80 stations in the Nationwide Differential Global Positioning System NDGPS DODDOT 2001a Complete coverage is expected for 2003 In Europe the beacon network nearly covers the complete coastline of the European coastal states see Fig 762 Within the EU ROFIX project tests are underway to use existing Loran C stations for the transmission of DGPS data Helwig et al 1997 The US National Geodetic Survey NGS runs the CORS network CORS stands for Continuously Operating Reference Stations It consists of about 200 stations and is still growing CORS will meet the postprocessing requirements of positioning users by providing code phase and carrier phase observation data in the RINEX format The data are freely accessible via Internet or anonymous ftp Depending on the station the data are recorded at 1 5 15 or 30 seconds intervals For details see Snay 2000 Canada is establishing the Canadian Base Network CNB with a spacing between 200 km and 1000 km depending on the area CNB consists only of pillar monuments and is connected to the Canadian Active Control System CACS CACS basically consists of a number of active stations 14 in 2002 partly remotely controlled The dual frequency pseudorange and carrier phase data are transmitted to a processing center in Ottawa and are being used as a backbone for estimating state vectors in wide area DGPS systems eg the Canadawide Differential GPS CDGPS see 753 In Japan a nationwide GPS control network also named GEONET is being estab lished under the responsibility of the Japanese Geographical Survey Institute GSI The network consist of about 900 sites equipped with dualfrequency GPS receivers and additional sensors like tiltmeters and meteorological stations The spatial density 334 7 The Global Positioning System GPS Spain Portugal Italy France Germany Switzerland Austria Slovania Croatia Serbia Hungary Romania Bosnia Bulgaria Albania Greece Macedonia United Kongdom Ireland Norway Belgium Netherlands Poland Belarus Lithuania Ukraine Estonia Russia Latvia Sweden Finland Denmark Morocco Algeria Tunisia Iceland Slovakia Czech Republic Luxembourg Moldova Figure 762 DGPS Beacons in Europe is very high the mean distance between stations is about 25 to 30 km The primary purpose of the network is the determination of crustal strain for earthquake monitoring and prediction 7622 The stations equally provide reference code and carrier data for surveying purposes both in realtime and for postprocessing In addition the data can be used to map tropospheric zenith delay and to contribute to weather forecasts 7629 In Brazil a continuously growing network of active reference stations the Rede Brasileira de Monitoramento Continuo RBMC coordinated with respect to SIRGAS provides reference data for precise post processing Fortes et al 1997 Relatively dense permanent networks are already running or being established in European countries Examples are SWIPOS in Switzerland SWEPOS in Sweden SATREF in Norway and SAPOS in Germany In Great Britain the Ordnance Sur vey National GPS Network consisting of 30 active stations provides RINEX data via Internet for users who thereby can directly access the national coordinate sys tem Additionally over 1000 passive GPS points are available to support surveying measurements Cruddace 2001 The above examples demonstrate the many activities and different approaches for DGPS services all over the world In the following the SAPOS project in Germany 75 Differential GPS and Permanent Reference Networks 335 will be explained in more detail because it provides a large variety of services SAPOS stands for Satellite Positioning Service and is organized by the German State Surveying Agencies AdV The final objective is to cover the complete area of Germany with a network consisting of about 250 permanent stations at a separation of about 40 to 70 km The rationale behind SAPOS is to provide services to many users who have different requirements concerning accuracy of position results required observation time and coverage SAPOS runs different services providing different accuracy levels namely Hankemeier 1996 EPS RealTime Positioning Service HEPS High Precision RealTime Positioning Service GPPS Geodetic Precise Positioning Service and GHPS Geodetic High Precision Positioning Service EPS is similar to many commercial and national DGPS services and provides an accuracy of 13 m sufficient for a broad variety of navigational applications The correction data are available free of charge via different communication channels HEPS is the principal precise realtime service and it can be used for many ap plications in surveying and GIS including cadaster The position accuracy is between 1 cm and 5 cm and depends on several influences in particular on the behavior of distance dependent errors In order to obtain 1 cm accuracy in realtime over distances larger than a few kilometers it is necessary to model the error state in the working area see 753 For the application of HEPS a special decoder and payment of user fees are required GPPS provides 1 s data from the reference stations for a limited time eg 10 days thereafter the data are reduced to 15 seconds Via mobile phone the data can be transmitted directly to the user in the field for precise near realtime positioning GHPS requires precise ephemerides and is a postprocessing service An overview of the SAPOS services is given in Table 718 Table 718 SAPOS products DGPS Positioning Positioning Data Data Data Service Accuracy Mode Format Transmission Rate EPS 1 3 m Realtime RTCM 20 LF UHF 3 5 s 2 m Band HEPS 1 5 cm Realtime RTCM 21 2 m Band 1 s Modified Cellular Phone GPPS 1 cm Quasi RINEX Cellular phone 1 s Realtime Fixed Phone 15 s Postprocessing Data Network GHPS 1 cm Postprocessing RINEX Data Network 1 s Data Storage 15 s 75 Differential GPS and Permanent Reference Networks 339 It would require a very large number of individual DGPS installations to cover a single country or even a whole continent A solution to this problem is the idea to interconnect several reference stations and to transmit their measurement data in realtime to a central processing station All data are used in a common filter to estimate the error state for the whole area and to separate the error components The state vector can then be applied to improve the corrections for the complete area as a function of the geographic user location resulting in much better accuracy and a much sparser density of reference stations Alternatively as a first step simple interpolation algorithms can be used This concept was developed early on under the name Wide Area Differential GPS WADGPS for the use of coderange measurements in continental networks 7531 Only recently a similar concept has been developed for high precision DGPS using carrier phase data in local regional or national networks The concept is known as Networked Reference Stations Virtual Reference Stations or Area Correction Param eter Approach 7532 Note that the terms are not uniformly used in the literature 7531 Wide Area Differential GPS The term Wide Area Differential GPS WADGPS was coined by C Kee and others in 1991 Kee et al 1999 The basic idea was to establish a sparse network of reference stations over an area as large as the continental US CONUS to provide high quality DGPS corrections to navigation users at land on sea in the air as well as in the near space A WADGPS system consists of see Fig 763 a sparse network of reference stations equipped with dual frequency GPS re ceivers high precision clocks and optional meteorological sensors a master control station that receives all measurements and estimates the differ ential corrections an upload station to broadcast the corrections possibly via GEO satellite to the users and monitor stations to control the system Themainobjectiveistoovercomethedecorrelationofthedistancedependenterrors by using suitable network algorithms An excellent overview of the basic algorithms is given by Mueller 1994 A rough separation is into measurement and statespace domain algorithms Measurement domain algorithms do not estimate the individual error components but form a weighted mean of all corrections from the participating reference stations The weighting scheme may use a distance weighting the nearest station gets the highest weight an elevation angle weighting higher elevation satellites get more weight an age weighting lower latency gets higher weight or other criteria State space domain algorithms try to identify the individual error sources and trans mit the information to the user in a suitable form The components are in particular 340 7 The Global Positioning System GPS GPS GPS GEOS Master Station Monitor Station Figure 763 Architecture of an Wide Area DGPS installation a 3D ephemeris error a satellite clock offset ionospheric delay parameters and tro pospheric parameters User apply this information as a function of their geographical location The measurement domain algorithms are the simplest and hence cheapest solu tions The corrections however are not independent of distance but degrade with growing separation from the center of the network The concept is hence seldom used The statespace domain approach is baseline independent and provides the highest accuracy The error components in the state vector also vary rather slowly so that the data transmission rate can be low For details about the algorithms see also Kee 1996 Kaplan 1996 The advantages of using WADGPS when compared with a single DGPS reference station are obvious coverage can be extended over inaccessible regions like water areas the number of reference stations can be reduced and the biases are nearly or completely distance independent The WADGPS concept has been realized in various services In the US the Federal Aviation Administration FAA is establishing the Wide Area Augmentation System WAAS to meet safetyrelated integrity requirements and to support as well the en route as the precision approach phases of flight FRNP 2001 see also 772 In Europe the European GPS Navigation Overlay System EGNOS has similar objectives 772 The same is true for the Japanese service MSAS All three augmentation systems will be interoperable to provide seamless global coverage In Canada the CanadaWide Differential GPS CDGPS provides accurate differential corrections via communication satellite for the whole country to support positioning and naviga tion at the meter level The service is however not intended for commercial aviation no integrity channel The aforementioned commercial services Skyfix and Omnistar like other global or regional commercial services also apply the WADGPS concept The approach of 75 Differential GPS and Permanent Reference Networks 341 Omnistar is very similar to the idea of virtual reference stations VRS see 7532 7532 High Precision Networked Reference Stations With the installation of reference stations providing carrier phase data for precise DGPS applications in realtime eg SAPOS in Germany 7513 the problem of distance dependent errors became evident When 1 cm accuracy is required the number of reference stations with the necessary density would be unrealistically high in particular during periods of strong ionospheric disturbances A solution to the problem comes from interconnection of the reference stations and the estimation of the error state in the working area in realtime statespace domain approach option iii in 7511 Fig 764 demonstrates the problem and its solution For ordinary baseline RTK without network the achievable accuracy decreases with increasing distance at the same time the TTFA increases In the networked solution the error state in the area is estimated and transmitted to the rover where the measurements can be corrected accordingly As a result the accuracy and the TTFA remain at a constant level independent from the distance Accuracy cm 1 2 3 TTFA min 5 10 15 20 25 km 1 2 3 5 10 15 20 25 km without Network with Network with Network without Network Figure 764 Modelling the distance dependent errors in an interconnected reference network ThecurrentdataformatsforDGPScorrectionsdonotallowtotransmitthecomplete state vector to the roving station hence the state vector needs to be represented by a simplified model The basic idea of this approach is as follows Wübbena Willgalis 2001 The observation equation for carrier phase observations between the antenna phase centers of satellite i and receiver j is PRi j Ri j δBi j λNi j εi j 7161 The equation can be written for each particular signal s the index s is omitted for clarity The bias term δBi j comprises the terms δCi j for clock related errors δDi j for distant dependent errors and δSi j for station dependent errors 342 7 The Global Positioning System GPS hence δBi j δCi j δDi j δSi j 7162 The clock related errors δCi j contain components originating in the satellite and the receiver clock and signal delays in the hardware of the satellite and the receiver The distance dependent errors δDi j are composed of the ionospheric delay δI i j the tropospheric delay δT i j and the orbit error vector δoi hence δDi j δI i j δT i j Ri j Ri jδoi 7163 The station dependent errors δSi j finally are composed of multipath and receiver antenna phase center variation PCV For completeness multipath and PCV at the satellite antenna can be included Precise positioning with carrier phases requires the correct determination of the phase ambiguities N As has been outlined in 732 two approaches are possible parameter elimination and parameter estimation In the parameter estimation approach all biases have to be estimated together with the coordinates and ambiguity terms The parameter estimation procedure with undiffer encedobservableshassomeadvantageswhencomparedwiththeparameterelimination process for example see also 7322 biases can be constrained by specific models precise clock models can be used absolute information is maintained more flexibility with changes in network design and different receiver types and different GNSS signals can be adapted more easily It is obvious that the parameter estimation concept is particularly well suited to be used in the state space approach because all biases can be separately modeled and the distancedependent biases can be applied as corrections Table 717 gives an overview of possible functional and stochastic models for the above mentioned error sources Once all state parameters are estimated with sufficient accuracy they can be trans mitted to the user who can eliminate the corresponding error terms from the obser vation equation As a result precise absolute coordinates for the user antenna can be determined This is basically the approach for precise point positioning PPP in global and regional networks see eg 734 and Muellerschoen et al 2001 For operational multistation networks for the time being a simplified state representation is used instead of the complete state vector In a first step a network solution with ambiguity fixing is established for the partici pating reference stations and all states are properly estimated The measured ranges at the reference stations are filtered using the state space model of the network The dif ferences between filtered and computed ranges for all satellites give residuals which 75 Differential GPS and Permanent Reference Networks 343 Table 719 Functional and stochastic description of GPS error sources afterWübbena Willgalis 2001 Bias Functional Model Stochastic Model Satellite clock 2nd order polynomial white noise process Signal delay SV constant white noise process Satellite orbit Cartesian elements 3D GaussMarkov process Ionospheric delay single layer model 3D GaussMarkov process Tropospheric delay modified Hopfield model 2 scaling parameterstation Receiver clock offset white noise process Signal delay rcv constant white noise process Satellite PCV Receiver PCV calibration Multipath rcv elevation dependent 1st order GaussMarkov weighting process Measurement noise white noise process Carrier phase ambiguity constant after fixing are separated into ionospheric orbit and tropospheric residuals This separation is pos sible because of the proper state estimation In some cases the orbit and tropospheric residuals are combined as geometrical residuals In a second step the residuals are interpolated between the reference stations Fig 765 demonstrates that a rover experiences an error δ1 by using the range cor rection ε1 only and an error δ2 by using the range correction ε2 With a linear interpolation between the reference stations RS1 and RS2 the interpolation error is just δε Investigations show that up to distances of 100 km a linear representation is sufficient Larger spacing between reference stations requires use of a polynomial of 2nd or higher order depending on the spatial decorrelation characteristics of the particular error sources From the various proposals of how to correct the measurements at the rover station two frequently applied procedures are the concepts of Area Correction Parameters ACP and Virtual Reference Stations VRS The interpolation between two stations as in Fig 765 only models the errors along one baseline For three reference stations the state residuals can be represented by a plane Fig 766 For each epoch the time variable parameters aϕt and aλt describing the inclination of the plane are determined The parameters aϕt and aλt are called area correction parameters ACP They are estimated at a rather slow rate of about 10 seconds separately for the two distance dependent error components the ionospheric component and the geometric component and transmitted in addition to the conventional PDGPS range corrections eg RTCM 21 from the reference station 76 Applications 345 Figure 767 Concept of precise realtime positioning in an interconnected network The concept of multiple reference stations for precise positioning in realtime is already applied in some areas for example in Germany within the SAPOS service 7513 Jahn Winter 2002 Other developments are reported in Vollath et al 2000 or Raquet Lachapelle 2001 In total however development is still in its early stages A next step will be the unification of existing networks and an extension of services Wübbena et al 2001b Wübbena 2002 Global state parameters orbit global ionosphere and troposphere can be taken from global networks like the IGS and introduced into the state modeling of regional or local networks The same is true for a combination of sparse national and dense regional networks The state parameters of the national network including solved ambiguities are forwarded to regional or local networks that are only established in more densely populated areas This concept of an adapted PDGPS network is in particular suitable for large countries where a uniform dense coverage is neither feasible nor required Willgalis et al 2002 76 Applications 761 Planning and Realization of GPS Observation In the early days of GPS the planning and execution of field projects resembled in many aspects the execution of Doppler projects with TRANSIT 66 Experience gained in the preparation organization and execution of Doppler projects could be transferred for the most part to GPS work and has influenced GPS practice It is hence of interest to study chapter 6 and to read some of the original TRANSIT publications Due to the much broader field of applications however the issue of 76 Applications 347 From the almanac data the current position vectors of the satellites can be cal culated in the CTS coordinate system using the formulas in 7153 With known Figure 768 Visibility diagram Sky Plot 4 hour period for Washington DC approximate absolute coordinates ϕ λ h of the observation site the satellites azimuth and elevation can be found as a function of time with standard formulas and used for the construction of visibility diagrams A corresponding visibility diagram in stereographic projection sky plot is shown in Fig 768 The related bar diagram is given in Fig 715 p 231 The sky plot shows a certain lack of symmetry in the distribution of satel lite tracks This comes from the fact that the inclination of the GPS orbits is 55 and hence defines an area of the ob servers sky shadow area where it will not be possible to make observations The shadow area is a function of the observers latitude and is equal for any longitude Fig 769 gives an example for equatorial polar and midlatitude ob servers Santerre 1991 For observers at northern midlatitudes the shadow area is also called the northern hole 30 30 225 225 225 o o o o o o o o o o o o o o o o 135 135 135 315 315 315 45 45 45 60 60 60 o S S S W W W E E E N N N ϕ 45 ϕ 0 ϕ 90 o o o Figure 769 Shadow area as a function of the observers geographic location Additional information for planning purposes is given by the computation of PDOP values that reflect the geometrical strength of the satellite configuration 742 As long as the complete satellite coverage had not yet been installed the PDOP values indicated the best time periods for observations observation window With the current status of GPS the importance of the PDOP criterion should not be overemphasized most 348 7 The Global Positioning System GPS geodetic receivers can track all visible satellites and do not require any preselection whilst for most geodetic applications the observation period is long enough to average out the influence of geometry With the full GPS constellation the PDOP is sufficiently low for most of the day Hence the PDOP criterion is of interest only for navigational purposes kinematic surveying and applications with satellites obscured by obstructions The necessary length of observation depends on the purpose of the survey the instrument type the desired accuracy the software capacity and logistic aspects The basic requirement for precise surveys is the resolution of phase ambiguities Once the ambiguities are resolved the observations can be finished Over short distances up to 10 km with sufficient satellites six or more dual frequency receivers and advanced software this period can be as short as a few minutes or even less 7323 In kinematic surveying the few centimeter level can be achieved continuously see 752 Over larger distances and under difficult environmental conditions such as iono spheric disturbances multipath several hours of observations are required to obtain a precise ambiguity float solution 7323 For the establishment of national or conti nental fundamental networks and for geodynamic purposes the observations can last 24 hours or even several days to average out orbital meteorological multipath and other timevariable effects Under difficult logistical conditions eg in areas with difficult access it is advis able to increase the usual observation time in order to avoid the need for reoccupation of sites in cases of poor data Hence the following observation scenarios can be dis tinguished 24 hours up to several days fundamental networks geodynamics several hours highest accuracy over larger distances or under difficult conditions 15 to 30 minutes control surveys with short distances up to 10 km and continuous measurements rapid methods and navigation With the installation of permanent networks and dense arrays of GPS receivers contin uous reference observations are available for many tasks The number of specifically organized GPSprojects will decrease Most observations in applied geodesy and surveying will be done with respect to existing reference stations or networks 7612 Practical Aspects in Field Observations Advance local reconnaissance can be essential for successful observations The obser vation sites should have unobstructed visibility and should be accessible to vehicles As a general rule a free line of sight down to the horizon is required in all directions In forested areas or near buildings a satellite visibility diagram sky plot cf Fig 768 helps in the site selection However if the sites are to remain usable for later observations with other satellite constellations it is recommended that the horizon be generally open at least down to a 10 angle of elevation Note that for precise 76 Applications 349 height determination observations down to 5 are advantageous 7623 Existing obstructions should be documented in the reconnaissance sheet in a shadow diagram Fig 770 225 15 25 35 135 315 45 o o o o o o o N dense trees two trees power line wooden pole building Figure 770 Shadow diagram indicating ob structions with elevations 10 The GPS technique requires and per mits selection criteria other than those of classical triangulation techniques Con trol points no longer have to be installed on topographic elevations or towers with mutual station intervisibility but rather where ever they are needed on eas ily accessible sites with a minimally obstructed horizon Also places near high buildings towers power lines and transmitting antennas are not suitable Nearby walls or other reflecting surfaces can cause multipath effects 7443 In wooded areas the antennas can be mounted on light masts In the case of noncentric observations however cen tering and plumbing must be done with the same accuracy with which the GPS mea surements can be evaluated that is centimeters to millimeters Note that eccentricity calculations have to be done in the 3D space cf 217 In the interest of convenient future use for topographic and surveying purposes points should be selected where centric observations can be made In many cases the followup surveying is done with conventional equipment for example with electronic tacheometers Points should be selected such that either a free sight is available to a nearby surveying mark or an intervisible second GPS point has to be installed a few hundred meters away The monumentation of station marks usually follows the general rules of the re sponsible surveying and mapping authorities Regarding the high accuracy potential of GPS the monuments should be established on stable ground if possible on rock or concrete blocks with sufficiently deep foundation The station marker should be defined to at least 1 mm for example with a fine grid mark on a corrosionresistant metallic rivet In such cases the GPS stations can also be used for control purposes and engineering surveying In addition the station markers should be suitable as an exact vertical reference The central survey marker is usually controlled by eccentric reference marks All essential information should be documented in a reconnaissance sheet Possi ble elements are station name and identification code description of site approximate coordinates and height accessibility car road conditions walking distance necessary antenna height tripod mast 350 7 The Global Positioning System GPS orientation marks and shadow diagram Power supply is no longer a major problem in practical field work as it was for older receiver types such as the TI 4100 7241 Modern instruments have a very low power consumption Internal batteries usually last for a whole working day or even longer For security reasons it is advisable to recharge batteries every other day Whereas older receivers could only be operated by skilled people modern receivers work completely automatically Dialogue with the receiver is possible but not required in standard operation Usually all visible satellites are tracked and no preselection or change of constellation is necessary The personnel should be able to carefully mount the tripod on the station mark measure the antenna height control the receiver operation work according to a given time schedule run the station control sheet station log and measure additional data if required meteorological data eccentric elements In most projects the measured GPS data have to be stored on suitable recording mediaforsubsequentcomputation egformultistationadjustments Modernreceivers havebuiltinsolidstatememories orpluginmemorycards Dependingonthememory capacity and the amount of data the recorded measurements have to be downloaded to a computer once a day or at the end of a campaign or the memory cards have to be exchanged In larger field projects it is recommended that the data are transferred to suitable mass storage in the observation area making a data check at the same time Data can also be transferred via cellular phone andor internet from the field to a central processing facility The amount of incoming data is enormous if the full data rate of modern receivers is exploited ie once or twice per second For most static applications a much lower data rate is completely sufficient for example every 15 or 30 seconds It is however essential that all receivers in one project sample at the same data rate This condition may cause problems if different receiver types are used In some cases the meteorological data are used in the subsequent multistation evaluation The data have to be recorded at adequate intervals for example every 30 minutes pressure 1 mm temperature 1 C and relative humidity 1 However note that meteorological station data can introduce biases into the multi station adjustment because they are not representative for the working area It is advisable to keep a station log entering not only the weather data but also the station identification code the receiver and antenna identification numbers the antenna position and height the observation schedule operation problems and other significant information of relevance to future data processing 7613 Observation Strategies and Network Design Three basic observation strategies can be distinguished cf 734 point positioning concept single receiver 76 Applications 351 baseline concept relative observations at two stations and multistation concept three and more receivers operating simultaneously Various procedures can be selected within the last category Of particular relevance are observations in connection with active multiple reference stations 753 The choice of the observation concept depends on the objective of the survey the required accuracy the number and type of receivers available and the logistic condi tions Hence a general classification is difficult and not appropriate As regards the necessary accuracy the following user classes may be defined though the boundaries are debatable Table 721 Table 721 GPS user classes Category Average required Corresponding relative accuracy accuracy in m distance dependent A Exploration geophysics Georeferencing low 1 104 1 50 accuracy GIS B Topographic map surveys Small scale engineering 1 105 02 1 Vehicle control systems C Cadastral surveys Engineering surveys of 5 1 106 001 02 mean accuracy D Geodesy Control surveys High precision 5 107 1 106 001 005 engineering surveys E Geodynamics Highest precision 1 107 0001 002 engineering surveys With a single receiver an absolute position determination can be achieved con tinuously navigation mode with an accuracy of 5 to 15 m without SA under the Standard Positioning Service SPS cf 716 741 Even after several hours of observation the achievable absolute accuracy is not better than several meters There fore only group A activities can be undertaken with a single receiver A new situation evolves with the use of precise ephemerides and clocks in the concept of Precise Point Positioning PPP In essence this is however an implicit form of differential GPS 734 For all other user groups only relative observation techniques with at least two simultaneously operating GPS receivers are worth considering The terms differential GPS and translocation observations are also used equivalently 352 7 The Global Positioning System GPS The concept of relative observations is extensively discussed in chapter 75 It applies for moving and static antennas The essential strength of relative techniques lies in the fact that a part of the error influences at neighboring stations is strongly correlated and is therefore cancelled out when a difference is taken cf 653 for the TRANSIT system This is especially true of orbit errors errors of the satellite clock and errors in the ionospheric modeling Comparison of Table 712 and Table 76 makes it clear that the systematic model errors and the observation noise of the code have more or less the same order of magnitude namely 1 to 10 m Hence in the navigation mode a relative navigational accuracy of 2 to 3 m is successfully achieved using code phase measurements and corrections from a reference station differential GPS 751 For a static receiver the extremely low observation noise of the carrier phase measurement which is three to four orders of magnitude less than the systematic error effects can be used to advantage only if the systematic components are eliminated by relative measurements In this way an accuracy increase by a factor 103 to 104 is brought about in the geodetic relative mode with at least two simultaneously operating receivers as com pared with the single receiver mode Relative techniques are particularly effective when the station distance is small compared with the satellite range 20 000 km The amount of correlation decreases as the distance increases however the correla tion is effective up to several thousand kilometers The adjustment models for relative observations are discussed in 734 and 75 A B C Figure 771 Baseline observations with two receivers A B C D 1 2 3 4 5 6 Figure 772 GPS network If two receivers are avail able a point field or network can be set up by the observa tion of baselines One possibil ity is to operate one instrument at a central station and occupy the adjacent points in a starshaped pattern Fig 771 Adjacent central stations A B C are linked through baseline observa tions The baselines between the nonsimultaneously occupied stations can then be derived by computation For control pur poses some of those trivial baselines cf 734 Fig 742 p 284 can be independently ob served Another possibility is to oc cupy neighboring points and form triangles or quadrangles Fig 772 This method leads 354 7 The Global Positioning System GPS must not be overemphasized because network configuration is only one aspect of a GPS mission As regards logistic and practical limitations the choice of an observation strategy willoftenbeguidedbyexperience withformaloptimizationcriteriaprovidingvaluable aid Since the accuracy of a local GPS network is only little dependent of the station distance the design aspects are mainly governed by logistic economic and reliability factors Some general rules from experience are that each station should be occupied at least twice under different conditions to identify blunders neighboring stations should be occupied simultaneously because the ambiguity resolution works best over short distances for mediumsized projects the use of 4 to 10 receivers is a good compromise with respect to logistics production rate and reliability and a certain number of baselines should be observed twice for accuracy checks These rules are valid for independent projects In active multiple reference station networks the situation is different insofar as a new station is always determined by a single receiver with respect to the whole network 753 Besides accuracy the reliability of a GPS network is an important issue of network quality Reliability means the ability of a network to selfcheck against blunders or systematicerrors Fig773givesanexampleAugath1988 StationsAandBareused II III IV I III II I I III I IV I IV I III A A B B Figure 773 Network with accuracy criteria left three sessions and reliability criteria right four sessions as reference points and are occupied during all sessions Four receivers are mobile The left part of Fig 773 demonstrates a network design with accuracy criteria only The right part yields more or less the same accuracy but in addition offers reliability because each point solid triangle is used in two sessions Additional constraints come through the permanent stations An even more controlled network is shown with Fig 774 76 Applications 355 Session 11 22 23 24 25 12 13 14 15 A B D C Session 21 Figure 774 Generic network densification with GPS The data set which results from a GPS multistation adjustment process has a high relative accuracy The ab solute coordinates however may have standard deviations of several meters be cause of the uncertainty in the realization of the satellite datum through observa tions cf 661 and 734 As a rule therefore newly determined GPS net works must be tied to previously exist ing known points either from the partic ular national control network or from fundamental stations which are deter mined by precise global techniques such as VLBI Laser or GPS tracking net works Examples of the latter group are International Earth Rotation Ser vice Terrestrial Reference Frame ITRF 212 1212 International Global Positioning System Service IGS 743 781 National or regional GPS tracking networks like the Canadian ACS the US CORS the Brazilian RBMC or the German SAPOS 751 and Continental or national fundamental GPS networks like EUREF SIRGAS and DREF 762 The tie can be made over one or several identical points for example A B C D in Fig 772 or nearby permanent stations For smaller working areas a single connection point may be sufficient The control points can be used as fixed points with minimum variances or as fiducial points with a predefined nonvanishing dispersion matrix The network datum is derived from the preexisting control points rather than from the GPS observations In active reference networks the datum comes from the network datum For detailed discussion see 1211 and 7621 When planning GPS projects in remote areas careful attention must be paid to connection to reference points with known precise geocentric coordinates Otherwise the errors in the absolute coordinates inherent in the actual GPS observations will propagate into the relative coordinates of the network solution 762 A good solution to the problem is to connect new measurements with IGS stations With the evolution of sufficiently dense global continental and national funda mental networks based on precise space techniques as well as on GPS the reference point or fiducial point concept will be the technique usually applied when establishing GPS networks In other words GPS will be mainly used as an interpolation technique for network densification in the working area A final generic example Fig 774 highlights some of the essential items that have been discussed in this chapter Stations A B C D are points of the existing network 356 7 The Global Positioning System GPS either from previous GPS campaigns or from a precise classical terrestrial network They are used as fixed or fiducial points The datum is completely defined through these stations Seven receivers are applied Two of them are operated on the fixed stations and five are moving Five sessions are observed each project section During the first section the fixed stations A and B are occupied and the roving receivers move in five sessions according to the solid lines During the second section stations C D are occupied and the receivers move according to the dashed lines Depending on the interstation distances the receiver types the available software and the project objective the individual sessions can last minutes hours or even days Note that the following principles are fulfilled for the newly determined points high accuracy caused by a sufficiently long observation period in each session following the project goals highly economic because the session number for double occupancy and the interstation travel times are minimized and high reliability because each new point is derived from two completely indepen dent determinations new antenna installation tied to different control points and mostly observed under a different satellite constellation For observation strategies using active reference networks see 753 and 7621 762 Possible Applications and Examples of GPS Observations Since GPS is an allweather realtime continuously available economic and very precise positioning technique almost unlimited possibilities are opened up for its use in geodesy surveying navigation and related fields including control surveys geodynamics altitude determination cadastral surveying and GIS monitoring and engineering precision navigation photogrammetry and remote sensing and marine and glacial geodesy Some typical fields and examples of GPS application will be discussed in the following The use of satellite methods is further reviewed in 12 It was recognized early on that GPS is a multipurpose system One major advantage is its capability of forming a powerful building block in integrated systems GPS together with a coordinate system and geographic information produces a map GPS together with a map facilitates navigation GPS together with a digital geometric data base a geographic information system GIS and a communication link produces a command and control system Gibbons 1991 With the establishment of continuously operating reference stations covering a whole country 75 the acceptance of GPS as a basic positioning tool will further grow The availability of position information in realtime at any level of required 76 Applications 357 accuracy and at any place will be taken for granted as today is the availability of precise time or of communication links Because of the fast growing application market only some basic concepts are described here For more information on the current discussion see journals like GPS World or symposia proceedings like ION GPS The statements in this chapter refer to NAVSTARGPSTheyare however alsovalidforotherGNSSsystemslikeGLONASS or the forthcoming European GALILEO 77 7621 Geodetic Control Surveys The following objectives can be identified a settingup of a completely new field of control points b densification or extension of existing networks c inspection analysis and improvement of existing networks and d establishment of a network of active reference stations The terms network and control point field are used as synonyms a New network The installation of a completely new network can be performed in three steps Since all densification work will be done with GPS techniques it is advisable to select a global geocentric datum compatible with the World Geodetic System WGS 84 216 WGS 84 is now defined with an accuracy level of about 1 cm Merrigan et al 2002 and corresponds at that level with the International Terrestrial Reference Frame ITRF 2122 1242 Areas with an insufficient coverage of ITRF sites for example Africa or some parts of Asia see Fig 24 are densified by stations of the IGS service 7432 781 with the same accuracy standard For most practical purposes the global network ITRF2000 and the IGS network can be considered as equivalent Starting from the global network three basic levels of Geodetic GPS Networks may be distinguished all with the same high accuracy standard namely about 1 cm Level A Continental or SubContinental Reference Frames Level B National Fundamental Networks and Level C All other GPS networks At Level A a continental or subcontinental GPS network is installed with the ITRFIGS sites as fiducial points The interstation distances are between 300 km and 500 km The station coordinates have to be determined with the highest achievable accuracy in general 1 cm This is possible with the fiducial point concept 7432 about one week of observations dual frequency receivers precise orbits and advanced software As an example see the EUREF European Reference Frame project EUREF has been built up since 1989 by successive GPS campaigns The existing ITRF stations in Europe Laser and VLBI were used as fiducial points The first campaign was performed in May 1989 with about 60 dualfrequency receivers In 1990 some 30 stations were added during the EUREF North campaign After 1990 in several cam paigns stations from Eastern Europe were included The European Reference System 358 7 The Global Positioning System GPS was defined as ETRS in agreement with the ITRS for the epoch 19890 Its realization is ETRF89 that coincides with the ITRF89 for stations in Europe The basic idea is that ETRF89 rotates with the stable part of the European plate and hence can remain unchanged for a long time period About 90 stations of the more than 200 EUREF sites form the permanent EUREF network 7513 Fig 775 with the objective to maintain the ETRS and to densify the IGS network in Europe Figure 775 EUREF Permanent Network source BKG Figure 776 SIRGAS 1995 source DGFI Similar basic reference frames have been or are being built up in other continents or subcontinents In South America the Sistema de Referencia Geocentrico para America del Sur SIRGAS was created in 1995 by 10 days of simultaneous GPS observations at nearly 60 stations Fig 776 Hoyer et al 1998 The network was tied toITRF94 Someofthestationscontinueaspermanentstations providereferencedata and maintain the frame The data are processed in the IGS Regional Network Associate Analysis Center for SIRGAS RNAAC SIR 781 and contribute to a densification of the IGS global network In 2000 the SIRGAS network was reobserved and enlarged including sites in Central and NorthAmerica In NorthAmerica the already mentioned US CORS network 751 and the Canadian Active Control System CACS play a similar role A continental network for Africa AFREF is under discussion At level B nationwide or statewide fundamental networks are installed with a spacing of 50 to 100 km depending on the size of the country and the objectives The stations of level A are kept fixed for use as fiducial points The accuracy of the individual GPS station with respect to the neighboring stations is again 1 cm hence providing a homogeneous set of coordinates for the whole country One example is the DREF campaign Fig 777 in Germany DREF was observed early in 1991 with 83 dual frequency receivers The network contains 109 stations with a mean spacing of 70 to 100 km Some 20 stations are EUREF sites from level A 76 Applications 359 It is advisable to use as many receivers as possible to provide a homogeneous set of observations In most cases it will not be possible to occupy all stations of a national network simultaneously The total network has then to be broken down into Figure 777 The DREF German Reference Frame network subnetworks and sessions The single subnetworks and sessions are intercon nected via fiducial stations from level A and by selected identical points at the rim of the individual subnetworks Most countries have established funda mental networks of this type or will do so within the near future Before using station coordinates fromlevelAasareferenceframeforden sification at level B the coordinates have tobecorrectedforcrustaldeformation if applicable Even small motions of say 2 cmyear will lead to a 10 cm deformation already after 5 years which is not toler able in precise geodetic networks The procedure is as follows Drewes 1998 Step 1 Transformation of level A co ordinates of the stations S used as connecting points fiducials from the epoch t0 of the reference frame level A to the epoch ti of the new observations Station velocities vS derived either from repeated observations or from crustal deformation models are applied according to XSti XSt0 vSti t0 7167 Step 2 Network adjustment of the new stations N level B using the observations at epoch ti together with the coordinates XSti of the fiducial points from level A Step 3 Transformation of the new station coordinates XN from observation epoch ti back to the epoch t0 of the reference frame level A using XNt0 XNti vNti t0 7168 This procedure ensures a homogeneous network of level B stations in the datum of level A Since station velocities of the new stations are not always available it is advisable to develop continuous deformation models for all continental plates 1241 At level C all other control points have to be connected to stations of level B again at the 1 cm accuracy level One advantage when compared with classical techniques is that no systematic densification is necessary Work can be done following a priority schedule where coordinates are required The densification procedure can follow the scheme of Fig 774 The classical division into geodetic networks of 1st to 4th order within a country will disappear and be mostly replaced by two levels 360 7 The Global Positioning System GPS the fundamental national reference frame level B and all other control points level C b Densification of an existing network This can be treated in different ways 1 A precise classical terrestrial network of 2nd or 3rd order exists In this case GPS is used as a modern surveying tool for precise network densification GPS is in nearly all cases much more economical than the classical methods The procedure is as outlined in Fig 774 see 7613 The existing control points are taken as fixed reference points The existing national datum is maintained This approach is used in many countries as a tool for rapidly providing precise geodetic control 2A terrestrial network of medium or low accuracy exists the old coordinates shall be maintained In this case the distortion of the traditional network is introduced into the precise GPS results GPS is only used as a method of costeffective interpolation into the existing national framework The GPS observations should be preserved for a rigorous adjustment once a fundamental GPS network has been established in the area at some later date This procedure is acceptable as an intermediate solution in particular in developing countries until a completely new network and datum based on satellite techniques can be established 3 The existing terrestrial network is combined with new GPS observations In this case the existing network datum is maintained however the complete network is readjusted and strengthened with the inclusion of GPS measurements New points are linked to the existing network in an optimal way All network coordinates are slightly changed The method only works if sufficient stochastic information on the existing network is available see 121 and related literature Leick 1995 Strang Borre 1997 A particular problem arises when multiple reference stations 7532 are estab lished in an area with existing geodetic control Even if the traditional network is of highest quality discrepancies at the several centimeter level have to be expected when distortionfree new GPS points derived from references stations at about 30 to 50 km distance are established in the direct neighborhood of existing distorted sur veying points Such discrepancies are often not acceptable in cadaster or engineering projects Two solutions are possible In a first step for the whole area local transformation parameters have to be derived from GPS observations at a sufficient number of existing control points These parameters are either used to transform all existing surveying points into the distortion freereferenceframedefinedbytheGPSreferencestations ortheyareusedtotransform the GPS determined coordinates of new object points into the existing distorted local frame realized through the conventional surveying points In the latter case the GPS results should be maintained in order to use them for a new coordination as soon as the former solution can be realized c Analysis of an existing network This procedure is of particular importance in countries where little information on the original observation and computation is available for example in developing countries 76 Applications 361 Figure 778 Residuals after a 7parameter trans formation between the DÖNAV network and the classical German network DHDN eg Campos et al 1989 The analysis however also offers a very important in sight into the present official networks of countries with an advanced cartographic tradition such as Germany For the analysis a certain number of existing sta tions is reoccupied with GPSThe resid uals after a sevenparameter Helmert transformation 246 are inspected Fig 778 shows residual vectors be tween an early GPS campaign in Ger many DÖNAV and the official ter restrial network DHDN Seeber et al 1987 The residuals reach up to 1 m A similar analysis is used to derive detailed expressions for a transformation formula between the datum of the GPS network and the existing local network d Active Reference Stations A modern tendency is to represent the fundamental reference frame in a coun try by a network of active control points that provide relative information for any authorized user on a routine basis see 7532 This service can be operated under the responsibility of the national survey ing authorities for example SAPOS in Germany The longterm rationale behind this concept is to substitute the reference frame exclusively through the active reference stations and to considerably decrease the number of monumented points Fig 779 shows some possible concepts of active reference station networks at level C In version a GPS data are collected at the reference stations and distributed to users via a control station In option b range corrections in the RTCM 20 or RTCM 21 format are broadcasted to users from the nearest reference stations In Data recording Data redistribution Data analysis Monitoring a b c Figure 779 Different concepts of permanent reference stations 362 7 The Global Positioning System GPS version c all stations are interconnected and work as monitor stations and analysis stations they all transmit range corrections andACP to the users 7532 The subject of network densification no longer arises 7622 Geodynamics The very high accuracy potential associated with comparatively easily transportable equipment makes GPS a suitable technique for determining recent crustal movements 1241 Until about 1985 crustal movements were mainly analyzed with Very Long Baseline Interferometry VLBI 111 and satellite laser ranging SLR 8 With VLBI longrange baselines can be determined precisely a few millimeters accuracy and precision over several thousand kilometers are achievable The main disadvantage of the VLBI method is the enormous technical expenditure and the limitation to a comparatively small number of fundamental stations only very few transportable systems are available With satellite laser instruments very precise and reliable movement rates have been derived from many years observation for example in the area of the San Andreas fault Watkins et al 1990 or along with the WEGENERMEDLAS project in the Mediterranean region Ambrosius et al 1991 Transportable satellite laser ranging systems are also in use 833 still the use of SLR technology involves high costs and long mobilization times For many areas of interest in particular if a large number of points are to be determined for higher spatial resolution GPS offers considerable advantages This is why since about the late 1980s besidesVLBI and SLR GPS is the technology of preference for the operational determination of crustal deformation and global plate motion In the early days of GPS one of the most important limiting factors in the error budget for precise baseline determination over large distances was orbit accuracy Following the rule of thumb 7134 an orbit error of about 25 m would propagate 1 cm error per 100 km into the baseline In view of the known motion rates of a few cmyear or only mmyear station spacing should then not be much greater than 100 km With todays orbit accuracy of 5 cm or better for IGS products 7432 the orbit is no longer a critical factor in crustal motion studies even over large distances Key factors of the error budget are rather 744745 modeling of atmospheric propagation effects antenna phase center variations PCV and multipath effects Much research has been invested in recent years into the modeling of tropospheric and ionospheric propagation effects 233 The use of data from GPS observations in LEO GPSMET see 7629 projects will further help to improve the models In addition an attempt can be made to raise the accuracy level through the use of water vapor radiometers 2332 7442 Tectonically active areas near the geomagnetic equator or in high latitudes will ex perience large ionospheric disturbances 7441 eg Wanninger Jahn 1991 Völk sen 2000 The use of dualfrequency receivers is hence essential Long observation periods over at least 24 hours help to average out residual effects 76 Applications 363 Site dependent effects can be minimized with absolutely calibrated antennas and multipath reducing observation techniques 7451 Even for identical antennas the PCV variation will not be cancelled in relative observations over very long baselines because of Earths curvature Menge Seeber 2000 Two strategies are being used to determine station velocities i repeated observations within dedicated campaigns and ii continuous observations at permanent installations Strategy i was mainly used during the development phase of GPS and it is still applied for smaller independent projects or in remote areas with difficult access A first epoch measurement establishes a network of well demarcated stations and repeated epoch observations are performed after one or several years A typical example is given with the Iceland campaigns in Fig 780 With the availability of fully automatic low power consumption GPS receivers and the possibility to transfer data over large distances strategy ii is more and more applied One main advantage compared with option i is that data are continuously available and sudden events like displacements due to earthquakes can be directly analyzed Two eminent examples are the IGS network and the GEONET in Japan 7513 The following main fields of application for crustal motion monitoring can be identified a global and continental plate motion and deformation analysis b regional crustal motion analysis and c local monitoring of deformation and subsidence Projects of group a show very impressive results after a couple of years of obser vations Comparisons between GPS and other space techniques like VLBI and SLR demonstrate an agreement at the centimeterlevel and hence prove the capability of GPS for global geodynamics Boucher et al 1999 A major breakthrough came with the establishment of the IGS 781 More than 300 globally distributed stations deliver data on a permanent basis and as such provide a continuous monitor of deformation The station velocities can be used to compute global stress maps and to determine a kinematic model of the individual plate rotation vectors see 1241 Fig 1213 p 529 Tab 123 p 528 Two examples are given for continental projects The motion of theAntarctic plate was determined with two epoch measurements in 1995 and 1998 Dietrich et al 2001 Three weeks of observations each time at about 45 stations on the Antarctic continent and the adjacent tectonic plates were taken to establish a precise reference network linked to the ITRF96 reference frame and to determine besides of local deformations the rotation of theAntarctic plate Based on a data analysis with four different software packages at seven analysis centers the combined solution yields an accuracy of 1 cm for the horizontal and 2 cm for the height components For details see Dietrich ed 2000 With horizontal velocities of about 2 to 3 cm per year an epoch difference of three years gives reliable results For the detection of height changes the situation is more critical A longer time span and even more sophisticated modeling is required see 7623 364 7 The Global Positioning System GPS The SIRGAS network in South America was observed in 1995 with 58 stations and again in 2000 with in total 184 stations The results from the repeated stations are used to derive their velocity vectors This information is also of high importance for followup geodetic work because SIRGAS 95 was adopted as a national datum by some of the participating countries About 20 of the SIRGAS stations deliver data on a continuous basis These data are included in the data set of the Regional IGS Network RNAAC SIR and continuously provide information on the motion of the South American Plate DGFI 2001 An extremely challenging endeavour in this project group is the connection of continental control points with submarine control points near plate boundaries or sub duction zones because GPS measurements on floating platforms have to be integrated with underwater acoustic measurements 1232 Chadwell et al 1998 Central vulcano with fissure swarm Reference point NE displacement Object point Glacier Scale of vectors 66 65 64 341 342 343 344 345 346 347 340 o o o o o o o o o o o 532 Askja Krafla 0 5 10 cm 7947 Figure 780 Displacement vectors from two consecutive epoch measurements in Iceland 19871990 Projects of group b already show significant results Investigations and epoch or continuous measurements have been started in nearly all tectonically ac tive parts of the world Well known examples are among many others con trol networks in California the CASA Central and South America and SAGA South American Geodynamic Activi ties GPS project the GEODYSSEA Geodynamics of South and SouthEast Asia project Wilson et al 1998 projects in the Mediterranean area Ka niuth et al 2001 and the neovolcanic rifting zone in Iceland Usually dis placement vectors are derived from the comparison of two or more epoch mea surements if no continuous measure ments are available Fig 780 shows the results derived from two early epoch measurements in 1987 and 1990 in the Northern Volcanic Zone of Iceland About 50 stations were controlled with seven TI 4100 dual frequency Pcode receivers The epoch accuracy of adjacent stations is about 1 to 2 cm The identified displacements in a postrifting period reach about 3 to 5 cmyear Subsequent epoch measurements in 1992 1993 and 1995 provided a deeper insight into the mechanisms and enabled geo physical modeling and interpretation Hofton Foulger 1996 Völksen Seeber 1998 Fig 781 shows deformations after the M 81 Antofagasta Earthquake on July 30 1995 Klotz et al 1996 One major difficulty in the analysis of a displacement field is the identification of stable reference points Powerful methods have been developed in the field of network deformation analysis to address this problem eg Mayer et al 2000 76 Applications 365 Niemeier et al 2000 One effective procedure is to relate all epoch measurements to ITRF In order to demonstrate the local deformation behavior it can be helpful to Longitude deg Salar de Atacama ARGENTINA Latitude deg Pacific Ocean Antofagasta CHILE Deformation vector 1m SAGA Station 71 70 69 68 23 24 25 23 24 25 71 70 69 68 Figure 781 Deformation after the M 81 Antofagasta Earthquake July 30 1995 after Klotz et al 1996 select stations in the center of the de formation field eg Fig 780 Völksen 2000 In areas of high risk eg of earth quake volcanic activities like the San Andreas Fault in California or in Japan continuously monitoring GPS arrays have been installed Bock et al 1997 A fixed network of GPS receivers tracks all GPS satellites 24 hours a day The data from all sites are transmitted via highspeed communication lines to the central facility and are analyzed to ob tain accurate snapshots of the relative positions of the network stations Sig nificant variations in these positions may indicate deformation caused by seismic or volcanic preevent coevent or postevent activities Projects of group c ie the monitoring of local deformation belong in most cases to the field of deformation analysis in engineering surveying Possible applications are the monitoring of land subsidence eg in mining areas and oil fields hang sliding and local geotectonics In most cases the point distances are very small about 1km hence an accuracy of a few millimeters can be achieved and very small deformations can be detected Depending on the objectives of the control and the expected rate of motion the measurements have to be repeated after a given time period for example days weeks or months At least one stable reference station is required In many cases rapid methods can be applied 735 In future more and more continuously monitoring arrays will be built up The data of the remote operating receivers have to be transmitted to the central station via cable radio data link or the internet A rather new and very promising field of GPS application in geodynamics is Earth orientation monitoring in particular the variation of LOD and polar motion 212 1242 Error analysis and comparison with other space techniques demonstrate the high potential of GPS to monitor daily and subdaily variations at the accuracy level of a few millimeters Earth rotation monitoring together with the delivery of precise orbits and station coordinates is one of the major objectives of the International Geodynamics GPS Service IGS 743 781 368 7 The Global Positioning System GPS control points the method delivers satisfying results Zhang 2000 Very good results have also been obtained with the use of finite elements to represent a height reference surface Jäger Schneid 2002 Where heights in the gravity field are known from levelling lines it is possible to directly derive geoid heights from GPS results This method can contribute consid erably to the determination of a precise geoid Other major problems to be solved with GPS altimetry are the connection of separated tide gauges eg Kakkuri 1995 Liebsch 1996 and the establishment of a global height datum This includes the determination of a precise marine geoid and of the sea surface topography 951 In coastal areas a precise geoid strongly supports the height determination for nearshore engineering and shore protection activities Seeber et al 1997b Very precise geoid profiles can be determined with a transportable digital zenith camera using the concept described in 52 in combination with GPS The camera providesthedirectionoftheplumblineinnearrealtime andtheGPSreceivergenerates geodetic coordinates as well as precise time Using the technique of astronomical levelling Torge 2001 a high resolution geoid profile and orthometric heights are provided online Hirt 2001 7624 Cadastral Surveying Geographic Information Systems Because of the high accuracy in connection with short observation time GPS can also be employed economically for detailed surveying in rural or urban environments Main fields of applications are in connection with the installation or maintenance of multipurpose cadaster or geographic information systems reference point GPS tacheometers reflectors for detailed surveying GPS and tacheometer point Figure 783 Combination of GPS with an elec tronic tacheometer One major problem in detailed sur veying is signal shadow caused by build ings trees towers bridges etc This is why the exclusive use of GPS in cadas tral surveying will be restricted to open areas With the presence of such ob structions GPS will be mainly used to determine rapidly the standpoints for electronic tacheometers or other conven tional surveying instruments Fig 783 illustrates the situation In areas of free sight like most ru ral areas or urban areas with broad streets low buildings and low vegetation rapid GPS methods can be used 735 in particular the RTK technique 7354 752 Fig 784 gives an artists view of a detailed survey with GPS The data can be stored in the moving receiver or transmitted via a data link to the reference receiver or vice versa With a continuously working data link the settingout of coordinates or a re identification of existing points or lost monuments will also be possible The precise coordinates of the moving antenna are calculated in the field in realtime and it is 76 Applications 369 indicated to the surveyor how far the antenna has to be moved to the final destination Integrated systems of this type are available from most major GPS manufacturers The procedure depicted in Fig 784 can be realized with a local temporarily established reference station case a or with respect to a continuously operating reference station case b GPS reference station data link display GPS reference station tacheometer setting out with GPS and tacheometer setting out with GPS only target N 20 30 10 standpoint GPS GPS Figure 784 Use of GPS in realtime detailed surveying Case a can be realized with conventional RTK equipment consisting of two GPS receivers and a radio The reference receiver has to be installed on an existing demar cated surveying point or the coordinates of the reference station have to be determined with respect to existing stations in the neighborhood This can be realized when the roving receiver occupies two or three of such stations along with the survey In mod ern surveying concepts it is no longer necessary to demarcate the temporary reference stations because the local field of surveying points is only represented by a strongly limited number of demarcated stations CasebhastheadvantagethatonlyoneGPSreceiverisrequiredinthefield Again in most cases GPS will be used to establish standpoints for a tacheometer whereas the object points boundary marks or housecorners are determined with conventional surveying tools Another advantage is that all coordinates are immediately given with respect to the official reference frame and that no additional time is needed for the reconstruction of existing surveying marks For high accuracy requirements it is necessary to work with networked reference stations 7532 For reliability purposes it is advised to occupy each object point twice GPS is a powerful means to support Geographic Information Systems GIS The role of GPS in this context is manyfold it contributes to a uniform basic geometric frame for example a coordinate system a digital map or a digital terrain model it contributes to the geometric location of objects that enter the GIS for example streets buildings power lines proprietary boundaries 370 7 The Global Positioning System GPS it allows the GIS to be taken out into the field with GPS directentry and it forms an integrated buildingblock in a command and control system for example for moving vehicles or machines that are navigating based on a digital terrain model In the following only some examples are given For all enterprises that provide services like energy water supply or traffic information a geographic information system forms the basis of most decisions As a first step all spatially related data and object data have to be collected Traditional maps are in many cases not sufficient Here GPS provides an economic and efficient tool for an automatic data flow into the GIS Vice versa all objects that are selected in a GIS can be immediately identified in the field eg Barrett 1997 Integrated GIS GPS concepts are offered by many manufacturers The market is rapidly growing Application examples are inventories for pipelines power lines fresh and waste water streets traffic signs railway tracks trees contaminated locations and so on Depending on accuracy requirements GPS provides continuous position informa tion at all scales of interest In some cases the accuracy of a single receiver 5 to 15 m is sufficient In most cases ordinary DGPS will be applied 05 to 2 m If highest accuracy is required few centimeters the services of multiple reference stations can be used 753 or even established for the purpose Another advantage is that 3 D information is available In connection with a digital geoid gravity field related height information eg orthometric heights can be supplied for applications involving the direction of water flow Reference station Figure 785 Car driven survey system Rapid digital data acquisition is pos sible with a car driven survey system for mobile mapping Fig 785 The posi tioning problem is solved by GPS in con nection with an inertial sensor or alter natively wheel sensors barometer and magnetic sensors The data are acquired and analyzed automatically with sev eral video cameras Benning Aussems 1998 ElSheimy 2000 Another fast growing field of appli cation is precision farming Based on a GIS including the topography soil qual ity and actual state data all steps in farming can be performed in an optimized way like finetuned fertilization or spray ing of infested areas Computerized controllers and GPSguided navigation form an optional part of farming equipment like sprayers or harvesters Table 722 gives an overview of accuracy requirements Demmel 2000 Many more examples could be given The integration of GPS and GIS together with a communication link is increasing and widely discussed in the GPS literature eg GPS World as well as in the general surveying and GIS literature 76 Applications 371 Table 722 Accuracy requirements for the use of GPS in precision farming Task Example Required accuracy Navigation Search working area 10 m Search deposit place Execution of work Work in the field with 1 m Information determination of returns Documentation fertilization plant protection soil samples Automatic data recording Vehicle guidance Connected tracks 10 cm Harvesterthresher Equipment guidance Mechanical weed removal 1 cm 7625 Fleet Management Telematics Location Based Services These services present important new challenges with a focus on realtime positioning communication and information They are mainly related to motorized vehicles like cars but also may concern pedestrians The denomination is not yet clearly defined all three terms are sometimes used for the same service Fleet management means the control of a large quantity of vehicles like trucks trains police and emergency cars public buses and so on Telematics is a new word composed from telecommunication and informatics and means the use of trafficrelated information Location Based Services LBS are mainly related to the use of cellular phones and mean the realtime availability of all kinds of positionrelated information to individual customers The backbone of all services is composed of these elements knowledge of the position of the client knowledge of the position of other participants in the system if required a geographical information system a personal digital assistant PDA palmtop with the client or a computer in the control center and a communication link The positions can either be provided by GPS GNSS or another positioning device like the cellular phone identification The GIS is either available in the PDA of the client or via cellular phone from a provider Considering the rapid development of communication technology and the high number of vehicles in industrial countries the market promises to develop fast Some examples follow Car navigation systems for individual users based on a digital map and a location service are already well established The inclusion of information on congestion snowfall or roadwork for instance will improve the service Additional features are automatic location transmission in case of emergency or theft 372 7 The Global Positioning System GPS Fleet management is essential for shipping agencies train and bus systems police and emergency services and fire brigades In connection with a traffic management system traffic light priority can be given to public transportation and emergency ve hicles At large construction sites a logistic system can be installed to organize and guide the construction vehicle traffic Each vehicle gets a certain time slot when entering the site and a GPS based local navigation equipment is deployed in each car as long as it operates inside the construction area A particular application is the mobility of blind people A precise DGPS system and a precise and detailed specific digital map connected to a voice generator enables a user to navigate in an unknown environment aided perhaps only by a stick A large potential market is developing for location based services Tourists can request information on nearby touristic highlights restaurants and public transporta tion Parents can supervise their children and persons with a critical health status can be remotely monitored by a medical center A particular application will be the automatic location of a mobile phone in con nection with the emergency calls E911 in the US or E112 in Europe A further step will be a combination of outdoor and indoor navigation within a single hybrid location device 7626 Engineering and Monitoring Almost unlimited possible uses and applications may be conceived in this field The corresponding observation and evaluation methods are as discussed in the previous sections Since the distances are usually small it is possible to achieve mm accuracy with routine methods Rapid methods 735 realtime solutions and integration with electronic tacheometers may be required Some fields of application are 1 Determination of geodetic control points Geographic Information Systems GIS cartography photogrammetry geophysical surveys inertial surveys antenna location in hydrographic surveying expeditions of all kinds and archaeological mapping 2 Monitoring object movements by repeated or continuous measurements ground subsidence mining ground water withdrawal land slides construction of dams subsidence of offshore structures and settlement of buildings 3 Setting out local networks for the control of engineering projects tunnel construction 76 Applications 373 particle accelerators bridge construction road construction pipelines and waterways 4 Realtime guidance and control of vehicles construction vehicles large excavators in opencast mining and forklifts in open storage areas eg container yards If two antennas and receivers units are used GPS can also be employed as a method of determining directions Usually the direction is derived from the coordi nates of the two antenna phase center positions hence precise carrier phase resolution and carefully designed and calibrated antennas are required Table 723 shows the relation between station spacing azimuth accuracy and required GPS relative position accuracy If 2 mm relative position accuracy is considered to be the accuracy limit it is possible to determine a 1 arcsecond azimuth over 400 m distance This may be of interest for setting out a tunnel axis Table 723 Azimuth reference control with GPS azimuth accuracy in seconds of arc 1 2 4 6 10 station spacing m GPS relative position accuracy in mm 100 1 2 3 5 200 1 2 4 5 10 300 2 3 6 9 14 400 2 4 8 12 19 500 3 5 10 14 24 600 3 6 12 18 29 For operational use a much shorter baseline can be selected With a 1 m antenna separation a directional accuracy of a few arcminutes can be achieved even in kine matic mode GPS can hence be used for compassing With three antennas the attitude of a moving platform can be controlled From the above list of possible applications two examples are given a control network for tunnel construction and a network for dam control The advantage of GPS can in particular be demonstrated for the tunnel network The main purpose of such a network is the settingout of the bearing of the shaft center line at both entrances PW portal west and PE portal east cf Fig 786 In classical engineering both portals had to be connected via a precise network covering the whole area This could be an extremely difficult task in mountainous or heavily forested areas With GPS it is sufficient to determine two control points each at both entrances for setting out the 374 7 The Global Positioning System GPS bearing of the center line For security reasons it is advisable to establish a second target pillar at each portal for reference bearings The distance should not be too large to enable sights under unfavorable atmospheric conditions TP TP TP tun nel cen ter l ine W1 PW W2 E1 PE E2 Figure 786 Generic tunnel network with GPS C C C P P P P P S S 1 1 1 2 2 i i n n crest C dam wall pressure area stable area check points 2 3 Figure 787 Dam control with GPS The relative location of the two portal networks can be determined with an accuracy level below 1 cm for distances up to 10 km The results are given in three dimensions In order to provide levelled heights via GPS it is necessary to include a precise local geoid 7623 If required the tunnel network can be easily connected with the nearest control points TP of the geodetic network via GPS techniques The second example refers to the permanent control of a dam during construction and after completion Fig 787 A difficult task is the selection of stable control points and the delimitation of the pressure zone from the stable area Usually the advice and support of experts is required One advantage of GPS is that the stable control points Si can be placed well away from the influence zone and that no direct sight connection to the nearconstruction control points Pi is required GPS can be used to establish stable control points Si establish and monitor control points in the pressure zone Pi and establish control points on the dam crest Ci Checkpoints attached to the dam wall remain to be controlled by other techniques either with electronic tacheometers or photogrammetry GPS is suited to determining and monitoring the coordinates of the tacheometer or camera standpoints Pi in the pressure zone GPS is also capable of identifying and analyzing point motion within the pressure zone Regarding the high potential of GPS concerning accuracy and cost effectiveness it is possible to install a dense network of control points in the potential pressure zone Deformationscanbederivedfromrepeatedobservation inintervalsofdays weeks or months depending on the situation In cases where there is suspicion of impending 76 Applications 375 structural distress the establishment of a continuous monitoring array can be taken into consideration One critical factor is the limited visibility of satellites from stations near the dam wall The situation will improve with the inclusion of other GNSS like GLONASS and GALILEO 77 but drawbacks result from unbalanced geometry and multipath effects Instead control points near the dam wall can be related to better placed control points by tacheometry GPS can also be used for deformation monitoring at the one millimeter or sub millimeter level when all acting error sources are eliminated or considerably reduced The most critical part multipath can be eliminated by forming sidereal differences 7443 because the satellite geometry repeats after 24 hours in sidereal time The technique has been successfully applied for the monitoring of deformation during the filling process of locks Seeber et al 1997a Wübbena et al 2001a 7627 Precise Marine Navigation Marine Geodesy and Hydrography Because of the realtime capability continuous availability and the high accuracy potential this field of use is very broad continuously growing and is developing fast In this chapter only a short overview is given For more information see 123 751 and the ample literature in symposia proceedings like INSMAP 94 INSMAP 98 or journals like Navigation GPS World Sea Technology The possible applications and the related accuracy requirements can be divided into three user groups a low accuracy requirements about 10 to 100 m in position and 1ms in velocity b medium accuracy requirements about 1 to 10 m in position and 01 ms in velocity and c high accuracy requirements better than 01 m in position and height and 001 ms in velocity User inquiries indicate that highest interest is in the group b ie a position require ment of a few meters User group a can be fully satisfied with a single CAcode navigation receiver aboard a ship GPS will provide continuous twodimensional position accuracy of about 10 to 30 m or better under the Standard Positioning Service 741 Important areas of employment in user group a are for example cf 123 1 general navigation tasks on the high seas 2 research in oceanography 3 ships positioning in small scale bathymetry with swath systems and 4 position and velocity in small scale gravimetric magnetic and seismic mea surements For some applications of tasks 3 and 4 the accuracy of a single operating receiver is not sufficient In these cases and for the majority of applications user group b in marine geodesy hydrography and precise navigation GPS must be operated in the relative mode Differential GPS see 751 Typical fields of application in user group b are for example cf 123 376 7 The Global Positioning System GPS 1 precise navigation in coastal waters 2 harbor approach 3 sea floor mapping in the Exclusive Economic Zone EEZ for the delimitation of seaward boundaries andor for scientific purposes cf Fig 1210 p 524 4 hydrography 5 precise gravimetric and seismic surveys 7 positioning of underwater sensors and samplers in marine prospecting for min eral resources and 6 calibration of transponder arrays In cases where the data are not required in realtime the final positions can be computed afterwards postmission in a postprocessing step However considering the huge amount of data it is advisable to determine the ships position in realtime and not to store the original raw data A further option of the differential mode is to use the carrier phase data at the remote station to smooth the code phase observations 736 with an appropriate filter algorithm 7108 p 296 This method works on a routine basis if an appropriate receiver is used and provides a continuous accuracy of 23 m for the moving antenna or even better The accuracy level satisfies most users of the above list in particular in hydrography and precise surveying activities An increasing user market requires an accuracy level of better than 01 m in particular in the height component user group c In this case the carrier phase observable has to be used as the primary quantity and the ambiguities have to be resolved The pure kinematic method 7354 with ambiguity resolution techniques on the way 7323 has to be applied The methods work well with postprocessing and also in realtime if a data link of sufficient capacity is available 7512 For larger areas the concept of multiple reference stations can be applied to model the distance dependent errors 753 Possible applications in user group c are 1 precise hydrographic surveying 2 monitoring silt accretion and erosion in rivers lakes estuaries coastal waters and harbor areas 3 realtime dredge guidance and control 4 support of coastal engineering 5 marine geodynamics Two further particular applications are 6 precise continuous height control and 7 attitude control of ships buoys floating platforms For precise echosounding and sea level monitoring a continuous height determination with an accuracy of a few centimeters is required and feasible Goldan 1996 Goffinet 2000 Böder 2002 The actual sea level at the location of the surveying vessel must be referred to the height reference onshore depth reduction The conventional method is to estimate the depth reduction dh from tidal and hydrodynamic models with respect to tide gauges onshore With GPS the reduction can be determined directly Fig 788 The GPS 76 Applications 377 GPS antenna echo sounder ellipsoid ϕ λ href dϕ dλ dh dh href t ht dhb hgauge hGPS Figure 788 Depth reduction for echosounding conventional and with GPS antenna phase center does not coincide with the reference point of the echosounder Fig 789 The horizontal and vertical corrections are given by dX X sin β γ S 7170 dZ Z cos β γ S 7171 Z β GNSS antenna γ S X S dX dZ dS echo sounder Figure 789 Inclination correction in echo sounding Figure 790 Attitude control with three GPS antennas To minimize the effect of ship inclina tion on the depth correction dZ it is recommended to install the GPS antenna directly above the sounder β 0 GPS onboard an anchored ship or a moored buoy can also be used to mon itor tidal variation The resolution is a few centimeters depending on the size and behavior of the platform a larger platform shows smaller noise Goldan 1996 A challenging application is continuous height control in calibration areas for altimeter satellites 933 see Fig 910 With three antennasreceivers on board a ship Fig 790 the time dependent spatial behavior of the plat form its attitude can be monitored in realtime Seeber Böder 1998 The achievable accuracy depends on the baseline length between the antennas and the noise in the GPS result Table 724 378 7 The Global Positioning System GPS Table 724 Relationship between a height error dx baseline length s and GPS derived orientation accuracy s dx 3 mm 1 cm 01 m 1 m 017 057 571 5 m 003 011 115 10 m 002 006 057 30 m 0006 002 019 In general a resolution of 01 is sufficient for example for the correction in 7171 Attitude control is of particular importance for the inclination correction of multibeam sonar systems in seabottom mapping 123 Fig 1210 p 524 and for the moni toring of floating GPS sensors at the sea surface in the precise location of submarine geodetic control markers cf 1232 Fig 1212 p 526 For the mathematics of attitude determination see Kleusberg 1995 Cohen 1996 Note that most developments in precise marine navigation with GPS can easily be applied in land navigation and remote vehicle control 7628 Photogrammetry Remote Sensing Airborne GPS The use of GPS contributes in several different ways for example a determination of ground control points in photogrammetry b navigation of sensor carrying airplanes and c determination of sensor platform coordinates and orientation Thedeterminationofgroundcontrolpoints groupaforphotogrammetricmapproduc tion corresponds completely to the procedures discussed in 7621 The technique and effort required depend on the desired map scale For cadastral purposes centimeter accuracy can be achieved with carrier phase adjustment Usually the photogrammetric products have to be related to the official reference frame via at least one control point with known coordinates 121 The accuracy requirements are much less for control points and ground truthing in satellite images eg SPOT LANDSAT The level of 1 to 5 m can be achieved by differential techniques using code or carriersmoothed code observations only without resolving ambiguities 751 The remote receiver can be operated over distances up to several hundred kilometers It is sufficient to collect only a few minutes of data on the site For the precise navigation group b of a survey aircraft the differential mode and a realtime data link are required Usually the transmission of range corrections 7511 is sufficient to assure an accuracy of several meters as long as at least four satellites are visible Conventional DGPS services are well suited to the task The most promising contribution of GPS to photogrammetry is the determination of the sensor orientation in particular the precise camera position group c in order 76 Applications 379 to support aerial triangulation Li 1992 Lee 1996 Schmitz 1998 Fig 791 GPS determined camera positions are introduced as precise observations into the combined Reference station Figure 791 The use of GPS for camera posi tioning in aerotriangulation block adjustment As a consequence the required number of ground control points can be reduced to about 10 per cent or even less of those required in conventional aerotriangulation Jacob sen 1997 2000 In order to achieve the required accu racy level of about 5 cm it is necessary to operate in the differential mode use code and carrier phase data and resolve the phase ambiguities Becauseofthecycleslipproblem inpar ticular in the turns between individual survey strips it is necessary to use ambi guity resolution techniques on the fly 7323 Receivers that provide suffi cient channels for all satellites both fre quencies and low noise code observa tions are particularly suitable The following problems or aspects have to be considered simultaneity of receiver and camera operation eccentricity between antenna phase center and camera projection center and loss of satellite track or cycle slips in turns Modern GPS receivers and aerial cameras allow nearly synchronous operation It is usually not possible for a GPS receiver to measure at arbitrary epochs hence the camera shutter has to be triggered by an output signal from the receiver For older aerial cameras it is advisable to operate the shutter manually or by some external device as near as possible to the GPS observation epoch and to register the midopen time of the shutter Considering the average speed of a photogrammetric aircraft asynchronous operation may introduce errors of up to several meters Another possibility is to interpolate the aircraft positions between the GPS positions with an inertial platform INS The integrated techniques of GPS and INS provide an accuracy of a few centimeters Lee 1996 Cramer 2001 The 3D eccentricity between the GPS antenna and the camera projection center Fig 792 includes the distance and the three orientation angles The distance is invariable and has to be measured by conventional means The orientation can be determined by a GPS based platform orientation unit with three GPS antennas cf 7627 as a byproduct of an inertial package onboard or with inclinometers 76 Applications 381 GPS meteorology Figure 793 Ice flow from GPS observations In glacial geodesy and Antarctic research GPS can be employed suc cessfully to determine the movement of glaciers or ice sheets Hinze 1990 If motion parameters velocity and az imuth are to be derived from repeated measurements over the years a quasi online reading suffices while a route is traversed with snow mobiles or a helicopter lands for a short time In the relative mode to a fixed station subdecimeter accuracy can be attained with short observation times depending on the distance to the reference station 751 so that correct results can be ex pected from repeated measurements af ter about 1 month in the same season Fig 793 gives an example from the Ek ström Ice Shelf near the German Antarctic station Georg v Neumeyer GPS is one of the most efficient means for operational global clock synchronization Table 725 gives an overview of the achievable accuracy Lombardi et al 2001 In most cases the socalled commonview technique is applied The time of arrival of the same signal from one satellite is observed at two stations and compared with the local reference clocks Afterwards the data are exchanged The signal travel time between the satellite and the station has to be calculated based on precise coordinates for both stations and precise satellite orbits Single channel technique means that the measure ments follow a predetermined tracking schedule In the multichannel commonview technique data from all satellites in view are recorded without a schedule The latter mode facilitates continuous comparison of standards with no gaps in the data Table 725 Accuracy of GPS time transfer Technique Timing Uncertainty Frequency Uncertainty 24 hours 2 σ 24 hours 2 σ OneWay 20 ns 2 1013 SingleChannel CommonView 10 ns 1 1013 MultiChannel CommonView 5 ns 5 1014 CarrierPhase CommonView 500 ps 5 1015 A station position error of 3 cm enters 100 picoseconds into the error budget The effect of orbital errors follows the rule of thumb 7134 hence an orbit accuracy of 382 7 The Global Positioning System GPS 01 m is required for 100 picoseconds time transfer over 5000 km The International GPS Service IGS 781 considerably supports operational high precision global time transfer through its station network and products A number of the stations are connected with external oscillators like Hmasers cesium and rubidium clocks IGS 2000 Several manufacturers offer dedicated GPS receivers for timetransfer For the nanosecond accuracy level all error influences including hardware delays have to be carefully modeled Realtime relative time transfer at the 100 picoseconds level has been demonstrated within the InternetBased Global Differential GPS project of the NASAJPL Powers et al 2002 see also 7512 For a topical treatment of GPS time transfer see for example Schildknecht Dudle 2000 Very powerful GPS Earth Science applications result from the deployment of GPS sensors on near Earth orbiting satellites socalled LEOs 342 The GPS data re ceived at the orbiting platform may serve for precise orbit determination of remote sensing satellites primarily altimeter satel lites 9 precise position and orbit determination of satellites probing Earths gravity field 10 attitude control of space vehicles and analysis of GPS signals after passing the atmosphere GPSMET One of the first demonstrations for precise orbit determination with GPS see 3323 was with the TOPEXPOSEIDON mission Melbourne et al 1994a Since then GPS receivers have been included in a number of missions in particular on LEO satellites like CHAMP GRACE JASON1 and ICESAT Precise orbit determination POD 3323 is supported by the orbit and clock products of the IGS The accuracy level is in the order of a few decimeters and may reach subdecimeter after tailored gravity field improvement Wickert et al 2001 On the other hand LEO data are of interest to IGS The IGS has started a pilot project to study the inclusion of LEO data into the regular IGS products IGS 2000 If the satellite carries three or more GPS antennas it is possible to determine its attitude Since the baseline between the antennas is always very small and only the carrier phase difference is required single frequency CAcode receivers can be used For details of the technique see for example Purivigraipong Unwin 2001 GPS contributes with two different techniques to the improvement of global weather data The continuous observations at more than 200 IGS sites are used to model the total zenith delay at a level of 3 to 5 mm that corresponds to better than 1 millimeter in water vapor IGS 2000 The data are available as a regular IGS product and can be used by meteorological institutions in numerical weather prediction models For details of the subject see also Schüler 2001 For very dense networks of monitor stations for example in Germany with a spacing of about 50 km the accuracy of the integrated water vapor was found to be 1 to 2 mm with a delay of only 40 minutes Reigber et al 2002 77 GNSS Global Navigation Satellite System 383 The second technique uses the observations made between GPS satellites and LEOs equipped with GPS receivers Fig 794 demonstrates how GPS contributes to atmospheric research Figure 794 The use of GPS in atmospheric research after Yunck Melbourne 1990 Due to the relative motion between the LEO satellite and a GPS satellite setting behindEarthsdisk thetangentialpointoftheradiolinkbetweenthetwospacevehicles moves downward with a geocentric velocity of about 25 to 3 kilometers per second Hocke Tsuda 2001 and scans the atmospheric layers from the high atmosphere down to Earths surface The signals are affected both by the ionosphere and the troposphere and can be used for ionospheric tomography as well as for mapping the integrated water vapor The technique is known as radio occultation or limb sounding A first experiment GPSMET was carried out with the launch of the MICROLAB satellite in 1995 Hocke Tsuda 2001 Other suitable satellites for radiooccultations are ÖRSTED launch January 1999 CHAMP and GRACE For details on the tech nique see eg Kleusberg 1998 First results from CHAMP radio occultations are reported in Wickert et al 2001 CHAMP measures at a rate of 50Hz and provides about 230 globally distributed vertical profiles of atmospheric parameters per day 77 GNSS Global Navigation Satellite System GPS is not the only satellitebased navigation system The Russian Federation is operating GLONASS and the European Union together with the ESA is planning GALILEO In addition various augmentations to GPS are under preparation The general name given to these systems is Global Navigation Satellite System GNSS Most of the material outlined in chapter 7 is also valid for other GNSS systems This is why in many publications instead of GPS the more general term GNSS is used The term GNSS was coined at the 10th Air Navigation Conference in 1991 when the International Civil Aviation Organization ICAO recognized that the primary 384 7 The Global Positioning System GPS standalone navigation system in the 21st century will be provided by the Global Navigation Satellite System GNSS Hein 2000 As commonly understood GNSS includes more than just satellitebased positioning Important features besides accu racy are integrity availability and continuity of service GPS and GLONASS being primarily military systems do not guarantee these capabilities On the way to establish GNSS several steps have been defined GNSS1 is based on GPS andor GLONASS as backbone and is augmented by additional civil components GNSS2 is a secondgeneration satellite navigation system which fulfills the above requirements such as GPS IIF or the European GALILEO In the following some of the particular features of GNSS developments are ex plained 771 GLONASS The former Soviet Union SU has since the 1970s been developing a navigation system very similar in design to GPS under the name GLONASS GLObal NAvigation Satellite System The Russian denomination is Globalnaya Navigatsionnaya Sput nikowaya Sistema Today GLONASS is continued by the Russian Federation Like GPS GLONASS is a military system but it has been offered to civil use by several declarations of the Russian Federal Government Slater et al 1999 The system was officially put into operation on September 24 1993 as a firststage constellation of twelve satellites By the end of 1995 the constellation was expanded to 24 satellites standard constellation Due to a lack of new launches the constellation has since then decreased considerably By the end of 2002 only 7 satellites were operational Similar to GPS with SPS and PPS 716 741 GLONASS provides a standard precision SP and a high precision HP navigation signal The SP signal is continu ously available to all civil users worldwide The specification for SP accuracy is 50 to 70 m horizontally and 70 m in height Information for civil users is available via the Coordinational Scientific Information Center CSIC of the Russian Space Forces In this section some basic information on GLONASS is given For further read ing with additional references see eg Kaplan 1996 chap 10 Daly Misra 1996 Habrich 2000 Roßbach 2001 A short introduction is given by Langley 1997a Table 726 compares GLONASS with GPS and indicates similarities and differences It is evident that the systems have strong similarities The main characteristics and differences are as follows a Satellite orbits In the baseline constellation both systems consist of twentyfour satellites including three spares Unlike GPS the GLONASS satellites are arranged in 3 orbital planes 110 apart Each orbital plane contains eight equally spaced satellites Fig 795 shows the complete configuration The ground tracks repeat every seventeen orbits or eight sidereal days The orbits are arranged in such a way that resonance phenomena do not occur and that in one 386 7 The Global Positioning System GPS Table 726 Comparison of GLONASS and GPS Parameter GLONASS NAVSTAR GPS Satellites Number of satellites in 21 3 spares 21 3 spares the baseline constellation Number of orbital planes 3 6 Inclination 648 55 Orbital altitude 19 100 km 20 180 km Orbital radius 25 510 km 26 560 km Orbital period sidereal time 11 hours 15 min 12 hours Repeat ground tracks every sidereal day every 8 sidereal days Navigation message Ephemeris 9 parameters Keplerian elements representation position velocity and interpolation acceleration in the coefficients ECEF Cartesian system Geodetic datum PZ90 WGS 84 Time base GLONASS system time GPS system time Related system time UTCSU UTCUSNO Almanac transmission 25 minutes 125 minutes Signals Satellite signal division Frequency division Code division Frequency band L1 16021615 MHz 1575 MHz Frequency band L2 12461256 MHz 1228 MHz Codes same for all satellites different for all satellites CAcode on L1 CAcode on L1 Pcode on L1 L2 Pcode on L1 L2 Code type PRN sequence Gold code Code frequency CAcode 0511 MHz 1023 MHz Code frequency Pcode 511 MHz 1023 MHz Clock data clock offset clock offset frequency offset frequency offset and rate frequencies to a somewhat lower domain In addition the number of frequency chan nels is cut in half socalled antipodal satellites ie satellites in the same orbital plane separated by 180 degrees in the argument of latitude share the same chan nel The reorganization of the frequency plan occurs in several steps From 1998 to 2005 the frequency numbers k 7 12 are applied and after 2005 the numbers k 7 4 5 6 for testing only The bands will hence be finally shifted to 15980625160425 MHz for L1 and 12429375124775 MHz for L2 77 GNSS Global Navigation Satellite System 387 c Navigation message The navigation data are biphase modulated onto the carrier at 50 bitss The binary sequence has a total length of 2 seconds called one line The digital data structure is formed by navigation superframes of 25 minutes in length A superframe consists of five frames of 30 seconds each and each frame consists of fifteen lines subframes As with GPS the GLONASS message contains precise orbital information ephemeris data about the individual satellites own position and status and less precise almanac information about other satellite positions Lines 14 of a frame contain the ephemeris data of the transmitting satellite and line 5 general information concerning the entire system Lines 615 contain the almanac data for five satellites The almanac data of the complete system hence require one superframe corresponding to 25 minutes Details of the data format can be found in the official GLONASS Interface Control Document ICDGLONASS or in the literature cited above The navigation message contains for example coordinates for the ith satellite in the ECEF reference frame for the reference time speed vector components for the ith satellite acceleration vector components caused by Earth and Moon gravity time scale correction to the GLONASS time scale for the ith satellite and satellite identification number status information reference time The GLONASS broadcast ephemerides are updated every 30 minutes and refer to the center of the 30 minutes time interval For a measurement epoch in between these half hour marks the satellite position has to be interpolated using the position velocity and acceleration data from the reference epochs before and after the observation epoch These data are used as initial values for an integration of the equation of motion 33 eg Roßbach 2001 d Control Segment The groundbased control segment is responsible for Kaplan 1996 prediction of satellite ephemerides uploading of ephemeris clock correction and almanac data into each satellite synchronization of the satellite clocks with GLONASS system time estimation of the offset between GLONASS system time and UTC SU and spacecraft control The ground segment consists of the System Control Center the Central Synchronizer several Command and Tracking Stations and Laser Tracking Stations The ground control center is in Moscow The monitoring stations are uniformly dis tributed over the territory of the former Soviet Union hence lacking global coverage The navigation and control parameters are uploaded twice per day to each satellite The central synchronizer forms the GLONASS system time and is related to the phase 390 7 The Global Positioning System GPS is depicted in Fig 796 The threeaxis stabilized satellite is equipped with a propul sion system for station keeping and relocation attitude control and laser cornercube Figure 796 GLONASS spacecraft reflectors The antenna beamwidth of 35 to 40 degrees provides navigation signal reception up to 2000 km above Earths surface The numbering scheme is many fold Besides the international satel lite ID number the GLONASS satellites are given numbers in the COSMOS se ries a sequential GLONASS number an orbital position number and a channel number The usual identification follows the channel number A new generation of spacecraft intended to replace older satellites is under prepa ration and commonly referred to as GLONASSM M for modified A first launch took place in December 2001 but as of December 31 2002 no GLONASSM spacecraft was operational The main advantages of the GLONASSM series are longer lifetime of five to seven years enhanced clock stability intersatellite communication autonomous spacecraft operation and modified structure of the navigation format For details on GLONASS satellites see Johnson 1994 Kaplan 1996 Due to the short design lifetime of the current spacecraft generation frequent launches are required to maintain the constellation During the first months of 1996 the constellation was fully deployed with 24 satellites Thereafter several spacecraft were withdrawn from service and not replaced Between January 1997 and January 1999 12 to 16 satellites were always available Since then the number has continuously decreased As of March 2003 the following eleven satellites were in service Plane 1 SV channel 2 7 8 9 12 Plane 3 SV channel 3 5 5 10 10 11 Note the use of the same channel on pairs of antipodal satellites h Use of GLONASS During the period of full deployment GLONASS showed a similar performance to GPS The advantages of GLONASS are that there has been no artificial signal degrada tion like SA and that the Pcode is fully available The user range error URE shows a standard deviation of 8 to 10 m Roßbach 2001 After 1992 several commercial receiver makes entered the market Two groups of user equipment can be distinguished navigation receivers L1 CA code and L1 carrier phase and geodetic receivers L1 CA and Pcode carrier phase L2 Pcode and carrier phase 77 GNSS Global Navigation Satellite System 391 Several advanced receivers offer the possibility to observe both GPS and GLONASS satellites Examples are the Ashtech Z18 the series of JPS receivers and the Novatel Millennium board Fig 797 shows the JPS Legacy dual frequency 40 channel receiver with the RegAnt antenna Figure 797 Combined GPSGLONASS re ceiver JPS Legacy with RegAnt antenna As with GPS plans were devel oped in Russia to establish a differen tial GLONASS DGLONASS service Because of the large size of the country the implementation went slowly Ganin 1995 Instead developments started to combine GPS and GLONASS into a combined DGNSS service Chistyakov et al 1996 An important prerequi site was fulfilled with the inclusion of DGLONASS correction data into the format RTCM 22 from January 1998 7512 GLONASS carrier phase data can be used either alone or together with GPS data for precise geodetic applications For observation equations modeling of ob servables and ambiguity resolution see eg Habrich 2000 or Roßbach 2001 In 19981999 a major effort was undertaken to exploit the potential of GLONASS for the geodetic community Under the auspices of the IAG and the IGS and also ION and IERS the International GLONASS Experiment IGEX98 was initiated and re alized The major objectives were to collect GLONASS data for several months from a worldwide network of tracking stations compute precise orbits evaluate receivers and resolve geodetic reference frame and time system issues Slater et al 1999 The campaign lasted six months from October 1998 untilApril 1999 Over 60 GLONASS tracking stations and 30 Satellite Laser Tracking SLR observatories in 25 countries participated Precise orbits were computed by several analysis centers using the SLR and GLONASS receiver data with accuracies of 2050 cm Datum transformation parameters relating PZ90 WGS 84 and ITRF were analyzed The most interest ing results were discussed at a meeting in September 1999 and are published in a comprehensive report Slater et al 1999 After the termination of IGEX98 a number of stations 32 as of December 2000 continued dual frequency tracking within the International GLONASS Service IG LOS Pilot Experiment under the auspices of the IGS The goals and objectives are IGS 2000 establish and maintain a global GLONASS tracking network produce precise 10centimeter level orbits satellite clock estimates and station coordinates monitor and assess GLONASS system performance investigate the use of GLONASS to improve Earth orientation parameters 392 7 The Global Positioning System GPS improve atmospheric products of the IGS and fully integrate GLONASS into IGS products operations and programs To support these goals three GLONASS satellites are tracked with high priority by Satellite Laser Ranging see 851 The longterm success of an International GLONASS Service certainly depends on the reliability and maintenance of the GLONASS constellation Many of the potential applications do not require a full constellation but take advantage of GLONASS as an augmentation to GPS This may however become a critical issue if not enough new launches take place and the number of usable satellites further goes down 772 GPSGLONASS Augmentations GPS and GLONASS are systems under military control and do not fulfill the re quirements for safe navigation in particular coming from the international aviation community These requirements are in particular accuracy integrity availability and continuity of service Accuracy requirements depend on the particular application for example 4 m vertical position accuracy in Category I aircraft approach landing FRNP 2001 Dif ferential techniques are required to meet these demands Integrity is the ability of a system to provide timely warnings to its users when it should not be used for navigation see 746 and Langley 1999b This service requires a network of control stations and channels to transmit the warnings in due time to the user Availability means the ability of the system to provide usable service within the specified coverage area and continuity of service means the availability of service without interruptions for the intended operations Hein 2000 In order to meet these requirements augmentation systems to the existing satellite navigation systems GPS and GLONASS have been established or are under devel opment These are the Wide Area Augmentation System WAAS in the USA 7531 European Geostationary Navigation Overlay System EGNOS in Europe Multifunctional Satellitebased Augmentation Service MSAS in Japan and Satellite Navigation Augmentation System SNAS in China All are contributions to a first generation of a Global Navigation Satellite System GNSS1 and intend to provide seamless coverage of the whole globe They are also known as SatelliteBased Augmentation Systems SBAS An alternative solution are GroundBased Regional Augmentation Systems GBRAS broadcasting corrections on VHF The generic architecture of a satellitebased augmentation system is as follows A network of GPS GLONASS stations at surveyed locations collects dual frequency 77 GNSS Global Navigation Satellite System 393 measurements of pseudorange and pseudorange rate for all spacecraft in view along with local meteorological data The data are processed and generate precise correc tions to the broadcast ephemerides and clock offsets These corrections together with system integrity messages are transmitted to the users via a dedicated package on geostationary satellites This technique also supports an additional GPSlike ranging signal between GEO and user Hence in total three additional signals are provided a ranging integrity and WAD wide area differential signal The European contribution to GNSS1 EGNOS Benedicto et al 1999 includes augmentations to GPS and GLONASS It is described in more detail as an example EGNOS is part of the European Satellite Navigation Program ESNP and is initi ated by the European Tripartite Group European Commission EC European Space Agency ESA EUROCONTROL since about 1993 The current EGNOS space segment is composed of transponders on two geostationary INMARSAT3 satellites positioned over the Atlantic Ocean Region East AORE and the Indian Ocean Re gion IOR These satellites provide extra ranging signals over Europe For the full operational capability FOC expected for 20042005 additional GEO transponders are required Soddu Razumovsky 2001 The EGNOS ground segment consists of about 40 Ranging and Integrity Monitor ing Stations RIMS mostly in Europe These RIMS collect ranging measurements from the GPS GLONASS and GEO navigation signals on L1 and L2 frequencies The collected data are transmitted to a set of redundant Mission Control Centers MCC where the integrity information differential corrections GEO satellite ephemerides and ionospheric delays are estimated These data together with the GEO ranging signal are uplinked to the GEO satellites from where they are transmitted on the GPS L1 frequency as GPS like navigation signals to the users It will be possible to receive EGNOS navigation data over Europe South America Africa Western Australia and a large part of Asia The US WAAS architecture is very similar to EGNOS For details see FRNP 2001 WAAS however does not include GLONASS satellites The system is pro jected to be fully operational by the end of 2003 Augmentation systems like WAAS EGNOS MSAS or others will make it possi ble for many applications to obtain DGPS accuracy without the cost of extra reference stations or radio data links and they offer continentwide coverage In the long term augmentation systems are likely to replace the conventional DGPS services 773 GALILEO The European Commission together with the European Space Agency ESA and European industry is building up a European Satellite Navigation System under the name GALILEO as Europes contribution to GNSS2 The system will be controlled by civil authorities and be interoperable with GPS and GLONASS It offers dual frequency as standard and will provide realtime positioning and timing services at different levels of accuracy integrity and availability Other than the existing satellite navigation systems GALILEO is a suitable system for safety critical applications 394 7 The Global Positioning System GPS such as landing aircraft guiding cars tracking hazardous materials and controlling rail traffic The GALILEO schedule comprises several phases The definition phase from 1999 to 2001 included the initial definition of requirements and system architecture Two major studies took place the EC study GALA on the system architecture and the ESA study GalileoSat on the space segment Based on the results of these studies a 4 years design and validation phase from 2002 to 2005 was initiated by the Euro pean Council EC on March 26 2002 This phase includes a consolidation of the requirements the development of satellites and ground based components and the inorbit validation A first experimental satellite will be launched by the end of 2004 Up to four operational satellites will be launched thereafter in 2005 and 2006 for final validation of the space and ground segment The remaining operational satellites will be launched in the deployment phase from 2006 to 2007 to reach the full operational phase in 2008 The information within this section is mainly taken from ESA documents and the cited literature eg Forrest 2002 Eisfeller 2002 Details are subject to changes dur ing the design and validation phase For updated information see the ESA homepage the journal Galileos World and conference proceedings like IONGPS a Space segment The GALILEO space segment when fully deployed consists of 30 satellites 27 operational 3 active spares in three circular Medium Earth Orbits MEO Fig 798 Figure 798 Probable GALILEO constellation This configuration is also called Walker constellation 2731 The inclination an gle is 56 degrees and the orbital alti tude 23 616 km The orbital period is 14 hours 4 minutes and the ground tracks repeat after about 10 days The constel lation is optimized for Europe and pro vides a good coverage up to a northern latitude of 75 degrees The GALILEO satellite Fig 799 has a mass of 625 kg and measures 27 12 11 m3 it hence belongs to the class of minisatellites The naviga tion payload includes 2 rubidium stan dards and 2 hydrogen masers Other than GPS each satellite carries laser reflectors for independent orbit determination Several deployment strategies are possible for example up to 8 GALILEO spacecraft simultaneously launched with ARIANE 5 or up to 6 spacecraft simultaneously with the PROTON launcher The injection is directly into the MEO orbit b Ground segment The GALILEO ground segment consists of two GALILEO Control Centers GCC One is responsible for the control of satellites and the generation of navigation and time 77 GNSS Global Navigation Satellite System 395 Figure 799 GALILEO satellite possible schematic view data the other is responsible for the control of integrity About 30 globally distributed monitor stations the GALILEO Sensor Stations GSS provide data for the GCCs Data transmission to the satellite is realized via 10 upload stations with Sband andor Cband antennas A further feature is the global Search and Rescue SAR function Each satellite is equipped with a transponder which is able to transmit emergency signals to a rescue center A particular link gives a feed back to the user In Europe the integrity service is closely related to the EGNOS system 772 c Services Several particular services will be offered within the GALILEO service framework Forrest 2002 satellite navigation signals only services combined services with other GNSS or with non GNSS and local services Among the satellite only services besides the search and rescue service are four position velocity and time services Open Service providing positioning navigation and time for a mass market free of charge Commercial Service with added value over the open service for professional use with service guarantee and user fees Safety of Life Service includes integrity in particular for landing approach and vehicle guidance Public Regulated Service for applications devoted to EuropeanNational secu rity For geodesy surveying and GIS the open service and the commercial service are of particular interest The accuracy with a single dual frequency receiver is estimated to be 4 m horizontal 8 m vertical 50 nsec time at the 95 level The commercial service will have some additional features such as augmentation with local elements like multiple reference stations 753 396 7 The Global Positioning System GPS d User segment The receiver architecture will be similar to those used with GPS but with modern elements in the digital signal processing and reference to the particular GALILEO signal structure Combined GPSGALILEO receivers will be designed at least for 4 frequencies The user market is predicted for 2005 as follows Eisfeller 2002 73 mobile phones 23 car navigation 1 aviation 1 fleet management 1 leisure and 1 surveying e Signal structure The GALILEO signal structure is not yet definitely decided Probably the carrier frequencies shown in Table 729 will be used in the lower middle and upper Lband Table 729 GALILEO carrier frequencies status August 2002 Carrier Middle frequency MHz E5a L5 117645 E5b 120714 E6 1278750 E2 L1 E1 157542 There are potential interferences with the GPS signals L1 and L5 mitigation of which will require particular modulation techniques On the other hand such signal overlap facilitates antenna design for hybrid receivers and guarantees maximum inter operability Difficulties also exist with the bandwidths For E1 and E5 the bandwidth is just 4 MHZ and rather small for a robust signal As shown E6 is not a protected band and hence its use is questionable In the future at least 5 civil signals will be available to combined GPSGALILEO receivers namely code pseudorange and carrier phase Modernized GPS L1 L2 L5 GALILEO E1L1E2 E5a b Simulations show Eisfeller 2002 that a combined evaluation of GPSGALILEO data for geodetic purposes has several advantages increased number of satellites 15 smaller PDOP 16 increased success rate of the ambiguity fixing and increased positioning accuracy by a factor of 2 for the horizontal and a factor of 3 for the vertical component An interoperable GNSS will enhance the use of satellitebased positioning in difficult environments like mountainous terrain urban canyons and around large structures like dams or industrial complexes 78 Services and Organizations Related to GPS 397 f Applications The expected field of possible applications is manyfold as with GPS 762 An overview is given in Table 730 Table 730 Possible application markets for GALILEO Forrest 2002 Professional Mass market Safety of life geodesy personal communication aviation precision survey and navigation maritime land survey GIS cars rail photogrammetry buses trucks police remote sensing commercial vehicles fire timing inland waterways emergency mining coastal waters ambulance oil and gas outdoor recreation search and rescue environment personal protection fleet management traffic surveillance precision agriculture EEZ delimitation fisheries vehicle control robotics construction engineering meteorology space application 78 Services and Organizations Related to GPS 781 The International GPS Service IGS The IGS was established by the InternationalAssociation of Geodesy IAG and started its activities formally on January 1 1994 after a pilot phase of about 1 year The IGS is a member of the Federation of Astronomical and Geophysical Data Analysis Services FAGS and it works in close cooperation with the International Earth Rotation Service IERS On January 1 1999 the name of the service was changed from the original International Global Positioning System GPS Service for Geodynamics IGS to International GPS Service IGS The information in this section is mainly taken from IGS documents like the IGS Annual Reports and the IGS Directory These documents are available from the IGS Central Bureau Following the IGS Terms of Reference IGS 2002a the primary objective of the IGS is to provide a service to support through GPS data and data products geodetic 398 7 The Global Positioning System GPS and geophysical research activities The IGS collects archives and distributes GPS observation data at a number of tracking stations These data sets are used by the IGS to generate data products namely high accuracy GPS satellite ephemerides Earth rotation parameters IGS tracking station coordinates and velocities GPS satellite and tracking station clock information ionospheric information and tropospheric information In order to fulfill its tasks the IGS has a certain structure Fig 7100 with several components Networks of Tracking Stations Data Centers Analysis and Associate Analysis CentersAnalysis Coordinator Working Groups and Pilot Projects Central Bureau and Governing Board IUGG IAG FAGS ICS International GPS Service International Governing Board Central Bureau Analysis Network Coordinator Coordinator Users Associate Analysis Centers Operational IGS Reference Frame Coordinator Data Centers Analysis Global Centers Regional Network Stations Pilot Projects and Working Groups Figure 7100 Structure of the IGS 78 Services and Organizations Related to GPS 399 The products of the IGS support scientific activities such as improving and extending the International Terrestrial Reference Frame ITRF monitoring deformations of the solid Earth monitoring Earth rotation monitoring variations in the liquid Earth sea level ice sheets determining orbits of scientific satellites monitoring the high atmosphere ionospheric tomography and climatological research contributions to weather prediction a Network of Tracking Stations The global IGS network of permanent dualfrequency GPS tracking stations included more than 300 stations in 2002 representing some 200 agencies around the world The number is still growing Fig 7101 shows the global station distribution The stations have to meet certain requirements in particular they need data transmission facilities for a rapid at least daily data transfer to the data centers The tracking data are analyzed by at least one Analysis Center or Associate Analysis Center IGS stations which are analyzed by at least three IGS Analysis Centers for the purpose of orbit generation are called IGS Global Stations numbering about 120 early in 2002 All IGS stations can be taken as reference stations for regional GPS analyses The tracking data are available in RINEX format from the Data Centers Approximately 90 IGS stations are producing hourly 30seconds RINEX files and about 35 stations are providing data in near realtime delivering 15 minute 1 Hz data files Schmidt Moore 2002 The ensemble of IGS stations form the IGS network or polyhedron In 2002 at about 50 stations GLONASS satellites were also tracked Figure 7101 IGS Network 2002 source IGS b Data Centers There are three categories of data centers Operational Regional and Global Data Centers The Operational Data Centers ODCs in total 25 at the end of 2000 are in direct contact to the tracking stations They maintain the data in local archives validate 400 7 The Global Positioning System GPS and reformat the data conversion to RINEX and data compression and transmit them to a regional or global data center Regional Data Centers RDCs in total five collect reformatted tracking data from several data centers maintain a local archive for users interested in stations of a particular region and transmit the data to the Global Data Centers The Global Data Centers GDCs are the main interfaces to the Analysis Centers and to the general user community Among other tasks they archive and provide on line access to tracking data and IGS products GDCs provide an online archive of at least 100 days of GPS data in the RINEX format including the data from all global IGS sites The GDCs also provide an online archive of derived products generated by the IGS analysis or associate analysis centers There is also online access to IGS products generated since the start of the IGS test campaign in 1992 The three Global Data Centers are CDDIS Crustal Dynamics Data Information System NASA Goddard Space Flight Center USA IGN Institut Géographique National France and SIO Scripps Institution of Oceanography USA c Analysis Centers There are two categories of analysis centers Analysis Centers ACs and Asso ciate Analysis Centers AACs The Analysis Centers receive and process track ing data from one or more data centers and generate IGS products as a minimum ephemerides Earth rotation parameters station coordinates and clock information as well as other recommended products The products are delivered to the Global Data Centers and to the IERS using designated standards The Analysis Centers are COD Center for Orbit Determination in Europe University of Berne Switzerland EMR Geodetic Resources Division Natural Resources Canada Ottawa Canada ESA European Space Operations Center European Space Agency Darmstadt Germany GFZ GeoForschungsZentrum Potsdam Germany JPL Jet Propulsion Laboratory California Institute of Technology Pasadena California USA NGS National Oceanic and Atmospheric AdministrationNational Geodetic Survey Silver Spring Maryland USA and SIO Scripps Institution of Oceanography University of California San Diego California USA The Associate Analysis Centers produce specialized products for example ionospheric maps or station coordinates and velocities for a global or regional subnetwork Of particular importance are the Global or Regional Network Associate Analysis Cen ters GNAACs or RNAACs producing weekly solutions of the global polyhedron or regional subsets thereof Examples for RNAACs are the EUREF NAREF or SIRGAS networks for Europe North and South America Blewitt 1998 78 Services and Organizations Related to GPS 401 The Analysis Coordinator monitors the activities of the Analysis Centers This person is also responsible for the appropriate combination of the Analysis Center products into a single set of products in particular a single IGS ephemeris for each GPS satellite d Working Groups and Pilot Projects A Working Group works on a particular topic A Pilot Project has the objective to develop a particular IGS product or service relying on the IGS infrastructure Active Working Groups and Pilot Projects by the end of 2002 were for example Reference Frame Densification Working Group IGSBIPM Time and Frequency Pilot Project Ionosphere Working Group Troposphere Working Group International GLONASS Service Pilot Project Low Earth Orbiter Pilot Project Realtime Working Group Tide Gauge Pilot Project and African Reference System AFREF Pilot Project e Central Bureau and Governing Board The Central Bureau CB is responsible for the general management of IGS and coor dinates all IGS activities The Governing Board GB sets the IGS policy and exercises a broad oversight of all IGS functions and components The Central Bureau for the time being is located at the Jet Propulsion Laboratory in Pasadena California and maintains an IGS Information System CBIS accessible at httpigscbjplnasagov World Wide Web The CBIS contains information on the availability of and access to tracking data and IGS products IGS orbits Earth rotation parameters and other data CBIS also gives access to IGS publications like annual reports and workshop proceedings An overview of current IGS products is given in Table 731 782 Other Services A large number of international and national services provide information on GPS and other GNSS systems Here only some indications are given Note that webaddresses may change For updated information see the regular Almanac pages in the August and December editions of GPS World CanadianSpaceGeodesyForum httpgaussggeunbcaCANSPACEhtml AserviceoftheUniversityofNewBruswick Canada PresentsdailyGPSconstellation status reports and ionospheric disturbance warnings News and discussion about GPS and other spacebased positioning systems US Coast Guard Navigation Center httpwwwnavcenuscggovgps GPS constellation status almanac data information on DGPS Loran C US National Geodetic Survey httpwwwngsnoaagovGPSGPShtml Precise and rapid orbits General information on GPS 402 7 The Global Positioning System GPS Table 731 IGS products status August 2002 source IGS Central Bureau Accuracy Latency Updates Sample Interval GPS Orbits Clocks Broadcast 260 cm 7 ns real time daily UltraRapid 25 cm 5 ns real time twice daily 15m15m Rapid 5 cm 02 ns 17 hours daily 15m5m Final 5 cm 01 ns 13 days weekly 15m5m GLONASS Orbits Final 30 cm 4 weeks weekly 15m Geocentric Coordinates IGS Tracking Stations Final horizvert position 3 mm 6mm 12 days weekly weekly Final horizvert velocity 2 mm 3 mm per yr 12 days weekly weekly Earth Rotation Rapid polar motion 02 mas 04 masd 17 hours daily daily polar motion rates LOD 0029 ms Final polar motion 01 mas 02 masd polar motion rates LOD 0020 ms 13 days weekly daily Atmospheric Parameters Final tropospheric 4 mm zenith path 4 weeks weekly 2 hours delay Ionospheric TEC grid under development for comparison Geodetic Survey Division NatRes Canada httpwwwgeodnrcangcca Provides access to data of the Canadian Spatial Reference System CSRS and Cana dian Active Control System CACS Scripps Orbit and Permanent Array Center SOPAC httpsopacucsdedu A service of the Scripps Institution of Oceanography University of California SOPAC provides precise rapid ultra rapid hourly and predicted orbits for the IGS in SP3 format Further SOPAC archives daily RINEX data from about 800 continuous GPS sites from various networks and arrays IGS SCIGN CORS EUREF and others SOPAC is also the operational Center for the California Spatial Reference Center National Imagery and Mapping Agency NIMA http164214259 GandGsathtml Offers precise GPS orbit information based on tracking data from US Air Force NIMA and IGS sites Daily precise ephemerides and satellite clock estimates in SP3 format Earth Orientation Parameter predictions National Mapping Division Australia AUSLIG httpwwwauslig govau Comprehensive wwwsite with information on various GPSrelated topics Data from 78 Services and Organizations Related to GPS 403 the Australian Regional GPS Network Online GPS processing service for RINEX data Federal Agency for Cartography and Geodesy BKG Germany httpgibs leipzigifagde The information site GIBS is a service of the Bundesamt für Kartographie und Geodäsie FankfurtLeipzig GIBS GPS Informations und Beobachtungssystem provides almanac data information on GPS status datum transformations satellite visibility precise ephemerides DGPS GLONASS status and almanac data The site also contains comprehensive information material on GPS and services like SAPOS For information on Galileo see Galileo Homepage httpwwwgalileopgmorg Genesis Office httpwwwgenesisofficeorg Genesis is a project providing support to the European Commission on its GALILEO activities GENESIS communicates and disseminates information related to GALILEO and also distributes a Galileo Newsletter 406 8 Laser Ranging solution of important tasks in geoscience This remains true in spite of the increasing efficiency of microwave techniques like GPS and DORIS The eminent advantages of the satellite laser ranging technique are among others the very high accuracy potential in particular because of the favorable propagation properties of light longevity of satellites without active elements long time series of observations and derived parameters determination of absolute geocentric coordinates in particular absolute heights independent control of other geodetic space techniques and backup for active orbit determination systems like PRARE DORIS GPS Possible disadvantages are strong dependence on suitable weather conditions high costs in building and maintaining the ground segment inhomogeneous data distribution compared to GPS DORIS or VLBI no or limited mobility of the ground segment and hence only limited operational capability For further reading on technical questions see the proceedings volumes of the International Workshop on Laser Ranging Instrumentation eg Schlüter et al 1999 ILRS2001 TheapplicationofSLRingeodesyandgeodynamicsiswidelydiscussed in the geodetic literature in proceedings of the IAG eg Schwarz ed 2000 in scientific journals like the Journal of Geophysical Research or the Journal of Geodesy and in the reports of the International Laser Ranging Service ILRS see 851 A short introduction is also given in Degnan Pavlis 1994 82 Satellites Equipped with Laser Reflectors Laser ranging is only possible to satellites equipped with appropriate reflectors The incoming laser light must be sent back in exactly the same direction from which it comes Such types of reflectors are also called retroreflectors they are mostly made from glass prisms A retroreflector can be created by cutting an evenly sized pyramid from the corner of a cube This is why they are often named corner cube reflectors Henriksen 1977 In order to attain the desired accuracy reflectors have to be carefully designed for the particular satellite geometry and orbital height in particular the energy balance has to be adjusted The reflector must be sufficiently large to reflect enough energy In most cases several single reflectors with a diameter of 2 to 4 cm are assembled in certain arrays to achieve the necessary energy level The alignment of the individual reflector requires extreme care in order to avoid pulse deformations caused by signal superposition The signal path within the cube corner must be known If the reflectors cannot be arranged symmetrically with respect to the spacecrafts center of mass for instance for multiplepurpose satellites the geometrical relationship between the individual reflector and the satellites center of mass is required 84 82 Satellites Equipped with Laser Reflectors 407 Reflectors are passive devices and can be fitted easily enough as additional com ponents on a given satellite This is why a fairly large number of space vehicles carry an array of laserreflectors Table 81 gives an overview of a selection of satellites carrying laser ranging targets The total number by 2002 amounts to about 70 In Table 81 Satellites carrying laser reflectors selection Satellite Name Launch Altitude Inclination year km degrees BEACONB 1964 890 80 BEACONC 1965 930 41 GEOS1 1965 1120 40 DIADEME1C 1967 540 40 DIADEME1D 1967 580 40 GEOS2 1968 1080 106 STARLETTE 1975 810 50 GEOS3 1975 840 115 LAGEOS1 1976 5850 110 SEASAT 1978 800 108 ASIJAI 1986 1480 50 ETALON1 1989 19100 65 ETALON2 1989 19100 65 GLONASS40 GLONASS88 19892001 19140 65 ERS1 1991 780 99 TOPEXPOSEIDON 1992 1350 66 LAGEOS2 1992 5630 53 STELLA 1993 810 99 GPS 35 1993 20100 54 GPS 36 1994 20100 55 ERS2 1995 800 99 GFZ1 1995 400 52 TIPS 1996 1020 63 GFO1 1998 800 108 WESTPAC 1998 830 98 SUNSAT 1999 400 93 CHAMP 2000 430470 87 STARSHINE3 2001 470 67 JASON 2001 1340 66 METEOR 3M 2001 1000 100 REFLECTOR 2001 1020 100 ENVISAT 2002 800 98 GRACE A 2002 480500 89 GRACE B 2002 480500 89 ICESAT 2003 600 94 408 8 Laser Ranging most cases the SLR technique is applied to provide precise orbital information for the particular satellite mission eg for altimeter satellites 9 or for gravity field missions 10 Today in most cases where precise orbits are required space vehicles are fitted with a reflector array as a backup system Some satellites have been launched with the sole objective of serving as precise targets in their orbits These space vehicles have been optimized in design and or bital parameters Dedicated laser satellites of this type are STARLETTE STELLA LAGEOS12 AJISAI ETALON12 GFZ1 and WESTPAC They are described below in more detail STARLETTE was launched by the French Space Agency CNES Centre National dEtudes Spatiales on February 6 1975 with the following characteristic data CNES 1975 perigee height 805 km apogee height 1 108 km orbit inclination 498 degrees period of perigee 110 days nodal period 91 days diameter 24 cm mass 47295 kg and retroreflectors 60 diameter 33 mm STARLETTE was the first satellite to be designed with minimized surface forces in order to allow highly precise laser ranging The core consists of Uranium 238 with a density of 187 gcm3 formed as an icosahedron with 20 triangular planes Each triangle carries a spherical aluminium cap with three integrated retroreflectors Due to the extremely favorable areamass ratio the disturbing forces drag and solar radiation pressure 323 are minimized and can be precisely modeled This is why gravitational forces acting on low orbiting satellites can be separated and well analyzed The main fields of application are the determination and analysis of 85 ocean tides and body tides main purpose Earths gravity field geocentric station coordinates polar motion Earth rotation and tidal friction Because of its rather low orbit STARLETTE is particularly suitable for the study of solid Earth tides and related elasticity models of the Earth 856 A virtually identical twin satellite named STELLA was launched into a sun synchronous orbit on September 26 1993 The orbital parameters are inclination 986 degrees height 800 km quasi circular orbit As with STARLETTE the main objectives are a contribution to the gravity field in particular tuning the field for sunsynchronous Earth observing satellites such as SPOT ERS and others a contribution to the modeling of nongravitational forces and 82 Satellites Equipped with Laser Reflectors 409 for modeling the Earth and ocean tides The anticipated lifetime of STARLETTE and STELLA is several centuries LAGEOS1 was launched by the American Space Agency NASA on May 4 1976 and LAGEOS2 as a joint USItalian project on October 22 1992 The orbital char acteristics are LAGEOS1 LAGEOS2 Perigee height 5860 km 5620 km Orbit inclination 10984 degrees 5264 degrees Eccentricity 00045 00135 Period 225 minutes 223 minutes Diameter 60 cm 60 cm Shape sphere sphere Mass 411 kg 405 kg Reflectors 426 corner cubes 426 corner cubes The design goals of LAGEOS were as for STARLETTE to minimize surface forces and to create a precise relationship between the satellites center of gravity and the individual reflectors Due to its greater altitude the LAGEOS orbit is less sensitive to atmospheric drag and short wavelength terms of Earths gravity field than is the STARLETTE orbit The retroreflectors are incorporated into an aluminum sphere surrounding a cylindric brass core Fig 83 422 silicon reflectors serve for the pulse range measurements Four additional germanium reflectors were designed for range rate observations with optical Doppler measurements The name LAGEOS stands for aluminium hemisphere brass core 175 kg retro reflectors 4762 mm radius 30 cm 275 cm 3176 cm Figure 83 LAGEOS Laser Geodynamics Satellite structure Laser Geodynamics Satellite originally Laser Geodetic Satellite and thus in dicates the main fields of application 85 installation and maintenance of a precise geodetic reference frame determination of tectonic plate motion and regional crustal move ments determination of Earth orientation parameters polar motion Earth rotation study of Earths gravity field The lifetime of the LAGEOS satellites is estimated to be several millions of years This is why a steel plaque indicating continental drift was added to the first spacecraft as a message to the future The Japanese Experimental Geodetic Satellite EGS also named AJISAI was launched on August 12 1986 into a circular orbit of 1 500 km altitude and 50 incli nation cf 432 The orbital period is 193 hours the rotation period of perigee 14253 days and the nodal period 11753 days The spherical satellite has a diameter 410 8 Laser Ranging of 214 cm a mass of 685 kg and carries 120 laser reflector assemblies The areamass ratio is hence less favorable than for STARLETTE and LAGEOS The satellite can be used for laser range and photographic direction measurements The original goal was to determine the location of isolated islands and to adjust the geodetic network of Japan Komaki et al 1985 In the meantime tracking of AJISAI has contributed considerably to the improvement of gravity field models and the geodetic reference frame Torrence 1999 In January and May 1989 the former Soviet Union launched two spherical satellites named ETALON1 and ETALON2 each time together with two GLONASS satellites 771 into rather high orbits The characteristic parameters are altitude 19 120 km eccentricity 000068 orbit inclination 65 degrees diameter of sphere 1294 m mass 1 415 kg period 675 minutes and reflector arrays 306 each with 14 corner cubes Ofthereflectors sixaremadeofgermaniumforpossiblefutureinfraredinterferometric measurements and they are placed symmetrically The original objective of the ETALON mission was to determine solar radiation pressure for the orbit control of GLONASS satellites Anodina Prilepin 1989 Be cause of the high orbital altitude the ETALON satellites together with LAGEOS form the basis of a highaccuracy global reference coordinate frame 854 Fur ther significant contributions are expected to the modeling of the low order gravita tional field parameters to the determination of the geocentric gravitational constant GM and station positions and to the estimation of Earth orientation parameters Figure 84 GFZ1 courtesy GFZ Potsdam photo L Grunwaldt Two particular dedicated laser tracking satellite are GFZ1 and WESTPAC1 GFZ stands for GeoForschungsZentrum Potsdam The small spherical satellite with a diameter of 215 cm and a mass of 206 kg Fig 84 carried 60 retro reflectors and was jettisoned from the Russian MIR space station on April 19 1995 into a low 400 km nearly circular Earth orbit of 516 degrees inclination From this initial altitude it was to decay naturally with a predicted lifetime of 35 to 5 years On June 23rd 1999 it burned up after nearly 24 000 orbits The last observation placed GFZ1 at an altitude of 230 km The mission objectives of GFZ1 were to determine variations in rotational char acteristics of the Earth and to recover high resolution parameters of the gravity field 83 Laser Ranging Systems and Components 411 Through the changing orbital height during the satellites lifetime it was possible to estimate a wide variety of higher order gravity coefficients 853 WESTPAC1 stands for Western Pacific Laser Tracking Network Satellite The satellite is of a similar size to GFZ1 and was launched on July 10 1998 into a sunsynchronous circular orbit of 835 km altitude and 98 degrees inclination The satellite has a diameter of 24 cm a mass of 23 kg and carries 60 corner cube reflectors WESTPAC1 was designed in particular to provide a high ranging accuracy The specific features are a centerofmass correction within 05 mm accuracy and that only a single cornercube will reflect at any shot In total at the end of the year 2002 eight dedicated lasersatellites are in orbit The tracking characteristics are quite different allowing multisatellite ranging for appropriate tracking systems 83 Table 82 shows some characteristic features of the most important dedicated targets Table 82 Tracking characteristics of dedicated satellite laser targets Satellite Mean Maximum pass Signal flight time altitude duration MinMax STARLETTESTELLA 810 km 10 min 614 ms AJISAI 1 490 km 15 min 1020 ms LAGEOS1 2 5 999 km 50 min 4057 ms ETALON1 2 19 100 km 330 min 127150 ms 83 Laser Ranging Systems and Components 831 Laser Oscillators The most important component of a laser ranging system is the laseroscillator The artificial word LASER Light Amplification by Stimulated Emission of Radiation de notes a configuration for the coherent amplification of electromagnetic oscillations in the optical spectral domain through induced emission In an optical resonator the electromagnetic wave interacts with excited material Besides the coherence ie the fixed phase coupling between the individual beams providing monochromatic light two more properties of the laser are exploited in satellite geodesy These are the high degree of collimation of the beam and the high power density Hence very highenergy sharply defined pulses can be transported over large distances In satellite geodesy two types of solid state pulsed lasers are widely used the ruby laser and the NeodymiumYAG laser The SLR systems of the first and second gener ation are almost exclusively equipped with ruby lasers whereas the third generation systems mostly use the NdYAG laser 412 8 Laser Ranging Ruby is the classic material of solid state lasers Ruby is a crystal absorbing green and blueviolet light and emitting sharp red spectral lines at 6943 nm By changing the resonator quality and opening the resonator at the predefined maximum of energy absorption single laser pulses can be generated with a pulse width of about 10 to 50 nanoseconds and a peak power of 1 GigaWatt The process is controlled by the socalled Qswitch Q stands for quality With a special arrangement of the Qswitch inside the resonator it becomes possible to reduce the pulse width to 25 ns This is however the upper limit of performance for a ruby laser Another way of generating short pulses is the coupling of longitudinal resonator oscillations the socalled modes through active modulators producing a defined se quence of short high energy pulses In particular the NeodymiumYAG laser YAG YttriumAluminiumGarnet is suited for the modecoupling This technique makes a reduction of the pulse width to 100 to 200 picoseconds possible It also requires less pumping energy and hence provides a better system performance and a higher pulse repetition rate Finally the frequency is doubled and with a wavelength of 530 nm green instead of 1060 nm infrared produces better conditions for the reception of return pulses Modern developments are directed toward eyesafe lasers ie lasers with low power and high repetition rate see 834 For an overview of the current status in satellite laser ranging technology see the proceedings of the biannual International Workshop on Laser Ranging eg Schlüter et al 1999 ILRS 2001 832 Other System Components a Telescope Mount The transmitter component must be able to follow moving targets This is possible with a mounting that permits changes in azimuth and elevation It is advisable to fit the receiver to the same mounting or to integrate the transmitter and receiver telescopes For first generation systems the laser apparatus was usually also mounted on the pointing assembly Third generation lasers are rather sensitive and hence need a well controlled environment Stationary systems are usually kept on a rigid bench in a particular cleanroom near the pointing assembly The laser pulses are directed via a series of prisms or optical conductors to the transmission telescope It is necessary to point the telescope with sufficient accuracy to the satellite For first generation systems tracking was often controlled visually with the help of a guidance telescope The pointing control of third generation systems usually works automatically with computer control based on precomputed ephemerides socalled IRVs InterRange Vector see 851 This is also required because of the ability to make daytime observations During the satellite pass corrections are derived from a comparison between the predeterminedandactualsatellitepositions Inordertoachieveahighreturnrate even for distant satellites a pointing accuracy of 1 or better is aimed for which is quite a demanding requirement for guidance and control The divergence of the outgoing laser beam can usually be adapted to different satellite ranges and for tracing the 414 8 Laser Ranging signal reflection at different retrocubes and relative motion between transmitter and reflector A careful pulseanalysis is required to determine the pulse center For modern systems working on the basis of single photonelectron detection no pulse analysis is possible In these cases the single photonelectrons have to be identified and analyzed with very fast detectors Current techniques use for example SPAD Single Photon Avalanche Diode techniques Prochazka et al 1999 Instead of using a single pulse techniques have been developed to use a train of 5 to 10 short pulses about 50 ps length at a fixed interval of a few nanoseconds From this train an electrooptical shutter passes about half the pulses the socalled semitrain containing 3 to 5 pulses Paunonen 1999 see also Hamal Prochazka 1989 This method increases the precision and decreases the single pulse energy d Time Base The signal travel time is measured by a propagation timer which is controlled by an extremely accurate clock Electronic counters are used with a resolution of about 10 ps The counters are controlled by atomic clocks with high longterm and short term stability in particular rubidium and cesium standards or hydrogen masers 225 Atomic clocks also define the station system time which is needed for determination of the observation epochs Regular comparisons with international time scales UTC are required and can be easily realized via an appropriate GPS receiver with an accuracy level of better than 20 ns 7629 e System Computer A suitable computer is required with the related software for the precalculation of satellite ephemerides and pointing elements the guidance and control of the instru ment mounting the control of the whole system calibration and control of system parameters data analysis data control and data transfer In modern systems multi tasking and network processors with realtime capability as well as remote control are required f Aircraft Detector In some areas with dense air traffic and near airports it may be required to make provisions against an airplane passing through the laser beam An optical or radar airplane detection system can be deployed that automatically interrupts the laser oper ation Because of the low energy of modern laser ranging systems eye safe operation the requirement for installing airplane detection devices is now less stringent 833 Currently Available Fixed and Transportable Laser Systems In 2002 about 40 systems were used worldwide for laser ranging to satellites Most of them now belong to the third generation or are new developments The majority has the capability of ranging to high satellites such as ETALON GLONASS and GPS while only three or four systems can reach the Moon Most systems installed are stationary although the number of transportable systems is increasing A current overview of systems contributing to global geodesy and geodynamics 85 is given in 83 Laser Ranging Systems and Components 415 the documents of the International Laser Ranging Service ILRS 851 Many of the older systems have been replaced or upgraded in recent years Husson 1999 Table83givesanoverviewonthesystemdataoftwomodernlaserrangingsystems the Wettzell Laser Ranging System WLRS operating in the fundamental station Wettzell Germany 125 and the MOBLAS7 operating at the Goddard Geophysical Astronomical Observatory GGAO in Greenbelt Md USA Table 83 System data of two laser ranging systems System WLRS MOBLAS7 Telescope 75 cm mirror 76 cm mirror Mount AltAz AltAz Lasertype NdYAG NdYAG Laserfrequency 532 nm 532 nm Operating mode single pulse 532nm 100ps 180 mJ single pulse single pulse 1064 nm 100 ps 360 mJ 200ps100 mJ pulse semitrain 48 pulses 300 mJ Pulse repetition rate 1 to 10 Hz 1 5 10 Hz Receiver Photomultiplier Avalanche diode Photomultiplier Microchannel plate photomultiplier Microchannel plate Streak camera photomultiplier Observation range satellites and Moon high satellites The global geographical distribution of laser systems see Fig 813 p 432 reflects national capabilities and interests and is often not very suitable for the analysis of regional and local geodynamical phenomena To allow more flexible applications in particular in the determination of crustal motion 851 1241 transportable systems of the newest laser technology are being developed Some of them have already been widely used in recent years for example in the Mediterranean area MEDLAS project 854 and in the NASA Crustal Dynamics Program 1241 The systems have a modular construction and can be transported with containers in regular airplanes They work with quite low energy and with single photon detection Typically mobile systems occupy sites for periods of 23 months and then require several days for relocation Examples of current transportable systems are FTRLS1 France TLRS Germany TROS China MTLRS1 Germany and MTLRS2 Netherlands Table 84 gives some system data All systems work with the single photon technique and allow daylight operation 416 8 Laser Ranging Table 84 System data of transportable laser ranging systems System MTLRS12 FTLRS TLRS Aperture 40 cm 13 cm 50 cm Weight 500 kg 300 kg 1700 kg incl cart Laser NdYAP 539 nm NdYAG 1064 nm Titan Sapphire 427 854 nm Pulse energy 10 mJ 100 mJ 30 mJ Pulse length 200 ps 100 ps 80 ps Repetition rate 10 Hz 10 Hz 10 Hz Time base cesium rubidium GPS 2 cesium controlled 2 hydrogen maser Range 6 000 km 6 000 km 36 000 km The Modular Transportable Laser Ranging Systems MTLRS1 and MTLRS2 have been operated successfully since 1984 for about 15 years mainly in the Mediter ranean for international geodynamic projects eg WEGENERMEDLAS The slight difference of wavelength as compared with the NdYAG laser comes from the use of a different laser active material named NdYAP YAP Yttrium OrthoAluminate a crystal of the mineral type Perovskite The normal point 842 accuracy is about 1 to 2 cm The French Transportable Laser Ranging Station FTRLS Pierron et al 1999 was developed by French organizations and entered its operational phase in 1996 The system is highly mobile weighing only 300 kg in 8 containers The system can reach satellites at LAGEOS height Its main objective is the installation of low cost laser stations in remote areas for research in geodynamics and the calibration of altimeter satellites 933 The TIGO Laser Ranging System TLRS is designed to measure ranges to satellites with an accuracy better than 1 cm simultaneously at two wavelengths The tracking range is from low orbit satellites at about 300 km altitude up to geostationary satel lites 36 000 km TIGO stands for Transportable Integrated Geodetic Observatory Besides the SLR module TIGO includes a VLBI module 111 GPS GLONASS and DORIS receivers a timekeeping laboratory and a superconducting gravity meter Schlüter et al 2000 The installation ofTIGO at a particular site is always anticipated for a duration of several years Since 2002 TIGO has been operating in Concepción Chile 1252 834 Trends in SLR System Developments Some of the main development trends are toward the following characteristics short pulse width down to 50 picoseconds or even less pulse trains high repetition rate 10 Hz low output signal strength 83 Laser Ranging Systems and Components 417 Figure 86 Wettzell Laser Ranging System courtesy BKG Figure 87 TIGO with SLR module Concepción Chile courtesy BKG single photon detection exploitation of quantumstatistic properties faster elec tronics improved photodetectors such as single photon avalanche diode or mi crochannel plate streak cameras eyesafe systems ie low energy 150 µJ and high repetition rate 2 KHz fully automatic operation remote control 24hour operation reduced station construction operating and maintenance costs higher mobility through lowweight optics realtime data processing and data transfer softwareoriented systems hence higher flexibility multiple satellite tracking capability low error budget 1 mm twocolor ranging and epoch synchronization down to 10 ns corresponding to 01 mm NASA is developing a modern SLR system meeting most of these requirements under the name SLR2000 SLR2000 is an autonomous eyesafe single photoncounting satellite laser ranging station with an expected single shot range precision of about one centimeter and a normal point precision better than 3 mm Degnan 2000 The system is designed to provide 24hour tracking coverage It is planned to build more than 10 systems with a replication cost of 1M per system The main features are Qswitched NdYAG microlaser frequencydoubled 532 nm 130 µJ of energy 2 KHz repetition rate highspeed quadrant microchannel plate photomultiplier highspeed high resolution event timer arcsecond precision tracking mount shelter and protective dome CCD camera for guidance control and focussing and daylight tracking capability to GPS 422 8 Laser Ranging proceedings of the biannual International Workshop on Laser Ranging eg Schlüter et al 1999 ILRS 2001 The most effective method of testing a satellite laser ranging system is by parallel observation with another system at the same site collocation test 842 Data Control Data Compression and Normal Points The observed raw data are controlled in a filtering and data compression process in order to detect and eliminate gross errors blunders evaluate the accuracy of the observations and reduce the amount of data for subsequent processing Gross errors may arise in particular during daytime observations if spurious return signals are acquired The quality of the single observations can be assessed through comparison of the individual measurements with a curve smoothed through all ob servations Data compression is necessary because modern SLR systems with pulse repetition rates of 10 Hz may produce several thousand data points per satellite pass These data are highly correlated because of instrumental and meteorological effects For subsequent investigations only one representative range mean is required for each time interval of about one or a few minutes Data control and data compression can be achieved operationally within one multi step process Several methods have been proposed in the interest of international co operation however the procedure recommended at the Herstmonceux Laser Work shop in 1984 Gaignebet ed 1985 is mostly used and has since been discussed and updated eg Sinclair 1999 In the first step the observed ranges d0 are compared with computed reference ranges dp predictions and a series of residuals dr is generated Fig 810 dr d0 dp 85 The reference ranges can be obtained from all available observations be they short arc or long arc approximations of the observed orbit 3333 This procedure demands a rather large computational effort high precision predictions are required with a best available estimate for a time bias The predicted range must include the refraction delay Data with gross differences outliers are eliminated using an adequate range window In the second step a suitable trend function f p is fitted to the residuals dr either using a set of orbital parameters preferable or a polynomial eg Chebyshev polynomials 3332 Care has to be taken not to introduce spurious high frequency signals by fitting a high order polynomial The deviations after the fit fr dr f p 86 are analyzed for any remaining outliers using a 3 σcriterion This approximation procedure can be repeated iteratively For systems that detect the first photoelectron a 25 σ criterion can be of advantage Sinclair 1999 84 Corrections Data Processing and Accuracy 423 d0 f p dp dp dr fr d0i fri fri NPi fr dr d0 f p Figure 810 Formation of normal points In the third step the observed trajectory is divided into fixed intervals socalled bins starting from 0h UTC The proposed interval sizes for various satellites are for example GPS GLONASS 300 seconds LAGEOS12 120 seconds STARLETTE STELLA 30 seconds ERS12 15 seconds and GRACE 5 seconds In each interval i a mean value of all deviations fri is formed and added to the trend function at the center of the interval This point NPi Fig 810 is called the normal point and represents all single observations of the particular interval The observation d0i with the fit residual fri nearest to the mean epoch of the accepted fit residuals in bin i leads to the normal point range dNPi dNPi d0i fri fri 87 The discrepancies between the single residuals fr with respect to the mean fr are used to determine the observation noise of the single distance measurement The precision of the mean laser range in the normal point 87 is used as the characteristic measure of the internal accuracy of the laser ranging equipment It is called the normal point precision and is about 1 to 2 cm for the third generation SLR configurations For modern systems like the SLR 2000 a normal point precision better than 3 mm is expected Degnan 2000 Systematic effects are not included they have to be estimated in the subsequent adjustment model Summarizing the following aspects have to be emphasized when forming normal points the essential information of the raw measurements is maintained outliers are eliminated from the data 424 8 Laser Ranging the remaining correlation between normal points is insignificant and the observation noise is removed Normal points are also referredto as quicklook data because they are generated very shortly after the satellite pass and can be used together with equivalent data from other stations for rapid orbit prediction Today normal point data are the primary product of SLR stations They have in most cases replaced the fullrate data 85 Applications of Satellite Laser Ranging Due to the very high accuracy potential of laser range observations to satellites a broad field of applications in geodesy and geodynamics opened early on Fig 811 gives an 3 m 1 m 30 cm 10 cm 3 cm 1 cm 1 3 mm Gravity Field Tides Earth Rotation Intra Plate Deformations High Resolution Earth Orientation Plate Tectonics Crustal Deformation 1965 1970 1975 1980 1985 1990 1995 Figure 811 SLR accuracy development and application fields overview of the development related to the achievable accuracy The main fields of application are in Gravity field and satellite precise determination of low degree orbits 853 and order coefficients tailored Earth models for particular satellite orbits precise orbit determination POD Positions position changes and absolute geocentric coordinates reference frames 854 absolute heights contribution to ITRF crustal deformations Earth Orientation Parameters polar motion variation of Earth EOP 855 rotation LOD and Particular applications 856 tides precise time transfer relativity 851 Realization of Observation Programs International Laser Ranging Service ILRS Progress in the different tasks listed above is only possible through international coop eration and by the use of data from globally distributed stations This is why from the beginning of SLR activities a close cooperation developed between the agencies and 85 Applications of Satellite Laser Ranging 425 groups responsible for SLR stations About 20 fixed stations and several mobile sys tems contributed permanently to the NASA Crustal Dynamics Project 1241 About 30 stations participated with SLR equipment within the framework of the MERIT cam paign Monitor Earth Rotation and Intercompare the Techniques Moritz Mueller 1987 The International Earth Rotation Service IERS during the first years after its establishment in 1988 was primarily based on continuous input from about 25 laser sites and still uses SLR data 855 1242 Several regional groups have worked together with dedicated objectives for example the MEDLAS Mediterranean Laser ranging project group within the WEGENER Working Group of European Geo scientists for the Establishment of Networks for Earthquake Research framework The meaningful use of the observation results is only possible if international standards are agreed upon for data production data reduction and data analysis Such standards were formulated in 1983 with the MERIT Standards Melbourne et al 1983 and they are maintained and updated as necessary with the IERS Standards and now the IERS Conventions McCarthy 2000 Today the role of laser ranging for some products and applications has decreased due to the strength of other technologies This holds in particular for the determination of recent crustal motion in regional projects where GPS is much more efficient or for the analysis of high resolution Earth orientation parameters where VLBI and GPS are of increasing importance On the other hand SLR data are mandatory for the determination of absolute coordinates they still form an essential part in gravity field models they are a backup system and sometimes the only means for precise orbit determination and they play an increasing role in various scientific space experiments With the objective to concentrate international efforts in the field of satellite and lunar laser ranging the International Laser Ranging Service ILRS was established in 1998 as a service of the IAG The objectives and organization of the ILRS are similar to the IGS 781 Following the Terms of Reference ILRS 2000 the ILRS provides global satellite and lunar laser ranging data and their related products to supportgeodeticandgeophysicalresearchactivitiesaswellasIERSproductsimportant to the maintenance of an accurate ITRF The ILRS collects archives and distributes SLR and LLR observation data sets of sufficient accuracy and uses the data to generate data products including Earth orientation parameters station coordinates and velocities timevarying geocenter coordinates static and timevarying coefficients of Earths gravity field centimeter accuracy satellite ephemerides fundamental physical constants lunar orientation parameters and lunar ephemerides and librations The organizational components of the ILRS are besides the Governing Board and the Central Bureau Tracking Stations and Subnetworks 426 8 Laser Ranging Operations Centers Global and Regional Data Centers Analysis and Associate Analysis Centers and Permanent and Temporary Working Groups Detailed information on the ILRS can be found in the annual reports and the ILRS website The global SLR network about 40 stations in 2002 is reflected in Fig 813 At the moment we can distinguish three regional subnetworks the European Laser Network EUROLAS incorporating the European stations the NASA network in North America with some stations in South America South Africa and the Pacific the Western Pacific Laser Tracking Network WPLTN encompassing Japan China Eastern Russia and Australia According to the System Performance Standards 834 the ILRS tracking stations are divided into three categories Core Stations meeting the highest standards of performance Contributing Stations contributing significantly to ILRS goals and Associate Stations presently providing intermittent variable quality data By the end of 2002 about two thirds of the total number of ILRS stations belong to the first two categories An essential prerequisite for sufficient data points and high quality data are good predictions of satellite passes Some of the Associate Analysis Centers serve as Pre diction Centers and provide socalled InterRange Vectors IRV or Tuned InterRange Vectors TIV to the stations Prediction centers compute precise orbits and extrapolate them forward An IRV file is derived from the predicted orbit and contains position and velocity of the satellite for a given epoch say 0000 UT each day The IRV are tuned such that a simple orbit integrator is capable to generate a prediction file at the particular tracking station The prediction file contains altitudes azimuths ranges and velocities at close intervals eg every minute and serves to control the observation process telescope motion and detector gating Alongtrack errors can be easily de tected and modeled onsite as a time bias For low orbiting satellites like CHAMP or GRACE more sophisticated force models and shorter tuning intervals eg 6 hours may be necessary Wood 1999 Satellites are tracked following an ILRS Tracking Priority List The general rules are that priorities decrease with increasing orbital altitude and increasing orbital inclination at a given altitude Particular satellites can be supported by higher priority namely active missions such as altimetry special campaigns such as the tandem mission ERS2ENVISAT and postlaunch intensive tracking phases Current lists are available from the ILRS website As of January 2003 a total of 22 satellites were included in the tracking priority list 85 Applications of Satellite Laser Ranging 427 852 Parameter Estimation In principle two different concepts can be used namely geometrical and dynamical methods 12 The geometrical method can only be applied for the determination of positions and baselines Basically simultaneous range measurements from at least four ground stations to a target satellite have to be carried out at identical epochs The distance between the participating ground stations can be derived in the concept of spatial trilateration cf Fig 12 p 3 or new stations can be related to a network of existing control points The method corresponds to the classical SECOR technique 441 It has concep tual advantages because no assumptions are needed for example in orbit modeling However from the practical point of view it cannot be applied because weather con ditions do not allow rigorous simultaneous observations at four or more stations The larger the station separation the smaller the probability of meeting favorable weather conditions at the same time Experiences from the geometrical BC4network 515 demonstrate that common observations are very rare at three stations and nearly im possible at four Consequently the pure geometric method of laser ranging is more of theoretical interest and has never been applied in practice For model calculations see Campbell et al 1973 In the dynamical method all observed ranges can be used The motion of the satellite is described with an adequate orbital model and relates all observations to each other To exploit the high accuracy level of the observations all forces acting on the satellite have to be carefully modeled and the rotational behavior of Earth with respect to the orbital plane has to be known The satellite motion refers to Earths center of mass hence geocentric coordinates are determined It is clear for the dynamical method that the determination of station coordinates is not an isolated problem Station coordinates have to be estimated together with other quantities in the course of a general parameter estimation process 41 Possible parameters are geocentric station coordinates gravity field coefficients pole components Earth rotation and universal time UT1 model parameters of Earth and ocean tides and additional parameters for the description of the satellite orbit It is not generally possible to derive all parameters of interest from the same set of observations because the solution system may become unstable cf 41 Usually the coefficients of Earths gravity field will be held fixed in the estimation of station coordinates or the station coordinates will be treated as known quantities in the de termination of Earth rotation parameters Hence we have two groups of parameters in dynamic modeling a parameters contained in the solution and b adopted parameters not contained in the solution 428 8 Laser Ranging Today the dynamic approach is almost exclusively used based on all available tracking data from the global SLR network In all parameter estimation processes the necessity arises to fit a precise trajectory to the observed data Usually the SLR analysis is performed in several steps eg Devoti et al 2001 In the first step satellite orbits are reduced piecemeal solving for arc dependent parameters like the state vector nongravitational forces and mea surement biases The arc length is shorter for low orbiting satellites eg five days for STARLETTE STELLA ERS2 and longer for high orbiting satellites eg between 1 week and 1 month for LAGEOS In a second step the arc solutions are combined in a multiarc solution and global parameters are estimated such as coordinates Earth orientation parameters and coefficients of the gravity field In a final step very long arcs over many years are analyzed to verify fundamental physical models or to solve for the secular drift of certain parameters like low order zonals Two particular effects were derived rather early from analysis of LAGEOS orbits over many years These are a secular nodal acceleration and an unexpected decrease in the semimajor axis at the submillimeterday level The nodal acceleration is related to a secular change of J2 and reflects a decrease of Earths flattening This effect can be explained by relaxation of the Earth since the last glaciation The decrease of the semimajor axis is mostly explained by thermal effects on the cornercube reflectors caused by Earths infrared radiation Rubicam 1986 The possibilities and techniques for orbit modeling have been continuously im proved since the launch of the first laser satellites A 1 month arc of the LAGEOS orbit can be modeled with about 1 to 2 cm accuracy For lower and hence more disturbed satellites like STARLETTE or ERS12 the accuracy in orbit modeling is about 5 cm or slightly better Fig 812 demonstrates the improvement over about 15 years in the modeling of 1 month LAGEOS arcs Pavlis et al 1991 0 10 20 30 40 50 76 78 80 82 84 86 88 90 RMS cm Year Figure 812 Accuracy improvement in the modeling of 1month LAGEOS arcs 853 Earth Gravity Field Precise Orbit Determination POD Because of their high accuracy laser distance measurements to satellites have been included in the computation of Earth models since the launch of the first satellites 85 Applications of Satellite Laser Ranging 429 equipped with retroreflectors cf 122 The last gravity field model in the pre LAGEOS era computed by the NASA Goddard Space Flight Center was named GEM 9 and contained about 200 000 laser ranges to 9 satellites The model was developed up to degree and order 20 Lerch et al 1979 Because of the decreasing sensitivity of satellite orbits to smaller gravity anomalies it is necessary to incorporate results from the direct mapping of the gravity field satellite altimetry 9 satellitetosatellite tracking gradiometry 10 or surface gravity data into the solutions with higher order coefficients It can be stated as a general rule that the limit of resolution of gravity field structures by orbit analysis is within a wavelength of about 1000 km The influence of highfrequency terms in the gravity field on the satellite orbits decreases with increasing height Because of this relationship between gravity field development and satellite orbital height it is very important to know precisely the low frequency components of the gravity field for the exact orbit modeling of dedicated satellites like STARLETTE STELLA LAGEOS or ETALON in order to meet the requirements of geodynamical research and reference frame stability Vice versa LAGEOS orbit analysis permits the isolation of long wavelength geopotential signals within gravity field solutions because LAGEOS is rather insensitive to the gravity field above degree 10 and is unaffected by terms above degree 20 Klosko 1999 Dedicated gravity fields of this type are called tailored gravity fields The GEM L2 solution Lerch et al 1983 is an early such tailored field for LAGEOS orbits the related longwave geoid can be modeled to degree and order 44 with an accuracy level of 8 cm An equivalent tailored gravity field has been designed for STARLETTE with the PGS1331 model up to degree and order 36 Marsh Lerch 1985 This model is also of value for other missions at a similar orbital height such as STELLA ERS1 and ERS2 With the availability of new precise laser ranging data to LAGEOS and other satellites and with the requirements for a precise modeling of the TOPEXPOSEIDON altimeter mission a new GEMseries of satellite based long wavelength gravity field models was started in 1987 The model GEMT1 was exclusively based upon direct satellite tracking observations It is complete to degree and order 36 Marsh et al 1987 and contains about 440 000 laser observations The followup model GEM T2 Marsh et al 1990 was improved by additional laser observations to LAGEOS STARLETTE andAJISAI as well as by older arcs of GEOS1 and GEOS2 GEMT3 Lerch 1992 was complete to degree 50 using tracking data from 31 satellites and in addition altimeter data from GEOS3 SEASAT and GEOSAT The availability of laser targets in low altitudes like GFZ1 gave rise to the de velopment of higher order satelliteonly gravity models About 74 000 laser data to GFZ1 together with 28 million older tracking observations were used to estimate the gravity field model GRIM4S4G complete to degree and order 60 with higher degree terms up to 100 in zonal and resonant bands König et al 1999 Many more gravity field models have been developed where the SLR data form a substantial part of the data base in particular for the longwavelength part Frequently 430 8 Laser Ranging used models are the Joint Gravity Model 3 JGM3 Tapley et al 1996 a tailored model for TOPEXPOSEIDON and complete to degree 70 and the NASA and NIMA Joint Geopotential Model EGM96 Lemoine et al 1998 complete to degree 360 An excellent overview of historical and current models is given by Rapp 1998 see also 122 The realization of the importance of SLR as a longlived passive tracking technique for the estimation and continuous improvement of gravity models is enlight ened by the fact that several old long abandoned satellites like BEC D1C D1D or GEOS3 have been included in new international tracking programs Klosko 1999 ILRS 2000 Laser ranging to geodetic satellites with stable orbits in particular LAGEOS1 and LAGEOS2 is useful to measure the evolution over time of the long wavelength part of the gravity field Several authors have reported time derivatives of the zonal coefficients J2 to J6 Devoti et al 2001 So far only the term J2 could be determined significantly J2 26 30 02 05 1011 yr The effect can be related to postglacial rebound the ongoing mass redistribution following Pleistocene deglaciation in the northern hemisphere LAGEOS is particularly suitable for the determination of the geocentric gravita tional constant GM cf 1222 because of its fairly undisturbed orbit and the high ranging accuracy The value of GM is estimated each time as part of a global solution The precision of the estimate has improved by an order of magnitude in each of the last two decades Smith et al 2000 The current value from recent LAGEOS estimations is GM 398 60044187 000020 km3sec2 88 The results are confirmed by estimates from SLR data from STELLA STARLETTE AJISAI and ETALON however with a much higher scatter The value of GM defines the scale in satellite orbit determination The value from recent LAGEOS observations is about 1ppb higher than the previously adopted value from SLR observations Ries et al 1992 This difference corresponds to a difference in orbital height of about 3 mm Smith et al 2000 For further discussion on gravity field determination from satellite data see 122 or Torge 2001 Precision Orbit Determination POD is one of the most important applications of todays SLR technology Based on a tailored gravity field for a particular satellite and an appropriate dynamical model all available SLR data from the ILRS tracking network are used to estimate a precise orbit The unique feature of SLR data is that the orbits are absolute in the sense that they refer to Earths center of mass In many cases the orbit determination is based on SLR and additional tracking systems such as GPS DORIS or PRARE In some cases SLR is the only tracking device because of a failure of the primary tracking system such as PRARE for ERS1 or GPS for GFO GEOSAT Follow On SLR is hence an excellent backup system with an extremely long lifetime that survives all other tracking systems 85 Applications of Satellite Laser Ranging 431 In combined orbit determination for example DORIS and SLR for TOPEX POSEIDON the DORIS data provide the main contribution to the overall orbit accu racy and SLR contributes in the crucial centering of the orbit Centering errors in the absolute height of altimeter satellites would introduce asymmetry in the estimated sea surface variations and hence corrupt the oceanographic interpretation Recent studies indicate a POD accuracy for TOPEXPOSEIDON of 2 to 3 cm in the radial direction ILRS 2000 The high accuracy of SLR determined orbits is of eminent importance for the absolute calibration of sensor errors in new missions This is in particular true for the radial altimeter errors such as in the JASON1 or ENVISAT1 mission 92 SLR also contributes in combination with GPS to the precise orbit determination of gravity field missions like CHAMP and GRACE 102 The high value of the SLR tracking data for orbit determination is illuminated in the long list of tracking priorities and SLR missions set up by the ILRS 851 For the technique of precise orbit determination including SLR data see 33 and eg Rim Schutz 1999 Montenbruck Gill 2000 854 Positions and Position Changes The dynamical modeling of satellite laser range data offers the possibility of estimating geocentric threedimensional positions If gravity field parameters form part of the solution the coordinates refer conceptually to the Earths center of gravity Today in most cases a tailored gravity field model is used such as JGM3 The scale is introduced through the velocity of light and the adopted GM value During the early years of satellite laser ranging the technique was mainly used for the determination of crustal motion along selected baselines or in regional networks One example is the continuous monitoring of crustal deformation along the San An dreas Fault For a 400 km baseline between Quincy and Monument Peak a significant deformation of about 6 cm 3 mmyear could be detected Watkins et al 1990 Another example is the WEGENERMEDLAS project in the Mediterranean Three transportable laser systems have provided accurate epoch positions for sites in Italy Greece and Turkey since 1985 The apparent motions with respect to a coordinate system that is rigidly attached to the Eurasian tectonic plate reach 20 to 40 mmyear Ambrosius et al 1991 Today particular SLR campaigns are no longer arranged instead the continuously available tracking data from the global ILRS network are used to estimate coordinates and coordinate changes Some of the ILRS analysis or associate analysis centers do this on a regular basis ILRS 2000 The usual procedure is firstly to compute weekly solutions or from similar short intervals up to one month for the total time span of analysis These solutions are used to clean the data and they offer a valuable insight into the quality of the station data The variations of the weekly coordinates are in the order of 2 cm for high performance laser stations In a second step improved weekly or monthly solutions for coordinates and velocities are generated which are combined in a final adjustment over the total time span of say several years Fig 813 shows as an example the results of a 10 years global solution for 40 global SLR stations based 438 8 Laser Ranging was mainly used for other astronomical purposes In the mid1980s a transition was made to the dedicated 076 m McDonald Laser Ranging System MLRS capable of ranging to artificial satellites as well as to the Moon Since 1984 another dedicated LLR station is continuously ranging to the Moon namely a French station near Grasse Observatoire de la Côte dAzur Centre dEtudes et de Recherche en Géodynamique et Astronomie OCACERGA Since about 1985 other observatories have also been successfully contributing to Lunar Laser Ranging for limited time periods These are Haleakala on the Island of Maui Hawaii the station Orroral inAustralia and the German fundamental stationWettzell Another joint SLRLLR station is being built up in Matera Italy Matera Laser Ranging Observatory MLRO The operational Lunar Laser Ranging Network LLRN of the ILRS hence for the time being only consists of two stations The earliest LLR ranges had accuracies of several meters and were improved to 20 cm during the 1980s Current measurement accuracies at the two LLRN observatories are about 1 to 3 cm This corresponds to a relative accuracy of better than one part in ten billion 11010 Subcentimeter normal point accuracy is aimed for Because of the high measurement accuracy it is necessary to formulate the analysis models in postNewtonian approximation The geometric relationship in the lunar laser ranging technique is explained in Fig 817 The basic observable is the range ρ between the Earthbased observatory O and the reflector R on the lunar surface E is the terrestrial center of mass and M the lunar center of mass B is the barycenter of the solar system The ephemerides of the Earth and lunar orbits refer to B B rB rO z rE E O x y mR mB ρ m z R mM M y x Figure 817 Geometrical relationship in lunar laser ranging The equation linking the coordinates of the telescope and of the reflector is written in the mean heliocentric barycentric coordinate system as rO mR ρ 812 86 Lunar Laser Ranging 439 Equation 812 is only fulfilled if several corrections are applied The coordinates rE of the telescope written in the Earthfixed reference system differ from the coordinates in the barycentric system because of Earth rotation pole coordinates precession and nutation Thereflectorcoordinates mR expressedinthebarycentricsystem havetobecorrected for lunar motions for example libration The measured ranges finally are influenced by tides aberration and other relativistic effects as well as by variations of the station coordinates due to crustal motion The modeling of the whole process hence constitutes a rather complicated problem of parameter estimation Dickey et al 1983 report on morethan80EarthMoonparameterstobeintroducedintothemodel Basicmodelsare given in the early literature for example Stolz 1979 Ballani 1982 For an analysis of LLR observations in the concept of a postNewtonian theory see eg Müller 1991 Nordtvedt 2001 The long series of what is now more than 30 years of continuous data provides an excellent opportunity for longterm as well as shortterm studies of the behavior of the EarthMoon system The LLR technique contributes andor is expected to contribute to among others the following problems Dickey et al 1994 Soffel Müller 1997 Global parameters of the EarthMoon system geocentric coordinates of the tracking stations including drift rates selenocentric reflector coordinates lunar orbit lunar rotation libration low harmonic coefficients of the lunar gravity field combined mass of Earth and Moon tidal friction momentum exchange between Earth and Moon Love number of the Moon and control of precession and nutation theories for a deformable Earth Earth rotation universal time UT0 length of the day LOD polar motion and longterm variation of the Earth rotation Gravitational physics and relativity test of Newtons law of gravitation possible GG test of the equivalence principle general relativity principles of special relativity eg Lorentz contraction and verification of the geodesic precession 87 Spaceborne Laser 441 for the determination of UT1 because Earth rotation variations cannot be separated from the pole components with only one input station Stolz 1979 Because of strong correlations between pole coordinates and errors in the lunar ephemerides as well as variations of UT1 lunar laser range observations are less suited for the determination of polar motion than are range measurements to artificial satellites Within the IERS therefore LLR does not contribute to the determination of pole coordinates For results and new insights from lunar laser ranging in gravitational physics and relativity see for example Dickey et al 1994 Soffel Müller 1997 Two notable findings are that the relativistic geodesic precession of 19 masyear is confirmed within 035 and that the gravitational constant G has no detectable rate for dGdtG within 11 1012year ILRS 2000 87 Spaceborne Laser The use of SLR equipment at a large number of terrestrial observation stations for the determination of precise coordinates is very expensive and time consuming This is why several proposals were made early on for reversing the principle that is to deploy the laser ranging system in an orbiting platform and to install reflectors on the ground eg Mueller 1975 Kahn et al 1980 Drewes Reigber 1982 Cohen et al 1990 The concept has many attractions because a dense network of ground reflector points can be installed in active tectonic areas and be controlled on a regular basis With the use of additional beacons in areas of tectonic stability fiducial stations the orbit of the spaceborne laser system can be precisely modeled Feasibilitystudieshavedemonstratedthatspacebornelasersystemscanberealized and would provide baseline accuracies on the order of a few cm over distances from a few km to 1000 km The concept however was never realized because GPS developed to be an extremely accurate and efficient tool to provide geodetic control for monitoring crustal deformation Instead a spaceborne laser altimeter mission was planned and has been realized with the Geoscience Laser Altimeter System GLAS as an integral part of the NASA Earth Observing System EOS program GLAS is the primary instrument on the Ice Cloud and Land Elevation Satellite ICESAT launched on January 12 2003 The main scientific objective of ICESAT is to better understand the mass balance of the polar ice sheets and their contribution to sea level change Furthermore cloud heights topography of land surfaces vegetation heights and seaice surface characteristics will be measured Schutz 1998 ICESAT flies in a near polar low Earth orbit LEO at an altitude of 600 km with an inclination of 94 degrees The mission orbit sets a 183 day repeat pattern which yields 15 km track spacing at the equator and 25 km at 80 degrees latitude The onboard dualfrequency GPS receiver is designed to provide 5 cm radial orbit position SLR reflectors serve as a backup system Onboard star cameras and gyros control the spacecraft orientation and laser pointing direction 442 8 Laser Ranging The GLAS instrument uses three Qswitched NdYAG lasers but only one will operate at a time The pulse length is 5 ns the shot repetition rate 40 Hz The laser beam nominally in nadir direction has a 0110 mrad divergence and illuminates a spot on Earths surface with a diameter of about 66 m footprint The surface reflected part of the signal is collected in a 1 m onboard telescope The laser pulse travel time provides the scalar altitude Together with the pointing information from the orientation system and the GPS position of the spacecraft an altitude vector can be determined which provides the ITRF location of the illumi nated spot on the surface The error budget is estimated as follows Schutz 1998 instrument precision 10 cm radial orbit determination 5 cm pointing determination 75 cm tropospheric delay 2 cm atmospheric scattering 2 cm other 1 cm total 138 cm The single shot error of about 14 cm enters an adjustment process as in satellite altimetry 94 using the crossover technique Considering the high number of possible crossovers in high latitudes error estimates indicate that the required accuracy of 15 cmyear can be met and the surface variability of large ice sheets in Antarctica and Greenland can be determined Schutz 1998 444 9 Satellite Altimetry from the possibility of scannning large ocean areas within a fairly short time period and determining a detailed representation of the sea surface with high resolution in space and time On the other hand satellite altimetry is a very good example of the interdisciplinary nature of satellite geodesy The quantity H namely the separation between the mean sea surface and the geoid is a disturbance noise to the geodesist who models the geoid but constitutes the observation signal for the physical oceanographer in the study of ocean dynamics 953 The geophysicist can from the large scale analysis of H derive valuable insight into the structure of the ocean floor and its tectonic features 952 A wealth of data has been obtained from existing altimeter missions and this has led to important scientific results in geodesy geophysics and oceanography Detailed discussions can be found in several dedicated issues of the Journal of Geophysical Research eg Vol 84 B8 1979 Vol 87 C5 1982 Vol 88 C3 1983 Vol 95 C3 1990 Vol 99 C12 1994 Vol 100 C12 1995 and in the excellent handbook edited by Fu et al 2001 In recent years several new satellite altimeter missions have been launched and further missions carrying radar altimeters 92 are planned for the near future Satel lite altimetry will hence remain one of the powerful methods in satellite geodesy 92 Satellites and Missions The technique of satellite altimetry was tested for the first time during the SKYLAB missions SL2 SL3 and SL4 19731974 over orbital arcs of about 750 km length The accuracy of the altimeter was about 1 to 2 m This opened the way to a direct comparison of the altimeter heights with a computed 5 5 gravimetric geoid Marsh Vincent 1975 Fig 92 shows this comparison for one orbital arc near the Puerto Rico Trench where the geoidal heights change by up to 20 m over quite short distances The correspondence is within a few meters all the main characteristic geoidal structures Puerto Rico Island geoidal height m Antilles Trench Puerto Rico Trench 30 40 50 60 70 80 90 100 110 15 15 30 15 16 00 15 16 30 15 17 00 15 17 30 h m s h h h h m m m m s s s s Figure 92 SKYLAB altimeter test are visible in the data of the SKYLAB altimeter solid line model geoid After the successful test during the SKYLAB missions new and improved altimeter versions were flown on the early satellites GEOS3 1975 and SEASAT1 1978 GEOS3 Geo dynamics Experimental Ocean Satellite Fig 411 p 150 launched on April 9 1975 was a multipurpose satellite 432 Besides the altimeter laser reflectors Doppler transmitters for pre cise orbit determination and a satellite tosatellite tracking package 102 92 Satellites and Missions 445 were installed on the spacecraft Primary mission goals were improvement of our knowledge of Earths gravity field the geoid ocean tides currents structure of Earths crust dynamics of the solid Earth and remote sensing technology Stanley 1979 The design lifetime of the altimeter was only 1 year however the total amount of altimeter data spans 35 years SEASAT1 also designated as SEASATA was launched on June 26 1978 Its main objective was the mapping of ocean surface data through remote sensing tech niques The sensor module includes five sensors with the following tasks altimeter satellite altitude wave height wind velocity scatterometer wind velocity wind direction microwave radiometer sea surface temperature wind velocity atmospheric water vapor synthetic aperture radar wavelength wave direction and visible and infrared radiometer feature identification On October 10 1978 after about three months of operation a shortcircuit occured onboard and prevented the operation of most sensors including the altimeter Never theless the majority of the mission objectives were reached In particular the amount and quality of the altimeter data fully met initial requirements 951 The US Navys GEOSAT Geodetic Satellite spacecraft was launched on March 12 1985 into an 800 km near circular orbit with an inclination of 108 Cheney et al 1986 McConathy Kilgus 1987 The main instrument is an improved version of the radar altimeter flown on SEASAT The precision for height measurements is about 35 cm Mac Arthur et al 1987 Additional subsystems are a dual frequency 150 and 400 MHz Doppler beacon for spacecraft tracking based on the TRANET network 63 and a Cband transponder 442 The attitude control subsystem a gravity gradient system in the form of a 6 m scissors boom with a 45 kg end mass was designed to point the radar altimeter to within 1 degree of nadir The satellite performed in succession two separate missions the primary Geode tic Mission GM with data collected from March 31 1985 through September 30 1986 and the subsequent Exact Repeat Mission ERM from November 8 1986 through January 5 1990 Marks et al 1991 The main objective of the primary geodetic mission was to map the marine geoid up to latitudes of 72 degrees at high resolution The ground track had a nearrepeat period of about 23 days The drifting orbit produced a dense network of sea level profiles with an average track spacing of about 4 km thus providing gravity fields of unprecedent accuracy and resolution The GM data were initially classified but released in their entirety for public use in 1995 The full GM data set in particular with recomputed orbits gave rise to valuable geophysical interpretation 952 In October 1986 upon termination of the GM phase the spacecraft was maneu vered into an orbit whose ground track repeated every 17 days and largely corresponded to the SEASAT ground tracks The data of this Exact Repeat Mission ERM were unclassified from the beginning and freely accessible for geodetic and oceanographic work The spacing between ERM ground tracks is 75 km at 60 latitude and hence 446 9 Satellite Altimetry much wider than that of GM tracks Fig 93 gives an example for the latitude 60S 3 Exact repeat means that the ground tracks repeat to within 1 km for each 17days repeat cycle The ERM mission covered 62 complete 17days cycles before a 57 S 60 S 63 S 205 E 220 E Figure 93 Ground track spacing of GEOSAT GM medium lines and ERM thick lines missions near 60 southern latitude SEASAT ground tracks thin lines for comparison from Marks1991 tape recorder failure in October 1989 terminated the global data set A limited amount of data was available by direct broadcasting in the North Atlantic and Gulf of Mexico until January 1990 The more than three years of ERM data are highly valuable for oceanographic studies such as sea level variations 953 however the gravity fields derived from these data are not able to resolve finescale features fully due to the wide spacing of the ground tracks 951 Reprocessed socalled geophysical data records GDRs were made available through NOAA in 1997 The data set includes the entirety of the GM ERM data with consistent JGM3 orbits and enhanced geophysical corrections NOAA 1997 The first European Remote Sensing Satellite ERS1 was launched on July 17 1991 into a sunsynchronous lowEarth nearly circular orbit of 780 km and with 985 inclination The satellite allowed allweather highresolution imaging over land coastal zones and polar ice caps measured ocean wave heights and wavelengths wind speeds and directions various ice parameters seasurface temperatures cloud cover atmospheric water vapor content and precise altimetry over oceans and ice The satellite carries a set of active microwave sensors supported by additional instruments Fig 94 Synthetic Aperture Radar SAR Radar Altimeter RA Along Track Scanning Radiometer ATSR Precise Range and RangeRate Equipment PRARE and Laser Retro Reflector Array RRA 92 Satellites and Missions 447 Wind Scatterometer Antenna SAR Antenna Radar Altimeter Antenna Laser Retroflector IDHT Antenna PRARE Along Track Scanning Radiometer Platform Solar Array Figure 94 ERS1 The total mass is 2 400 kg and the over all height is 118 m The RA antenna has a diameter of 12 m ERS1 carries an attitude and orbit control system AOCS to main tain the platform orientation in flight This system contains inter alia infrared Earth sensors sunsensors an inertial core of six gyros and three orthogonal reaction wheels OBrien Prata 1990 The primary onboard system for precise orbit determination was PRARE 4333 Unfortunately PRARE failed during the ini tial tests hence precise orbits depend on satellite laser ranging The radar altimeter operates in the Ku band in two modes the ocean mode and the ice mode Because of the near polar orbit ERS1 provides valuable data over ice and permits the study of the polar regions The design accuracy of the ERS1 altimeter was 10 cm The results however revealed a performance similar to the GEOSAT altimeter 35 cm Because of the multidisciplinary nature of satellite altimetry different phases of operation were planned and realized Two 3dayrepetition cycles were initiated for 3 months each during theArctic winter to monitor ice coverage ice phase During 1992 and 1993 ERS1 operated in the multidisciplinary phase with a ground track repetition rate of 35 days In 1994 for primarily geodetic applications ERS1 was maneuvered into a 176day cycle the altimeter phase or geodetic phase The equatorial ground track spacing was about 900 km for the ice phase 80 km for the multidisciplinary phase and 18 km for the altimeter phase The expected lifetime was about three years ERS1 however worked three times as long This is why a completely new space technique Interferometric SAR InSAR 112 could be applied in a tandem phase with ERS2 soon after its launch in April 1995 ERS1 operation was terminated on March 10 2000 because of a failure in the attitude control system Table 91 gives an overview of the different mission phases Schöne 1997 TOPEXPOSEIDON Fig 95 often abbreviated as TP is a satellite mission that carries a radar altimeter system as the primary instruments and is jointly con ducted by the NASA and the French Space Agency CNES TOPEX stands for Ocean TOPography EXperiment The spacecraft was successfully launched on August 10 1992 into a circular nonsunsynchronous orbit at an altitude of 1340 km and with an inclination of 66 The mission includes two altimeters The primary instrument is a dualfrequency altimeter operating simultaneously at 136 GHz Ku band and 53 GHz C band 448 9 Satellite Altimetry Table 91 ERS1 mission phases Operation phases Orbit Duration start and test 17071991 30071991 commissioning phase 3days 01081991 12121991 first ice phase 3days 28121991 10031992 multidisciplinary phase 35days 14041992 15121993 second ice phase 3days 24121993 01041994 geodetic phase 168days 10041994 19031995 tandem mission phase 35days 21031995 10032000 The measurements can hence be corrected for errors caused by free electrons in the ionosphere As a byproduct the total electron content can be obtained This altimeter is the first to use twochannel measurements for ionospheric range corrections Figure 95 TOPEXPOSEIDON courtesy NASAJPLCaltech The second instrument POSEI DON is a solidstate radar altime ter experimental sensor CNES op erating at a single frequency of 1365 GHz The main objective of the experimental sensor is valida tion of lowpower lowweight al timeter technology for future Earth observing missions The orbit determination is sup ported by a laser retroreflector array and the French DORIS Doppler Or bitography and Radiopositioning In tegrated by Satellite tracking system 67 In addition an experimental GPS receiver is flown onboard A radiometer provides estimates of the total water vapor content along the signal path and is used to correct the altimeter measurements The satellite is operated through NASAs Tracking and Data Relay Satellite System TDRSS The TOPEXPOSEIDON mission is mainly designed to explore ocean circulation and its interaction with the atmosphere 953 The ground tracks repeat exactly after about 10 days with a spacing of about 315 km at the equator The footprint is 3 to 5 km in diameter for typical wave heights Measurements are taken approximately once per second giving a spacing of about 6 km The design lifetime of the mission was 3 to 5 years At the time of this writing however this highly successful satellite is still delivering data after more than 10 years having also flown several months in a tandem formation with its successor satellite JASON1 ERS2 the followon mission to ERS1 was launched by the European Space Agency ESA on April 21 1995 into a nearly identical orbit to ERS1 with the 92 Satellites and Missions 449 objective to continue its work Additional instruments measure the ozone content of the atmosphere Global Ozone Monitoring Experiment GOME Both SLR and PRARE are used for precision orbit determination Because of the longevity of ERS1 both satellites were placed in a tandem configuration separated by 400 km for nearly five years The orbital period is 35 days and the ground track spacing at the equator is 80 km GEOSAT followon GFO is a US Navy satellite mission to study physical oceanography GFO was launched on February 10 1998 into a nearcircular orbit at 800 km altitude with 108 degrees inclination The satellite carries a single fre quency radar altimeter water vapor radiometer Doppler beacon four GPS receivers and a laser retroreflector array The mission lifetime is scheduled to be about 10 years following the GEOSAT Exact Repeat Mission ERM orbit with a repetition rate of 17 days after 244 revolutions Due to problems with the onboard GPS receivers precise orbit determination is mainly supported by SLR JASON1 is a followon mission to TP again as a joint project of NASA and CNES JASON1 was launched on December 7 2001 into a circular orbit very similar to that of TP namely with an altitude of 1336 km and an inclination of 66 degrees The onboard instrumentation is tracking and data relay satellite transmitter microwave radiometer dual frequency altimeter POSEIDON2 DORIS dual frequency receiver GPS receiver TRSR and laser retroreflector array As with TOPEXPOSEIDON three independent techniques are used for precise orbit determination The satellite weighs just 500 kg one fifth the weight of its predecessor The design lifetime is 5 years The main objective is to continue the mission started by TP to monitor world ocean circulation and to study interactions of the oceans and atmosphere TP time series are not long enough to resolve all scientific issues in oceanography Oceanic oscillations with periods over 10 years can only be recovered by continued timeseries 953 The Environmental Satellite ENVISAT1 is the successor to the European Space Agency ESA Remote Sensing Satellites ERS1 and ERS2 The satellite was launched on March 1 2002 into a nearcircular sunsynchronous nearpolar orbit of 800 km altitude and 985 degrees inclination The orbital period is 35 days as for ERS2 and some phases of ERS1 ENVISAT1 is a multipurpose satellite for environmental studies and observes Earths atmosphere ocean land and ice over a 5year period using ten complementary instruments The most important sensors for research related to geodesy are Advanced Synthetic Aperture Radar Radar Altimeter RA2 Microwave Radiometer DORIS Receiver and Retroreflector Array 450 9 Satellite Altimetry Table 92 gives an overview of the system data of the cited altimeter missions It is evident that a wealth of data for research in geodesy oceanography and geophysics has been provided by so many missions Since TOPEXPOSEIDON altimeter noise levels are as low as 2 to 3 cm corresponding to the noise level of the other space techniques TP and ERS2 are already far beyond their expected lifetime But three current missions and planned successors promise that satellite altimetry will remain a powerful technique in satellite geodesy Table 92 Characteristic data of altimeter missions Mission SKYLAB GEOS3 SEASAT1 GEOSAT ERS1 Mission begin 1973 1975 1978 1985 1991 Mission end 1973 1978 1978 1989 1996 Duration months days 44 4 54 57 Mean altitude km 435 840 800 785 785 Inclination 115 108 108 985 Max latitude 65 72 72 815 Cycle repeat days 2317 335168 Track division km 475 9338016 Frequency GHz 135 135 Altimeter noise cm 100 60 10 4 4 RadiometerFrequ yes no yes2 Orbit determination SLR Doppler Doppler SLR Doppler PRARE Mission TOPEX ERS2 GFO JASON1 ENVISAT1 POSEIDON Mission begin 1992 1995 1998 2001 2002 Mission end Duration months Mean altitude km 1340 780 800 1340 800 Inclination 66 985 108 66 985 Max latitude 66 815 72 66 815 Cycle repeat days 10 35 17 10 35 Track division km 316 80 165 316 80 Frequency GHz 53136 135 135 53136 32136 Altimeter noise cm 2 3 35 15 2 RadiometerFrequ yes2 yes3 yes2 yes3 yes2 Orbit determination SLR GPS SLR SLR GPS SLR GPS SLR DORIS PRARE Doppler DORIS DORIS For the near future two more missions are planned or are already realized ICE SAT carrying a laser altimeter GLAS 87 was launched on January 12 2003 CRYOSAT an altimetry satellite built by ESA will be dedicated to polar observations 452 9 Satellite Altimetry anomalies from sea gravity observations do not refer to the geoid but to the mean sea surface The sea surface topography can further be separated into one part caused by atmospheric pressure also called inverted barometric effect and into another part the mean ocean dynamic topography mainly caused by ocean circulation Tapley Kim 2001 Note that the denomination is not uniform in literature The term sea surface height or sea surface topography may either refer to the ellipsoid or the geoid In this book SST is defined with respect to the geoid 932 Data Generation The satellite altimeter antenna transmits a short rectangular impulse which is reflected back from the sea surface at the moment of contact The simultaneously reflecting ie the completely illuminated circular area is called the footprint The footprint size depends on the sensor altitude a above the sea the signal propagation velocity c and the pulsewidth τ The maximum radius of the circular area cf Fig 97 b Chelton et al 2001 is R 2cτh 94 h R a b c d τ θA Figure 97 Variation of the illuminated reflecting area for a radar pulse penetrating the sea surface Equation 94 is valid for a quiet sea surface With increasing wave height the footprint radius expands because the effective pulselength is amplified as Rummel Sanso 1993 τ τ 2 SWH c SWH is the significant waveheight see 933 For ERS1 and ERS2 with h 800 km and τ 3 ns the footprint radius R varies between 12 km for quiet sea and about 6 km for rough sea SWH 10 m 93 Measurements Corrections Accuracy 453 The reflected energy depends directly on the size of the reflecting area Conse quently the returning energy continuously increases until the radar pulse is completely submerged in the reflecting surface Fig 97 a b As soon as the outer edge of the pulse has arrived at the surface the reflecting area converts into an annular form with a nearly constant area until the edge of the beam is reached Fig 97 c d Altimeter systems where the size of the footprint depends on the length of the transmitted pulse in the above described way are called pulselengthlimited systems Another possibility is to define the footprint size by the beamwidth θA of the radar beam Such beamwidthlimited systems require a very precise nadir adjustment of the antenna A detailed discussion of footprint sizes and their dependence on wave heights is given by Chelton et al 2001 Fig 98 shows the idealized form of the return impulse in pulselengthlimited systems The leading edge has the length of the transmitted impulse 125 ns for GEOS3 and is followed by a constant level until the final edge transmitted pulse 125 ns time return pulse time 125 ns Figure 98 Transmitted pulse and return pulse The range observable is derived from the time delay between the instant of pulse transmission and the moment when the return pulse reaches half of the maximum amplitude The size of the reflecting area and the real form of the return pulse depend on the quality of the reflecting surface water ice land and on the roughness of the surface wave heights Information on the sea state can be derived from a pulse analysis The wave crests and troughs within the footprint are averaged out Remaining systematic effects depending on the sea state have to be determined by calibration measurements in special test areas ground truth The altimeter pulse frequency is usually about 1 KHz The single pulses are condensed to 10 Hz and then reduced to 1 second mean values This process leads to a strong limitation of the observation noise The precision of a 1secondmean altimeter observation is about 2 cm for current missions see Table 92 To convert the altimeter measurements into sea surface heights requires several corrections such as for instrumental influences atmospheric delays sea state and orbit improvement see 933 The final accuracy for current missions is about 6 to 8 cm 94 Altimeter measurements or sea surface heights are given along the satellite ground track with a spacing of about 7 km The spacing between tracks can be much larger depending on the mission objectives Geodetic missions with the aim to determine a high resolution gravity field aim for a dense spacing and low repetition rate Examples 454 9 Satellite Altimetry are 4 km for the GEOSAT GM mission and about 16 km for the ERS1 geodetic phase see Table 92 Oceanographic missions aiming at measurements of sea level varia tions need frequent repetition rates and thus accept a larger spacing A good example is TOPEXPOSEIDON with a track spacing of 316 km The European satellites select a multidisciplinary compromise with 80 km track spacing Fig 914 p 462 shows the track pattern of SEASAT for a period of 18 days Altimeter data and data products are available to users through particular data centers under the control of the responsible space agencies The data and products are provided in a missiondependent format and also include corrections orbit information and waveform analysis The ENVISAT products for example are categorized into three distinct levels Benveniste et al 2001 Level 0 raw unprocessed data as it comes from the instrument Level 1 engineering data converted to engineering units with instrumental calibration applied and Level 2 geophysical data converted to geophysical units with datation geo location including retracked data such as range wind speed wave height Retracking means improvement of the altimeter data based on analysis of the return signal Heidland 1994 Different techniques are applied referring to the specific properties of the reflecting surfaces such as water continental ice shelf ice or sea ice Data products of modern altimeter missions are available either in nearrealtime 3 hours in quasi nearrealtime 23 days or with the highest precision offline after several weeks The generation of nearrealtime products is supported by onboard orbit determination for example with the DORISDIODE capability 67 Significant advantages are to be gained by merging the data from two or more altimetry missions with different orbital patterns see Fig 913 such as ERS and TP or ENVISAT and JASON In some cases historic altimeter measurements are reprocessed with improved orbital data based on refined gravity models This is in particular true for the GEOSAT GM data set NOAA 1997 Data formats and standards are not yet homogeneous The establishment of an International Altimeter Service similar to the existing services for GPS SLR and VLBI is under discussion The main objective is to harmonize the use of heterogeneous data for MultiMission Satellite Altimetry MMSA 933 Corrections and Error Budget Three groups of corrections have to be considered each of them contributes to the level of achievable accuracy 1 deviation of the real orbit from the calculated orbit orbit error 2 influences along the signal propagation path altimeter error and 3 deviation of the instantaneous sea surface from the geoid 1 Orbit errors These are mainly caused by 32 93 Measurements Corrections Accuracy 455 limited resolution and accuracy of the terrestrial gravity field used in the orbit computation errors in the coordinates of the tracking stations errors or limitations in the tracking system Doppler Laser and mismodeling in the orbit computation The predominant influence in particular for the early altimeter missions comes from the terrestrial gravity field Each satellite is particularly sensitive to a certain subset of harmonic coefficients it is therefore advisable to develop tailored gravity models including observations of the particular satellite or satellites with a similar orbit This has been done for example with the gravity model GEM 10 for GEOS3 1222 that improved the orbit accuracy from 10 m to 1 to 2 m Lerch et al 1979 The tailored gravity models PGSS1 to PGSS4 were developed for SEASAT and have improved the orbit accuracy from 5 m initially to 1 m Fig 99 Wakker et al 1987 These models could also be used for ERS1 because of its similar orbital 2 1 3 4 5 6 0 1 2 3 4 5 6 5 years 1 2 3 launch m 4 σr Figure 99 Improvement of the radial or bit accuracy for SEASAT 1 before launch 2 5 additional data from SEASAT laser GEOS3 altimetry SEASAT altimetry TRANET Doppler 6 final accuracy elements Precise GEOSAT orbits at the level of 50 cm have been com puted based on the GEMT2 geopo tential model Marsh et al 1990 GEMT3 was a refined version Lerch 1992 with the inclusion of altime ter data from GEOS3 SEASAT and GEOSAT Based on GEMT3 the se ries of Joint Gravity Models JGM was developed to compute precise orbits for TOPEXPOSEIDON Since none of the previously used satellites had a sim ilar orbit a refinement of the pre launch model JGM1 was started with TP laser and DORIS tracking data and direct altimetry data from GEOS 3 SEASAT and GEOSAT resulting in JGM2 The inclusion of additional SLR data DORIS and GPS tracking of TP resulted in JGM3 Tapley et al 1996 This model provided an orbit accuracy of 10 cm for reprocessing of the GEOSAT data and it is also appropriate for JASON Based on JGM3 a tuned model has been developed to provide improved orbits for the ERS satellites Scharroo Visser 1998 and hence also for ENVISAT The most recent model is EGM96 Lemoine et al 1998 including additional data with a much higher spatial resolution than models such as JGM3 With the various new models at hand the orbits of altimeter satellites can be modeled with an accuracy of better than 10 cm in the radial component Chelton et al 2001 The gravity field is hence no longer the dominant factor for precise orbit determination in satellite altimetry 93 Measurements Corrections Accuracy 457 propagation errors The most important instrumental influences are the distance between the phase center of the radar antenna and the spacecraft center of mass center of gravity correction propagation delay in the altimeter electronics and timing error in the measuring system These effects can be minimized and estimated as the altimeter instrument is built The overall effect of the instrumental errors the altimeter bias is determined and controlled in the altimeter calibration over precisely surveyed test areas ground truth Satellite passes through the zenith of laser ground stations are in particular suitable For GEOS3 a mean calibration value of 530 m was determined Berbert Carney 1979 For SEASAT1 the calibration value did not differ significantly from zero Kolenkiewicz Martin 1982 For TOPEXPOSEIDON calibration sites have been maintained at a platform off the coast of Southern California and near Lampedusa Island in the Mediterranean Sea Chelton et al 2001 Besides SLR GPS and DORIS are also used Fig 910 Sea surface height is determined independently by the altimeter and direct in situ measurements with tide gauges Magnitudes of the biases for recent altimeter missions GPS GPS GPS GPS GPS DORIS DORIS Orbit Ellipsoid Laser Tide gauge h N a Figure 910 Geometry of in situ altimeter cali bration after Chelton et al 2001 range from 40 cm for ERS1 to near zero for the two altimeters onboard TP In addition validation of JASON and ENVISAT is assisted by a worldwide network of tide gauges collocated by DORIS and GPS measurements For the study of changes in the global mean sea level 953 it is important to detect and calibrate potential drifts in the measurement system Considering a eustatic sea level rise of less than 2 mmyear it is necessary to detect any drifts at the 1 mmyear level This re quires continuous calibrations at the cal ibration sites over several years Another instrumental error may be caused by deviation of the beam direction from the vertical nadir error The influence depends on the pulse length and the beam width and can be minimized by technical means The effect of the nadir error can be neglected for the pulselength limited systems cf Fig 97 because the footprint is then defined by the pulselength Signal propagation errors are caused by the influence of the ionosphere and the troposphere on the propagation velocity 233 The influence of the ionospheric refraction in the frequency domain of 14 GHz is about 5 cm to 20 cm depending on the level of ionization As with other microwave systems used in satellite geodesy 642 744 the ionospheric effect can be modeled with measurements at two frequencies 93 Measurements Corrections Accuracy 459 The response of the sea surface to atmospheric loading is about 1 cm mbar1 This socalled inverted barometer effect causes global deformations of the sea surface between 10 and 20 cm Regional effects in particular in the tropics are smaller Sea surface pressure values are taken from numerical weather prediction models with an uncertainty of 2 to 4 mbars corresponding to 2 to 4 cm The inverted barometer effect is hence still a major error source in the precise analysis of seasurface height For detailed information on the subject see eg Wunsch Stammer 1997 The principal part of the variable deformation is induced by ocean tides In the open ocean tidal amplitudes reach about 10 to 60 cm with larger values near the coasts and in shallow marginal seas Before the launch of TP knowledge of tides was mainly based on hydrodynamical models with empirical constraints from globally distributed tide gauges The global ocean tide model of Schwiderski 1984 with an accuracy of about 01 m was widely used With the inclusion of TP data the tides can now be estimated to an accuracy of 23 cm LeProvost 2001 One example is the CSR30 model Eanes Bettadpur 1996 In shallow seas such as the North Sea deviations from the global model can reach quite large amounts in such cases local or regional tidal models must be applied Solid Earth tides cause deformations of the Earth body of several decimeters in height They include the effect of direct astronomical forcing the body tide and the effect of crustal deformation by ocean tides tidal upload The modeling accuracy is about 1 cm or better Zahran 2000 Both solid Earth and ocean tides have to be removed from altimeter data before they can be used for the study of ocean circulation Chelton et al 2001 The constant part H Fig 96 the sea surface topography also named dynamic sea surface height shows amplitudes up to about 2 meters 931 953 Depending on the subject the quantity H can be regarded as a correction or as the signal of interest If altimeter observations are used in the determination of a marine geoid the sea surface topography has to be taken as a correction to the measurements from oceanographic models Traditionally dynamic heights are computed from hydrographic data with respect to a reference level of equal pressure at great depths several thousand meters The accuracy of these models is debatable and is at best about 20 cm Fu et al 2001 In oceanography the dynamic sea surface height is of interest and the geoid un dulation is taken as a correction Precise geoid information over the oceans without the inclusion of altimeter data is available for long wavelenghts only For shorter wavelengths with the inclusion of altimeter data the current accuracy estimate is at the few decimeter level Chelton et al 2001 Thedifficultyinseparatingthegeoidundulation N andtheseasurfacetopography H hence constitutes a basic problem in the use of satellite altimetry in geodesy as well as in oceanography Several solution concepts exist to improve the situation by the inclusion of additional information on ocean flow or satellite orbits Rummel Sanso 1993 The best solution will be an independent geoid improvement for shorter wavelengths which can be expected from the new gravity field missions 10 460 9 Satellite Altimetry 94 Determination of the Mean Sea Surface The altimeter data are available as a sequence of altitude values of the mean sea surface above the selected reference ellipsoid along the subsatellite track cf Fig 912 The distance between adjacent subsatellite points varies according to the satellite and the 58 57 6 8 5 m Figure 912 Example of altimeter data in the North Sea observation mode for current missions it is about 7 km The spacing between the tracks varies from 80 to 316 km for current missions and it was 4 and 16 km for the geodetic missions of GEOSAT and ERS1 Afterapplyingallthecorrectionsdis cussed in 93 a systematic vertical er ror remains which is partly due to the radial orbit error 933 and which con tains all other residual errors The subsequent data processing makes use of the fact that the same ocean area is covered several times so that the altitude of the mean sea surface N H must be identical in the intersections of the ascending and the descending satellite ground tracks This socalled crossover technique is widely used in the evaluation of altimeter measurements eg Rummel Sanso 1993 Fig 912 demonstrates the principle for a small section of the North Sea and GEOS3 data Monka 1984 After correction of the altimeter measurements the differences in the crosspoints are more or less identical to the differences in the radial orbit errors of the contributing satellite orbits and residual altimeter biases As a first step the crossover points have to be located This can be achieved in an iterative process based on the geographical coordinates of the satellite groundtracks Other methods start from the satellite ephemerides Kim 1997 Then the heights at the crossover points are interpolated from the sequence of measured altimeter heights along the ground tracks Simple linear or quadratic interpolation formulas can be used or advanced interpolation techniques like the Kalman or Wiener filter The differences between the interpolated values at the crossover points are dij hi hj di dj εi εj 96 with hi hj interpolated altimeter observations along the ground tracks i and j for the crossover point di dj orbit errors of the satellite orbits i and j for the crossover point and εi εj observation errors The orbit error can be modeled along the satellite orbit by use of a polynomial in distance or time In the simplest case a shift or inclination of the orbital arc is 462 9 Satellite Altimetry geodesy the wealth of data from satellite altimetry provides the best overall approach for determination of the marine gravity field 951 The fine structure of the mean sea surface derived from high resolution satellite altimeters such as GEOSAT and TP reflects ocean bottom topography and tectonic structuresoftheoceaniclithosphere andcontributessignificantlytomarinegeophysics 952 The high frequency of track repetitions together with the centimeter resolu tion of modern missions like TP JASON and ERSENVISAT provides a powerful means for continuous monitoring of ocean surface variability and related processes in oceanography 953 Dedicated missions with high orbit inclination like ERS12 ICESAT and the forthcoming CRYOSAT offer unprecedented opportunities to map the polar icesheets 953 Whereas the first altimeter missions were mainly directed to the mapping of a detailed marine gravity field also with the objective to improve the precise orbit determinationofthealtimetersatellites themodernmissions withtheirhighresolution in the time domain are more committed to monitor time variable effects 951 Geoid and Gravity Field Determination To a first approximation the mean sea surface and the marine geoid can be considered as equal The mean sea surface heights along a satellite subtrack resulting from an altimeter mission 94 can hence be treated as geoidal heights N Fig 914 shows as an example the global coverage with SEASAT satellite tracks for a period of 18 days The complete data set is accordingly much denser 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 72 60 50 40 30 20 10 0 10 20 30 40 50 60 72 Figure 914 18day global coverage with SEASAT1 data Marsh Martin 1982 In total about 5 million height values are available for the GEOS3 mission as well as for the SEASAT1 mission about one half are useful after data screening Because of the inclination of the satellite orbits the data are restricted to a belt between 72 north and south In spite of the very short lifetime of SEASAT1 both data sets are about equal in size SEASAT1 delivered data for 1648 hours from 3 months of operation and GEOS3 provided data for 1745 hours from 35 years of operation These sea surface heights can be used to determine an evenlyspaced grid of glob ally distributed heights based on suitable interpolation techniques Based on the grid 95 Applications of Satellite Altimetry 463 points a representation with contour lines can be derived Fig 915 gives as an ex ample the representation of the mean sea surface based on the data of Fig 914 This surface roughly corresponds to the geoid and demonstrates that the early altimeter missions provided excellent global coverage and new insights into the structure of the marine geoid 72 60 50 40 30 20 10 0 10 20 30 40 50 60 72 0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360 Figure 915 Sea surface topography from SEASAT data Marsh Martin 1982 The global altimeter data base was improved considerably after the release of the GEOSAT data from the geodetic mission GM In total 30 million GEOSAT data and 20 million data from the ERS1 geodetic phase are available Knudsen Andersen 1997 The track spacing is between 4 and 8 km A further breakthrough came with the TP data and its high radial orbit accuracy of 3 to 4 cm By about 1995 combined solutions of several altimeter missions led to sea surface models of about 1 dm precision By averaging over several years and reprocessing of older data with improved gravity field models the current uncertainty of the mean sea surface representation is a the 1 cm level Tapley Kim 2001 Altimeter data are used as a data base to derive gravity anomalies with Stokes inverse integral formulas Torge 2001 For example the GEOSAT GM data first gave 5 5 mean altimeter heights and were then converted into 5 5 mean gravity anomalies Trimmer Manning 1996 Usually the sea surface topography is first removed with a global model Altimeter data are included in all recent Earth models 1222 While the classical analysis of satellite orbits only allows the determination of the long wavelength part of the potential field the inclusion of altimeter data together with surface gravity data gives a much higher resolution up to degree and order 360 360 and even higher The use of heterogeneous data from different sources has to be supported by proper weighting Appropriate strategies have to be applied to account for the dynamic sea surface topography EGM96 for example solves for a separate spherical harmonic expansion of the dynamic SST TOPEX ERS1 and GEOSAT to degree 464 9 Satellite Altimetry and order 20 Lemoine et al 1998 Comparisons between TP mean sea surface over two years with an independent hydrographic SST model and EGM96 show an agreement of about 10 cm Lemoine et al 1998 Tapley Kim 2001 It seems that this number is the current accuracy limit for an ocean geoid model derived from altimetry For a better separation between geoid and dynamic sea surface topography it will be necessary to include data from the current and forthcoming gravity field missions CHAMP GRACE and GOCE 10 For more information on the subject see Tapley Kim 2001 or the series of IAG symposia on topics related to geoid determination eg Rapp et al 1996 Segawa et al 1997 Forsberg et al 1998 952 Geophysical Interpretation Except for the 1 to 2 m dynamic sea surface topography associated with oceano graphic features 953 the geoid and the sea surface coincide The SST can be represented by rather long wavelengths Altimeter data with a precision of a few cm can thus resolve geoid signals associated with seafloor topography This is particu larly true for the denselygridded data from the ERS1 geodetic mission 19941995 and the originallyclassified GEOSAT GM data released in 1995 These data pro vide a detailed view of the marine gravity field with a spatial resolution of better than 5 km Previously undetected seamounts submarine elevations uncharted fracture zones and deep sea trenches can be identified and located and they can be made visible in suitable representations Continental margins rifts and the orientation of fracture zones can be traced over thousands of kilometers and give a wealth of information for geophysical interpretation Midocean spreading ridges the longest mountain chains on Earth are now nearly entirely mapped Lineations have been detected in every ocean basin that are the result of tectonic plate motions Satellite altimetry hence provides a confirmation of plate tectonics For detailed information on the subject see Cazenave Royer 2001 with many impressive pictures Geoid anomalies related to submarine tectonic features have wavelengths below about 3000 km Hence as a first step in analysis a long wavelength reference geoid such as JGM3 is subtracted from the data Another procedure is to use a high pass filter For detailed investigation it can be useful to remove wavelength components larger than 200 km by filtering The remaining data allow detailed mapping of the seafloor tectonic fabric Fig 916 demonstrates the relationship in the case of a seamount Such seamounts generate an excess of mass relative to the adjacent oceanic plain This excess produces deformations little bumps on the mean sea surface in the geoid height that can be measured by the satellite altimeters The height variation corresponds to variations in shipborne gravity The geoid anomaly reaches about 1 to 2 m for a 1 to 3 km high seamount with a typical base diameter of 10 to 50 km The related gravity anomaly varies between 20 and 200 mGal More than 10 000 seamounts have been identified alone on the Pacific plate Cazenave Royer 2001 95 Applications of Satellite Altimetry 467 Muir seamount 120 cm change due to Gulf stream meander 100 50 0 0 100 200 N 310 W 645 N 410 W 564 cm km April 23 1977 September 28 1977 Figure 918 Variation of the sea surface topography due to a Gulf stream meander models derived from TP data have an accuracy of about 2 to 3 cm Desai Wahr 1995 Fu Chelton 2001 The study of sea level changes shows periodic as well as secular effects The results have been verified by comparisons to globally distributed tide gauges Cazenave et al 1999 Each cycle 10 days for TP and JASON delivers a model of the mean sea state which can be gridded For the grid points the sequence of altimeter heights can be analyzed in a time series eg a Fourier series Annual periods show amplitudes up to 20 cm the secular trend indicates a sea level rise of about 2 mmyear The annual variations can be referred to as ocean seasons caused by variable temperature The differences between spring and autumn reach about 20 cm Well known is the El Niño effect resulting in a sea level anomaly of about 10 cm caused by increased water temperature Altimeter data can identify the eastward wander of this anomaly over several monthlong periods across the Pacific Ocean Satellite altimetry hence contributes to global climate studies Oscillations with periods over 10 years will be recovered from the long time series of TOPEXPOSEIDON now continued with JASON1 One particular advantage of satellite altimetry as compared to tide gauge readings is that an absolute sea level can be determined referred to Earths center of mass and independent of crustal motion This contributes for example in connecting separated tide gauges and distinct height reference systems with the objective of creating a unified global height datum Fig 919 GPS observations at the tide gauges provide the precise geometrical connection between the stations 7623 Characteristic features of the sea state waves and wind can be analyzed from the shape and intensity of the return pulse wave form A calm sea is a good reflector and returns a strong pulse rough seas scatter the signal and hence return a weak pulse The 468 9 Satellite Altimetry height datum tide gauge topography mean sea surface geoid ellipsoid Figure 919 Relationship between separated tide gauges amount of scattered power can be used to identify the sea state observe sea ice extent and the rate of accumulation of snow on glaciers Heidland 1994 Zwally Brenner 2001 Due to the nearpolar orbits of altimeter missions like ERS1 92 significant contributions were expected to the mapping of ice topography and ice sheet variability For ERS1 two particular icephases with a 3day repetition cycle were realized The orbital parameters allowed mapping of the whole Greenland ice sheet and about 80 of Antarctica ERS2 and ENVISAT continue the observations Polar ice sheets and sea ice play an important role in the global climate system because of their high albedo and their role as a large store of fresh water With ERS altimeters it has been possible to monitor ice sheet mass balance and changes in sea ice thickness since 1992 This monitoring has already revealed a significant thinning of Antarctic glaciers Benveniste et al 2001 that can continue to be observed with ENVISAT A current difficulty in mass balance estimation is controlling the wave penetration within the snowpack Rémy et al 2001 Twofrequency altimeters will improve the estimation of ice accumulation Further improvement of our knowledge on ice mass balance is expected from the GLAS laser altimeter on ICESAT 87 and the CRYOSAT altimeter devoted to the survey of ice sheets and sea ice 10 Gravity Field Missions 101 Basic Considerations According to Newtons law of gravitation the attraction between two particles is pro portional to the product of their masses and inversely proportional to the square of the distance between them 312 accordingly the gravitational effect of mass anoma lies on the orbit of a nearEarth satellite must decrease with the square of increasing orbital height The relationship is explained simply in Fig 101 Rummel 1986 P Figure 101 Mass inhomogeneity and satellite orbit A mass inhomogeneity at 1 km depth causes a certain gravity signal at the point P on Earths surface In order to generate an identical signal at P a mass inhomogeneity at 10 km depth must be one hundred times as large To produce the same signal at a satellite orbiting at 200kmaltitude theinhomogeneitymust be stronger by a factor of 40 000 This consideration demonstrates that only a highly sensitive satellite sensor is capa ble of measuring small inhomogeneities of Earths gravity field The terrestrial gravity field is usually expressedintermsofaseriesofspherical harmonics up to a maximum degree N 3221 122 which can be associated with a shortest resolvable wavelength λ at Earths surface according to λ 360 N o 101 An equivalent representation refers to a certain block size S on the sphere in relation to representative mean values such as mean free air anomalies Torge 2001 The resolution of the associated gravity field expansion is as given in Table 101 In many cases the half wavelength λ2 is considered The factor aern in equation 3116 describes attenuation of the field with the altitude of the satellite orbit The series in 3116 is usually truncated at the maximum resolvable degree n N which is then transformed into the corresponding spatial resolution with the wavelength λ or half wavelength D given in km with D 20 000N The degree of development is for example N 25 for LAGEOS h 6000 km N 50 for STARLETTE h 950 km N 60 for ERS h 780 km 101 Basic Considerations 471 probes in Earths gravity field To overcome the limitations of ground tracked satellites as they are present in traditional tracking techniques three fundamental criteria have to be fulfilled orbit altitude as low as possible 200 to 500 km uninterrupted tracking over large orbital arcs in 3 spatial dimensions and discrimination between gravitational and nongravitational forces acting on the satellite Two concepts are under consideration and have already been tested see also Rummel et al 2002 These are satellitetosatellite tracking range and rangerate measurements between satel lites and satellite gravity gradiometry measurement of gravity differences within the satellite In the first concept we distinguish between the highlow and the lowlow configuration Fig 102 a to c demonstrates all three techniques GPS reference Mass anomaly Mass anomaly GPS reference GPS reference 3 D accelerometer Mass anomaly Eart hs sur fa ce Eart hs sur fa ce Eart hs sur fa ce A A A A A D a b c A Figure 102 Different concepts of dedicated gravity field missions SSTHL a SSTLL b SGG c after Rummel et al 2002 Satellitetosatellite tracking in the highlow mode SSTHL Fig 102 a means that a LEO spacecraft is tracked by high orbiting satellites like GPS GLONASS or GALILEO relative to a network of ground stations The nongravitational forces acting on the low orbiter are measured by accelerometers The LEO is a probe in the Earths gravity field which can be precisely tracked without interruption The observed 3D accelerations correspond to gravity accelerations Satellitetosatellite tracking in the lowlow mode SSTLL Fig 102 b means that two LEO satellites are placed in the same low orbit separated by several hundred kilometers and that the range D between both spacecrafts is measured by an inter satellite link with the highest possible accuracy Again the effect of nongravitational forces acting on the two LEOs can either be measured or compensated see 4331 In essence the acceleration difference between the two LEOs is measured The LL configuration can be combined with the HLconcept One advantage over the pure HLtechnique is that differencing of observables provides a much higher sensitivity 472 10 Gravity Field Missions Satellite gravity gradiometry SGG Fig 102 c means that acceleration differ ences are measured directly in the satellite Since the spacecraft is in free fall the accelerations have to be measured away from the satellites center of mass ideally in all three dimensions One important advantage compared with the SST technique is that nongravitational accelerations are the same for all measurements inside the spacecraft and hence vanish by differencing In the first case SSTHL the first derivatives of the gravitational potential are measured and in the second case SSTLL the difference of the first derivatives over a long baseline In the third case SGG the second derivatives are determined In short the methods can be characterized as Rummel et al 2002 SSTHL measurement of accelerations of one LEO SSTLL measurement of acceleration differences between two LEOs SGG in situ measurement of acceleration gradients within one LEO A large number of proposals has been elaborated for all three concepts during the last 30 years or so among them the Geopotential Research Mission GRM Keating et al 1986 ARISTOTELES Visser et al 1994 or STEP Satellite Test of the Equivalence Principle For an overview see Sneeuw Ilk 1997 Although these projects were not realized the principles developed for them have nevertheless entered most of the existing or planned dedicated gravity field missions It is remarkable that all three above mentioned techniques could be or will be realized during the first decade of the new century with the missions CHAMP GRACE and GOCE This period is therefore dubbed the Decade of Geopotential Research The missions have different characteristics and hence satisfy different aspects of high precision gravity field determination Fig 103 gives an impression All three missions will considerably improve the best existing gravity field model EGM96 by several Cumulative Geoid Height Error m EGM96 Error CHA MP E rror GRACE Error GOCE Error Degree 100 200 300 10 10 10 10 10 10 10 10 10 10 10 10 0 1 2 3 4 5 5 4 3 2 1 0 100 200 300 Figure 103 Cumulative geoid errors for EGM96 gravity field and dedicated gravity field missions after Gruber et al 2000 102 SatellitetoSatellite Tracking SST 473 orders of magnitude CHAMP up to coefficients of degree and order 70 GRACE up to about 140 and GOCE up to about 350 Whereas GRACE shows the highest accuracy for the low harmonics up to 70 and hence can detect gravity field variations with time at this scale GOCE shows best performance between degrees 70 and 350 and can hence also provide a 1 cm geoid for short half wavelengths down to about 80 km More details about concepts and missions are given in the next two sections and in the cited literature 102 SatellitetoSatellite Tracking SST 1021 Concepts In this method range changes between two satellites are measured with a very high resolution The method belongs to group 3 in 12 Space to Space Two concepts can be applied as has been indicated before 1 highlow concept between a highorbiting satellite geostationary GPS GLONASS or GALILEO and a loworbiting spacecraft possibly launched from the space shuttle Fig 102 a and 2 lowlow concept based on two satellites following each other along the same orbit a few hundred kilometers apart Fig 102 b For both concepts the spacecraft in the low orbit are the sensors in Earths gravity field Oneway and twoway microwave intersatellite tracking systems can be used to measure the relative velocities The irregular variations of this velocity contain gravitational information The lower the satellites orbit the more pronounced and detailed this information becomes The basic observable is the radial velocity range rate between the two spacecraft Rummel et al 1978 ρ X12e12 102 The intersatellite range is ρ X12 X2 X1 is the difference in the velocities of the two satellites S1 and S2 Fig 104 and e12 X2 X1 X2 X1 X12 ρ 103 is the unit vector from S1 to S2 The range rate change is then Reigber et al 1987 ρ X12e12 X12e12 X12e12 X12 X12 ρe12ρ1 104 X12e12 X122 ρ2ρ1 because e12 d dt X12ρ1 X12 ρe12ρ1 Cρ1 105 476 10 Gravity Field Missions 1022 HighLow Mode CHAMP The concept of satellitetosatellite tracking was proposed and tested quite early in the 1960s SST in the highlow mode was applied during the NASA lunar APOLLO program for Earthbased control of the lunar orbiter Vonbun 1977b Subsequent analysis of the data led to the discovery of strong anomalies in the lunar gravity field Sjögren et al 1972 With respect to Earths gravity field SST in the highlow mode was tested in 1975 with measurements between the geostationary satellite ATS6 and the low orbiting space vehicles GEOS3 NIMBUS6 and APOLLOSOYUZ From a comparison between measured range rates ρm and the computed range rates ρc based on a global gravity model GEM 7 the anomalous gravity structures of the Java Trench and the Himalayan mountains for example were clearly visi ble Fig 106 The efficiency of the method was demonstrated in this test However a Himalaya anomaly revolution 7 revolution 82 revolution 22 0 0 0 20 20 20 40 40 40 time min 60 60 60 48 48 48 36 36 36 24 24 24 12 12 0 0 24 24 12 12 36 36 48 48 48 60 60 60 24 36 cms Figure 106 Recovery of anomalous gravity structures from rangerate observations in the highlow mode Vonbun 1977b dedicated satellite mission with a much higher resolution in the range and rangerate observations has only been realized after about 25 years with the CHAMP mission Figure 107 Challenging MiniSatellite CHAMP courtesy GFZ The Challenging MiniSatellite Pay load for Geophysical Research and Ap plication CHAMP was launched un der the scientific responsibility of the GeoForschungsZentrum GFZ Pots dam Germany on July 15 2000 into an almost circular near polar orbit of about 450 km altitude and an inclination of about 873 degrees The design lifetime of the satellite is 5 years Due to atmo spheric drag the altitude will decrease over the mission time to about 300 km or less This change in altitude is inten tional and makes the satellite sensitive to a broad variety of coefficients The spacecraft Fig 107 only weighs 500 kg 102 SatellitetoSatellite Tracking SST 477 The main scientific goals of the mission are mapping of the global gravity field mapping of the global magnetic field and profiling of the ionosphere and troposphere To achieve these goals the satellite carries the following scientific instruments a spaceborne 16 channel dualfrequency GPS receiver connected to a multiple antenna system a threeaxis accelerometer at the spacecrafts center of mass to measure the nongravitational accelerations acting on the spacecraft a laserretro reflector LRR for backup tracking from the ground a magnetometer and a digital ion drift meter The low orbiting CHAMP satellite is a sensor in free fall in Earths gravity field The gravitational orbit perturbations are continuously monitored with respect to the high orbiting GPS satellites using precise GPS orbits 7432 based on a worldwide tracking network 781 The concept of differential GPS 75 can be applied and provides position and velocity information for the CHAMP spacecraft with an accuracy of a few centimeters CHAMP is not a dragfree satellite 4331 For gravity field modeling the grav itational perturbations alone are required hence the nongravitational perturbations from drag solar radiation pressure albedo thrust and so on 323 have to be mea sured independently This is done by the threeaxis STAR accelerometer from ONERA Touboul et al 1998 with a resolution of about 3109ms2 To avoid misalignment the accelerometer has to be placed as close as possible to the spacecrafts center of mass and the satellites orientation has to be controlled by star sensors 531 With CHAMP data it is expected to improve the accuracy of existing gravity field models at long and medium wavelengths by a factor of about 5 to 10 Sneeuw Ilk 1997 Gruber et al 2000 see also Fig 103 Earths magnetic field is measured by scalar and vector magnetometers fixed to the end of a 4 m boom together with the star sensors Reigber et al 1999 Two particular GPS antennas at the rear of CHAMP receive signals from setting GPS satellites at the spacecrafts horizon these signals are used for the technique of limb sounding 7629 For more details on the CHAMP mission see eg Balmino et al 1999 Reigber et al 1999 and the forthcoming literature on CHAMP results 1023 LowLow Mode GRACE The first experiment in the lowlow mode was carried out during theAPOLLOSOYUZ rendezvous maneuver in 1975 Vonbun 1977b The results however were not sig nificant because of the low resolution in the observables NASA was for several years developing a promising lowlow mission under the name Geopotential Research 478 10 Gravity Field Missions Mission GRM Keating et al 1986 The mission is no longer being pursued Nev ertheless the GRM concept is still a viable technical option for precisely modeling Earths gravity field In this concept two coorbiting space vehicles would be posi tioned from the Space Shuttle in a 160 km altitude circular polar orbit at an adjustable separation between 150 and 550 km The selected orbital height is always a compromise between the technical effort involved in maintaining a low orbit and the desired resolution of the gravity field 10 8 6 4 2 0 10 8 6 4 2 10 12 8 8 6 6 4 4 2 2 0 ms anomaly 1 1 1 mgal µ h 200 km h 160 km Figure 108 SST signal 1 1 1 mgal gravity anomaly GRM mission Fig 108 demonstrates this relationship for two orbital heights 160 km and 200 km It is evident that the relative veloc ity between both satellites must be mea sured with an accuracy of about 1 µms Because of the low orbital height the space vehicles are exposed to strong surface forces in particular air drag 3233 For mapping of the gravity field however it is required that only the velocity changes that are due to gravita tional effects are measured The space craft must hence either carry a Distur bance Compensation System DISCOS 4331 which measures and immedi ately corrects the dislocation of the space vehicle caused by external forces or the non gravitationalforceshavetobemeasuredindependentlywithathreeaxisaccelerometer A rather large amount of propellant is required for orbit corrections and to maintain the orbital height An alternative is to start with a larger altitude and to accept the decrease of the semimajor axis during the missions total lifetime Instead of GRM the GRACE mission with very similar parameters and objec tives has been realized GRACE is a joint project between NASA and the German GPS navigation antenna Signals from GPS Satellites GPS navigation antenna 24 32GHz Crosslink GPS occultation antenna Signals from GPS Satellites Figure 109 GRACE mission Space Agency DLR The name stands for Gravity Recovery and Climate Ex periment Besides the high resolu tion precise mapping of Earths grav ity field the secondary science objec tive of GRACE is limb sounding for the determination of tropospheric and iono spheric parameters 7629 Two identical satellites were launched on March 17 2002 into a nearpolar orbit of about 500 km altitude with an inclination of 89 In the nominal configuration the satellites fly inechelon 220 km apart within 50 km Orbit maneuvers are necessary every one or two months in order to maintain the 102 SatellitetoSatellite Tracking SST 479 separation between the two spacecraft The design lifetime of the mission is 5 years Each satellite is about 3 m long weighs about 480 kg and carries the following scientific instruments mostly redundant ultrastable oscillator USO GPS receiver accelerometer SuperSTAR Kband ranging system KBR star cameras and laser retro reflectors LRR The GPS receivers can track up to 10 satellites and provide navigation data as well as range and rangerate in the highlow mode As with CHAMP the STAR accelerometer is required to separate gravitational and nongravitational disturbances The sensor unit consists of a metallic proof mass inside an electrode cage In order to make precise measurements of the nongravitational accelerations the proof mass must be located within 01 mm of the center of gravity of the spacecraft The LRR array is used for precise absolute orbit determination and the star cameras are required for precise pointing of the satellites towards one another The key instrument is the KBand Ranging System KBR Each satellite transmits carrier phase signals to the other satellite at two frequencies 24 and 32 GHz allowing for ionospheric corrections Two oneway ranges between both satellites are obtained each by comparing the onboard generated phase with the received phase Both phases are generated by the same ultrastable oscillator The ranges are obtained at a sam pling rate of 10 Hz and are then filtered to produce rangerates and rangeraterates accelerations in the line of sight at a sampling rate of 01 Hz The estimated accuracy of the filtered rangerate is 106 ms Jekeli 2000 In essence the twin GRACE satellites can be considered as one instrument in which variations in the gravity field cause variations in the range between the two satellites areas of stronger gravity will affect the lead satellite first and accelerate it away from the following satellite range variations are measured by a highaccuracy microwave link the relation ship to the global reference frame is given by GPS and the observed range variations are corrected for nongravitational effects by a precise accelerometer The observations will produce monthly global gravity maps with a spatial resolution of about 300 km on the ground and a precision superior by a factor of up to 100 over existing models see Fig 103 Besides mapping a static global gravity field down to mean wavelengths with unprecedent accuracy GRACE will in particular be able to monitor fluctuations in the gravity field Changes in the geoid can be monitored to a submillimeter level per year These variations contain information on changes in the distribution of masses between the atmosphere oceans and solid Earth and contribute to the monitoring of surface and deep currents in the ocean ground water storage on land masses 480 10 Gravity Field Missions mass variations within the Earth and exchange between ice sheets glaciers and the oceans The GRACE concept can also be regarded as a onedimensional gradiometer with a very long baseline The original GRACE observations can be used to derive gravity gradients with an accuracy comparable to the planned gradiometer missions 103 Keller Heß 1999 Another of GRACEs mission goals is to provide a better knowledge on the atmo sphere by limb sounding 7629 103 Satellite Gravity Gradiometry 1031 Concepts A gradiometer is a sensor that can measure the change of the gravity acceleration in space ie the gravity gradient The first derivatives of Earths gravitational potential V V X Y Z are given with the vector g of the gravity acceleration A gra diometer is hence capable of measuring the second derivatives In total the second derivatives given by Vij 2V ij form a tensor the gravity gradient tensor or Eötvöstensor V VXX VXY VXZ VYX VYY VYZ VZX VZY VZZ 109 X Y Z is an orthogonal triple Only five of the 9 elements in the Eötvöstensor are mutually independent It holds that VXY VYX VXZ VZX VYZ VZY 1010 as does the Laplace condition ie a vanishing trace of the tensor VXX VYY VZZ 0 A gravity gradiometer which measures all of the elements contained in the tensor 109 is called a fulltensor gradiometer The components of the tensor describe the local structure of the gravity field by the curvature of this field This implies a conceptual superiority of the gradiometer if compared with other sensors for the mapping of the gravity field The development of gravity gradiometers can be traced back to the Hungarian baron Roland von Eötvös who built a stationary torsion balance in about 1900 based on the early work of Cavendish 17311810 and others Torge 1989 Eötvös was able to measure one part of the components of the second derivatives of the gravitational field at the surface 482 10 Gravity Field Missions 15 10 10 5 10 0 1 10 1 mgal 2u 1 5 10 15 20 3 3 2 3 EU u 150 km u 100 km u 50 km Figure 1010 Signal of the vertical gravity gradient at 200 km altitude caused by a 1 mGal isolated anomaly at Earths surface after Balmino Bernard 1986 1032 GOCE mission Several proposals and studies over the last about 20 years for example Balmino et al 1984 or Rummel Schrama 1991 finally led to the GOCE mission which is sched uled for launch early in 2006 GOCE stands for Gravity Field and SteadyState Ocean Circulation Explorer and forms part of the ESA Earth Explorer program The mission is based on a sensor fusion technique see Fig 102 c namely a combination of very precise orbit determination using GPS highlow SST and satellite gravity gradiometry SGG GOCE will be flown in a nearly circular near polar sun synchronous orbit of about 97 inclination and an altitude of 240250 km The satellite will have a launch mass of about 1000 kg and a small cross section of about 09 m2 It will be totally symmetrical to minimize the influences of nongravitational surface forces The mission duration will be about 2 years Continuous data will be generated in two eclipsefree cycles of 6 months each The main objective is to measure the geoid with an accuracy of about 1 cm gravity anomalies of 1mGal and a spatial halfwavelength resolution of about 70 km The two core instruments of GOCE are a GNSS GPSGLONASS receiver and a gravity gradiometer The GNSS receiver will play twin roles It will be used for precise orbit determination location of the gravity gradiometer at the 1 cm level and for an analysis of the long and medium wavelength features of the gravity field by the SSTHL technique 1022 The gravity gradiometer consists of three pairs of highly sensitive accelerometers locatedintheclosevicinityofthesatellitescenterofmass Observablesaredifferences of accelerations over a short baseline of about 50 cm The six threeaxis accelerom eters are mounted in a socalled diamond configuration Sneeuw et al 2001 Two accelerometers are placed on each axis of the instrument triad 484 10 Gravity Field Missions be expected In oceanography a 1 cm geoid completely fulfills the requirements for large scale and mesoscale ocean circulation models 953 The development of satellite gradiometry is still at its beginning The forthcom ing satellite gravity gradiometry missions will certainly give rise to further intensive theoretical developments and broad discussion in the literature 11 Related Space Techniques 111 Very Long Baseline Interferometry Very Long Baseline Interferometry VLBI is not strictly speaking a method of satel lite geodesy Nevertheless the fundamentals of this technique and its possible appli cations in geodesy and geodynamics have been included in this book because VLBI is a geodetic space technique that is used solely or in combination with other satellite techniques in the recovery of geodetic astrometric and geody namic parameters the observation and adjustment techniques for the geodetic use of the GPS 7 were significantly influenced by the VLBI technology and satelliteborne VLBI missions 1114 are in their initial stages of realization 1111 Basic Concept Observation Equations and Error Budget The technique of long baseline interferometry was developed in radio astronomy with the objective of studying the detailed structure of compact radio sources with a high angular resolution Hey 1984 Wohlleben et al 1991 Rohlfs Wilson 1996 Sovers et al 1998 The frequencies usually applied are between 05 and 22 GHz 75 cm to 13 cm in the socalled radio window of the terrestrial atmosphere 233 Receivers for 43 GHz 86 GHz and above are being added Walker 2000 In order to improve the rather low angular sensitivity and resolution of a radio telescope the effective diameter of an antenna dish is amplified by interconnecting several individual telescopes The approximate relation is ε λ d 111 with ε resolution λ wavelength of the particular radiation and d telescope diameter For the emission wavelength of cosmic hydrogen λ 21 cm the telescope diameter or the distance between the connected individual telescopes must be at least 42 km if the required angular resolution ε is 1 Cable connections over these distances are technically difficult and very expensive VLBI overcomes this problem by linking the independently operating telescopes via precise atomic clocks With this technique the distance between the participating telescopes is no longer a problem and even telescopes on different continents can be integrated The maximum telescope size is nearly the diameter of the Earth and the corresponding angular resolution is better than 0001 or 1 mas milliarcsecond A generic interferometer cf 426 consists of two antennas arranged at a fixed distance b the interferometer base and an appropriate processing unit The 488 11 Related Space Techniques with the bandwidth synthesis technique Here the total recorded bandwidth is split into several smaller units and distributed over the much wider receiver unit window With modern analysis techniques for the 84 GHz Xband frequency used for geodetic VLBI a bandwidth of 720 MHz can be spanned Fringe analysis allows determination of the group delay to about 1 of the peak width corresponding to 15 picoseconds or 5 mm Campbell 2000b Other than with GPS the phase delay cannot be used successfully for geodetic VLBI because timing errors cannot be eliminated by single or doubledifferencing 732 The antenna can only be pointed to one source at a time Simultaneous observation of different sources is not possible because the signals emitted by quasars 2121 are at least six orders of magnitude weaker than signals emitted by GPS satellites Campbell 2000a According to the observation equation 112 and 115 a total of 3 2n fun damental parameters are introduced into the basic parameter estimation process for a single baseline These are 3 components of the baseline vector bx by bz and 2 coordinates α δ for each radio source In the linearized observation model these are the corrections to the approximate values In practice more parameters are included in the adjustment process In a typical experiment in astrometry and geodesy several stations make simulta neous observations Station location and clock parameters of one reference station are fixed For each remaining station 3 site coordinates 1 zenith tropospheric parameter and 2 linear clock parameters are introduced Global parameters common to the entire network are among others Earth orientation 5 parameters polar motion UT1 nutation and position of the radio sources 2 parameters The right ascension α for one radio source has to be kept fixed to obtain the origin in the celestial frame In addition a certain number of physical parameters and hardware effects have to be considered to fit the observations to the model An extended list of parameters including the already formulated principal terms in the observation equations is Shapiro 1978 Campbell 1979 2000b 1 general and special relativity aberration 2 precession nutation 3 proper motion and structural changes in the radio sources 4 hardware effects oscillator instabilities signal delays in the receiver electronics deformation of the telescope 5 signal propagation effects ionospheric refraction tropospheric refraction 111 Very Long Baseline Interferometry 489 6 geodynamical effects polar motion variable Earth rotation solid Earth tides crustal deformation The mathematical and physical details of the individual parameters are exhaus tively discussed in the literature eg Shapiro 1978 Schuh 1987 Preuß Campbell 1992 A comprehensive modern review is given by Sovers et al 1998 An excellent short overview of the development of models from its basic form up to the extensive relativistic formulation is given by Campbell 2000b In accordance with current accuracy requirements modeling of observables and determination of instrumental and environmental corrections have to be performed at the level of 01 mas and several millimeters respectively Themodelingofthebasicgeocentricobservationequationsee112includesterms for diurnal and annual aberration relativistic light deflection and general and special relativity The model is formulated in the barycentric reference system Campbell 2000b parameter group 1 The orientation of Earth with respect to the celestial system precession nutation shows periodic variations with amplitudes of about 5 to 10 mas when compared with the IAU 1980 nutation series 2123 The new PrecessionNutation Model IAU 2000 will account for these effects parameter group 2 The international celestial reference frame ICRF is based on radio sources quasars well outside our galaxy ensuring minimal proper motions The physical nature of quasars is still under debate but numerous astrophysical studies during the last two decades have demonstrated that these compact extragalactic radio sources be inhomogeneous showing internal structure at the level of several mas Changes in the structure of ICRF sources limit the accuracy of a reference frame based on them Per manent monitoring of sourcesstructure however is possible with the sameVLBI data alongside with the other analyses Structure correction will become routine for ex tended radio sources used in geodeticastrometric work Sovers et al 1998 Campbell 2000b parameter group 3 The necessary stability of the time base is achieved through an assembly of atomic clocks including hydrogen masers 225 Usually second order polynomials are used as clock models To account for sudden breaks an additional delay is included that models the station clock behavior as a piecewise quadratic function of time Sovers et al 1998 The instrumental delay changes are monitored by the calibration system which is part of the adjustment procedure In general these effects can be modeled as clock errors Large telescopes exhibit elevation dependent changes in the focal dis tance which can be modeled to the level of millimeters Campbell 2000b parameter group 4 Atmospheric effects on VLBI observations are considered to be the most critical factors limiting the achievable accuracy VLBI stations are widely separated hence the elevations of the telescopes during an observation session are quite different as are the meteorological conditions along the signal paths The ionosphere is a dispersive 490 11 Related Space Techniques mediumforradiofrequencies2331andcanhencebemodeledbyusingtwodifferent observing frequencies In geodeticVLBI a frequency pair of 23 GHz Sband and 84 GHz Xband is selected throughout In most cases in order to model the influence of water vapor on tropospheric signal propagation 2332 water vapor radiometers are used at VLBI stations For the dry part of the correction an appropriate mapping function has to be selected The situation is similar to that in GPS It can be expected that the forthcoming availability of near realtime global and regional tropospheric models coming from groundbased and spacebased GPS observations will contribute to improved data correction Schüler 2001 see 7442 parameter group 5 Of particular interest to applications in geodesy and geodynamics are the parame ters of group 6 The motion of Earths axis with respect to the crust polar motion has to be determined with the same accuracy as all the other parameters ie 01 mas corresponding to 3 mm The same is true for the phase angle of Earths rotation which corresponds to the requirement to determine the UT1variations variations in the length of the day LOD to better than 001 ms of time Our understanding of the geophysical processes behind these variations has not yet reached this level of accu racy hence the variations form part of the unknown parameters in the data adjustment The periodic crustal deformations caused by tidal effects could be seen rather early in VLBI data Campbell 2000b Solid Earth tides cause diurnal and semidiurnal variations with vertical amplitudes of about 40 cm and horizontal displacements of about 10 of the vertical effect The tidal loading effects of the oceans amount to about a decimeter for coastal and island sites Models are being improved Zahran 2000 The VLBI stations are also subject to horizontal and vertical crustal motion as sociated with plate tectonics In order to define a terrestrial reference frame a priori constraints are required for example the nonet rotation assumption 1241 Prob lemsmayarisewhendifferentsetsofdefiningstationsareselectedintheglobalnetwork Campbell 2000b The parameters of group 6 as mentioned above together with the parameters of group 2 and the radio source positions group 3 are of particular interest in geodesy astrometry and geodynamics They are dealt with in more detail in section 1112 Currently two modes of observations are carried out 24hour multistation ses sions and 90minute singlebaseline sessions While the first mode is appropriate to provide all components of Earth orientation parameters and contributes to celestial and terrestrial reference frames the second is used for rapid determination of UT1UTC see 1112 Within one session various sources quasars are observed following a preprogrammed schedule The correlation and adjustment process is done with a sophisticated hard and software installation at particular processing centers The Mark III system has been widely used since about 1980 with several refinements until 1999 The transition to the next generation Mark IV configuration started in 2000 With the Mark III data recording and processing system it was possible to record a data stream of 112 Megabits per second on 28 parallel tracks of tape The Mark IV system is designed to 111 Very Long Baseline Interferometry 491 handle 1 Gigabit per second Campbell 2000b Up to 4 independent experiments or subnets or up to 16 stations can be processed simultaneously The transition to the Mark 5 system has already started by 2002 The discbased data system will directly replace the Mark IV tape drives The storage capacity of the discs will increase to 1000 GB within the next years The Mark 5 system will also support electronic transmission of VLBI data eVLBI it is hence an important prerequisite for future near realtime processing of VLBI data 1112 Applications As it has been stated above the main contributions of VLBI to space geodesy are to establish and maintain the International Celestial Reference Frame ICRF to establish and maintain the International Terrestrial Reference Frame ITRF and to establish and maintain the time dependent Earth Orientation Parameters EOP that relate the ITRF to the ICRF VLBI is unique in that it is the only technique for establishing and maintaining the ICRF and the relationship between the ITRF and the ICRF by directly monitoring the nutation parameters and UT1 As well as this it is the only geodetic space technique that contributes to all three of the above mentioned items Other advantages when compared with satellite techniques come from the fact that VLBI is independent of the gravity field As a consequence Drewes 2000 VLBI is not affected by satellite orbit errors caused by gravity field mismodeling VLBI is not influenced by variations of the geocenter and VLBI is independent of the uncertainty of the GM value and hence of the related scale problems Compared with satellite laser ranging 8 VLBI has the advantage of being weather independent Disadvantages can be stated as follows VLBIisaratherexpensivetechnology henceonlyalimitednumberoftelescopes is available instrumental errors like telescope deformation are difficult to handle and results are not yet available in realtime VLBI also does not provide absolute coordinates with respect to the geocenter but baselines between stations or relative coordinates with respect to some arbitrarily selected origin Due to the high efficiency of modern satellite techniques like GPS the VLBI technology is not used for operational positioning in geodesy and geodynamics VLBI due to its unique capacities will however remain the primary geodetic technique for maintaining the fundamental reference frames and their interrelationship Inertial Reference Frame and Source Positions Under the assumption of a nonrotating universe Walter Sovers 2000 only extra galacticobjectsquasars whichdonotparticipateintherotationofthegalaxy canpro vide stable fiducial points for the establishment of an inertial reference frame 2121 492 11 Related Space Techniques VLBI is at present the only astrometric technique for the determination of directions to quasars with good accuracy The ICRF see Fig 23 p 15 is realized by the coordinates of 608 extragalactic radio sources positioned with an accuracy between 04 mas and 1 mas They are divided into three categories following quality criteria Capitaine 2002 212 defining sources best observed set of sources 294 candidate sources and 102 other sources The stability of the axes derived from the defining sources is estimated as 20 mi croarcseconds The coordinates are based on the analysis of about 16 million observations between 1979 and 1995 using 24hour VLBI sessions The observations continue with the objective to improve the source position accuracy to 025 mas for as many sources as possible and to improve the overall sky distribution of sources Schuh et al 2002 In particular the absence of proper motions or structural changes of the sources at the submilliarcsecond level is essential Walter Sovers 2000 For details about the definition and realization of the ICRS see Ma et al 1997 as well as the already cited literature Baselines Plate Motion and Terrestrial Reference Frame The possibility of determining precise baselines with radio telescopes over very large distances was recognized at an early stage and has been applied within the scope of the NASA Crustal Dynamics Program and its predecessors since about 1972 Routine observations over several baselines in particular in North America started Figure 113 20m VLBI telescope Wettzell courtesy BKG Frankfurt in about 1980 Anderle Malyevac 1983 A major early problem encoun tered by the technique was that the great majority of radio telescopes was primar ily used in astronomical research so that only very little and sporadic observation time could be assigned to geodetic ap plications For this reason a number of dedicated VLBI telescopes for geodetic geodynamic programs has been installed in subsequent years The 20m radio telescope at Wettzell Fig 113 belongs to this group It has been incorporated since 1983 into numerous international projects During the NASA Crustal Dynamics Program CDP 19791991 vector base lines between selected sites were mea sured repeatedly In 1990 the global VLBInetwork consisted of about 20 111 Very Long Baseline Interferometry 493 fixed stations participating regularly in geodeticVLBI projects and about 40 platforms for mobile stations with at least one occupation per year A VLBI experiment usually Figure 114 Transportable 6mVLBI telescope TIGO cf 1252 courtesy BKG Frankfurt lasted 24 hours and included observations of 12 to 18 dif ferent radio sources Campbell et al 1992 The CDP was phased out by 1991 and substi tuted by the DOSE Dynamics of the Solid Earth program in cluding the VLBI activities The CDP provided the first contem porary measurements of relative motions between Earths tectonic plates and it demonstrated the in ternal rigidity of the continental and oceanic plates Since station coordinates form part of the solution in most observing programs station velocities for as many as 60 sites are today available from historical data Currently about 30 stations are observing within the framework of the International VLBI Service IVS 1113 cf Fig 116 In most cases the baseline length changes detected by VLBI confirm the tectonic models to a surprisingly high degree Schuh 2000 Fig 115 shows the evolution of the baseline length between Wettzell Germany and Westford USA over 17 years The 6000 km baseline shows an increase of 170 cm 001 cmyear The predictions of WettzellWestford 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 200 160 120 80 40 0 120 160 80 40 200 Year Baseline length residuals in mm Figure 115 Evolution of the 6000 km VLBI baseline WettzellWestford source Geodetic Institute University Bonn 494 11 Related Space Techniques the NUVEL geotectonic model for the same baseline is 19 cmyear The increasing precision with time is clearly visible In future it should be possible to discern non linear effects in the baseline evolution such as periodic or episodic changes if they occur One problem in the determination of global plate motions withVLBI is the fact that some of the VLBI stations are placed in deformation zones between the stable plates Campbell Nothnagel 1998 The stability of reference stations has to be carefully established with local surveys for example using dense GPS control networks Current accuracies for coordinates are 520 mm from 24 hours of observation and 14 mm for annual solutions The accuracies of coordinate velocities from the annual solutions are estimated to be 01 to 1 mm per year Schuh et al 2002 The Terrestrial Reference Frame TRF may be determined from single session so lutions or from a global solution Station positions and velocities are usually computed from the same 24 hour sessions that are used for the estimation of Earth Orientation Parameters In most cases a global VLBI solution including all available sessions is introduced into the formation of the ITRF by the responsible IERS product center see 1242 For the creation of the ITRF2000 for example 3 global VLBI solutions spanning 20 years of data have been included IERS 2001 For a detailed description of the analysis procedure see the related ITRF documents A particular strength of VLBI is its contribution to the scale of the ITRF Schuh et al 2002 Current disadvantages are the unequal global distribution of stations especially the lack of stations in the southern hemisphere For the future it would be desirable and sufficient to have two or three stations in stable areas on each of the major tectonic plates Campbell Nothnagel 1998 Earth Orientation Parameters Traditionally the Earth orientation parameters EOP are understood to include polar motion and Earth rotation see 2123 In modern discussion as in the documents of the IERS the EOP group is understood to include also the conventional precession nutation model and the differences between this model and observations named celes tial pole offsets The EOP hence include all parameters describing the transformation between the CRF and the TRF These are xp yp pole coordinates of the Celestial Ephemeris Pole CEP relative to the IERS Reference Pole IRP UT1 related to the Greenwich mean sidereal time GMST and expressed as the difference UT1UTC and dψ dε celestial pole offsets in longitude and in obliquity with respect to its position defined by the conventional IAU precessionnutation theory VLBI is unique in its ability to make rapid accurate measurements of all five param eters UT1UTC and the nutation offsets within the final IERS EOP solution come exclusively from VLBI Typically the EOP are observed in several 24 hour sessions per week within regional networks of five or more stations see 1113 In addition socalled intensive sessions of 60 minutes take place on a single long baseline several times per week The intensive session can only be used to determine UT1UTC The 111 Very Long Baseline Interferometry 495 currently achievable accuracy for the pole coordinates is 200 µas for xp and 100 µas for yp The difference is due to the unfavourable geometry of the station networks UT1 can be determined with an accuracy of 5 µs over 24 hours and 20 µs over the one hour intensive sessions Schuh et al 2002 An impression of polar motion during recent years is given in Fig 1214 p 533 taken from the IERS Annual Report 2000 The Earth rotation data have revealed various new phenomena for example the atmospheric excitation of Earths rotation due to winds in the upper atmosphere or effects like El Niño A rich spectrum of oscillations can be detected in UT1 including tidally induced phenomena Schuh 2000 An even deeper insight into the complete spectrum of oscillations can be expected as soon as continuous VLBI observations 7 days a week become available Based on VLBI observations new theoretical models could be developed in nuta tion theory The new IAU 2000 precessionnutation model is mainly based on VLBI observations A comparison of the model with VLBI observations shows an agree ment at the order of 200 µas Capitaine 2002 With future continuous observations an improvement of a factor of 5 to 10 can be expected Schuh 2000 The effects of precession and nutation are caused by the gravitational forces of the Sun and the Moon on Earth Earths response to these forces depends on its structure This is why precise VLBI data and the analysis of precessionnutation serve as highly sensitive probes of Earths interior structure In addition to the above mentioned geodetic products VLBI contributes informa tiononsolidEarthtides oceanloading andatmosphericloadingaswellastropospheric zenith delay gradients ionospheric parameters and the relativistic light deflection pa rameter γ Schuh et al 2002 Table 111 gives a summarizing overview of the currently achievable accuracy of VLBI products Table 111 Present status of geodetic and astrometric VLBI cf Schuh et al 2002 Type Product Accuracy Frequency Resolution Delay CRF α δ 0253 mas 1 year 36 months TRF session coordinates 520 mm 3dweek 1d 34 months annual coordinates 14 mm 1 y 36 months velocities 011 mmy EOP UT1 from 24h session 5 microsec 3dweek 1d 14 months 60min sess 20 microsec 4dweek 1d 1 week xp 200 µas 3dweek 1d 14 months yp 100 µas 3dweek 1d 14 months dε dψ 0104 mas 3dweek 1d 14 months 496 11 Related Space Techniques 1113 International Cooperation International VLBI Service IVS VLBI experiments require international cooperation In particular the regular determi nation of Earth orientation parameters is only possible when several stations cooperate following a strict schedule and when the data flow and the correlation process is well organized The VLBI part of the NASA Crustal Dynamics Program was organized based on the experiment by experiment philosophy By about 1980 the monitoring concept was formulated with the objective to increase the frequency of observing sessions to a level that allowed continuous monitoring of EOP Campbell 2000b After the successful participation of severalVLBI observatories during the MERIT campaigns in 1980 and 19831984 Robertson Carter 1985 1242 a number of observatories continued with geodeticastrometric VLBI on a regular basis The control network POLARIS Polar Motion Analysis by Radio Interferometric Surveying originally established in North America was expanded to include tele scopes on other continents in the IRIS International Radio Interferometric Surveying network From 1984 to 1990 IRIS observed routinely at a 5day interval Afterwards it was continued under the responsibility of NASA and the US Naval Observatory USNO under the acronym NEOS National Earth Orientation Service NEOS op eration consists of one 24 hour observing session per week for EOP and a daily one hour or 90minute intensive observation on one baseline for UT1 A network of 4 to 6 stations surrounding the Atlantic ocean has been in operation since 1986 as IRIS South IRISS under the responsibility of the University of Bonn IRISS observes monthly 24 hour sessions for stabilization of EOP and TRF It is the longest running VLBI series In 1997 a program named CORE Continuous Observation of the Rotation of the Earth was proposed by NASA with the objective to coordinate VLBI observations in subnetworks of about 5 stations each observing on different days of the week Two subnetworks CORE1 and CORE2 started in 2000 with monthly sessions IERS 2001 Other examples of cooperation are the Very Long Baseline Array VLBA a 10 station network operated in NorthAmerica and the European geodeticVLBI network VLBA is mainly devoted to astronomical research but six observing days per year are allocated for geodesyastrometry The European geodetic VLBI network includes up to 10 stations and is mainly devoted to the determination of vertical crustal motion in Europe Campbell et al 2002 Based on the experience of many years international cooperation and stimulated by the great success of the International GPS Service IGS the geodetic VLBI community decided to establish the International VLBI Service for Geodesy and As trometry IVS and to continue and coordinate all international activities under this umbrella The IVS started as a service of the International Association of Geodesy IAG on July 1 1999 and has also been recognized as a service of the International Union of Astronomy IAU since August 2000 It cooperates closely with the Inter national Earth Rotation Service IERS The organizational structure is similar to that of the IGS Besides a Directing Board which determines policies adopts standards 111 Very Long Baseline Interferometry 497 and sets the scientific goals for the observing programs the IVS status 2002 consists of Vandenberg et al 2002 31 Network Stations acquiring high performance VLBI data 3 Operation Centers coordinating the activities of the Network Stations 6 Correlators processing the acquired data and providing processed data for anal ysis 6 Data Centers distributing products to users storing and archiving data 21 Analysis Centers analyzing the data and producing the results and products 7 Technology Development Centers developing new VLBI technology and 1 Coordinating Center coordinating daily and long term activities Details can be taken from the IVS Annual Reports eg Vandenberg et al 2002 These publications also contain information on all participating telescopes A global map with the current distribution of participating VLBI stations is shown in Fig 116 The inhomogeneous distribution is clearly visible A future goal is to operate 3 to 4 telescopes on each of the major tectonic plates if possible outside of deformation zones This objective can be contributed to by transportable VLBI telescopes like the VLBI component of the Transportable Integrated Geodetic Observatory TIGO 1252 cf Fig 114 Onsala Svetloe Simeiz Noto Wettzell Matera Medicina Mizusawa Kashima 34 Kashima 11 Miura Koganei Tateyama Nanshan Seshan Tsukuba Syowa O Higgins Concepcion Fortaleza Algonquin Kokee Park Yellowknife Gilmore Creek Hartebeesthoek IVS Site Greenbelt Ny Alesund Yebes Figure 116 Network Stations of the International VLBI Service Status 2002 The IVS started with a continuation of existing programs such as IRISS NEOS and CORE and has defined its own observing programs since 2002 The long term goals are among others eg Schuh et al 2002 improve EOP and TRF by a factor of two to four improve the sky distribution of the CRF decrease the average time delay for the delivery of products and increase the frequency of observing sessions up to 7 sessions per week 111 Very Long Baseline Interferometry 499 The basic principle of equation 1111 namely the direct observation of the prop agation time delay through correlation of GPS signals received at two antennas was proposed by Mac Doran 1979 In this technique which was called Satellite Emission Radio Interferometric Earth Surveying SERIES the GPS signals are considered to be pure noise The realization of this proposal requires rather bulky instruments this is the reason why the proposal was not successful in GPS technology A modified version uses the binary structure of the GPS time signals Mac Doran 1983 but at a rather low accuracy level Some of these early ideas for the codeless use of GPS were taken up again in modern GPS receiver technology to gain access to the full carrier signal of L2 under activated AS 723 One major advantage of satellite signals when compared with radio sources is the much stronger signal and the existence of predetermined structures Hence much simpler concepts can be used for the receiver design and the data processing techniques The proposals originally developed for GPS may be used again for future satellite systems If signals from GPS satellites and from radio stars are observed with the same radio telescopes the GPS observations could be linked directly to the CIS reference frame 2121 1112 Proposals were made early on to launch radio telescopes into Earth orbit and to integrate them into the ground based VLBI networks Fejes Mihály 1991 Fejes 1994 This SpaceVLBI offers a wide range of applications in the field of geodynamics and satellite dynamics One potential application is related to the connection and unification of reference frames The TRF can be tied directly to the CRF because the space antenna is related by interferometric baselines to the TRF realized by the network of groundbased antennas Another aspect is the inclusion of directional information into the space data for gravity field determination Ádám 1999 Because of the lengthened baseline a detailed study of the structure of sources used in the establishment of the CRF will be possible Particular difficulties are that precise orbit information is required and that the correction for ionospheric delay may be difficult if no dual frequency observations from the spacetelescope are available The feasibility of SpaceVLBI was at first demonstrated experimentally using the 5 m diameter antenna of a geosynchronous TDRS satellite 432 A first dedicated SpaceVLBI satellite named HALCA was launched successfully on February 12 1997 from Japan into an elliptic orbit HALCA with its 8 m diameter antenna forms the orbiting element of the international VLBI Space Observatory Program VSOP It operates at 16 GHz and 5 GHz Together with groundbased telescopes HALCA creates an effective telescope diameter up to 30 000 km The Russian RADIOASTRON satellite has been approved but the launch is de layed until the second half of this decade due to funding problems The satellite carries a 10 m antenna and will be launched into an elliptical orbit An apogee radius in the range of up to 350 000 km is under discussion This enormous baseline will allow the study of quasar structure with unprecedented angular resolution SpaceVLBIprojectsareprimarilydedicatedtoastrophysicalresearch butwillalso contribute to geodesy and geodynamics First experiments with data from HALCA gave encouraging results Meyer et al 2000 500 11 Related Space Techniques 112 Interferometric Synthetic Aperture Radar InSAR Satellite borne radar techniques do not belong to satellite geodesy but are usually treated within the field of remote sensing Still some fundamentals and possible ap plications are addressed here because of their close relationship to satellite geodesy and other geodetic techniques Most spacecraft carrying SAR equipment like ERS 12 ENVISAT are also used in satellite altimetry 92 and some of the results from differential InSAR can be considered as complementary to GPS in geodynamic defor mation studies Further connections are the determination of satellite orbits the signal propagation and the use of GPS for spacecraft and ground control InSAR is a rather complicated and very demanding discipline requiring a comprehensive treatment of its own Within this text only a very rough and basic idea is presented For further studies the reader is referred to the special literature eg Leberl 1990 Bamler 1998 Gens 1998 Lillesand Kiefer 2000 1121 Basic Concepts Synthetic Aperture Radar SAR RADAR stands for Radio Detecting and Ranging A radar instrument illuminates an area with microwaves and measures the traveltime and strength of the returned signal From these the range between the reflecting object and the radar antenna can be determined Typical wavelengths are 3 cm Xband 6 cm Cband and 24 cm Lband One problem encountered by radar techniques is the low resolution of microwaves In general this is determined by the frequency the range of the object and the size of the aperture see also equation 111 For satellites at a height of about 800 km a several hundred meter long antenna would be required to achieve the aperture necessary for a resolution of 100 m on the ground This is technically not feasible However when the radar measurements are taken from a moving platform satellite or airplane then the reflected signals along the flight path can be collected and combined The aperture is hence created synthetically during the signal processing This technique is called Synthetic Aperture Radar SAR As a consequence the radar achieves a high resolution in the alongtrack direction also called the azimuth direction In the range direction perpendicular to the flight path the resolution is determined by the duration of the transmitted pulse In practice frequency modulated pulses are transmitted and the phase of the return signal is measured Fig 118 demonstrates the basic principle Bamler 1997 A SAR transmitting antenna illuminates the Earths surface in a sidelooking mode The return signals are recorded with respect to intensity magnitude and phase Phase means a relative shift of the received sine signal with respect to the transmitted signal The resolution in range and azimuth defines the smallest picture element pixel For ERS the pixel size is 112 Interferometric Synthetic Aperture Radar InSAR 501 about 125 m 125 m Fig 118 also explains that the SAR process transforms a 3D object eg the topography into a twodimensional radar image with the coordinates Range resolution Azimuth resolution Pixel Azimuth Range Figure 118 Basic principle of SAR range and azimuth This type of geom etry creates distortions and makes inter pretation of SAR images difficult in par ticular over mountainous terrain Compared with traditional optical methods SAR images have particu lar properties and advantages Bamler 2000 microwave radiation is not af fected by clouds or heavy rain and can produce images in all weather conditions it also can penetrate partially snow and soil SAR is an active source technique and hence is independent of sun light continuous day and night operation is possible SAR can be considered as a technique complementary to optical remote sensing different properties of the same objects can be recorded SAR is a coherent imaging method this makes the interferometric approach possible and SAR is capable of observing dynamic processes such as ocean currents or sea ice motion On the other hand SAR has some disadvantages The resolution is rather low and the received signals are heavily affected by a noiselike phenomenon termed speckle caused by a large number of scatterers in the image formation process A SAR image contains geometric and radiometric information Each pixels bright nessisdeterminedbythebackscatteredradiationfromasurfaceelementontheground A strong signal results in a bright pixel value The signal strength depends on many influences such as topography size of scatterers radar wavelength surface humidity and incident angle The interpretation of a SAR image hence requires a profound understanding of the image formation process see eg Bamler 1998 The use of spaceborne imaging radar in remote sensing started with the launch of SEASAT1 92 in 1978 In spite of the short lifetime of this satellite the capability of SAR for mapping the Earths surface was demonstrated The first complete maps of some entire countries in particular those in tropical areas covered by clouds were generated in 1992 using ERS1 A particular use of SAR in topographic mapping was NASAs Magellan mission to planet Venus that is permanently covered by dense clouds SAR maps of the Venusian surface were generated in 1990 Another important field of SAR uses besides topographic mapping is environ mental monitoring Examples are land use erosion deforestation desertification 112 Interferometric Synthetic Aperture Radar InSAR 505 1123 Differential Radar Interferometry When three or more SAR images of the same area are generated from different passes at approximately the same antenna position it is possible to derive at least two inter ferograms These can be differenced and used to produce a differential interferogram or doubledifference interferogram The differential interferogram shows phase changes only where surface changes occured between the times of observation and hence have caused a change in the slant range to the antenna One complete phase cycle corresponds to about 3 cm for ERS1 Hence the method reveals surface changes like swelling and buckling with a resolution of centimeters or even millimeters The potential of differential radar interferometry was recognized early in 1989 Gabriel et al 1989 and was applied to the determination of surface deformation in volcanic or seismically active areas Famous examples are the Landers Earthquake in Southern California Massonet et al 1993 and the deflation of Mount Etna Mas sonet 1997 Applications are seen for earthquake and volcanic research research into tectonic processes and crustal deformation glaciology ice sheet monitoring and monitoring land sliding and subsidence Differential InSAR can be effectively combined with other geodetic techniques like continuous GPS arrays 7622 to provide a highly detailed and accurate picture of crustal deformation An early example is the Landers Earthquake where several GPS stations monitored continuously during the event Bock Williams 1997 One main advantage of GPS is the highly accurate few mm continuous monitoring of ab solute 3D displacements over large areas One main disadvantage is that observations are taken at an irregularly spaced set of stations not all of which are optimally placed with respect to the earthquake displacement zone The main advantage of InSAR is its much better spatial coverage On the other hand InSAR interferograms are restricted to smaller regions and the temporal resolution is limited Images can be easily decor related by changing conditions in vegetation and humidity A short review of some strengths and weaknesses is given in Table 113 Table 113 Comparison of GPS and DInSAR after Bock Williams 1997 Continuous GPS Differential InSAR Strengths high temporal density high spatial density 3D positioning remotely sensed mm accuracy no monumentation necessary Weaknesses limited spatial density limited temporal density stable monumentation 1D scalar measurement siting difficulties image decorrelation 508 12 Overview and Applications The satellite coordinates and also the derived station coordinates are by nature geocentric because the satellite motion is referred to the gravitational center of the central body geocenter No datum problem exists in the dynamical concept Absolute coordinates are determined in the same reference frame as that in which the satellite orbit is computed Most of todays operational observation techniques in satellite geodesy deliver absolute coordinates in the related satellite datum for example GPS 7 in the World Geodetic System WGS 84 One important feature of absolute methods in satellite geodesy is that coordinates can be determined from observations at one station only The methods are therefore appropriate for navigational purposes Some of the characteristic elements of absolute and relative positioning are sum marized in Table 121 For the absolute methods the achievable accuracy of the coor dinates is directly dependent on the accuracy of the available orbit data 33 This is of particular interest for the operational satellite navigation systems The broadcast orbits mostly suffer from difficult to model surface forces like drag 3233 or solar radiation pressure 3234 and from the inhomogeneous distribution of tracking stations The GPS orbits for many years were corrupted by intentional accuracy limitations 716 As a consequence the absolute accuracy of the position determination is usually far inferior to the relative accuracy For GPS the difference may reach as much as three orders of magnitude 1 cm against 10 to 20 m Table 121 Characteristic aspects of dynamical and geometrical methods in satellite positioning Dynamical methods Geometrical methods datum provided by satellite orbits datum undetermined datum defect absolute coordinates relative coordinates point positioning concept possible simultaneous multistation concept single station necessary absolute coordinate accuracy eg GPS relative coordinate accuracy eg GPS 515 m 1 cm Depending on the task absolute as well as relative information is extracted from the observables for the solution of practical problems This means that the necessary da tum information comes partly from the satellite orbits and partly from the terrestrial networks or from other sources With this background in mind the question of da tum transformation and the combination of satellite and terrestrial networks may be assessed The following levels in the use of datum information can be distinguished 1 The complete datum is taken from the satellite orbit This is for example the case in navigation with a single receiver or in point posi tioning with GPS GLONASS or the future GALILEO The related accuracy is about 5 15 m for GPS without SA With activated SA it only was 30 100 m The 121 Positioning 509 position results refer to the datum of the satellite system for example WGS 84 216 The coordinates obtained from the observations can be regarded as a realization of the satellite datum for the given epoch at the given place with a given uncertainty The transformation into a particular local reference system can be done with gener ally accepted datumtransformation parameters 215 However the accuracy of the transformation is no better than the related accuracy of the actual datumrealization ie 3 15 m for GPS If several stations are operating simultaneously or if they are interconnected through a network in the working area all observations can be used and provide a mean realization of the datum during the observation period The accuracy of the realization corresponds approximately to the realization accuracy of observations at a single station However the simultaneously observed stations show a high relative accuracy caused by the high correlations between the simultaneous observations The results hence contain absolute and relative information 2 Only one part of the datum is taken from the satellite orbit a Orientation and scale This may be the case if two satellite receivers are operated simultaneously eg DGPS or RTK 75 and the resulting baseline vectors are used to connect new points to existing control points of the terrestrial network eg Fig 771 in 7613 The position information of the datum here comes from the terrestrial network b Scale only This is the case if for example GPS observations with two receivers are exclusively used as a ranging method for terrestrial trilateration This mode was frequently used during the first years of GPS application in surveying c Orientation or one part of the orientation only This depends on the kind of parameter selection in the transformation formulas between the satellite network and the terrestrial network 215 3 No part of the datum is taken from the satellite orbit This is the case if the satellite network is first computed from only the simultaneous satellite observations case 1 and is then transformed with a 7parameter trans formation via identical points onto a terrestrial network In this case the complete datum is taken from the terrestrial network the information from the satellite datum is eliminated in the transformation process The satellite observations are only used to determine the geometry of the network This is also the case for networked GPS reference stations 7532 4 The satellite orbit is partly or completely recomputed a The satellite orbit is recomputed over the observation area b The satellite orbit is provided by an agency like IGS The procedure a is also referred to as the short arc technique or semi short arc technique 3333 41 The satellite orbit is recomputed over the observation area or is given some degrees of freedom based on the current observations In these cases part of the datum comes from the broadcast orbit part stems from the coordinates of the existing network and part is taken from the orbit adjustment model with the 510 12 Overview and Applications input gravity field Geometric as well as dynamic elements enter the solution The datum information in the broadcast satellite orbit is improved using the datum infor mation inherent in existing coordinates of a selected number of control points This lastmentioned aspect is for example of importance for highprecision application of GPS in geodynamic research if reference observations are available from fundamen tal stations with precisely known geocentric coordinates This is the case for ITRF andor IGS stations The procedure is also called the fiducial point concept Fiducial stations can be introduced either as errorless or with appropriate variances A proper weighting of all observations entering the network adjustment is essential The IGS orbits for GPS satellites 7432 procedure b are completely recom puted and refer to ITRF2000 which is essentially identical to WGS 84 216 For observations at a single station precise point positioning 734 the datum is fully derived from the precise postprocessed ephemerides When IGS orbits are used to gether with observation data from IGS stations as fiducial points both data sets are fully compatible and new stations are interpolated into the datum of the IGS stations which is practically identical to ITRF2000 1212 Global and Regional Networks One of the fundamental objectives in satellite geodesy identified from the beginning is to determine precise geocentric coordinates for globally distributed control stations within a uniform reference frame cf 11 12 One early contribution to this fundamental task was made with the purely geometric BC4 world network 515 Another geometric solution was provided with the equatorial SECOR network 441 With the inclusion of TRANSIT Doppler observations both sets of coordinates were made nearly geocentric Most of the early global sets of coordinates for a given number of observation stations formed part of comprehensive dynamical solutions where gravity field param eters were adjusted along with the station coordinates These socalled Earth models are discussed in chapter 122 The Smithsonian Astrophysical Observatory Stan dard Earths SAOSE and the Goddard Earth Models GEM belong to this category A comprehensive review and discussion of several of the early solutions is given by Mueller 1975 and is also included in the report on the US National Geodetic Satellite Program Henriksen 1977 With the worldwide use of TRANSIT and GPS an increasingly dense field of geo centric station coordinates has been built up If broadcast ephemerides have been used the absolute coordinates refer to WGS 84 or to WGS 72 for TRANSIT before 1988 and for GPS before 1987 The accuracy of the station coordinates was quite different Where precise ephemerides were used for the reduction of TRANSIT Doppler mea surements the absolute accuracy of the single station coordinates was about 1 to 2 m depending on the geographical location 622 The total number of Doppler sta tions determined with precise ephemerides may reach several thousand This global set of precise Doppler coordinates was one of the best sources for geocentric station coordinates until about 1990 121 Positioning 511 Sets of global station coordinates can be supplemented and densified by regional campaigns and solutions Regional Doppler campaigns with the inclusion of a large number of simultaneously operating TRANSIT receivers were very successful Exam ples are the European Doppler Campaign EDOC Boucher et al 1979 the German Austrian Doppler Campaign DÖDOC Rinner et al 1982 and the African Doppler Survey ADOS Chodota 1987 These projects provided sets of absolute coordinates for the working areas with the related system accuracy as well as sets of relative coordinates for all participating stations with a much higher accuracy The focus of interest since about 1985 has been the installation and monitoring of a very precise set of station coordinates for the establishment of a Conventional Terrestrial Reference System COTES based on all available geodetic space methods In the course of the MERIT campaign 19831984 1242 several solutions mainly based on SLR and VLBI were computed for 15 to 35 stations and compared with one another The absolute coordinates at that time showed differences of up to 10 to 20 cm between the individual solutions Since then new solutions have been produced nearly every year with increasing accuracy Since 1988 the organization responsible for compiling a combined set of coordinates has been the International Earth Rotation Service IERS 1242 The current status can be found in the annual reports of the IERS eg IERS 2001 Recent solutions agree at an accuracy level of about 1 cm The latest solution is the ITRF2000 2122 Laser ranging to the LAGEOS satellites provides particularly significant contribu tions Geocentric coordinates with a standard deviation below 1 cm can be deter mined from the analysis of long orbital arcs for appropriately equipped laser tracking stations 854 SLR is hence of particular importance to the ITRF origin VLBI pro vides global relative accuracies at the order of a few millimeters and also contributes significantly to the scale 1112 SLR and VLBI form the backbone of the global reference frame which is then densified mainly by DORIS 67 and GPS 7621 Contributions from GLONASS and GALILEO can be expected One early regional densification project is the Euro pean reference frame EUREF since 1989 ITRF stations in Europe Laser and VLBI were used as fiducials and densified by GPS Another example is SIRGAS for South America 7621 1213 Operational Positioning The reader is referred to the comprehensive discussion in 762 With respect to the instrumental effort until about 1986 it was mainly the TRANSIT Doppler method which was applied in operational positioning 66 For the time being GPS techniques are almost exclusively used Three main fields of application can be distinguished 1 geodynamics crustal deformation 2 control surveys and 3 special surveys 512 12 Overview and Applications 1 Geodynamics Relative position information is primarily needed for the analysis of crustal deforma tion The required accuracy of the coordinates is in most cases 1 cm or better This corresponds to 1 106 relative accuracy for 10 km station separation 1 107 relative accuracy for 100 km station separation and 1 108 relative accuracy for 1000 km station separation The only applicable operational observation technique so far is GPS 762 With respect to the required high accuracy level only dualfrequency receivers should be used even over very short distances cf ionospheric disturbances 7441 Precise orbits are available from the IGS Observations should always be connected to ITRF or IGS stations as fiducial points if necessary via some densification stations based on several days or even weeks of GPS data collection In areas of high risk eg earthquake volcanic activities permanent GPS arrays play an increasingly important role 7622 Geodynamic processes can also be monitored at stations equipped with DORIS receivers 67 2 Control surveys Considering the high accuracy potential and the three dimensional character of oper ational satellite techniques a fundamental network in the satellite datum ie WGS 84 or ITRF will be required for all countries even in already wellsurveyed areas All followup surveys must be related to this fundamental network Fig 777 p 359 gives an example the German GPS reference network DREF 7621 In the first step a homogeneous network has to be established with as many simul taneously working satellite receivers as possible The interstation distances may vary between 50 and 150 km depending on the situation The network should be tied via simultaneous observations to an existing geocentric datum in general the latest ITRF solution or a densification thereof with GPS The DREF network is tied to about 15 EUREF stations most of them have been determinedbySLRorVLBITheinterstationdistancesareabout100km Inmostcases the number of available satellite receivers is not sufficient to observe all stations in the national network simultaneously The connection between the individual observation phases sessions is achieved through permanently operating reference stations and a certain number of overlapping stations If the network is not tied to ITRF stations or regional densifications like EUREF or SIRGAS the set of coordinates after the network adjustment provides a mean realization of the satellite datum mostly WGS 84 for the observation period The absolute accuracy is only a few meters for GPS under activated SA it only was 30 to 100 meters This classical method of datum realization through observations today is no longer adequate If the network is tied to one or more reference stations which are already linked to ITRF the datum of the network is taken partly or completely from the reference points 1211 Observations in WGS 84 can easily be used for the interpolation of new stations in the ITRF reference frame 121 Positioning 513 The set of coordinates in the fundamental network once it has been determined in one of the ways described must be held fixed for subsequent densification work because the high accuracies desired can only be achieved in the relative mode The set of coordinates represents the satellite datum in the particular country at a partic ular epoch With respect to the increasing international cooperation in geodesy it is advisable to link the national network to the latest solution of the ITRF For the densification of the fundamental network see 7621 In order to avoid misunderstanding it should again be stressed that network densification with satellite methods is only possible with observations made relative to at least one known station Otherwise the uncertainty of the datum realization several meters to tens of meters would enter the result This is also true if precise datum transformation parameters are available for the area Because of the high accuracy requirements even in areas with existing classical geodetic control the GPS technique will in future nearly exclusively be used for the establishment and densification of networks possibly alongside GLONASS and GALILEO The issue of combining satellite networks with existing terrestrial geodetic control will continue to wane in importance For some years of transition the existing terrestrial networks will be maintained as national geodetic reference frame in many countries and GPS will only be used as a method of densification Because of the distortions and inhomogeneities in most classical networks GPS results have to be incorporated into existing networks using local transformation parameters Usually the high internal homogeneity and relative accuracy of the satellite results is lost due to this procedure On a longterm basis it is hence advisable to transform all existing surveying points into the distortionfree reference frame defined by GPS reference stations 7621 The hierarchic structure of classical networks from first to third or fourth order will disappear and be substituted by a new hierarchy The future structure of this hierarchy and its accuracy standards is already discernible cf 7621 and includes three levels A Continental or SubContinental Reference Frame based on the ITRF with interstation distances between 200 and 500 km and an accuracy goal of 1 cm over 500 km B Nationwide Fundamental Network with interstation distances of 50 to 100 km and an accuracy goal of 1 cm over 100 km C All other GPS measurements which must be connected to stations of level B Accuracy standards correspond to the particular purpose For control surveys the requirement is to maintain 1 cm relative accuracy 3 Special Surveys This group of tasks belongs to level C The accuracy requirements may be quite differ ent and range between meters for GIS applications and millimeters for high precision engineering surveys For details see 7624 7626 122 Gravity Field and Earth Models 517 that f 3 2J2 m 2 9 8J 2 2 15 28J2m 3 56m2 1215 with m a2 ebω2 GM The currently adopted best value is Moritz 2000 f 1 298257 North pole 20 m 0 10 20 10 m 10 m 10 0 0 0 10 20 20 m 30 South pole equator 10 20 Figure 125 Pearshape of the Earth due to the zonal coefficient J3 that forms part of the Geodetic Refer ence System 1980 The value given in the IERS Conventions 2000 is 1f 29825642 000001 The existence of a coefficient J3 was confirmed very early on through satel lite observations J3 denotes an asym metry in Earths figure with respect to the equator Fig 125 This discovery became famous at the time as Earths pearshape This assignment is mis leading however because the asymme try if compared with Earths flattening is smaller by a factor of 103 Even geoid undulations are much larger in some parts of the world In the general concept of dynamical satellite geodesy cf 41 the parameters describing the geometrical figure and Earths gravity field and the elements of the satellite orbits are solved for simultaneously The basic concept is as follows cf Sigl 1984 starting from equation 121 rS rB ρ with rS geocentric position vector of satellite S rB geocentric position vector of station B and ρ topocentric observation vector of S from B 121 is rewritten in a generalized form as rT S t rB S t 1216 The left hand side is computed as the theoretical satellite vector from orbital theory as rT S t rT S t α1 α6 p1 pn 1217 with 122 Gravity Field and Earth Models 519 solution the zonal harmonic coefficients can be determined with comparatively high accuracy beforehand and then be introduced as known parameters in the adjustment of the longitudedependent tesseral coefficients In a similar way the station coordinates can be determined first and then held fixed in the solution of the gravity field models 1222 Earth Models Satellite observations have been collected and introduced into data banks since the launch of the first artificial satellites and they are used from time to time for refined Earth model computations Up to 1997 more than 60 such models have been published and their number is still growing A current overview is given by Rapp 1998 In the following some of the bestknown models are summarized 1 Standard Earths of the Smithsonian Astrophysical Observatory SAOSE The first SAO Standard Earth was published as early as 1966 Lundquist Veis 1966 and was based on more than 45 000 directional observations with BakerNunn cameras from 12 ground stations to 13 satellites As a result geocentric coordinates of the 12 tracking stations zonal coefficients up to J14 and a complete development of the potential field up to degree and order 8 were published In addition numerical values were determined for GM and ae GM 398 6032 km3s2 and ae 6 378 165 m In 1969 an updated Standard Earth SAOSE II was published and in 1973 another update with SAOSE III Gaposchkin 1973 In SE II the first laser measurements to satellites were included In SE III camera and laser observations to a total of 25 satellites and surface gravity data were used The parameters of the gravity field were complete up to l 18 Geocentric coordinates were determined for 90 tracking stations 2 Goddard Earth Models GEM A long series of Earth models has been determined at the NASA Goddard Space Flight Center GSFC The first model GEM 1 exclusively based on satellite data was published in 1972 and included a development of the gravity potential field up to l 12 The model GEM 9 from 1979 was the last model in this series to be exclusively derived from satellite observations In total 840 000 observations to satellites were included namely 150 000 camera observations 51 477 000 electronic observations 44 6 and 213 000 laser ranges 8 The potential development is complete up to l 20 geocentric coordinates were determined for about 150 tracking stations Since the sensitivity of orbital analysis stopped at about l 20 altimeter data 9 and surface gravity data were included for further refinements The related GEM models are Lerch et al 1978 520 12 Overview and Applications GEM 10 1977 l 22 satellites surface gravity 1 GEM 10A 1978 l 30 satellites surface gravity 1 altimetry 1 GEM 10B 1978 l 36 satellites surface gravity 1 altimetry 2 GEM 10C 1978 l 180 satellites surface gravity 2 altimetry 3 About 700 altimeter passes from GEOS3 are contained in GEM 10B the model GEM 10C includes 2 300 altimeter arcs from GEOS3 and in addition 384 000 mean 1 1 gravity anomalies from surface data GEM 10C was for many years one of the most used high resolution spherical harmonic models Along with the adjustment of the models GEM 9 and GEM 10 an improved numerical value for GM was determined mainly based on LAGEOS laser ranging GM 398 60064 km3s2 The semimajor axis of a bestfitting global ellipsoid was determined from an analysis of the geocentric station coordinates as ae 6 378 139 m The dedicated tailored gravity model GEML2 was published in 1983 for analysis of LAGEOS observations Lerch et al 1983 The model was developed up to l 20 and was based on about 400 000 laser ranges to LAGEOS from 25 years in addition to the GEM 9 data The geocentric coordinates of the 20 tracking stations involved were known to an accuracy of 6 cm In particular the longwave components up to l 4 were extremely precise and allowed the modeling of the related geoid with an accuracy of better than 10 cm The GM value of the solution is GM 398 600440 km3s2 With respect to the TOPEXPOSEIDON mission 92 new tailored models were developed for precise orbit determination The prelaunch model GEMT1 was com plete to degree 36 and based on satellite tracking data from 27 satellites GEMT3 Lerch 1992 was complete to degree 50 and included in addition satellite altimeter data from GEOS3 SEASAT and GEOSAT as well as surface gravity data 3 GRIM Earth Models The first Earth model GRIM 1 was published in 1976 jointly by German and French research groups Balmino et al 1976a GRIM 1 was exclusively based on satellite observations and was developed up to l 10 A combination of the satellite solution with 1 1 surface gravity anomalies GRIM 2 was developed up to l 30 and published in the same year Balmino et al 1976b ThesolutionGRIM3Reigberetal1983yieldsacompletepotentialdevelopment up to l 36 and geocentric coordinates of 95 tracking stations The solution is based on camera laser and Doppler observations to 22 satellites some 25 000 1 1 terrestrialgravityanomalies andnearly28 00011 gravityanomaliesfromGEOS3 altimetry 122 Gravity Field and Earth Models 521 The development of the GRIM 4 series of solutions started in 1991 Schwintzer et al 1992 The last version was GRIM4 S4 GRIM4 C4 Schwintzer et al 1997 S stands for satelliteonly model and C for combined model GRIM4 S4 includes in total 265 million single observations to 34 satellites with orbital heights between 800 km and 20 000 km The model is complete to degree l 72 and order m 72 This corresponds to a spatial half wavelength of D 300 km For several years GRIM4S4 was considered to be one of the best available satelliteonly geopotential models Rummel et al 2002 The GM value for GRIM4 S2 is Schwintzer et al 1992 GM 398 6004369 00028 km3s2 The latest solution is GRIM 5 including observations to GFZ1 and has been available since October 1997 Schwintzer et al 2000 The satelliteonly solution GRIM 5S1 includes data from 21 satellites and is developed to degree l 99 and order m 95 Fig 126 The combination model GRIM 5C1 includes in addition Figure 126 GRIM5S1 Geoid 5 m contour lines Schwintzer et al 2000 gravity anomalies from surface data and altimeter data The degree of development is l m 120 4 Other Earth Models A large number of other Earth models exists they cannot all be mentioned in this book Reviews are given by Wenzel 1985 Rapp 1998 Torge 2001 High resolution models are always based on a combination of satellite data with terrestrial data An ultrahigh resolution model with 1800 1800 coefficients was developed by Wenzel 1999 Several dedicated gravity models have been developed for particular satellites like LAGEOS STARLETTE 853 GEOS3 SEASAT1 GEOSAT and ERS12 TOPEXPOSEIDON 933 One of the currently most used models is the Joint Geopotential Model EGM96 complete to degree and order 360 Lemoine et al 1998 see also 853 522 12 Overview and Applications 6 378 400 300 200 100 6 378 000 semimajor axis 1900 1920 1940 1960 1980 1909 1924 19381948 1967 1975 1979 388 388 245 099 160 140 137 HAYFORD IUGG IUGG IUGG KRASSOWSKJ IAG JEFREYS Figure 127 Numerical values for the semi major axis of a mean Earth ellipsoid since 1900 Together with the determination of Earth models and with the increasing amount of satellite tracking data the nu merical value for the semimajor axis ae of a best fitting mean Earth ellip soid can also be continuously improved Fig 127 shows the development of our knowledge of ae over the course of the last century The result from 1967 con tains for the first time satellite track ing data The latest value from the IERS Conventions 2000 is ae 6 378 1366 m 5 Geocentric Gravitational Constant GM The product GM of the mass of the Earth M and the universal gravitational constant G is a very important parameter in dynamical satellite geodesy because it contributes to the scale in the coordinate results GM is one of the defining constants in the Geodetic Reference System 1980 and is usually treated as an errorless quantity The parameter is always given in the form of the product because this can be derived from satellite observations with a much higher accuracy than can the single factors In astronomical research GM has been derived from analysis of the lunar orbit following Keplers 3rd law A much higher accuracy can be achieved from observation of the free fall acceleration acting on space vehicles in particular on interplanetary probes and distant satellites This is explained by the fact that during the first days of a space flight the motion of the space vehicle is primarily governed by the central term of the terrestrial gravitation 24 22 20 18 16 14 12 10 08 06 04 02 00 1966 1968 1970 1972 1974 1976 1978 Ranger 8 Surveyor 5 Ranger 9 Mariner 5 Surveyor 6 Mariner 9 final Pioneer 7 Lunar Ranging Mariner 9 preliminary Lunar Orbiter 2 Viking 2 Viking 1 VLBI and Lunar Ranging Verena 4 5 6 7 Lagos ATS6GEOS3 SatellitetoSatellite Tracking 398 600 km s 3 2 Mariner 10 Figure 128 Development in the determina tion of the geocentric gravitational constant GM Martin Oh 1979 The first reliable results were ob tained from analyses of the Mariner Ranger Surveyor LunarOrbiter and Venera probes NGSP 1977 Vol 1 p 292 The most accurate numbers to day come from several years of analysis of laser ranging to the Moon and to LA GEOS Some results are given in Table 122 Low orbiting satellites are less suited for the determination of GM because of the rather strong nongravitational per turbations Fig 128 illustrates develop ment in the determination of GM The dramatic improvement of the related ac curacy is noticeable 123 Navigation and Marine Geodesy 523 Table 122 Different determinations of GM km3 s2 MethodSource Numerical Value Lunar orbit OKeefe 1958 398 620 6 C20 C40 terrestrial data Rabe 1962 398 603 6 Ranger 69 1966 398 601 07 Mariner 9 1971 398 6012 25 Venera 46 398 60037 10 Laser ranging to the moon Williams et al 1987 398 600444 0010 Laser ranging to LAGEOS Smith et al 1985 398 600434 0002 Laser ranging to the Moon Dickey et al 1994 398 600443 0004 Laser ranging to LAGEOS Smith et al 2000 398 60044187 000020 Geodetic Reference System 1980 398 6005 05 MERIT Standards 1983 398 600448 IERS Conventions McCarthy 2000 398 6004418 00008 123 Navigation and Marine Geodesy 1231 PossibleApplications andAccuracy Requirements in Marine Positioning The accuracy requirements for marine positioning on the sea surface and the ocean floor are increasing along with the growing interest in the ocean areas with respect to economy sea traffic mineral and living resources their associated legal aspects and global geodynamics The following main fields of interest can be identified a Law of the Seas and Marine Boundaries 60 60 58 58 56 56 54 54 52 52 2 2 0 4 6 8 10 2 2 0 4 6 8 4 10 Denmark Netherlands Germany Belgium Norway DAN FRIGG BERYL FORTIES EKOFISK Great Britain 0 100 200 km Figure 129 Median lines in the North Sea and some oil and gas fields Due to the new codified Law of the Seas large parts of the open oceans are now characterized as Exclusive Economic Zones EEZ under the au thority of the adjacent states Bound aries have to be defined fixed and set out sometimes several hundred miles off the coast In cases where the median line between two states runs through areas with oil and gas de posits or other resources of economic interest cf Fig 129 the accuracy requirements may be less than 5 me ters Delimitation of the outer edge of the continental shelf may require de tailed mapping of sediment thick ness and inclination of the continental slope 524 12 Overview and Applications b Offshore Industry and Exploration This field of interest is concerned with such applications as geological mapping of the seafloor with seismic techniques installation of drilling sites and offshore structures laying and control of pipelines recovery of closed boreholes and the exploration and extraction of mineral resources such as manganese nodules or hydrothermal de posits The most demanding requirements are related to detailed seismic surveying 3D seismic and to the exploration and exploitation of smallscale deposits in deep sea areas c Sea Floor Mapping Figure 1210 Sea bottom mapping with multi beam sonar systems and differential GPS Detailed highresolution mapping of the ocean floor with multibeam sonar systems like SEABEAM or HYDROSWEEP has developed into one of the most powerful techniques in marine geoscience Schenke 1991 Schenke et al 1998 An essential requirement is knowledge of the precise relationship between the ships position and the multibeam data Fig 1210 including the ships attitude 7627 d Geodynamic Research Tectonic plate boundaries run mainly through marine areas In order to derive a representative pattern of recent global tectonics it is necessary to include the ocean floor in motion and deformation studies Deformation rates of 1 to 5 centimeters per year have to be determined This very demanding task can only be solved by a combination of satellite techniques eg GPS with acoustic underwater range measurements 1232 e Global Sea Level and the Marine Geoid For the establishment of a global height system differences in absolute sea level must be known over large oceanic areas cf Fig 919 p 468 In precise marine gravimetric surveying for the contribution to a marine geoid the height component must be known to about 01 m and ships velocity components to about 103 ms Gravimetric observations are also important in marine geophysics for the detailed study of features below the sea floor The precise position of buoys is required for the calibration of altimeter missions 933 1232 Marine Positioning Techniques The requirements in marine positioning indicated above can be met with various observation techniques either alone or combined Fig 1211 These are shore based radio navigation techniques 123 Navigation and Marine Geodesy 525 satellite radio navigation techniques acoustic techniques inertial techniques and integrated techniques Figure 1211 Different techniques in marine positioning Shorebased radio navigation techniques Egge Seeber 1979 Forsell 1991 played an important role in marine po sitioning until about 1995 but are to day mostly outdated In most cases they could only fulfill many accuracy re quirements near the coastThe only pre cise positioning techniques available at a global scale are the satellite meth ods Acoustic techniques are required for guidance positioning and control of underwater objects and in marine geo dynamics Inertial techniques have sel dom been used because of the high costs they may be of more interest in the future as a supplement to GPS in particular for attitude control andor for bridging data gaps in hydrographic surveying Böder 2002 Integrated techniques have been for many years the only officially recognized and globally applicable methods for higher accu racy demands Their significance has changed with the increasing availability of GPS In the following some particular aspects of marine positioning will be addressed in short Use of the Satellite Doppler Technique The TRANSIT system 6 using the Doppler effect for radio signals was originally developed for marine navigation its possible application to precise positioning on land was recognized and exploited much later One of the characteristic features of this method is that positioning data can only be obtained for a limited period of 15 to 18 minutes during a particular satellite pass Between two consecutive satellite passes the observer has to wait for up to several hours depending on the satellite constellation and the geographic location The following principal limitations are associated with the Doppler method for a moving user 662 position information can only be derived from a single satellite pass insufficiently known the observers velocity severely corrupts the computed an tenna position and position information from other sources must be available for the time gaps between two satellite passes These limitations together with the rather low accuracy were the main reasons for a nearly complete substitution of the Doppler techniques by GPS after 1990 In princi ple the DORIS system 67 can also be used for marine positioning and navigation However due to the limited realtime accuracy for moving platforms the benefits of DORIS are preferably seen in the determination of satellite orbits and station locations 526 12 Overview and Applications Global Positioning System The NAVSTAR GPS is the system par excellence for marine positioning and navi gation because at least four but in most cases more satellites are visible from any position in the world at any time offering 24 hours of worldwide navigation capability the positions are available in realtime the achievable accuracy for a standalone user is after the deactivation of SA in many cases sufficient for general navigation for precise positioning and navigation requirements it is possible to use correc tion services DGPS for most parts of the world and if required it is also possible to achieve an accuracy at centimeter level The conditions and possibilities of GPS use in the marine environment are discussed at length in chapters 75 and 7627 and so they will not be repeated here It can be expected that the Russian system GLONASS 771 and the European system GALILEO 773 will augment the constellation and in particular will contribute to the availability and integrity of services 772 Sea Floor Positioning One of the most demanding tasks in marine geodesy is the determination of seabottom control points at centimeter level for monitoring of crustal deformation Fig 1212 explains the situation An array of control points is installed in active zones each Communication Satellite GPS GPS GPS Receiver at Reference Point Buoy Precision Transponders Figure 1212 Seafloor positioning in geodynamic research after Chadwell et al 1998 of which must be related to control points on land case 2 In addi tion the internal geometry between the seabottom points has to be mon itored case 1 Case 1 is of interest at midocean ridges where control points can be established on either side of the di verging plate boundary In general it will be difficult to measure directly between the control points because of ray bending of acoustic waves in water Hence it may be necessary to include a platform moored buoy ship at the sea surface or inside the water body as a relay station Case 2 hastheobjectivetodeterminemotion between an oceanic plate and a continental plate The distance between the control points can reach several hundred or even several thousand kilometers In both cases the position and motion of a seasurface platform has to be monitored The task includes two different surveying techniques Only acoustic waves can propagate in water hence acoustic techniques have to be applied to determine the position of sea bottom markers and to control the relationship between the bottom 124 Geodynamics 527 control points and the moving platform The propagation of sound in seawater depends on many conditions salinity temperature pressure and is very difficult to model with the required high precision The connection between the platform and a landbased reference station is via GPS using longrange kinematic techniques 75 For details and experiences see eg Chadwell et al 1998 124 Geodynamics Geodynamics is an extremely broad field and it is developing fast Turcotte Schubert 2002 Results from satellite geodesy are contributing considerably For an overview of current developments see the results of the regular meetings spring or autumn of the American Geophysical Union AGU the series of IAG symposia proceedings as well as the Journal of Geophysical Research JGR or Journal of Geodesy Within this section only the topics crustal motion Earth rotation and reference frames are briefly summarized Another important field of application is the analysis of tides of the ocean and solid Earth cf 3232 856 1241 Recent Crustal Movements The increasing accuracy of satellitebased geodetic positioning techniques makes it possible to derive information on the kinematics of tectonic plates from repeated or continuous observations This can be regarded as one of the most important contribu tions of satellite geodesy to geodynamics According to the model of plate tectonics eg Le Pichon et al 1973 Turcotte Schubert 2002 the crust of the Earth is divided in a number of thin rigid plates moving with respect to each other Plates are continu ously being added to along the oceanic ridges from uprising material In the collision zones between plates mountain chains deep sea trenches and island arcs form At trenches one plate dives beneath the other in a process named subduction forming subduction zones Plate boundaries are defined by seismic activity and may also be characterized by volcanoes On this basis several larger tectonic plates can be identified the Pacific North American SouthAmerican Eurasian IndianAfricanAustralian andAntarctic plates In addition several smaller plates are known such as the Caribbean Nacza Cocos and Arabian plate The overall pattern of motion is fairly complicated and can give rise to short lived microplates especially in intraoceanic settings Detailed knowledge of the kinematic behavior of these plates is fundamental to our understanding of its driving mechanism and could contribute to a better understanding and perhaps prediction of seismic activity It is also of importance for the maintenance of terrestrial reference frames 7621 Global models of plate tectonics can be established based on geological palaeo magnetic and seismic investigations and derived from accumulated motion rates over large periods of time One generally recognized model was published by Minster Jor dan 1978 and has since been refined several times The motion rates vary between 1 124 Geodynamics 529 to derive an Actual Plate Kinematic and Deformation Model APKIM from present day geodetic observations such as VLBI SLR and GPS A series of such models has been developed Drewes 1999 In the latest solution APKIM2000 about 280 site velocities were used to estimate 12 plate rotation vectors The adjustment process allows to distinguish between rigid plates and deformation zones DrewesAngermann 2001 In general the agreement between APKIM2000 and NUVEL1A is very high Significant differences however are visible in deformation zones Fig 1213 gives an impression on the motion rates based on the geophysical model NNRNUVEL1A and the actual kinematic plate model APKIM Figure 1213 Main plate boundaries and expected motion rates cmyear source DGFI The available observations can be regarded as zero observations but they already give promising results As time goes on and with continuing observations the results will become more and more reliable The longest series of observations was created within the framework of the NASA Crustal Dynamics Program CDP since 1979 based on repeated observations from approximately 35 Laser and 30 VLBI stations status end 1991 The NASA CDP ended in 1991 and was replaced by the Dynamics of the Solid Earth DOSE program in 1992 Observations are now continued within the international services ILS IVS and IGS By 2002 about 40 to 50 SLR stations and about 30 VLBI stations cooperated with regular observations within international projects These stations form the backbone to which are added more than 300 perma nent GPS stations As can be seen from the ITRF2000 network Fig 24 the global station distribution is not yet homogeneous Nevertheless the results from the regular solutions give an excellent insight into the detailed pattern of global plate motion and deformation A number of regional projects and arrays such as those in California Iceland or Japan and WEGENER in Europe complete the picture 7622 854 1242 Earth Rotation Reference Frames IERS The possible use of satellite observation techniques for the establishment of a terrestrial reference frame and models of the rotational behavior of the Earth has been discussed 530 12 Overview and Applications in detail in previous sections 212 7621 854 855 86 1112 Several comments can be given to summarize Since about the beginning of the last century polar motion and Earth rotation have been determined by international services through astronomical observations with fundamental instruments eg photographic zenith tube Danjon astrolabe The responsible organizations were the International Polar Motion Service IPMS pre viously the International Latitude Service ILS and the International Time Bureau Bureau International de lHeure BIH About 50 globally distributed stations con tributed with astrometric instruments on a regular basis The accuracy was about 01 corresponding to 3 m for the pole coordinates and 07 ms for Earths rotational velocity The related reference system was determined in 1968 through the adoption of the astronomical geographical coordinates of the total of 68 stations involved in the determination of Earth rotation BIH System 1968 Since 1967 almost as a byproduct of the computation of precise ephemerides pole coordinates have been determined by the Defense MappingAgency from Doppler observations to TRANSIT satellites 662 Since 1972 the results have been used by the BIH on a routine basis This was the first operational use of satellite methods for the determination of Earth rotation parameters and their capability and superiority was demonstrated The coordinates of the pole were derived with an accuracy of 40 cm from twoday solutions In the following years the efficiency and capability of new space methods was demonstrated in particular forVLBI and for laser ranging to satellites and to the Moon Within the framework of several independent national and international projects Earth rotation parameters were derived from observations with the new space techniques and compared with the BIH products The results were discussed at numerous international conferences Gaposchkin et al 1981 and led to the establishment of two working groups named MERIT Monitor Earth Rotation and Intercompare the Techniques of observation and analysis and COTES Conventional Terrestrial Reference System WithinthescopeofMERITtheMERITShortCampaign wasobservedfromAugust to October 1980 and the MERIT Main Campaign for a period of 14 months one Chandler period from September 1 1983 until October 31 1984 Classical as well as all available modern observation techniques for the determination of Earth rotation parameters and station coordinates were applied in a worldwide cooperative effort Of particular interest was the participation of stations where different types of instruments were operated collocation sites which could be used to detect systematic differences between the techniques and their related reference frames Observation stations were operated in 35 countries During the Main Campaign the following types of observations were carried out Optical Astrometry OA 61 stations Doppler Observations with TRANSIT DTS 20 stations 124 Geodynamics 531 Satellite Laser Ranging SLR 27 stations Lunar Laser Ranging LLR 3 stations Connected Elements Interferometry CEI 1 station Very Long Baseline Interferometry VLBI 8 stations A set of constants parameters and correction models the MERIT Standards Mel bourne et al 1983 was defined to support the data analysis These standards have since been widely used in the international scientific community and resulted later in the IERS standards and conventions The MERIT observations were of equal use for the objectives of COTES namely the installation of a conventional terrestrial reference system To support this objec tive a 3month Intensive Campaign was performed with among others daily VLBI observations in order to study the relationship between the particular reference frames as materialized through the individual observation techniques The scientific results of MERIT and COTES have been published in the proceed ings of the International Conference on Earth Rotation and the Terrestrial Reference Frame July 31 to August 2 1985 Columbus Ohio USA Mueller Wei 1985 The observation results are documented in Part III of this report Feissel 1986 They consist in each case of one or two lists Set of Station Coordinates SSC and Earth Rotation Parameters ERP TheSSClistsaresimplytherealizationofageocentricreferenceframe theERPresults are compatible with the related SSC It was demonstrated that the determination of polar motion and Earth rotation with SLR and VLBI was 5 to 6 times more accurate than the results of the existing service based on astrometric and Doppler techniques cf 855 1112 Some of the analysis centers continued with their work after the end of the MERIT project as the forthcoming International Earth Rotation Service was already in view The results were published annually until 1988 in part D Earth Rotation and Related Reference Systems of the BIH Annual Report In 1984 the BIH established a new reference system based on the geocentric co ordinates of those fundamental stations where geodetic space techniques were applied The system was called the BIH Terrestrial System BTS and it coincided within the related observational accuracy with the former reference frame established by astro nomical observations Boucher Feissel 1984 The last realization BTS 87 was derived from the SSCs of seven analysis centers contributing to the ERP series BIH 1988 Based on the experiences with MERIT and COTES it was proposed Wilkins Mueller 1986 that a new International Service be established for monitoring Earth rotation parameters and the maintenance of a conventional terrestrial reference frame This service was to replace the IPMS and the Earth rotation section of the BIH The new International Earth Rotation Service IERS was established in 1987 by the International Astronomical Union IAU and the International Union of Geodesy and Geophysics IUGG and started operation on January 1 1988 cf 2123 Boucher Altamini 1989 based on the following space techniques 532 12 Overview and Applications Very Long Baseline Interferometry VLBI Satellite Laser Ranging SLR and Lunar Laser Ranging LLR At a later date GPS data from the International GPS Geodynamics Service IGS and DORIS data were also included Following the terms of reference IERS 2001 the primary objectives of the IERS are to serve the astronomical geodetic and geophysical communities by providing the following the International Celestial Reference System ICRS and its realization the International Celestial Reference Frame ICRF the International Terrestrial Reference System ITRS and its realization the International Terrestrial Reference Frame ITRF Earth orientation parameters required to study Earth orientation variations and to transform between the ICRF and the ITRF geophysical data to interpret timespace variations in the ICRF ITRF or Earth orientation parameters and model such variations standards constants and models ie conventions encouraging international adherence Like the other services of interest to satellite geodesy namely the IGS 781 the ILRS 851 and the IVS 1113 the IERS fulfills its tasks within several components namely Technique Centers Product Centers Combination Centers Analysis Coordinator Central Bureau and Directing Board For details see theAnnual Reports of the IERS On January 1 2001 the Central Bureau was transferred from the Paris Observatory to the Bundesamt für Kartographie und Geodäsie BKG Frankfurt Germany The products of the IERS include among others the following International Celestial Reference Frame ICRF International Terrestrial Reference Frame ITRF monthly Earth orientation data daily rapid service Earth orientation data and predictions leap second announcements long term Earth orientation information annual reports technical notes and conventions The ICRF is realized through the coordinates of compact radio sources and is based on VLBI observations cf 2121 1112 The sky distribution of sources is depicted in Fig 23 The latest ITRF realization is ITRF2000 2122 It is based on about 800 stations located at about 500 sites The solution is based on observations by VLBI LLR SLR GPS and DORIS Fig 24 shows the global distribution of the 124 Geodynamics 533 primary sites and indicates the collocated techniques The datum is defined as follows IERS 2001 the origin and its rate are derived from the most consistent SLR solutions the scale and its rate are based on VLBI and SLR solutions the orientation is aligned to that of ITRF97 and its rate is such that there is nonetrotation with respect to NUVEL1A The longterm stability of ITRF2000 is estimated to be better than 4 mm in origin and better than 05 ppb in scale This last figure corresponds to a shift in station height of about 3 mm over Earths surface The Earth orientation parameters EOP are based on VLBI SLR and GPS Table 124showsthecontributionofeachtechnique Itbecomesevidentthatpolarmotionand the variation of Earth rotation LOD length of day are nearly exclusively determined by GPS LOD is the difference between the astronomically determined duration of the day and 86400 seconds of TAI Table 124 Percentage of contribution in the final IERS EOP solution IERS 2001 Technique Polar Motion UT1UTC LOD Nutation offset IERS VLBI 20 100 10 100 IERS SLR 10 IERS GPS 70 90 The polar motion between 1996 and 2000 and the mean pole displacement for the last century is illustrated in Fig 1214 x y Figure 1214 Polar motion 19962000 and mean pole displacement 19002000 IERS 2001 534 12 Overview and Applications As of April 2003 the name of the service was changed to International Earth Rotation and Reference Systems Service IERS in order to reflect the broader spectrum of generated products 125 Combination of Geodetic Space Techniques 1251 Basic Considerations Geodetic space techniques can be combined to achieve more reliable and consistent results The individual geodetic procedures have particular strengths and weaknesses the objective of a combination is to compensate the shortcomings of one method with the strengths of the other The strengths of the different observing techniques are for example SLR relationship to the geocenter and to Earths gravity field VLBI relationship to the inertial reference frame DORIS homogeneous global distribution of tracking stations GPS highly operational system for the densification of the terrestrial reference frame CHAMP GRACE GOCE high resolution Earth gravity field Altimetry structure and variation of sea level connection of height systems Links between the different geodetic space techniques are possible Rothacher 2002 a at the level of stations b at the level of satellites and c at the level of parameters a Stations serve as a link when different types of observations are realized at the same location Such sites are named collocation sites The rationale behind the collocation of various techniques is that the same results are to be expected for example station positions and velocities and that the observations are not influenced by different atmospheric effects It is essential to determine the local ties between the reference points of the participating instruments at the level of 1 to 2 mm The combination can be realized by forming a simple weighted mean between the individual results or by more sophisticated means using the complete variancecovariance matrix b Satellites serve as a link when a given satellite is tracked by different observation techniques Precise orbit determination POD is supported by SLR GPS DORIS and altimetry The satellite par excellence is TOPEXPOSEIDON where all four techniques can be used Two GPS satellites SVN35 and SVN 36 and all GLONASS satellites carry SLR retroreflectors The observation of GPS or GLONASS signals with VLBI offers a direct link between the satellite orbits and the ICRF c The link at the level of parameters offers various possibilities because most parameters can be determined by different techniques Table 125 gives an overview The common parameters can be combined at the level of the normal equations or at the level of observations The second approach is more flexible but also more demanding because only a few computer programs exist that are capable of treating all different data types in a consistent way Rothacher 2002 It is evident that consistent 536 12 Overview and Applications The station Wettzell located in Bavaria in Southern Germany includes all relevant geodetic space techniques These are currently Schlüter 2002 a 20 m radio telescope dedicated to geodetic VLBI 1112 the Wettzell Laser Ranging System WLRS designed for measurements to satellites SLR and to the Moon LLR 833 several GPS receivers Wettzell is an IGS corestation 781 a large number 45 in 2001 of remote controlled permanent GPS stations con tributing to IGS EUREF and the German reference network GREF 7513 a time and frequency laboratory 3 cesium oscillators and 3 hydrogen masers 225 a superconducting gravity meter for monitoring local gravity variations eg due to tides a ring laser gyro for the determination of Earth rotation and meteorological sensors and a water vapor radiometer 2332 In addition a high precision local network has been established to link all individual observing systems at an accuracy level of 1 to 2 mm Seismic measurements are carried out for monitoring earthquakes Fig 1215 gives an impression of the site Figure 1215 Fundamental Station Wettzell courtesy BKG Frankfurt The Transportable Integrated Geodetic Observatory TIGO is a transportable fundamental station built by the Bundesamt für Kartographie und Geodäsie BKG in Germany Its purpose is to provide observations for international services from a remote location in order to improve the realization and maintenance of global reference frames Schlüter et al 2000 TIGO includes all relevant geodetic space techniques namely Very Long Baseline Interferometry 6 m radio telescope Satellite Laser Ranging two color system range up to 36 000 km and 125 Combination of Geodetic Space Techniques 537 Microwave systems like GPS and GLONASS In addition various sensors for local measurements are provided time and frequency to generate a local time scale two cesium standards two hydrogen masers GPS time receivers gravity measurements for monitoring Earth tides superconducting gravity me ter seismic measurements for monitoring earthquakes broad spectrum seismome ter meteorological measurements meteorological station and water vapor radiome ter and local survey measurements for monitoring site stability and for linking the in strument reference points high precision tacheometer and digital levelling in strument After an international request a site in Concepción Chile was selected where TIGO is to be operated for several years jointly by a Chilean consortium and BKG Schlüter et al 2002 Operations started in April 2002 Fig 87 p 417 and Fig 114 p 493 show some of the TIGO components 1253 Integrated Global Geodetic Observing System IGGOS The integration of all geodetic space techniques and their services under one roof can be defined as an Integrated Global Geodetic Observing System IGGOS The concept of IGGOS has been widely discussed in the scientific geodetic community Rummel et al 2000 Drewes et al 2002 and proposed as a Project in the new structure of the IAG effective from 2003 IGGOS shall act as an interface between the IAG com missions the IAG related services and international nongeodetic organizations for example the Committee on Space Research COSPAR the International Lithosphere Program ILP or the Scientific Committee on Antarctic Research SCAR The new IAG commissions are 1 Reference Frames 2 Gravity Field 3 Earth Rotation and Geodynamics 4 Positioning and Applications The existing services of IAG are International GPS Service International VLBI Service International Laser Ranging Service International Earth Rotation Service International Gravimetric Bureau International Geoid Service International Center of Earth Tides Permanent Service for Mean Sea Level International Service of Weights and Measures Time Section Bibliography Abbreviations frequently used AVN Allgemeine Vermessungsnachrichten H Wichmann Karlsruhe Bull Géod Bulletin Géodésique Springer BerlinHeidelbergNew York CSTG Bull International Coordination of Space Techniques for Geodesy and Geodynamics Bulletin ColumbusMunich DGK Veröffentlichungen der Deutschen Geodätischen Kommission bei der Bayerischen Akademie der Wissenschaften München EOS Transactions American Geophysical Union Washington DC IONGPS Proceedings of the Internat Technical Meeting of the Satellite Division of The Institute of Navigation J Geod Journal of Geodesy Springer BerlinHeidelbergNew York JGR Journal of Geophysical Research American Geophysical Union Washington DC Man geod manuscripta geodaetica Springer Berlin Navigation Journal of the Institute of Navigation OSU Rep Reports of the Department of Geodetic Science The Ohio State University Columbus Ohio SAO Spec Rep SAO Special Reports Smithsonian Institution Astrophysical Observatory Cambridge Mass Wiss Arb Univ Hannover Wissenschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover ZfV Zeitschrift für Vermessungswesen K Wittwer Stuttgart Aardoom L Gelder B V Vermaat E 1982 Aspects of the analysis and utilization of satellite laser ranging at the Kootwijk observatory In Feestbundel ter gelegenheid van de 65ste verjaardag van Professor Baarda Delft Vol 2 276317 Abidin H Wells D 1990 Extrawidelaning for on the fly ambiguity resolution simu lation of ionospheric effects Proc Second Int Symp Precise Positioning with the Global Positioning System GPS90 Ottawa 12171233 Ádám J 1999 Spaceborne VLBI beyond 2000 In Quo vadis geodesia Techn Rep Dep Geod GeoInform Univ Stuttgart 19996 13 Ádám J Augath W Boucher C et al 2000 The European Reference System coming of age In Schwarz ed 2000 4754 Agnieray P 1997 The DORIS system performances and evolutions CSTG Bull No 14 2027 AguirreMartinez M Cesare S 1999 GOCE mission concept error derivation and perfor mances Boll Geof Teor Appl 40 295302 Akos D Luo M Pullen S Enge P 2001 UltraWideband and GPS Can They Coexist GPS World 12 9 5970 Allan D 1987 Time and Frequency TimeDomain Characterization Estimation and Pre diction of Precision Clocks and Oscillators IEEE Transactions on Ultrasonic Ferroelectrics and Frequency Control Vol UFFC34 No 6 647654 540 Bibliography Allan D Ashby N Hodge C 1997 The Science of Time Keeping Hewlett Packard Appli cation Note 1289 Altamimi Z Angermann D Argus D 22 more authors 2001 The Terrestrial Reference Frame and the Dynamic Earth EOS 82 No25 Ambrosius B Noomen R Overgaanw B Wakker K 1991 Geodetic coordinates solutions from SLR and GPS measurements IAG Symp on Permanent Satellite Tracking Networks for Geodesy and Geodynamics XX General Assembly IUGG Vienna Anderle R 1973 Determination of polar motion from satellite observations Geophysical Surveys 1 147161 Anderle R 1974 Transformation of terrestral survey data to Doppler satellite datum JGR 79 53195331 Anderle R 1979 Geodetic applications of the NAVSTAR Global Positioning System Proc Int Symp Use of Artificial Satellites in Geodesy and Geodynamics II 117ff Athens Anderle R 1986 Doppler satellite measurements and their interpretation In A JAnderson A Cazenave eds Space geodesy and geodynamics Academic Press London Anderle R Malyevac C 1983 Current plate motions based on Doppler satellite observa tions Geophysical Research Letters 10 1 6790 Angermann D Müller H Gerstl M Kelm R Seemüller W Vei M 2001 Laserentfer nungsmessungen zu LAGEOS1 und LAGEOS2 und ihr Beitrag zu globalen Referenzsyste men ZfV 126 250256 Anodina T Prilepin M 1989 The GLONASS System Proc 5th Intern Geod Symp Satellite Positioning Las Cruzes Vol 1 1318 Aoki S Guinot B Kaplan G Kinoshita H McCarthy D Seidelmann P 1982 The new definition of universal time AstronAstrophys 105 359361 Argus D Gordon R 1991 Nonet rotation model of current plate velocities incorporating plate motion model NUVEL1 GeophysResLett 18 20392042 Arnold K 1970 Methoden der Satellitengeodäsie AkademieVerlag Berlin Ashby N Spilker J 1996 Introduction to Relativistic Effects on the Global Positioning System In Parkinson Spilker eds 1996 Vol 1 Chap 18 623697 Ashford A 2001 Star Catalogues for the 21st Century Sky Telescope July 6567 Ashjaee J 1989 Precision survey with Ashtech XII the allinone allinview Proc 5th Intern Geod Symp Satellite Positioning Las Cruzes Vol 1 316329 Ashjaee J Lorenz R 1992 Precision GPS surveying after Ycode Proc ION GPS92 Albuquerque 657659 Augath W 1988 Experiences with Trimble receivers in the control network of the FGR In Groten Strauss eds 1988 131143 Ballani L 1982 Die Bestimmung geodätischgeodynamischer Parameter mit Hilfe von Laserdinstanzmessungen zum Mond Gerl Beitr Geophysik 91 2 121140 Balmino G 1973 Analytical expressions for earth tide perturbations on close earth satellites ProcIntSymp Use of Artificial Satellites for Geodesy and Geodynamics Athens 313322 Balmino G 1983 The surface gravity data available for improvement of the global knowledge of the geopotential Proc IAG Symp GenAssembly Hamburg 1983 Columbus OhioVol 1 365387 Bibliography 541 Balmino G Bernard A 1986 Satellite gravity gradiometry for the determination of the geopotential Proc ESA Workshop Solid Earth Science Application Mission for Europe SESAME ESA SP1080 95101 Balmino G Perosanz F Rummel R Sneeuw N Sünkel H 1999 CHAMP GRACE and GOCE mission concepts and simulations Boll Geof Teor Appl 40 309319 Balmino G Reigber C Moynot B 1976a A geopotential model determined from recent satellite observing campaigns GRIM1 Man geod 1 Balmino G Reigber C Moynot B 1976b The GRIM2 earth gravity field model DGK A 86 München Balmino G et al 1984 Le projet Gradio et la determination à haute resolution du geopo tentiel Bull Géod 58 2 151179 Bamler R 1997 Digital Terrain Models from Radar Interferometry Photogrammetrische Woche Stuttgart 1997 93105 Bamler R 1998 Synthetic aperture radar interferometry Inverse Problems 14 R1R54 IOP Publishing Ltd Bamler R 1999 The SRTM Mission A WorldWide 30 m Resolution DEM from SAR Inter ferometry in 11 Days Photogrammetrische Woche Stuttgart 1999 145154 Bamler R 2000 Principles of SyntheticAperture Radar Surveys in Geophysics 21 147157 Barrett J 1997 Inventorying interstate pipelines with GPS GPS World 8 10 4043 Bastian U 1998 The small astrometric interferometry satellite DIVA In Brosche P ed The Message of the Angles Astrometry from 1798 to 1998 207212 Verlag H Deutsch Thun und Frankfurt Bastos M Landau H 1988 Fixing cycle slips in dualfrequency kinematic GPS applications using Kahman filtering Man geod 13 4 249256 Bate R Mueller D White J 1971 Fundamentals of Astrodynamics Dover Publications New York Battin R Croopnick S Lenox E 1978 The epoch state navigation filter J of Guidance and Control 1 5 359364 Bauch A Fischer B Heindorff P Hetzel G Petit G Schröder R Wolf P 2000 Comparison of the PTB primary clocks with TAI Metrologia 37 683692 Bedrich S 1998 Hochgenaue satellitengestützte Zeitübertragung mit PRARE Scientific Technical Report STR9824 GeoForschungsZentrum Potsdam Benedicto J Michel PVenturaTraveset J Maier T 1999 EGNOS European Geostation ary Navigation Overlay ServiceBasic Technical Background Rep Geod 44 3 267276 Benning W Aussems T 1998 Mobile mapping digitale Datenerfassung mittels CDSS und automatisierte Auswertung von Videosequenzen ZfV 123 202209 Benveniste J Roca M Levrini G 5 more authors 2001 The Radar Altimeter Mission RA2 MWR DORIS and LRR ESA Bull 106 6776 Berbert J Carney D 1979 Intercomparison of GEOS3 tracking system JGR 84 B8 39333943 Berroth A Hofmann W 1960 Kosmische Geodäsie Verlag G Braun Karlsruhe Bertiger W BarSever Y Haines B 11 more authors 1999 A Prototype RealTime Wide Area Differential GPS System Navigation 44 4 433447 542 Bibliography Beutler G Bauersima I Gurtner W Rothacker M Schildknecht T 1988 Static posi tioning with the Global Positioning System GPS state of the art In Groten Strauss eds 1988 363380 Beutler G Eanes R Engeln J Herring T 6 more authors 1997 SLR Review Committee Report International Laser Ranging Service Beutler G Gurtner W Bauersima I Rothacker M 1987 Correlation between simultane ous GPS double difference carrier phase observations in the multistation mode Implemen tation considerations and first experiences Man geod 12 4044 Beutler G Gurtner W Rothacher M Wild U Frei E 1990 Relative static positioning with the Global Positioning System basic technical considerations In Bock Leppard eds 1990 123 Beutler G Hein G Melbourne W Seeber G eds 1996 GPS trends in precise terrestrial airborne and spaceborne applications IAG Symp Proceed 115 SpringerVerlag Berlin HeidelbergNew York Beutler G Weber R Hugentobler U Rothacher MVerdunA 1998 GPS Satellite Orbits In Teunissen Kleusberg 1998 Chap 2 43109 Bianco G Selden M Bieneman M 9 more authors 1999 TwoColor Ranging Upgrade for the MLRO System In Schlüter Schreiber Dassing 1999 346352 BIH 1988 Annual Report Bureau International de l Heure until 1988 Paris BIPM 2002 Annual Report Bureau International des Poids et Mesures Sèvres Published yearly Bisnath S Beran T Langley R 2002 Precise Platform Positioning with a Single GPS Receiver GPS World 13 4 4249 Bisnath S Kim D Langley R 2001 A New Approach to an Old Problem CarrierPhase Cycle Slips GPS World 12 5 4651 Black H 1978 An easily implemented algorithm for the tropospehric range correction JGR 83 B4 Black H 1980 The TRANSIT system 1977 Performance plans and potential Phil Trans Royal Soc London A 294 217236 Blewitt G 1998 IGS Densification Program In IGS Annual Report 1997 2425 Blewitt G et al 1988 GPS geodesy with centimeter accuracy In Groten Strauss eds 1988 3040 Bock Y Leppard N eds 1990 Global Positioning System An Overview Symposium No 102 Edinburgh August 78 1989 International Association of Geodesy Symposia SpringerVerlag New York Bock Y Wdowinski S Fang P 18 more authors 1997 Southern California Permanent GPS Geodetic Array JGR 102 B8 1801318033 Bock Y Williams S 1997 Integrated Satellite Interferometry in Southern California EOS 78 29 293 299300 BockY et al 1986 Interferometric analysis of GPS phase observations Man geod 11 4 282288 Böder V 2002 Zur hochpräzisen GPS Positions und Lagebestimmung unter besonderer Berücksichtigung mariner Anwendungen Wiss Arb Univ Hannover Nr 245 Bibliography 543 Böder V Menge F Seeber G Wübbena G Schmitz M 2001 How to deal with station dependend errors New developments of the absolute field calibration of PCV and phase multipath IONGPS 2001 Böhler W 1972 Über die Satellitenbeobachtungen des deutschen Meßtrupps im Weltnetz US CGS DGK C 182 München Bossler J Goad C Bender L 1980 Using the Global Positioning System GPS for geodetic positioning Bull Géod 54 4 553563 Boucher CAltamini Z 1989 The initial IERS Terrestrial Reference Frame IERS Technical Note 1 Paris 1989 Boucher C Altamini Z Sillard P 1999 The 1997 International Terrestrial Reference Frame ITRF97 IERS Technical Note 27 Boucher C Feissel M 1984 Realization of the BIH Terrestrial System Int Symp on Space Techniques for Geodynamics Sopron Vol 1 235254 Boucher C Feissel M Lestrade J 1988 Concepts and methods of the Central Bureau of the International Earth Rotation Service Bull Geod 62 4 511519 Boucher C Paquet P Wilson P 1979 The second European Doppler Observation Cam paign EDOC2 Proc 2nd Intern Geodetic Symp Satellite Doppler Positioning Austin 819850 Boucher C Wilkins G eds 1990 Earth rotation and coordinate reference frames IAG Symposium No 105 Edinburgh August 1011 1989 SpringerVerlag New YorkBerlin Braasch M 1996 Multipath Effects In Parkinson Spilker eds 1996 Vol 1 Chap 14 547568 Bretterbauer K 1997 Eine Renaissance der Astrometrie in der Geodäsie Österr Z Vermes sungswesen und Geoinformatik 197 1520 Bretterbauer K 2001 Die parallaktische Refraktion ZfV 126 211213 Breuer B Campbell J Müller A 1993 GPS Meß und Auswerteverfahren unter opera tionellen GPSBedingungen J Satellite Based Positioning Navigation amd Communication SPN 2 3 8290 Brouwer D 1959 Solution of the problem of artificial satellite theory without drag Astro nomical Journal 64 378397 Brouwer D Clemence G 1961 Methods of Celestial Meachanics Academic Press New York London BrownA 1990 A multisensor approach to assuring GPS integrity GPS World 1 2 4448 Brown D 1970 Near term prospects for potential accuracies of 01 to 10 meters from satellite geodesy USAirforce Cambridge Research Laboratories ReportAFCRL700501 Bedford Mass Brunner F 1992 Refraction refractive index and dispersion some relevant history In DeMunck Spoelstra eds 1992 39 Brunner F ed 1998 Advances in Positioning and Reference Frames IAG Symp Proceed 118 SpringerVerlag BerlinHeidelbergNew York Bruns H 1878 Die Figur der Erde Publ Königl Preuß Geod Inst Berlin Bürki B Kahle HG 1995 MikrowellenWasserdampfradiometrie für hochgenaue Mes sungen mit GPS Vermessung Photogrammetrie und Kulturtechnik 1995 232240 Campbell J 1979 Die Radiointerferometrie auf langen Basen als geodätisches Meßprinzip hoher Genauigkeit DGK C 254 München 544 Bibliography Campbell J 2000a From Quasars to Benchmarks VLBI Links Heaven and Earth In Vandenberg Baver eds 2000 1934 Campbell J 2000b Very Long Baseline Interferometry a high precision tool for geodesy and astrometry C R Acad Sci Paris t1 Série IV 12551265 Campbell J Cloppenburg H Lohmar FJ 1984 Estimating the ionospheric refraction effect on interferometric GPSmeasurements Proc Int Symp SpaceTechniques for Geodyn Sopron Vol 2 196206 Campbell J Haas R Nothnagel A 2002 Measurement of Vertical Crustal Motion in Europe by VLBI Scientific Report European Commission TRM Network FMRXCT96 0071 Geodetic Institute University of Bonn Campbell J NothnagelA 1998 Erdkrustenbewegungen und Bezugssysteme neuere Ergeb nisse aus VLBIMessungen ZfV 123 4248 Campbell J Nothnagel A Schuh H 1992 VLBIMessungen für geodynamische Fragestel lungen ZfV 117 214227 Campbell J Seeber GWitte B1973 KombinationvonDoppler Laserundphotographis chen Beobachtungen in Satellitennetzen DGK B 200 München Campbell JWitte B 1978 Grundlagen und geodätischeAnwendung derVery Long Baseline Interferometry VLBI ZfV 103 1020 Campos M 1987 Controle da rede geodésica Brasileira por meio de satélites do sistema NNSS PhD thesis Curitiba Campos M Seeber G Wübbena G 1989 Positioning with GPS in Brazil Proc 5th Intern Geod Symp Satellite Positioning Las Cruzes Vol 1 526535 Capitaine N 2002 The Essential Contribution of VLBI to Fundamental Astronomy In IVS General Meeting Proceedings 2002 1423 Capitaine N et al 2002 Proceedings of the IERS Workshop on the Implementation of the New IAU Resolutions IERS Technical Note No 29 Frankfurt am Main Capitaine N Guinot B McCarthy D 2000 Definition of the Celestial Ephemeris Origin and of UT1 in the International Celestial Reference Frame AstronAstrophys 355 398405 Cappelari J Velez C Fuchs A 1976 Mathematical Theory of the Goddard Trajectory Determination System GSFC Document X5827677 Greenbelt Cazenave A Dominh K Soudarin F P L Cretaux J Provost C L 1999 Sea level changes from TopexPoseidon altimetry and tide gauges and vertical crustal motions from DORIS Geophys Res Letters 26 14 20772080 Cazenave A Royer J 2001 Applications to Marine Geophysics In Fu Cazenave eds 2001 Chap 11 407439 Chadwell D Spiess F Hildebrand J Young L Purcell G Dragert H 1998 DeepSea Geodesy Monitoring the Ocean Floor GPS World 9 9 4455 Chelton D Ries J C Haines B Fu L Callahan P 2001 Satellite Altimetry In Fu Cazenave eds 2001 Chap 1 1131 Chen D Lachapelle G 1995 A comparison of the FASF and leastsquares search algorithms for onthefly ambiguity resolution Navigation 42 2 371390 Cheney R Douglas B Green R Miller L Milbert D Porter D 1986 The GEOSAT altimeter mission a milestone in satellite oceanography EOS 67 Dec 2 Bibliography 545 Cheney R Douglas B Sandwell D Marsh J Martin T McCarthy J 1984 Applications of satellite altimetry to oceanography and geophysics Marine Geophysical Researches 7 1732 Chistyakov V Filatchenkov S Khimulin V Kornyenko V 1996 Double Duty Russias DGPSDGLONASS Maritime Service GPS World 7 3 5962 Chobotov V 1991 Orbital Mechanics American Institute of Aeronautics and Astronautics Washington DC Chodota M 1987 Present status of the African Doppler Survey Project ADOS CSTG Bull No 9 München Chodota M 1990 Post ADOS strategy for unified networks for Africa Proc 4th Symp on Geodesy in Africa Tunis CNES 1975 STARLETTE Centre National dEtudes Spatiales Toulouse CNES 2000 Proceedings DORIS DAYS Centre National dÉtudes Spatiales Cocard M 1995 High Precision GPS Processing in Kinematic Mode Geod Geophys Arb Schweiz Vol 52 Zürich Coco D 1991 GPSsatellites of opportunity for ionospheric monitoring GPS World 2 9 4750 Cohen C 1996 Attitude Determination In Parkinson Spilker eds 1996Vol 2 Chap19 519538 Cohen S Chinn D Dunn P 1990 Geoscience laser ranging system GLRS characteristics and expected performance in geodynamic applications In Vyskocil Reigber Cross eds 1990 5663 Collins P Langley R 1999 Tropospheric Delay prediction for the WAAS User GPS World 10 7 5258 Colombo O 1984 The global mapping of gravity with two satellites Netherlands Geodetic Commission New Series 7 Delft Colombo O 1989 Advanced techniques for highresolution mapping of the gravitational field In Sansò Rummel eds 1989 335372 Colombo O Bhapkar U Evens A 1999 Inertialaided cycleslip detectioncorrection for precise longbaseline kinematic GPS ION GPS99 19151921 Costes M 1997 DORIS system status and perspectives CSTG Bull 13 6466 Counselman C Shapiro I 1979 Miniature interferometer terminals for earth surveying Bull Géod 53 2 139163 Counselman C Steinbrecher D 1982 The Macrometer A compact radio interferometry terminal for geodesy with GPS Proc 3rd Int Symp on Satellite Doppler Positioning Las Cruzes Vol 2 11651172 Cracknell A Hayes L 1991 Introduction to remote sensing Taylor Francis London New York Cramer M 2001 Genauigkeitsuntersuchungen zur GPSINSIntegration in der Aeropho togrammetrie DGK C 537 München Cross P Ahmad N 1988 Field validation of GPS phase measurements In Groten Strauss eds 1988 349360 Cruddace P 2001 Ordnance Surveys National GPS GEO Informatics JulyAugust 1213 546 Bibliography Cugusi L Proverbio E 1978 Relativistic effects on the motion of Earths artificial satellites Astron Astrophys 69 321325 Cui C Mareyen M 1992 Gausss equations of motion in terms of Hill variables and first applications to numerical integration of satellite orbits Man geod 17 155163 Dach R 1999 Einfluss von Auflasteffekten auf präzise GPSMessungen DGK C 519 München Daly P Misra P 1996 GPS and Global Navigation Satellite System GLONASS In Parkinson Spilker eds 1996 Vol II Chap 9 243274 Davies K 1990 Ionospheric Radio IEEE ElectromagneticWaves Series 31 Peter Peregrinus London Davis J Herring T Shapiro I Rogers A Elgered G 1985 Geodesy by radio interferom etry Effects of atmospheric modelling errors on estimates of baseline length Radio Science 20 6 15931607 Degnan J 2000 An Overview of SLR2000 Engineering Progress and Potential Future Up grades 12th Int Laser Workshop on Laser Ranging Matera Italy Degnan J Pavlis E 1994 Laser Ranging to GPS Satellites with Centimeter Accuracy GPS World 5 9 6270 Delikaraoglou D 1989 On principles methods and recent advances in studies towards a GPSbased control system for geodesy and geodynamics NASA Techn Memo 100716 Greenbelt Md DeMets C Gordon RArgus D Stein S 1994 Effect of recent revisions to the geomagnetic reversal time scale on estimates of current plate motions Geophys Res Lett 21 21912194 Demmel M 2000 Satellitenortung in der Landwirtschaft Möglichkeiten und Anforderun gen Proc 3 SAPOS Symp München 3852 DeMunck J Spoelstra TA eds 1992 Refraction ofTransatmospheric Signals in Geodesy Symp Proceed Publication on Geodesy No 36 Netherlands Geodetic Commission Delft Denker H Torge W 1998 The European gravimetric quasigeoid EGG97 and IAG sup ported continental enterprise In Forsberg Feissel Dietrich eds 1998 249254 Desai S Wahr J 1995 Empirical ocean tide models estimated from TOPEXPOSEIDON altimetry JGR 100 C12 25 20525 228 Devoti R Luceri V Sciarretta C Bianco G Donato G D Vermeersen L Sabadini R 2001 The SLR secular gravity variations and their impact on the interference of mantle rheology and lithospheric thickness Geophys Res Letters 28 5 855858 DGFI 2001 Deutsches Geodätisches Forschungsinstitut Annual Report 20002001 DGFI München Dickey J Bender P Faller J Newhall X 8 more authors 1994 Lunar Laser Ranging A continuing Legacy of the Apollo Program Science Vol 265 482490 Dickey J Williams J Newhall X Yoder C 1983 Geophysical applications of Lunar Laser Ranging Proc IAG Symp Gen Ass Hamburg Vol 2 509521 Columbus Ohio Dietrich R Dach R Engelhardt G et al 2001 ITRF coordinates and plate velocities from repeated GPS campaigns in Antarctica an analysis based on different individual solutions Journal of Geodesy 74 No 1112 Dietrich R ed 2000 Deutsche Beiträge zu GPSKampagnen des Scientific Committee on Antarctic Research SCAR 19951998 DGK B 310 München Bibliography 547 DOD 2001 Global Positioning System Standard Positioning Service Performance Standard Department of Defense Document October 2001 DODDOT 2001a Federal Radio Navigation Plan Department of Defense DoD Depart ment of Transportation DOT DODDOT 2001b Federal Radio Navigation Systems Department of Defense DoD De partment of Transportation DOT Douglas B Agreen R 1983 The sea state correction for GEOS3 and SEASAT satellite altimeter data JGR 88 C3 16551661 Douglas B Cheney R 1990 GEOSAT Beginning a new era in satellite oceanography JGR 95 C3 28332836 Douglas B Goad C Morrison F 1980 Determination of the geopotential from satellite tosatellite tracking data NOAA Techn Memo NOS NGS 24 Rockville Dow J 1988 Ocean Tides and Plate Motions from LAGEOS DGK C 317 München Drew A 1983 Glacial movements in Greenland from Doppler satellite observations Inst of Polar Studies Ohio State University Report No 81 Columbus Drewes H 1998 Time Evolution of the SIRGAS Reference Frame In Brunner ed 1998 174179 Drewes H1999 RealisierungdeskinematischenterrestrischenReferenzsystemsohneglobale Rotation no net rotation Mitt Bundesamt f Kart u Geod 5 120125 Frankfurt a M Drewes H 2000 The Role of VLBI Among the Geodetic Space Techniques Within CSTG In Vandenberg Baver eds 2000 3541 Drewes H Angermann D 2001 The Actual Plate Kinematic and Crustal Deformation Model 2000 APKIM2000 as a Geodetic Reference System IAG 2001 Scientific Assembly Budapest Drewes H Beutler G Rummel R 2002 Challenges for VLBI Within an Integrated Global Geodetic Observing System Proceed IVS 2002 General Meeting 2432 Drewes H Reigber C 1982 Untersuchungen zu einem satellitengetragenen Laser Entfernungsmeßsystem zur präzisen Punktbestimmung ZfV 107 396405 Eanes R Bettadpur S 1996 The CSR30 global ocean tidal model Diurnal and semidiurnal ocean tides from TOPEXPOSEIDON altimetry Techn Rep CSRTM9605 University of Texas Center for Space Research Eanes R Schutz B Tapley B 1983 Earth and Ocean Tide Effects on Lageos and Starlette Proc 9th Int Symp on Earth Tides 239249 Egge D 1982 Investigations on the effect of small antenna movements in Transit Doppler Positioning Proc 3rd Int Geod Symp Satellite Doppler Positioning Las Cruces Vol 2 953968 Egge D 1985 Zur sequentiellen Auswertung von DopplerSatellitenbeobachtungen Wiss Arb Univ Hannover No 93 Egge D Seeber G 1979 Meßverfahren zur genauen Positionsbestimmung im Meeresbe reich Wiss Arb Univ Hannover No93 Ehlert D 1991 Differentielle Verschiebungen und Drehungen in dreidimensionalen Koordi natensystemen DGK B 295 München Eichhorn H 1974 Astronomy of Star Positions F Ungar PublCo New York Eisfeller B 2002 Das Europäische Satellitennavigationssystem GALILEO 4 SAPOS Symp Hannover 214226 548 Bibliography Eisner A et al 1982 NOVA1 The newest Transit satellite a status report Proc 3rd Int Geod Symp on Doppler Satellite Positioning Las Cruces Vol 2 843862 ElSheimy N 2000 Mobile multisensor system The new trend in mapping and GIS appli cations In Schwarz ed 2000 319330 Elgered G Jarlemark P 1998 Groundbased microwave radiometry and longterm obser vations of atmospheric water vapor Radio Science 33 707717 Engelis T 1987 Radial orbit error reduction and sea surface topography determination using satellite altimetry OSU Rep 377 Escobal P 1965 Methods of orbit determination John Wiley New York London Sydney Fagard H Orsoni A 2000 Current status and evolution prospects of the DORIS network Proceed DORIS days 2000 Fashir H Abdalla K 1991 Doppler geoid in Africa Survey Review 31 175180 Fedrizzi M de Paula E Kantor I Langley R Santos M Komjathy A 2001 The Low Latitude Ionosphere Monitoring its Behavior with GPS Proc ION GPS 2001 24682475 also GPS World 13 2 4147 Feissel M 1986 Observational results on Earth rotation and reference systems Report on MERITCOTES Part III Bureau International de lHeure Paris Fejes I 1994 Techniques and Methods in Geodynamical Research Space VLBI Acta Geod Geoph Hung 29 443456 Fejes I Mihály S 1991 Application of Space VLBI to satellite dynamics Adv Space Res 11 429437 Fell P 1980 Geodetic Positioning using a Global Positioning System OSU Rep 299 Flechtner F 2000 Bestimmung des Gesamtelektroneninhalts der Ionosphäre aus PRARE Entfernungs und Dopplerbeobachtungen Scientific Technical Report STR0002 Geo ForschungsZentrum Potsdam Fliegel H Gallini T 1989 Radiaton pressure models for Block II GPS satellites Proceed 5th Int Geod Symp Sat Positioning Las Cruzes 789798 Fliegel H Gallini T Swift E 1992 Global Positioning System Radiation Force Model for Geodetic Applications JGR 97 B1 559568 Fontana R Cheung W Stansell T 2001 The Modernized L2 Civil Signal GPS World 12 9 2832 Forrest W 2002 GALILEO Proc 39th CGSIC Conference Springfield Virginia 18th April 2002 Forsberg R Feissel M Dietrich R eds 1998 Geodesy on the Move Gravity Geoid Geo dynamics and Antarctica IAG Symp Proceed 119 SpringerVerlag BerlinHeidelberg New York Forsell B 1991 Radionavigation Systems Prentice Hall New York Fortes L Luz R Pereira K Costa S Blitzkow D 1997 The Brazilian Network for Continuous Monitoring of GPS RBMC Operation and Products In Brunner ed 1998 7378 Forward R 1974 Review of artificial satellite gravity gradiometer techniques for geodesy Proc Symp on The Use of Artificial Satellites for Geodesy and Geodynamics Athens 157192 Fosu C 1998 Astrogeodetic Levelling by the Combination of GPS and CCD Zenith Camera Studiengang Vermessungswesen Schriftenreihe UniBw München 62 Bibliography 549 Frei E Beutler G 1989 Some considerations concerning an adaptive optimized technique to resolve the initial phase ambiguities for static and kinematik GPS surveying techniques Proceed 5th Int Symp Satellite Positioning Las Cruces Vol 2 671686 Frei E Beutler G 1990 Rapid static positioning based on the fast ambiguity resolution approach the alternative to kinematic positioning Proceed GPS 90 Ottawa 11961216 Fricke W Schwan H Lederle T 1988 Fifth Fundamental Catalogue FK5 Part I The Basic Fundamental Stars Astronomisches Recheninstitut Heidelberg Veröffentlichungen Nr 32 Verlag G Braun Karlsruhe FRNP 2001 Federal Radio Navigation Plan 2001 Rep No DOTVNTSCRSPA013DOD 46505 NatTechnInfService Springfield Virginia USA Fu L Cazenave A eds 2001 Satellite Altimetry and Earth Sciences Academic Press San DiegoLondon Fu L Chelton D 2001 LargeScale Ocean Circulation In Fu Cazenave eds 2001 Chap 2 133169 Gabriel A Goldstein R M Zebker H A 1989 Mapping Small Elevation Changes Over Large Areas Differential Radar Interferometry JGR 94 B7 91839191 Gaignebet J ed 1985 5th Int Workshop on Laser Ranging Instrumentation Herstmonceux 1984 Vol 1 and Vol 2 Bonn Ganin A 1995 Differential GLONASS in Russia The Ways of Development Proceed ION GPS95 10491052 GaoY Zuofa L 1999 Cycle Slip Detection and Ambiguity Resolution Algorithms for Dual Frequency GPS Data Processing Marine Geodesy 22 3 169181 Gaposchkin E 1973 Smithsonian Standard Earth III SAO Spec Rep 353 Cambridge Mass Gaposchkin E Kolaczek B eds 1981 Reference coordinate systems for Earth dynamics Proc 56th Colloquium IAU Warschau 1980 Astrophysics and Space Science Library Vol 56 D Reidel DordrechtBostonLondon Gelb A ed 1974 Applied Optimal Estimation MIT Press Cambridge Mass Gendt G 2000 IGS Tropospheric Products IGS Annual Report 2000 Gens R 1998 Quality assessment of SAR data Wiss Arb Univ Hannover Nr 226 Georgiadou Y Kleusberg A 1988 On carrier signal multipath effects in relative GPS positioning Man geod 13 172179 GeorgiadouY Kleusberg A 1990 Multipath effects in static and kinematic GPS surveying In Bock Leppard eds 1990 8289 Gerstbach G 1999 CCD und AstroGeodäsie Unterwegs zur automatischen Lotrich tungsmessung Geowiss Mitt 50 4558 Giacaglia G 1973 Lunar perturbations on artificial satellites of the Earth SAO Special Report 352 Cambridge Mass Gibbons G 1991 GPS and friends integrating technology GPS World 2 5 10 Gibbons G Maynard G 1990 Odysseys of geodesy GPS World 1 2 2028 Goad C 1977 Application of digital filtering to satellite geodesy NOAA Techn Report NOS71 NGS 6 Rockville Md Goad C 1985 Precise relative position determination using Global Positioning System car rier phase measurements in a nondifference mode Proceed 1st Int Symp Precise Position ing with GPS Rockville Vol 1 347356 550 Bibliography Goad C 1998 Short Distance GPS Models In Teunissen Kleusberg 1998 Chap 11 457481 Goad C C Müller A 1988 An automated procedure for generating an optimum set of independent double difference observables using GPS carrier phase measurement Man geod 13 365369 Goffinet P 2000 Qualitätssteigerung der Seevermessung und Navigation durch neuartige Beschickungsverfahren Wiss Arb Univ Hannover Nr 235 Goldan H 1996 Beiträge zur GPS gestützten Höhenbestimmung im Küstenbereich Wiss Arb Univ Hannover Nr 215 Görres B 1996 Bestimmung von Höhenänderungen in regionalen Netzen mit dem Global Positioning System DGK C 461 München Görres B Campbell J 1998 Bestimmung vertikaler Punktbewegungen mit GPS ZfV 123 222230 Green R 1985 Spherical Astronomy Cambridge University Press Cambridge Großmann W 1976 Geodätische Rechnungen und Abbildungen in der Landesvermessung 3 Aufl Wittwer Stuttgart Groten E 1979 1980 Geodesy and the earths gravity field Vol I Principles and conven tional methods Vol II Geodynamics and advanced methods Dümmler Bonn Groten E Mathes A Becker M Sauermann K 2001 GNSS Information AVN 42001 p 154 Groten E Strauss R eds 1988 GPStechniques applied to geodesy and surveying Lecture Notes in Earth Sciences 19 SpringerVerlag BerlinHeidelberg Gruber T Reigber C Schwintzer P 2000 The 1999 preCHAMP high resolution gravity model In Schwarz ed 2000 8995 Guier W 1962 Navigation using artificial satellitesthe TRANSIT System Proceed 1st Int Symp Use of Art Satellites for Geodesy Washington DC 261277 Guier W Weiffenbach G 1960 A satellite Doppler navigation system Proceed IRE 48 Guier W Weiffenbach G 1998 Genesis of Satellite Navigation Johns Hopkins APL Tech nical Digest Vol 19 No 1 1417 Guinot B 1979 Basic Problems in the Kinematics of the Rotation of the Earth In McCarthy and Pilkington eds Time and the Earths Rotation IAU Symp No 82 716 Guinot B 1995 Scales of Time Metrologia 31 431440 Gurtner W 1994 RINEX The Receiver Independent Exchange Format GPS World 5 7 4852 GurtnerW2001 RINEXTheReceiverIndependentExchangeFormatVersion210Available via Internet from IGS Gurtner W Beutler G Bauersima I Schildtknecht T 1985 Evaluation of GPS carrier difference observations the Bernese second generation software package Proc 1st Int Symp Precise Positioning with GPS Rockville Vol I 363372 Gurtner W Mader G Macarthur D 1989 A common exchange format for GPS data Proc 5th Int Geod Symp Satellite Positioning Las Cruces USA Vol 2 920931 Habrich H 2000 Geodetic Applications of the Global Navigation Satellite System GLONASS and of GLONASSGPS Combinations Mitt Bundesamt für Kartographie und Geodäsie Bd 15 Frankfurt a M Bibliography 551 Hahn J 1999 Aspekte der Uhrensynchronisation Zeithaltung und verteilung bei der Konzep tion zukünftiger SatellitenNavigationssysteme Forschungsbericht 199946 Deutsches Zen trum für Luft und Raumfahrt Oberpfaffenhofen Hamal K Prochazka I 1989 Prospect of laser ranging using a semitrain versus a single pulse In Veillet ed 1989 209214 Han S Rizos C 1997 Comparing GPS ambiguity Resolution Techniques GPS World 8 5 5461 Hankemeier P 1996 The DGPS Service for the FRG Concept and Status In Beutler Hein Melbourne Seeber eds 1996 7584 Hartl P Thiel KH Wu X Xia Y 1995 Earth Observation by Means of SAR Present State and Future Possibilities Photogrammetrische Woche Stuttgart 1995 127137 Hartmann G Leitinger R 1984 Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz Bull Geod 58 109136 Hatch R 1982a Its about time TRANSIT time Proc 3rd Int Geod Symp Sat Doppler Pos Las Cruces Vol 2 903915 Hatch R 1982b The synergism of GPS code and carrier measurements Proc 3rd Int Geod Symp on Doppler Positioning Las Cruces Vol 2 12131232 Hatch R 1991 Instantaneous ambiguity resolution In Schwarz Lachapelle eds 1991 299308 Hatch R Jung J Enge P Pervan B 2000 Civilian GPSThe Benefits ofThree Frequencies GPS Solutions 3 4 19 Hatch R Keegan R Stansell T A 1992 Kinematic receiver technology from Magnavox Magnavox Electronic Systems Company Torrance CA Hay C 2000 The GPS Accuracy Improvement Initiative GPS World 11 6 5661 Hay C Wong J 2000 Tropospheric Delay Prediction at the Master Control Station GPS World 11 6 5662 Heidland C 1994 Satellitenaltimetrie über Eis Ber Polarforsch 141 Bremerhaven Hein G 1983 Erdmessungen als Teil einer integrierten Geodäsie Begründung Stand und Entwicklungstendenzen ZfV 108 93104 Hein G 2000 From GPS and GLONASS via EGNOS to GALILEO Positioning and Navi gation in the Third Millennium GPS Solutions 3 4 3947 HeiskanenWA Moritz H 1967 Physical Geodesy WH Freeman San Francisco London Helmert F R 18801884 Die mathematischen und physikalischen Theorien der höheren Geodäsie Teubner Leipzig Reprint Minerva GmbH Frankfurt aM 1961 Helwig A Offerans G van Willigen D 1997 Eurofix DGPS Service Through the Sylt LoranC Transmitter Static and Dynamic Test Results Proc 26th Annual Convention and Technical Symposium International Loran Association Ottawa Henriksen S 1977 National Geodetic Satellite ProgramIntroduction In NGSP Washing ton Vol I 385 Herring T 1992 Modeling atmospheric delays in the analysis of space geodetic data In DeMunck Spoelstra eds 1992 157164 Hey J 1984 Das Radiouniversum Einführung in die Radioastronomie Weinheim 1974 The Radio Universe 3 ed Oxford Hieber S 1983 Satellite systems for geodesy and geodynamics CSTG Bull No 6 253261 552 Bibliography Hilla S 2002 Extending the Standard Product 3 SP3 Orbit Format IGS Network Data and Analysis Center Workshop Ottawa 2002 Hinze H 1990 Zum Einsatz von SatellitenPositionierungsverfahren für glaziologische Auf gaben in der Antarktis Wiss Arb Univ Hannover Nr 163 Hirt C 2001 Automatic Determination of Vertical Deflections in RealTime by Combining GPS and Digital Zenith Camera for Solving the GPSHeightProblem Proc ION GPS 2001 Salt Lake City Hocke K Tsuda T 2001 Using GPS Satellites to Study Plasma Irregularities GPS World 12 7 3436 HofmannWellenhof B Lichtenegger H Collins J 2001 Global Positioning System The ory and Practice 6th ed SpringerVerlag WienNew York HofmannWellenhof B Remondi B 1988 The antenna exchange one aspect of high precision GPS kinematic survey In Groten Strauß eds 261277 Berlin Hofton M Foulger G 1996 Postrifting unelastic deformation around the spreading plate boundary North Iceland JGR 101 2540325421 Hog E Fabricius C others 2000 Construction and Verification of the Tycho2 Catalogue Astron Astrophys 357 1 367386 Hopfield H 1969 Twoquartic tropospheric refractivity profile for correcting satellite data JGR 74 18 Hopfield H 1971 Tropospheric effect on electromagnetically measured range prediction from surface weather data Radio Science 6 3 357367 Hoyer M 1982 Satellitendopplermessungen als unterstützende Beobachtungen bei der Kon trolle und Verbesserung eines geodätischen Netzes in Venezuela Wiss Arb Univ Hannover Nr 111 Hoyer M Arciniegas S Pereira K Fagard H Maturana R Torchetti R Drewes H Kumar M Seeber G 1998 The definition and realization of the reference system in the SIRGAS project In Brunner ed 1998 168173 Hugentobler U 1998 Astrometry and Satellite Orbits Theoretical Considerations and Typ ical Applications Geod Geophys Arb Schweiz Vol 57 Hugentobler U Schaer S Fridez P 2001 Bernese GPS Software Version 42 University of Berne Switzerland Husson S 1999 SLR Global Performance Evaluation In Schlüter Schreiber Dassing 1999 Vol 2 645649 ICD 1993 Interface Control Document Navstar GPS Space SegmentNavigation User Inter faces ICDGPS200C ARINC Research Corporation Revision IRN200C004 12 April 2000 IERS 2001 International Earth Rotation Service Annual Report 2000 BKG Frankfurt IGS 1996 SINEX Solution Independent Exchange Format Version 100 International GPS Service IGS 2000 IGS Annual Report 2000 International GPS Service Central Bureau NASAJPL IGS 2002a Homepage of the Central Bureau in theWorldWideWeb Httpigscbjplnasagov IGS 2002b Towards Real Time Network Data and Analysis Center Workshop 2002 Pro ceedings Ottawa Canada IGS Website Ilk K 1990 Zukünftige Möglichkeiten der globalen hochauflösenden Schwerefeldbestim mung In Schneider ed 1990 213255 Bibliography 553 ILRS 2000 ILRS Annual Report International Laser Ranging Service ILRS 2001 Proceed 12th International Workshop on Laser Ranging Matera Italy 1317 November 2000 ILRS Website ILRS 2002 International Laser Ranging Service ILRS Website Jacobsen K 1992 Recent experiences in combined block adjustment with kinematic GPS data XVII Congress International Society for Photogrammetry and Remote Sensing IUSM Session on GPS Washington DC USA Jacobsen K 1997 Operational Block Adjustment without Control Points ASPRS Annual Convention Seattle 1997 Jacobsen K 2000 Potential and Limitation of Direct Sensor Orientation IntArchPhRS 33 ISPRS Amsterdam 2000 B3a 429435 Jäger R 1990 Optimum positions for GPS points and supporting fixpoints in geodetic networks In Bock Leppard eds 1990 254261 Jäger R Schneid S 2002 Passpunktfreie direkte Höhenbestimmung mittels DFHBF ein Konzept für Positionierungsdienste wie SAPOPS Proceed 4 SAPOS Symposium Hannover 149166 Jahn CH Seeber G Foulger G Einarsson P 1991 GPS epoch measurements across the MidAtlantic plate boundary in Northern Iceland 19871990 IUGG Symp U5 Application of Gravimetry and Space Techniques for Geodynamics and Ocean Dynamics Vienna Jahn CH Winter R 2002 SAPOSHEPS in Niedersachsen 4 SAPOS Symposium Han nover 2236 Janiczek P ed 1986 Global Positioning System Papers published in Navigation Wash ington DC Vol I 1980 Vol II 1984 Vol III 1986 Jayles J Berthias JP Laurichesse D 2000 DORISDIODE From SPOT4 to JASON1 Proceed DORIS days 2000 Jefferson D BarSever Y 2000 Accuracy and Consistency of Broadcast GPS Ephemeris Data Proceed ION GPS2000 391395 Jekeli C 2000 Calibrationvalidation methods for GRACE In Schwarz ed 2000 8388 Johannessen R 1997 Interference Sources and Symptoms GPS World 8 11 4548 Johnson N 1994 GLONASS Spacecraft GPS World 5 11 5158 de Jong K 2001 GPS and the Internet GEO Informatics JanuaryFebruary 1213 Joosten P Tiberius C 2000 Fixing the Ambiguities Are you Sure Theyre Right GPS World 11 5 4651 Kahmen H 1978 Elektronische Messverfahren in der Geodäsie 2 Aufl Wichmann Karl sruhe Kahmen H Feig W 1988 Surveying W de Gruyter BerlinNew York Kahn W Vonbun F Smith D Englar T Gibbs B 1980 Performance analysis of the spaceborne laser ranging system Bull Géod 54 2 165180 Kakkuri J 1995 Final Results of the Baltic Sea Level 1993 GPS Campain Rep Finnish Geod Inst 942 Kang Z 1998 Präzise Bahnbestimmung niedrigfliegender Satelliten mittels GPS und die Nutzung für die globale Schwerefeldmodellierung Scientific Technical Report STR9825 GeoForschungsZentrum Potsdam 554 Bibliography Kaniuth K Drewes H Stuber K Tremel H 2001 Bestimmung rezenter Krustendeforma tionen im zentralen Mittelmeer mit GPS ZfV 126 256262 Kaniuth K Kleuren D Tremel H 1998 Sensitivity of GPS Height Estimates to Tropo spheric Delay Modelling AVN 105 200207 Kaniuth K Stuber K 1999 Einfluss von AntennenRadomen auf die GPS Höhenbestimmung AVN 106 234238 Kaplan E 1996 Understanding GPS Principles and Applications Artech House Boston London Kaplan M 1976 Modern spacecraft dynamics control New York Karslioglu M 2000 Probleme der Mess und Regeltechnik bei der geodätischen Nutzung künstlicher Erdsatelliten Scientific Technical Report STR0006 GeoForschungsZentrum Potsdam Kaula W 1966 Theory of satellite geodesy Blaisdell Publ Comp London Keating T Taylor P Kahn W Lerch F 1986 Geopotential Research Mission science engineering and program summary NASA Technical Memorandum 86240 Kee C 1996 Wide Area Differential GPS In Parkinson Spilker eds 1996 Vol 2 Chap 3 81115 Kee C Parkinson B Axelrad P 1999 Wide Area Differential GPS Navigation Vol 38 No2 Keller W Heß D 1999 Gradiometrie mit GRACE ZfV 124 137144 205211 Khan M 1983 Satellite contributions to geophysical exploration at sea In Geyer R A ed CRC Handbook of Geophysical Exploration at Sea 368 Boca Raton Florida Kim D Langley R 1999 An optimized leastsquares technique for improving ambiguity resolution performance and computational efficiency Proceed ION GPS99 15791588 Kim D Langley R 2000 GPS Ambiguity Resolution andValidation methodologies Trends and Issues Int Symp GPSGNSS Seoul Korea Kim M 1997 Theory of satellite groundtrack crossovers J Geod 71 749767 King R Masters R Rizos C Stolz A 1987 Surveying with GPS University of New South Wales Australia 1985 Verlag F Dümmler Bonn 1987 KingHele D 1958 The effect of the Earths oblateness on the orbit of a near satellite Proceed Roy Soc SerA 247 4972 KingHele D Merson R H 1958 Use of artificial satellites to explore the Earths gravity field Results from Sputnik 2 Nature 182 640641 Kirchner G Koidl F Prochazka I Hamal K 1999 SPAD Time Walk Compensation and Return Energy Dependent Ranging In Schlüter Schreiber Dassing 1999Vol 2 521525 Klees R Koop R Visser P van den IJssel J 2000 Data analysis for the GOCE mission In Schwarz ed 2000 6874 Kleusberg A 1984 Diagnose und Therapie von Geodätischen Satellitennetzen vom Typ Doppler DGK C 293 München Kleusberg A 1990 A review of kinematic and static GPS surveying procedures Proceed GPS90 Ottawa 11021113 Kleusberg A 1995 Mathematics of attitude determination with GPS GPS World 6 9 7278 Bibliography 555 Kleusberg A 1998 Atmospheric Models from GPS In Teunissen Kleusberg 1998 Chap 15 599623 Klobuchar J 1987 Ionospheric timedelay algorithm for singlefrequency GPS users IEEE Transactions on Aerospace and Electronic Systems Vol AES23 No3 Klobuchar J 1991 Ionospheric Effects on GPS GPS World 2 4 4851 Klobuchar J 1996 Ionospheric Effects on GPS In Parkinson Spilker eds 1996 Vol 1 Chap 12 485515 Klokoˇcník 1982 A review of methods of comparison of resonant lumped coefficients Bull Astron Inst Czechl 33 89104 Klosko S 1999 SLR Contributions to Determining the Gravitational Field and itsVariations In Schlüter Schreiber Dassing 1999 Vol 1 2840 Klotz J Reinking D Angermann D 1996 Die Vermessung der Deformation der Erdober fläche Geowissenschaften 14 389394 Knudsen P Andersen O 1997 Improved Recovery of the Global Marine Gravity Field from the GEOSAT and the ERS1 Geodetic Mission Altimetry In Segawa Fujimoto Okubo eds 1997 429436 Koch K 1990 Parameter estimation and hypothesis testing in linear models Dümmler Bonn Kolb W 1999 Interferenzprobleme bei GPSSignalen DVW Schriftenreihe 35 161198 Kolenkiewicz R Martin C 1982 SEASAT altimeter height calibration JGR 87 C5 31893197 Komaki K Sasaki M Hashimoto H 1985 Plan for satellite geodesy in Japan CSTG Bull No 8 5863 München König R Chen Z Reigber C Schwintzer P 1999 Improvement in global gravity field recovery using GFZ1 satellite laser tracking data J Geod 73 398406 Kouba J 1983a A review of geodetic and geodynamic satellite Doppler positioning Review Geophys Space Phys 21 1 2740 Kouba J 1983b An efficient shortarc orbit computation Bull Géod 57 2 138145 Kouba J 1983c GEODOP VGeodetic Doppler Positioning Programs Version V Earth Physics Branch Ottawa Kovalevsky J 1971 Mécanique Céleste In Levallois JJ Géodésie Générale Tome IV 85268 Editions Eyrolles Paris Kovalevsky J 1990 Astrométrie moderne Lecture Notes in Physics 358 SpringerVerlag BerlinHeidelbergNew York Kovalevsky J 1995 Modern Astrometry SpringerVerlag BerlinHeidelbergNew York Kovalevsky J Lindegren L Perryman M 22 more authors 1997 The Hipparcos Catalogue as a realisation of the extragalactic reference system Astron Astrophys 323 620633 Kovalevsky J Mueller I Kolaczek B eds 1989 Reference frames in astronomy and geophysics Astrophysics and Space Science Library Vol 154 D Reidel Dor drechtBostonLondon Kozai Y 1959 On the effects of the sun and the moon upon the motion of a close Earth satellite SAO Special Report 22 Cambridge Mass Kozai Y 1966 Lunisolar perturbations with short periods SAO Special Report 235 Cam bridge Mass 556 Bibliography Krynski J 1983 Study on satellitetosatellite data processing In Schwarz Lachapelle eds Geodesy in Transition 313326 Calgary Kumar M Maul G eds 1991 Proc Int Symp on Marine Positioning INSMAP 90 University of Miami Oct 1519 1990 Marine Technology Society Washington DC USA Lachapelle G 1990 GPS in the marine environment status trends and prospects FIG XIX Int Congress Helsinki Comm4 108118 Lachapelle G 1991 GPS observables and error sources for kinematic positioning In Schwarz Lachapelle eds 1991 1726 Lachapelle G Hagglund J Falkenberg W Bellemare P Eaton M Casey M 1986 GPS land kinematic positioning experiments Proceed 4th Int Geod Symp on Satellite Positioning Austin Vol 2 13271344 Ladd J Counselmann C Gourewitsch S 1985 The Macrometer II DualBand Interfer ometric Surveyor Proc 1st Int Symp Precise Positioning with GPS Rockville Vol 1 175180 Ladd J Welshe R Brown A Sturza M 1986 MiniMac A new generation dualband surveyor Bull Géod 60 3 221228 Lambeck K Cazenave A Balmino G 1975 Solid earth and fluid tides from satellite orbit analysis In Proceed Int Symp Use ofArtificial Satellites for Geodesy and Geodynamics Athens 353393 Landau H 1988 Zur Nutzung des Global Positioning Systems in Geodäsie und Geodynamik Studiengang Vermessungswesen Schriftenreihe UniBw München 36 Landau H 1990 Precise GPS positioning with the multistationmultisession softwareTOPAS In GPS for Geodesy and Geodynamics Luxembourg 6168 Landau H Hagmeier D 1986 Analysis of the required force modeling for NAVSTAR GPS satellites Studiengang Vermessungswesen Schriftenreihe UniBw 19 193208 Langley R 1990 Why is the GPS signal so complex GPS World 1 3 5659 Langley R 1991a The GPS receiver an introduction GPS World 2 1 5053 Langley R 1991b Time Clocks and GPS GPS World 2 11 3842 Langley R 1997a GLONASS Review and Update GPS World 8 7 4651 Langley R 1997b GPS Receiver System Noise GPS World 8 6 4045 Langley R 1998a A Primer on GPS Antennas GPS World 9 7 5054 Langley R 1998b Propagation of the GPS Signals In Teunissen Kleusberg 1998 Chap 3 111149 Langley R 1998c RTK GPS GPS World 9 9 7076 Langley R 1999a The GPS EndofWeekRollover GPS World 9 11 4047 Langley R 1999b The Integrity of GPS GPS World 10 3 6063 Langley R 2000a GPS the Ionosphere and the Solar Maximum GPS World 11 7 4449 Langley R 2000b The Evolution of the GPS Receiver GPS World 11 4 5458 Le Pichon X Francheteau J Bonnin J 1973 PlateTectonics Development in Geotectonics Vol 6 AmsterdamLondonNew York Leberl F 1990 Radargrammetric Image Processing Artech House Norwood MA USA Lee J 1996 Untersuchung von Verfahren zur kombinierten Aerotriangulation mittels inte griertem GPSINS Wiss Arb Univ Hannover Nr 220 Bibliography 557 Lefebvre M Cazenave A Escudier P Biancale R Cretaux J Soudarin L Valette J 1995 Space Tracking System Improves Accuracy of Geodetic Measurements EOS 77 4 2529 Leick A 1995 GPS satellite surveying 2nd Edition John Wiley New York Lelgemann D 1979 Eine lineare Lösung der Hillschen kanonischen Gleichungen für die Bewegung eines Satelliten im Gravitationsfeld der Erde Astr Geod Arb 39 351359 München Lemoine F Smith D et al 1998 The development of the joint NASA GSFC and the National Imagery and Mapping Agency NIMA Geopotential Model EGM96 NASATP 1998206861 Goddard Space Flight Center Greenbelt Maryland Leppard N 1980 Satellite Doppler fixation and international boundaries Phil Trans Roy Soc London Ser A Vol 294 289298 LeProvost C 2001 Ocean Tides In Fu Cazenave eds 2001 Chap 6 267303 LeProvost C Lyard L Kolines J Genco M Rabilloud F 1998 A hydrodynamic ocean tide model improved by assimilating a satellite altimeter derived dataset JGR 103 C3 55135529 Lerch F Klosko S Laubscher R Wagner C 1979 Gravity model improvement using GEOS3 GEM9 and 10 JGR 84 B 8 38973916 Lerch F Klosko S Patel G 1983 A refined gravity model from LAGEOS GEML2 NASA Techn Mem 84986 Lerch F Wagner C Klosko S Belott R 1978 Goddard Earth Model development for oceanographic applications Proceed Marine Geodesy Symposium Miami Lerch F J 1992 Geopotential models of the Earth from satellite tracking altimeter and surface gravity observations GEMT3 and GEMT3S NASA Tech Mem 104555 Lewandowski W Azpubib J Klepszynski W 1999 GPS Primary Tool for Time Transfer Proc IEEE Vol 87 1 163172 Li K 1992 Empirische Untersuchungen zur GPSgestützten kombinierten Blockausglei chung Wiss Arb Univ Hannover Nr 175 Lichten S 1990 High accuracy Global Positioning System orbit determination Progress and prospects In Bock Leppard eds 1990 146164 Lichtenegger H HofmannWellenhof B 1990 GPSData preprocessing for cycle slip de tection In Bock Leppard eds 1990 5768 Liebsch G 1996 Aufbereitung und Nutzung von Pegelmessungen für geodätische und gody namische Zielstellungen Doctor Dissertation University Dresden Lillesand T Kiefer R 2000 Remote Sensing and Image Interpretation 4th Edition J Wiley Sons New York Logsdon T 1998 Orbital Mechanics Theory and Applications John Wiley Sons New York Lohmar F 1985 Zur Berechnung ionosphärischer Refraktionskorrekturen fürVLBIBeobach tungen aus simultanen Dopplermessungen nach Satelliten Mitt Geod Inst Univ Bonn Nr67 Lombardi M Nelson L Novick A Zhang V 2001 Time and Frequency Measurement Using the Global Positioning System GPS Int J of Metrology 8 2633 Lorrain P Corson D Lorrain F 1988 Electromagnetic fields and waves including electric circuits 3rd edition Freeman New York 558 Bibliography Lundquist CVeis G1966 Geodeticparametersfora1966SmithsonianInstitutionStandard Earth SAO SpecRep 200 Lutgens F Tarbuck E 1998 The atmosphere an introduction to meteorology 7 ed Prentice Hall Upper Saddle River NJ Ma C Arias E Eubanks T a 1998 The International Celestial Reference Frame based on VLBI Observations of Extragalactic Radio Sources Astron J 116 516546 Ma C Feissel M eds 1997 Definition and Realization of the International Celestial Reference System by VLBI Astrometry of Extragalactic Objects IERS Technical Note 23 Observatoire de Paris Paris Mac Arthur J Marth P Wall J 1987 The GEOSAT radar altimeter Johns Hopkins APL Technical Digest Laurel Md 8 2 176181 Mac Doran P 1979 Satellite emission radio interferometric earth surveying SERIESGPS geodetic system Bull Géod 53 117 Mac Doran P 1983 SERIESGPS codeless pseudoranging positioning technology CSTG Bull No5 4655 Mackie J 1985 The elements of astronomy for surveyors 9th edition Charles Griffin Company High Wycombe Mader G 1990 Ambiguity function techniques for GPS phase initialization and kinematic solutions In GPS90 Ottawa 12481256 Mader G 1999 GPS Antenna Calibration at the National Geodetic Survey GPS Solutions 3 1 5058 Mader G Czopek F 2002 The Block IIa Satellite Calibrating Antenna Phase Center GPS World 13 5 4046 Maenpa J Balodis M Sandholzer J Walter G 1997 New Interference Rejection technol ogy from Leica Proceed ION GPS97 Kansas City Malys S Slater J 1994 Maintenance and Enhancement of the World Geodetic System 1984 Proceed ION GPS94 Salt Lake City Utah 1724 Mangs G Mittal S Stansell T 2001 Worldwide Beacon DGPS Sea Technology May 2001 3945 Maniatis A Campbell J Müller A Schuh H Seeger H 1987 Zur Auswertung von geodätischen GPSBeobachtungen AVN 94 919 Maral G Bousquet P 1986 Satellite communication systems John Wiley Sons Chi chesterNew York Marini J 1972 Correction of satellite tracking data for an arbitrary atmospheric profile Radio Science 7 2 223231 Markovitz W 1954 Photographic determination of the moons position and applications to the measure of time rotation of the earth and geodesy Astron J 59 6973 Marks K DC M A Sandwell D 1991 GEOSAT GM data reveal new details of ocean floor EOS 72 14 145 MarquisW Krier C2000 ExaminationoftheGPSBlockIIRSolarPressureModel Proceed ION GPS2000 407416 Marsh J Lerch F 1985 Precision geodesy and geodynamics using STARLETTE laser ranging JGR 90 B11 93359345 Marsh J Lerch F et al 1990 The GEMT2 gravitational model JGR 95 B13 22 043 22 071 Bibliography 559 Marsh J Martin T 1982 The SEASAT altimeter mean sea surface model JGR 87 C5 32693280 Marsh J Vincent S 1975 Gravimetric geoid computations and comparisons with Skylab altimeter data in the GEOSC calibration area Gen Ass IUGG Grenoble Marsh J et al 1987 An improved model of the Earths gravitational field GEMT1 NASA Technical Memorandum 4019 Martin D Oh I 1979 Utilization of satellitetosatellite tracking data for determination of the geocentric gravitational constant GM JGR 84 B8 39443950 Massonet D 1997 RadarInterferometrie zur Messung der Erdkrustendynamik Spektrum der Wissenschaft H 9 5665 Massonet D et al 1993 The Displacement Field of the Landers Earthquake Mapped by Radar Interferometry Nature 364 138142 Maul G 1985 Introduction to satellite oceanography Martinus Nijhoff Publ Dordrecht Mayer M Lindner K Kutterer H Heck B 2000 Deformationsanalyse zur Aufdeckung von Punkt und Blockbewegungen im Bereich der Antarktischen Halbinsel In Dietrich ed 2000 127144 McCarthy D 2000 IERS Conventions 2000 IERS Technical Note International Earth Rotation Service McConathy D Kilgus C 1987 The Navy GEOSAT mission an overview Johns Hopkins APL Technical Digest 8 2 170175 Laurel Md McDonald K 1999 Opportunity Knocks Will GPS Modernization Open Doors GPS World 10 9 3646 Meehan T Srinivasan J Spitzmesser D Dunn C JY TEN J T MUNSON T DUNCAN C 1992 The TurboRogue receiver 6th Int Geod Symp Satellite Positioning Columbus Ohio USA Melbourne W Davis E Duncan C 6 more authors 1994a The applications of spaceborne GPS to atmospheric limb sounding and global change monitoring JPL Publication 9418 NASA Jet Propulsion Laboratory Pasadena Melbourne W Dixon T Thorton C 1985 GPSbased geodesy in Mexico and the Caribean CSTG Bull 8 182190 München Melbourne W Tapley B Davis E Yunck T 1994b The GPS flight experiment on TOPEXPoseidon Geophys Res Lett 21 7 Melbourne W et al 1983 Project Merit Standards US Naval Observatory Circular No167 Dec 27 Mendes V Langley R 1994 A Comprehensive Analysis of Mapping Functions Used in Modelling Tropospheric Propagation Delay in Space Geodetic Data Proceed KIS 94 8792 Mendes V Langley R 1999 Tropospheric Zenith Delay Prediction Accuracy for High Precision GPS Positioning and Navigation Navigation J of the Institute of Navigation 46 1 2534 Mendes V Prates G Pavlis E Pavlis D Langley R 2001 Improved Mapping Functions for Atmospheric Refraction Correction in SLR Geophys Res Lett Menge F Seeber G 2000 Untersuchungen und Beiträge zur Problematik der Phasenzen trumsvariationen von GPS Antennen In Dietrich ed 2000 181194 560 Bibliography Merrigan M Swift E Wong R Saffel J 2002 A Refinement to the World Geodetic System 1984 Reference Frame IONGPS 2002 Portland OR Sept 2002 Meyer U Charlot P Biancale R 2000 GINS A New MultiTechnique Software for VLBI Analysis In Vandenberg Baver eds 2000 324328 Milani A Nobili A Farinella P 1987 Nongravitational perturbations and satellite geodesy Adam Hilger Ltd Bristol Milliken R Zoller C 1980 Principles of NAVSTAR and system characteristics Navigation 25 2 1978 In Janiczek ed 1986 Vol 1 314 Minster J Jordan T 1978 Presentday plate motions JGR 83 B11 53315354 Misra P Enge P 2001 Global Positioning System Signals Measurement and Performance GangaJamuna Press Lincoln Massachusetts Misra P Pratt M Muchnik R Burke B Hall T 1996 GLONASS Performance Mesure ment Data Quality and System Upkeep Proceed ION GPS96 Kansas City 261270 Monka F 1984 Zur Aufbereitung und Auswertung von GEOS3 Satellitenradaraltimetermes sungen Wiss Arb Univ Hannover Nr134 Montag H 1984 Zur Untersuchung des Erdrotationsvektors mit Hilfe von Laserentfer nungsmessungen zu künstlichen Erdsatelliten Veröff Zentralinstitut Physik der Erde Nr 80 Berlin Montenbruck O Gill E 2000 Satellite Orbits Models Methods and Applications SpringerVerlag BerlinHeidelberg Moritz H 1970 Methoden zur Berechnung von Satellitentriangulationen AVN 77 353359 Moritz H 1990 The figure of the Earth Theoretical geodesy and the Earths interior H Wichmann Karlsruhe Moritz H 2000 Geodetic Reference System 1980 J Geod 74 128133 Moritz H Mueller I 1987 Earth Rotation Theory and Observation The Ungar Publ Comp New York Mueller I 1964 Introduction to satellite geodesy The Ungar Publ Comp New York Mueller I 1969 Spherical and practical astronomy as applied to geodesy The Ungar Publ Comp New York Mueller I 1975 Tracking station positioning from artificial satellite observations Geo physical Surveys 2 243276 Mueller I Wei Z 1985 MERIT Main Campaign Reference frame intercomparisons Geodetic and Geophysical Research Institute Hungarian Academy of Sciences Papers in Honour of Antal TarzyHornoch 85 110117 Sopron Mueller T 1994 Wide Area Differential GPS GPS World 5 6 3644 Muellerschoen R BarSever Y Bertiger W Stowers D 2001 NASAs Global DGPS for High Precision Users GPS World 12 1 1420 Muellerschoen R W B Lough M Stowers D Dong D 2000 An InternetBased Global Differential GPS System Initial Results ION National Technical Meeting Anaheim CA Jan 2000 Müller J 1991 Analyse von Lasermessungen zum Mond im Rahmen einer postNewtonschen Theorie DGK C 383 München Müller J 2001 Die Satellitengradiometriemission GOCE Theorie technische Realisierung und wissenschaftliche Bedeutung DGK C 541 München Bibliography 561 Nakiboglu S Krakiwski E Schwarz K Buffet B Wanless A 1985 A multistation multipass approach to Global Positioning System improvement and precise positioning GeodSurvCanada Ottawa Report 85003 NGS 1986 Geodetic Glossary National Geodetic Survey Rockville NGSP 1977 National Geodetic Satellite Program 2 Volumes Washington DC Niell A 1996 Global mapping functions for the atmospheric delay at radio wavelengths JGR 101 B2 32273246 Niemeier W 2002 Ausgleichungsrechnung W de Gruyter BerlinNew York Niemeier W Rennen M Salbach H 2000 Bestimmung regionaler und globaler Deforma tionen im Bereich der Antarktischen Halbinsel In Dietrich ed 2000 109126 NIMA 2000 Department of Defense World Geodetic System 1984 Technical Report TR83502 3ed National Imagery and Mapping Agency Washington DC USA NOAA 1997 The GEOSAT Altimeter JGM3 GDRs on CDROM NODC Laboratory for Satellite Altimetry Silver Spring MD 20910 USA Nordtvedt K 2001 Lunar Laser Ranging A Comprehensive Probe of the PostNewtonian Long Range Interaction In C Lämmerzahl C W F Francis and F W Hehl eds Lecture Notes in Physics 526 317329 Nothnagel A 2000 Der Einfluss des Wasserdampfes auf die modernen raumgestützten Messverfahren Mitt Bd 6 Bundesamt für Kartographie und Geodäsie Frankfurt Nothnagel A 2002 Third IVS Analysis Workshop IVS Newsletter Issue 2 April 2002 Noton M 1998 Spacecraft Navigation and Guidance SpringerVerlag BerlinHeidelberg New York OBrien D Prata A 1990 Navigation of ERS1 alongtrack scanning radiometer ATSR images ESA Journal 14 4 447466 OKeefe J 1958 Oblateness of the Earth by artificial satellites Harvard Coll Obs An nouncement Card 1408 Otsubo T Amagai J Kunimori H 1999 Measuring Asijais spin motion In Schlüter Schreiber Dassing 1999 Vol 2 674677 Parkinson B Enge P 1996 Differential GPS In Parkinson Spilker eds 1996 Vol 2 Chap 1 350 Parkinson B Spilker J eds 1996 Global Positioning System Theory and Applications American Institute of Aeronautics and Astronautics 2 volumes Washington DC Paunonen M 1999 The new satellite laser ranging system at Metsähovi In Schlüter Schreiber Dassing 1999 Vol 1 139144 Pavlis E Smith D Torrence M 1991 A global reference frame for geodynamics SL71 XX IUGG General Assembly Vienna Pearlman M et al 1983 Early experience of the SAO Satellite Tracking Program EOS 64 June 21 417 Pearlman M R 1977 National Geodetic Satellite Program Smithsonian Astrophysical Observatory Instrumentation In NGSP 1977 Vol2 797811 Pelzer H 1985 Grundlagen der mathematischen Statistik und der Ausgleichsrechnung In Pelzer H ed Geodätische Netze in Landes und Ingenieurvermessung II 3120 Konrad Wittwer Stuttgart 562 Bibliography Perryman M Pace O 2000 GAIA Unravelling the Origin and Evolution of Our Galaxy Esa bulletin 103 2635 Pierron F Nicolas J Kasser M Haase J 1999 Status and new capabilities of the French Transportable Laser Ranging System In Schlüter Schreiber Dassing 1999 Vol 1 104112 Pisacane V ed 1998 The Legacy of Transit Johns Hopkins APL Technical Digest Vol 19 No 1 Ploner M 1996 CCD Astrometrie von Objekten des geostationären Ringes Geow Mitt TU Wien H 46 Ploner M Jackson P 1999 Satellitenastrometrie mit CCD In Festschrift K Bretterbauer Geow Mitt TU Wien 50 2944 Pospelov S Botchkovki A 2000 GNSS Software Receivers GPS Solutions 4 1 4855 Powers E et al 2002 RealTime UltraPrecise Time Transfer to UTC Using the NASA Differntial GPS System IGS Workshop Towards Real Time Ottawa April 811 2002 Preuß E Campbell J 1992 Verylongbaseline interferometry in astro geo and gravita tional physics In Ehlers Schäfer eds Proc of Heraeus Seminar Recent Developments in Relativistic Gravity Research Bad Honnef 26 Sept 1991 Lecture Notes in Physics SpringerVerlag Berlin Priester W Hergenhahn G 1958 Bahnbestimmung von Erdsatelliten aus DopplerEffekt Messungen Wiss Arb AGF Nordrhein Westfalen Vol 82 Prochazka I Hamal K Blazej J 1999 Millimetre Ranging and Echo Signal Strength Monitoring with SPAD Detectors In Schlüter Schreiber Dassing 1999 Vol 2 452457 PTTI 2000 Proceedings of the Annual Precise Time and Time Interval PTTI Applications and Planning Meeting USNaval Observatory Washington DC published yearly Purivigraipong S Unwin M 2001 Determining the Attitude of a Minisatellite by GPS GPS World 13 6 6066 Quine B 1996 Spacecraft Guidance Systems Attitude Determination using Star Camera Data PhD Dissertation University of Oxford Rabe E 1962 Comparison of terrestrial and astronomical results for GM Proc 1st Int Symp Use of Artificial Satellites for Geodesy 383386 Washington DC Rapp R 1998 Past and future developments in geopotential modeling In Forsberg Feissel Dietrich eds 1998 5878 Rapp R Cazenave A Nerem R eds 1996 Global Gravity Field and Its Temporal Variations IAG Symp Proceed 116 SpringerVerlag BerlinHeidelbergNew York Raquet J Lachapelle G 2001 RTK Positioning with Multiple Reference Stations GPS World 12 4 4853 Reigber C 1981 Representation of orbital element variations and force function with respect to various reference systems Bull Géod 55 1 111131 Reigber C Balmino G Moynot B Mueller H 1983 The GRIM 3 Earth Gravity Field Model Man geod 8 93138 Reigber C Gendt G Dick G Tomassini M 2002 Near realtime water vapor monitoring for weather forcasts GPS World 13 1 1827 Reigber C Hartl P 1989 PRAREPRAREE system development status CSTG Bull 11 157164 München Bibliography 563 Reigber C Hartl P 1990 Das Satellitenbeobachtungssystem PRARE ZfV 115 512519 Reigber C Schwintzer P Hartl P Ilk K Rummel R M van Gelder E S Wakker K Ambrosius B Leemann H 1987 Study of a SatellitetoSatellite Tracking Gravity Mission ESTECContract No 655785NL PPSC München Reigber C Schwintzer P Lühr H 1999 The CHAMP geopotential mission Boll Geof Teor Appl 40 285289 Remondi B 1984 Using the Global Positioning System phase observable for relative geodesy Modelling processing and results PhD Dissertation University of Texas Austin Remondi B 1985 Performing centimeters accuracy relative surveys in seconds using GPS carrier phase Proc 1st Int Symp Precise Positioning with GPS RockvilleVol 2 789797 Remondi B 1986 Performing centimeterlevel surveys in seconds with GPS carrier phase Initial results Proc 4th Int Geodetic Symposium on Satellite Positioning Austin Vol 1 12291250 Remondi B 1990 Recent advances in pseudokinematic surveying In ION GPS90 106114 Remondi B 1991 NGS second Generation ASCII and Binary Orbit Formats and Associated Interpolated Studies Proc IUGG XXth GenAssembly Vienna August1991 Rémy F Legresy B Testut L 2001 Ice sheet and satellite altimetry Surveys in Geophysics 22 129 Renken H 1999 Ein Verfahren der bildverarbeitenden Erkennung von unbekannten Stern musternzurautonomenund3axialenLagebestimmungvonRaumflugkörpern ShakerVerlag Aachen Richardus P 1984 Project Surveying 2 Edition Balkema RotterdamBoston Riepl S 1998 Lasermessungen nach Erdsatelliten auf zwei Wellenlängen unter Verwendung einer StreakKamera DGK C 495 München Ries J 1997 Nongravitational force modeling effects on satellite orbits CSTG Bull 14 7380 München Ries J Eanes R Shum C Watkins M 1992 Progress in the determination of the gravi tational coefficient of the Earth Geophys Res Lett 19 6 529531 Ries J Tapley B 1999 Centimeter level orbit determination for the TOPEXPOSEIDON altimeter satellite Adv Astronautical Sci 102 583598 Rim H Schutz B 1999 Precision Orbit Determination POD Geoscience Laser Al timeter System GLASAlgorithm Theoretical Basis Document Center of Space Research University of Texas Austin Rinner K Killian K Meissl P 1969 Beiträge zur Theorie der geodätischen Netze im Raum DGK A 61 München Rinner K Seeber G Seeger H eds 1982 Die DeutschÖsterreichische Dopplerkam pagne DGK B 269 München Rizos C Stolz A 1985 Force modelling for GPS satellites orbits 1st Int Symp Precise Positioning with GPS Rockville Md Vol 1 8798 Robertson D Carter W 1985 Earth orientation determined from VLBI observations Pro ceed Int Conf Earth Rotation and Terrestrial Reference Frame Columbus Vol 1 296306 Robinson I 1995 Satellite Oceanography Wiley Chichester New York Rohlfs K Wilson T 1996 Tools of Radio Astronomy 3rd ed SpringerVerlag BerlinNew York 564 Bibliography Roßbach U 2001 Positioning and Navigation Using the Russian Satellite System GLONASS Studiengang Geodäsie und Geoinformation Schriftenreihe HsBw 70 München Roßbach U Habrich H Zarraoa N 1996 Transformation Parameters Between PZ90 and WGS 84 Proceed ION GPS90 Kansas City 279285 Rothacher M 1992 Orbits of Satellite Systems in Space Geodesy Geod Geophys Arb Schweiz Schweizerische Geodätische Kommission Zürich Vol 46 Rothacher M2000a ComparisonsofAbsoluteandRelativeAntennaPhaseCenterVariations GPS Solutions 4 4 Rothacher M 2000b Toward an Integrated Global Geodetic Observing System In Rummel Drewes Bosch Hornik 2000 4152 Rothacher M 2002 Combination of SpaceGeodetic Techniques Proceed IVS 2002 General Meeting 3343 Rothacher M Mervart L 1996 Bernese GPS Software Version 40 University of Berne Switzerland Rothacher M Schaer S Mervart L Beutler G 1995 Determination of Antenna Phase Center Variations Using GPS Data Proceed IGS Workshop May 1517 Potsdam Rothacher M Springer T Schaer S Beutler G 1998 Processing strategies for regional GPS networks In Brunner ed 1998 93100 Roy A 1978 Orbital Motion Adam Hilger Bristol RTCM 2001 RTCM Recommended Standards for Differential GNSS Global Navigation Satellite Systems Service Version 23 Radio Technical Commission for Marine Services 1800 Diagonal Road Suite 600 Alexandria VA 223142840 USA Rubicam D 1986 Lageos orbit decay due to infrared radiation from Earth EOS 67 16 Rummel R 1979 Determination of shortwavelength components of the gravity field from satellitetosatellitetrackingorsatellitegradiometryanattempttoanidenficationofproblem areas Man geod 4 107148 Rummel R 1985 Satellitengradiometrie ZfV 110 242257 Rummel R 1986 The Earths Gravity Field Proceed ESA Special Workshop on Solid Earth Science Application Mission for Europe SESAME ESA SP1080 6976 Rummel R Balmino G Johannessen J Visser P Woodworth P 2002 Dedicated gravity field missions principles and aims J of Geodynamics 33 320 Rummel R Drewes H Bosch W Hornik H 2000 Towards an Integrated Global Geodetic Observing System IGGOS IAG Symp Proceed 120 SpringerVerlag BerlinHeidelberg New York Rummel R Reigber C Ilk K 1978 The use of satellitetosatellite tracking for gravity parameter recovery Proc ESA Workshop on Space Oceanography Navigation and Geody namics SONG ESASP137 151161 Rummel R Sanso F 1993 Satellite altimetry in geodesy and oceanography Lecture notes in Earth sciences Vol 50 SpringerVerlag Berlin Rummel R Schrama E 1991 Two complementary systems onboard ARISTOTELES Gra dio and GPS ESA Journal 15 1 135139 Russel S Schaibly J 1980 Control segment and user performance Navigation 25 2 1978 In Janiczek ed 1986 Vol 1 7480 Rutscheid E 1972 Preliminary results of the SECOR Equatorial Network In Henriksen ed The Use of Artificial Satellites for Geodesy Washington DC Bibliography 565 Saastamoinen J 1973 Contributions to the theory of atmospheric refraction Bull Géod 107 1 1334 Samain E Fridelance P 1998 Time Transfer by Laser Link T2L2 experiment on Mir Metrologia 35 151159 Sandwell D Milbert D Douglas B 1986 Global nondynamic orbit improvement for altimetric satellites JGR 91 B9 94479451 Sansò F Rummel R eds 1989 Theory of satellite geodesy and gravity field determination Lecture Notes in Earth Sciences 25 SpringerVerlag BerlinNew York Santerre R 1991 Impact of GPS satellite sky distribution Man geod 16 1 2853 Sasaki M 1983 On a laser ranging system at Simosato Hydrographic Observatory CSTG Bull 5 8086 Schaer S Gurtner W Feltens J 1998 IONEX The IONosphere Map EXchnge Format Version I Proceed 1998 IGS Analysis Center Workshop Darmstadt 233247 Scharroo R Visser P 1998 Precise orbit determination and gravity field improvement for the ERS satellites JGR 103 81138127 Scheneweck M et al 1990 Status of CIGNET and orbit determination at the National Geodetic Survey In GPS90 179189 Schenke H 1984 Untersuchungen zur Genauigkeit von DopplerSatellitenbeobachtungen im Testnetz Westharz Wiss Arb Univ Hannover Nr 129 Schenke H 1991 Impact of GPS on the accuracy of bathymetric charts from multi beam sonar surveys In Kumar Maul eds 1991 147170 Schenke H Dijkstra S Niederjasper F Hinze H Hoppmann B Schöne T 1998 The New Bathymetric Charts of the Weddell Sea AWI BCWS AGU Antarctic Research Series Vol 75 371380 Schildknecht T 1994 Optical Astrometry of Fast Moving Objects Using CCD Detectors Geod Geophys Arb Schweiz Vol 49 Schildknecht T Dudle G 2000 Time and Frequency Transfer High Precision Using GPS Phase Measurements GPS World 11 2 4852 Schlüter W 2002 Die Aktivitäten der Fundamentalstation Wettzell DGK A 118 148151 München Schlüter W Hase H Böer A Riepl S Alarez J Cecioni A 2000 Progress of the TIGOproject CSTG Bull 16 7784 Schlüter W Hase H Boer A Riepl S Cecioni A 2002 TIGO starts its operations in Concepción in 2002 CSTG Bull 17 9293 München Schlüter W Pesec P 1982 Mathematisches Modell zur Auswertung von Dopplermessungen DGK B 260 3754 München Schlüter W Schreiber U Dassing R 1999 Proceedings 11th International Workshop on Laser Ranging Deggendorf Germany Sept 2025 1998 Mitt BKG Bd 10 1999 Schmid H 1974 Worldwide geometric satellite triangulation JGR 79 35 53495476 Schmid H 1977 National Geodetic Satellite ProgramNational Geodetic Survey In NGSP 1977 Vol 2 525644 Schmidt M MooreA 2002 Network Issues Position Paper IGS Network Data andAnalysis Center Workshop 2002 Ottawa Canada 566 Bibliography Schmitz M 1998 Untersuchungen zur strengen GPS Parametrisierung in der gemeinsamen Ausgleichung von kinematischem GPS und Aerotriangulation Wiss Arb Univ Hannover Nr225 Schneider M 1981 Himmelsmechanik BI Wissenschaftsverlag Mannheim Wien Zürich Schneider M 1988 Satellitengeodäsie MannheimWienZürich Schneider M 1993 Himmelsmechanik Bd 2 BI Wissenschaftsverlag Mannheim Wien Zürich Schneider M ed 1990 Satellitengeodäsie Ergebnisse aus dem gleichnamigen Sonder forschungsbereich VCH Verlagsgesellschaft Weinheim Schödlbauer A 2000 Geodätische Astronomie W de Gruyter BerlinNew York Schöne T 1997 The Gravity Field in the Weddell Sea Antarctica by Radar Altimetry from GEOSAT and ERS1 in German Ber Polarforsch 220 AWI Bremerhaven Schuh H 1987 Die Radiointerferometrie auf langen Basen zur Bestimmung von Punkt verschiebungen und Erdrotationsparametern DGK C 328 München Schuh H 2000 Contribution of VLBI to Space Geodesy In Rummel Drewes Bosch Hornik 2000 3340 Schuh H Charlot P Hase H 10 more authors 2002 IVS Working Group 2 for Product Specification and Observing Programs Final Report In IVS Annual Report 2001 ed by N R Vandenberg and K D Baver NASA 2002 Schüler T 2001 On GroundBased GPS Tropospheric Delay Estimation Studiengang Geodäsie und Geoinformation Schriftenreihe UniBw 73 München Schupler B 1994 Signal Characteristics of GPS User Antennas Navigation 41 3 Schupler B Clark T 2001 Characterizing the Behavior of Geodetic GPS Antennas GPS World 12 2 4855 Schutz B 1998 Spaceborne Laser Altimetry 2001 and beyond In Plag H P ed WEGENER98 Norwegian Mapping Authority Honefoss Norway Schuyer M 1997 European Capability and Prospects for a Spaceborne Gravimetric Mission In Lecture Notes in Earth Sciences Vol 65 569588 SpringerVerlag BerlinHeidelberg Schwarz K 1980 Inertial surveying systems experience and prognosis The Canadian Surveyor 34 Schwarz K 1983 Inertial surveying and geodesy Reviews of Geophysics and Space Physics 21 4 878890 Schwarz K 1991 Kinematic modellingprogress and problems In Schwarz Lachapelle eds 1991 1726 Schwarz K ed 2000 Geodesy Beyond 2000 The Challenges of the First Decade IAG Symp Proceed 121 SpringerVerlag BerlinHeidelbergNew York Schwarz K Glennie C Bruton A 1997 Improving accuracy and reliability of airborne gravimetry by multiple system configurations In Forsberg Feissel Dietrich eds 1998 1117 Schwarz K Lachapelle G eds 1991 Kinematic systems in geodesy surveying and remote sensing Papers from a Symp held in Bauff Canada Sept 1990 IAG Symp 107 New YorkBerlin Schwarz K Sideris M 1993 Heights and GPS GPS World 4 2 5056 Bibliography 567 Schwiderski H 1984 Combined hydrodynamical and empirical modeling of ocean tides In Seeber Apel eds Geodetic Features of the Ocean Surface and their Implications 215229 D Reidel Dordrecht Schwintzer P et al 1997 LongWavelength Global Gravity Models GRIM4S4 GRIM4C4 J Geod 71 189208 Schwintzer P et al 2000 A new global Earths gravity field model from satellite orbit perturbations GRIM5S1 Geophys Research Letters 27 36113614 Schwintzer P Kang Z Reigber C Zhu S 1995 GPS satellitetosatellite tracking for TOPEXPoseidon precise orbit determination and gravity field model improvement J Geo dynamics 20 2 155166 Schwintzer P Reigber C Biancale R Balmino G et al 1992 GRIM4 Globale Erd schwerefeldmodelle ZfV 117 227247 Seeber G 1972 Über das stochastische Verhalten von photographisch bestimmten Stern und Satelliten Koordinaten DGK C 178 München Seeber G 1979 Inertiale Vermessungssysteme und ihre Anwendungsmöglichkeiten in der Geodäsie ZfV 104 460471 Seeber G 1983 The current role of Transit Doppler measurements for precise marine posi tioning Proceed Symp Point Positioning in Marine Geodesy Maracaibo 119128 Seeber G 1989a Anwendungsmöglichkeiten von GPS in Geodäsie und Nachbargebieten Erfahrungen mit dem TI 4100 NAVSTAR Navigator Verm Phot Kulturtechnik 87 479489 Seeber G 1989b Satellitengeodäsie W de Gruyter BerlinNew York Seeber G 1993 Satellite Geodesy Foundations Methods and Applications W de Gruyter BerlinNew York Seeber G Böder V 1998 Precise RealTime Positioning in Hydrography with DGPS and INSDevelopments and Results Proceed 4th Int Symp Marine Positioning INSMAP 98 Melbourne Florida 265275 Seeber G Egge D 1981 Positionsbestimmung mit SatellitenDopplerverfahren in bewegter Situation ZfV 106 123131 Seeber G Egge D Schuchardt A Siebold J Wübbena G 1985 Experiences with the TI4100 NAVSTAR Navigator at the University of Hannover Proceed 1st Int Symp Precise Positioning with GPS Rockville Vol 1 215226 Seeber G et al 1987 Status Report on DÖNAV Symp Impact of Global Positioning System on Geophysics IUGG Gen Assembly Vancouver Seeber G Hinze H 1984 Bestimmung von Gletscherbewegungen mit DopplerSatelli tenmessungen in derAntaktis In SchödlbauerWelsch eds SatellitenDopplermessungen Studiengang Vermessungswesen Schriftenreihe HSBw Nr 16 München Seeber G Menge FVölksen CWübbena G Schmitz M1997a PreciseGPSPositioning Improvements by Reducing Antenna and Site Dependent Effects In Brunner ed 1998 237244 Seeber G Seeger H 1984 SatellitenDopplermessungen im Deutschen Hauptdreiecks netz In Schödlbauer Welsch eds SatellitenDopplermessungen Studiengang Vermes sungswesen Schriftenreihe HSBw Nr 16 München Seeber G Torge W Denker H Goldan HJ 1997b Präzise Höhenbestimmung des Helgoländer Pegels Die Küste 59 3961 568 Bibliography Seeber G Wübbena G 1989 Kinematic positioning with carrier phases and on the way ambiguity solution Proceed 5th Int Geod Symp on Satellite Positioning Las Cruces Vol 2 606609 Seeger H 1984 Zur Geoidbestimmung im Alpenraum mit Hilfe von DopplerSatellitenmes sungen im NNSS ALGEDOP In Schödlbauer Welsch eds SatellitenDopplermes sungen Studiengang Vermessungswesen Schriftenreihe HSBw Nr 15 249266 Seemüller W Drewes H 2000 Annual Report 1999 of RNAAC SIRGAS 1999 Technical Reports IGS Central Bureau Segawa J Fujimoto H Okubo S eds 1997 Gravity Geoid and Marine Geodesy IAG Symp Proceed 117 SpringerVerlag BerlinHeidelbergNew York Seidelmann P ed 1992 Explanatory Supplement to the Astronomical Almanac US Naval Observatory Washington DC Seidelmann P Fukushima T 1992 Why new time scales AstronAstrophys 265 833838 Seidelmann P Guinot B Doggelt L 1992 Time In Seidelmann ed 1992 Chap 2 3994 Seidelmann P Johnston K et al 1998 Fizeau Astrometric Mapping Explorer FAME Satellite AAS 98154 763782 Shapiro I 1978 Principles of VeryLongBaseline Interferometry Proceed 9th GEOP Conf OSU Rep 280 2933 Shelus P Veillet C Dickey J 1996 Recent Developments in Lunar Laser Ranging CSTG Bull 12 4752 Munich Shum C Yuan D Ries J Smith J Schutz B Tapley B 1990 Precision orbit determi nation for the GEOSAT Exact Repeat Mission JGR 95 C3 28872898 Sidi M 1997 Spacecraft Dynamics and Control CambridgeAerospace Series 7 Cambridge University Press Sigl R 1984 The contribution of satellite geodesy to the geosciences Geo Journal 8 341362 Sinclair A 1999 Data Screening and Normal Point Formation International Laser Ranging Service Sinnott R 2001 The Best Star Catalogue Ever Sky Telescope July 2001 2223 Sjöberg L 1999 An efficient iterative solution to transform rectangular geocentric coordi nates to geodetic coordinates ZfV 124 295297 Sjögren D Gottlieb P Muller P Wollenhaupt W 1972 Lunar gravity via Apollo 14 Doppler radio tracking Science 175 165168 Slater J Malys S 1997 WGS 84 Past Present and Future In Brunner ed 1998 17 Slater J Noll C Gowey K eds 1999 International GLONASS Experiment IGEX98 Proceed IGEX98 Workshop IGS Central Bureau Smart W 1977 Textbook on Spherical Astronomy 6th ed University Press Cambridge Smith D et al 1985 A global geodetic reference frame from LAGEOS ranging SL51AP JGR 90 92219233 Smith D Kolenkiewicz R Dunn P Torrence M 2000 Earth scale below a part per billion from Satellite Laser Ranging In Schwarz ed 2000 312 Smith D Milbert D 1999 The GEOID96 highresolution geoid height model for the United States J Geod 73 219236 Bibliography 569 Snay R 2000 The National and Cooperative CORS System in 2000 and Beyond Proceed ION GPS2000 5558 Sneeuw N Doborantu R Gerlach C Müller J Oberndorfer H Rummel R 5 more authors 2001 Simulation of the GOCE gravity field mission In Proceed IV Hotine MarussiSymposiumonMathematicalGeodesy IAGSympVol122 1432 SpringerVerlag BerlinHeidelbergNew York Sneeuw N Ilk K 1997 The status of spaceborne gravity field mission conceps a compar ative simulation study In Segawa Fujimoto Okubo eds 1997 171178 Soddu C Razumovsky O 2001 GPS Augmentation Inmarsats New Navigation Payload GPS World 12 11 2432 Soffel M Müller J 1997 Lasermessungen der Monddistanz Sterne und Weltraum 36 646651 Soop E 1983 Introduction to geostationary orbits ESA SP1053 Sovers O Fanselow J CSJacobs 1998 Astrometry and geodesy with radio interferometry experiments models results Reviews of Modern Physics 70 4 13931454 Spilker J 1980 GPS signal structure and performance characteristicas Navigation USA 25 1978 In Janiczek ed 1986 Vol 1 2954 Spilker J 1996a Foliage Attenuation for Land Mobile Users In Parkinson Spilker eds 1996 Vol 1 Chap 15 569583 Spilker J 1996b GPS Signal Structure and Theoretical Performance In Parkinson Spilker eds 1996 Vol 1 Chap 3 57119 Spilker J 1996c Satellite Constellation and Geometric Dilution of Precision In Parkinson Spilker eds 1996 Vol 1 Chap 5 177208 Spilker J 1996d Tropospheric Effects on GPS In Parkinson Spilker eds 1996 Vol 1 Chap 13 517546 Stanley H 1979 The Geos3 project JGR 84 B8 37793783 Stansell T 1979 The MX 1502 Satellite Surveyor 2nd Int Geod Symp on Satellite Doppler Positioning Austin Vol 1 497534 Stewart M Tsakari M 1998 GLONASS Broadcast Orbit Computation GPS Solutions 2 1627 Stolz A 1979 Precise modeling aspects of lunar measurements and their use for the im provement of geodetic parameters DGK A 90 München Strang G Borre K 1997 Linear Algebra Geodesy and GPS WellesleyCambridge Press Stumpff K 195919651974 Himmelsmechnik IIII 3 Vol VEB Deutscher Verlag der Wissenschaften Berlin Swift E 1985 NSWCs GPS OrbitClock determination system Proceed 1st Int Symp on Precise Positioning with the GPS System Rockville Vol 1 5962 Taff L 1985 Celestial Mechanics a computational guide for the practitioner John Wiley Sons New York Tapley B Kim M 2001 Applications to Geodesy In Fu Cazenave eds 2001 Chap 10 371406 Tapley B Watkins M Ries J et al 1996 The Joint Gravity Model 3 JGR 101 B12 28 02928 049 Tavernier G Larson K Noll C Ries J Soudarin L Willis P 2000 Current status of the DORIS pilot experiment Proceed DORIS days 2000 570 Bibliography Tetewsky A Mullen F 1997 Carrier Phase Wrapup Induced by Rotating GPS Antennas GPS World 8 2 5157 Teunissen P 1998 GPS Carrier Phase Ambiguity Fixing In Teunissen Kleusberg 1998 Chap 8 319388 Teunissen P de Jonge P Tiberius C 1995 A New Way to Fix Carrier Phase Ambiguities GPS World 6 4 5861 Teunissen P J G Kleusberg A 1998 GPS for Geodesy Second Edition SpringerVerlag BerlinHeidelbergNew York Torge W 1980 Geodätisches Datum und Datumstransformation In Pelzer ed Geodätis che Netze in Ingenieur und Landesvermessung 113130 K Wittwer Stuttgart Torge W 1989 Gravimetry W de Gruyter BerlinNew York Torge W 1991 Geodesy 2nd ed W de Gruyter BerlinNew York Torge W 2001 Geodesy 3rd ed W de Gruyter BerlinNew York Torge W 2003 Geodäsie 2nd ed W de Gruyter BerlinNew York Torrence M 1999 Realization of the EGM96 Reference Frame In Schlüter Schreiber Dassing 1999 Vol 2 777785 Touboul P Willemenot E Josselin B F V 1998 Accelerometers for CHAMP GRACE and GOCE space missions synergy and evolution Boll Geof Teor Appl 40 321327 Trimmer R Manning D 1996 The altimetry derived gravity anomalies to be used in com puting the DMANASA Earth gravity model In Rapp Cazenave Nerem eds 1996 7181 Tscherning C Rapp R Goad C 1983 A Comparison of Methods for Computing Gravimet ric Quantities from High Degree Spherical Harmonic Expansions Man geod 8 249272 Tsui J BY 2000 Fundamentals of Global Positioning System Receivers a Software Ap proach John Wiley Sons Tucker A 1998 Computerized Ionospheric Tomography Johns Hopkins APL Technical Digest Vol 19 No 1 6671 Turcotte D Schubert G 2002 Geodynamics 2nd ed Cambridge University Press Cam bridge UK Väisälä Y 1946 An astronomical method of triangulation Sitz Finn Akad Wiss 99107 Van Dierendonck A 1995 Understanding GPS Receiver Terminology A Tutorial GPS World 6 1 3444 Van Dierendonck A Hegarty C 2000 The New L5 Civil GPS Signal GPS World 11 9 6471 Van Dierendonck A Russel S Kopitzke E Birnbaum M 1980 The GPS Navigation Message Navigation 25 2 1979 also in Janiczek ed 1986 Vol 1 5573 Van Diggelen F 1998 GPS Accuracy Lies Damn Lies and Statistics GPS World 9 1 4148 Van Melle M 1990 Cesium and rubidium standards and performance on the GPS program In ION GPS90 123130 Vandenberg N Baver K eds 2000 International VLBI Service 2000 General Meeting Proceedings NASACP2000209893 Vandenberg N Baver K eds 2002 International VLBI Service for geodesy and astrometry 2001 Annual Report NASATP2002210001 Bibliography 571 Vaníˇcek P Krakiwsky E 1986 Geodesy The Concepts 2 rev ed Elsevier Science Publ AmsterdamNew York de Vegt C 1999 The New Astronomical Reference Frame Mitt Bundesamt Kart Geod 5 6569 Frankfurt a M Veillet C ed 1989 Seventh International Workshop on Laser Ranging Instrumentation Matera Italy 28 Oct 1989 OCACERGA Av CopernicF06130 Grasse Vinti J 1998 Orbital and Celestial Mechanics Edited by G J Der and N L Bonavito American Institute of Aeronautics and Astronautics Reston Virginia Visser P Wakker KAmbrosius B 1994 Global gravity field recovery from the ARISTOTE LES satellite mission JGR 99 B2 28412851 Völksen C 2000 Die Nutzung von GPS für die Deformationsanalyse in regionalen Netzen am Beispiel Islands Wiss Arb Univ Hannover No237 Völksen C Seeber G 1998 Nachweis von rezenten Krustendeformationen in Nordisland mit GPS ZfV 123 6875 Vollath U Birnbach S Landau H FraileOrdonez J MartinNeira M 1999 Analysis of threecarrier ambiguity resolutiontechnique for precise relative positioning in GNSS2 Navigation 46 1 1324 Vollath U Buecherl A Landau H Pagels C Wagner B 2000 MultiBase RTK Posiiton ing Using Virtual Reference Stations Proceed ION GPS2000 123131 Vonbun F 1977a Goddard laser systems and their accuracies Phil Trans Roy Soc London A 284 443450 Vonbun F 1977b Probing the Earths gravity field by means of satellitetosatellite tracking Phil Trans Roy Soc London A 284 475483 Vyskocil P Reigber C Cross P eds 1990 Global and Regional Geodynamics IAG Symp No101 Edinburgh 1989 SpringerVerlag New YorkBerlin Wahr J 1981 The forced nutation of an elliptical rotating elastic and oceanless Earth Geophys J R Astr Soc 64 705727 Wakker K Ambrosius B Zandbergen R Geldrop G V 1987 Precise orbit computation gravity model adjustment and altimeter data processing for the ERS1 altimetry mission ESA Report Delft Walker R 2000 Astronomical VLBI Comparison and Contrast with GeodeticAstrometric VLBI In Vandenberg Baver eds 2000 4251 Walker R Kubik K 1996 Numerical Modelling of GPS Signal Propagation Proceed ION GPS96 709717 Walter H Sovers J 2000 Astrometry of Fundamental Catalogues SpringerVerlag Berlin HeidelbergNew York Wanninger L 1992 Monitoring total electron content and ionospheric irregularities with GPS In DeMunck Spoelstra eds 1992 141146 Wanninger L 1994 Der Einfluss der Ionosphäre auf die Positionierung mit GPS Wiss Arb Univ Hannover Nr 201 Wanninger L 1998 Realtime Differential GPS Error Modelling in Regional Reference Sta tion Networks In Brunner ed 1998 8692 Wanninger L 2000 Präzise Positionierung in regionalen GPSReferenznetzen DGK C 508 München 572 Bibliography Wanninger L Jahn CH 1991 Effects of severe ionospheric conditions on GPS data pro cessing IAG Symp G2 Permanent Satellite Tracking Networks for Geodesy and Geody namics IUGG General Assembly Vienna Watkins M Eanes R Tapley B Schutz B 1990 Station positions and plate motion from LAGEOS long arc LLA8903 In Vyskocil Reigber Cross eds 1990 110 Webb F Zumberge J 1993 An Introduction to GIPSYOASISII Jet Propulsion Laboratory Pasadena USA Webb J Penney R 1981 Six years of inertial surveying at the Geodetic Survey in Canada Proc 2nd Int Symp of Inertial Technology for Surveying and Geodesy 325342 Banff Weber G 2002 DGPSRTKDienste über Internet Proceed 4 SAPOS Symposium Han nover 2002 5461 Weber L Tiwari A 1995 DGPS Architecture Based on Separating Error Components Virtual Reference Stations and FM Subcarrier Broadcast Proceed 51st Annual Meeting of ION Colorado Springs 191200 Webster I Kleusberg A 1992 Regional modelling of the ionosphere for single frequency users of the Global Positioning System Proceed 6th Int Symp Satellite Positioning Colum bus Ohio Vol 1 230239 Weill L 1997 Conquering Multipath The GPS Accuracy Battle GPS World 8 4 5966 Wells D 1974 Doppler Satellite Control UNB TechnRep 29 Fredericton NB Canada Wells D ed 1986 Guide to GPS Positioning Fredericton NB Canada Wenzel H 1985 Hochauflösende Kugelfunktionsmodelle für das Gravitationspotential der Erde Wiss Arb Univ Hannover Nr 137 Wenzel H 1999 Schwerefeldmodellierung durch ultrahochauflösende Kugelfunktionsmod elle ZfV 124 144154 Westrop J Napier M Ashkenazi V 1990 The use of phase for kinematic positioning by GPS In Bock Leppard eds 1990 334339 White L 1980 Spheroidal and Cartesian Coordinates Survey Review 285286 Wickert J Reigber C Beyerle G 8 more authors 2001 Atmospheric sounding by GPS radio occultation First results from CHAMP Geophys Res Lett Wild U 1994 Ionospheric and Geodetic Satellite Systems Permanent GPS Tracking Data for Modelling and Monitoring Geod Geophys Arb Schweiz Schweizerische Geodätische Kommission Zürich Vol 48 Wilkins G Mueller I 1986 On the rotation of the Earth and the terrestrial reference system Bull Géod 60 85100 Willgalis S Seeber G Krueger C Romao V 2002 A Real Time GPS Reference Network for Recife Brazil Enabling Pricise and Reliable Cadastral Surveys FIG XXII International Congress Washington DC Williams J Newhall X Dickey J 1987 GM Earth from Lunar Laser Ranging LLR EOS 68 16 281 Williamson R Marsh J 1985 Starlette Geodynamics The Earths tidal response JGR 90 B11 93469352 Wilson P Michel G eds 1998 The Geodynamics of S and SE Asia GEODYSSEA Project Scientific Technical Report STR 9814 GeoForschungsZentrum Potsdam 1998 Wohlleben R Mattes H Krichbaum T 1991 Interferometry in radioastrometry and radar techniques Kluwer Academic Publishers Dordrecht Bibliography 573 Wolf H 1967 Computation of satellite triangulation by spatial fitting of the orbit DGK B 153 München Wolf H 1970 Short Arc Methode und räumliche Bahnglättung in der Satellitentriangulation ZfV 94 3741 Wolf H 1975 Ausgleichungsrechnung Formeln zur praktischen Anwendung Dümmler Bonn Wolf H 1984 SatellitenDopplermessungen in der Berechnung des Europäischen Dreieck snetzes RETrig In Schödlbauer Welsch ed SatellitenDopplermessungen Studiengang Vermessungswesen Schriftenreihe HSBw Nr 15 221230 Wolf H 1985 Fortschritte der Geodäsie Satelliten und terrestrische Methoden mit ihren Möglichkeiten Vorträge RheinWestf Akad Wiss Nr338 Opladen Wood R 1999 Improving Orbit Predictions In Schlüter Schreiber Dassing 1999 Vol 2 615620 Wübbena G 1985 Model and program developments for cmpositioning with GPS Proceed FIG Joint Meeting Inertial Doppler and GPS Measurements for National and Engineering Surveys 553565 München Wübbena G 1988 GPS carrier phase and clock modeling In Groten Strauss eds 1988 381392 Wübbena G 1989 The GPS adjustment software package GEONAP Concepts and models Proceed 5th Int Geod Symp Satellite Positioning Las Cruces Vol 1 452461 Wübbena G 1991 Zur Modellierung von GPS Beobachtungen für die hochgenaue Positions bestimmung Wiss Arb Univ Hannover Nr 168 Wübbena G 2002 Zu großräumigen Vernetzung von GNSS Referenzstationen Proceed 4 SAPOS Symposium Hannover 2002 139148 Wübbena G Bagge A Boettcher G Schmitz M Andree P 2001a Permanent Object Monitoring with GPS with 1 Millimeter Accuracy Proceed ION GPS2001 Salt Lake City Wübbena G Bagge A Schmitz M 2001b RTK Networks based on Geo GNSMART Concepts Implementation Results Proc ION GPS2001 Salt Lake City Wübbena G Bagge A Seeber G Böder V Hankemeier P 1996 Reducing Distance De pendent errors for RealTime Precise DGPSApplications by Establishing Reference Station Networks Proceed ION GPS1996 18451852 Wübbena G Menge F Schmitz M Seeber G Völksen C 1997 A New Approach for Field Calibation of Absolute Antenna Phase Center Variations Journal Navigation Vol 44 2 247255 Wübbena G Schmitz M Menge F Böder V Seeber G 2000 Automated Absolute Field Calibration of GPS Antennas in RealTime Proceed ION GPS2000 25142522 Wübbena G Willgalis S 2001 State Space Approach for Precise Real Time Positioning in GPS Reference Networks Proceed KIS 2001 Banff Canada Wunsch C Stammer D 1997 Atmospheric loading and the oceanic inverted barometer effect Rev Geophys 35 79107 Young C Neilan R Bletzacker F 1985 GPS satellite multipath An experimental investi gation Proceed 1st Int Symp Precise Positioning with GPS Rockville 423432 Yunck T 1996 Orbit Determination In Parkinson Spilker eds 1996 Vol 2 Chap 21 559592 574 Bibliography Yunck T Melbourne W 1990 Geoscience from GPS tracking by Earth satellite In Bock Leppard eds 1990 351369 Zacharias N Urban S Zacharias M Hall D Wycoff G Rafferty T Germain M Holdenried E JPohlmann Gauss F Monet D Winter L 2000 The First United States Naval Observatory CCD Astrograph Catalog The Astronomical Journal Vol 120 Zahran K2000 AccuracyAssesmentofOceanTideLoadingComputationsforpreciseGeode tic Observations Wiss Arb Univ Hannover Nr 238 Zhang S 2000 Interpolation of GeoidalQuasigeoidal Surfaces for Height Determination with GPS Wiss Arb Univ Hannover Nr 236 Ziebart M Cross PAdhya S 2002 Modeling Photon Pressure The Key to HighPrecision GPS Satellite Orbits GPS World 13 1 4350 Zielinski J 1989 GPS baseline error caused by the orbit uncertainty Man geod 14 117124 Zwally H Brenner A 2001 Ice Sheet Dynamics and Mass Balance In Fu Cazenave eds 2001 Chap 9 351369 Index Aberration 193 486 correction Doppler 198 Accelerometer 147 153 154 477 Accuracy Improvement Initiative 233 306 Accuracy measures GPS 302 Acoustic surveying 526 Active reference stations 361 Active satellites 148 AdamMoulton orbit integration 119 ADOS Doppler network 205 Aircraft detector laser ranging 414 Albedo 104 105 Allan variance 40 Almanac 228 346 Altimeter bias 457 calibration 457 Ambiguity 142 254 Ambiguity resolution 269 ambiguity function 271 antenna swapping 276 cascade technique 275 codecarrier combination 271 extra wide lane 264 316 FARA 273 fixed solution 270 float solution 270 276 geometric method 269 LAMBDA 273 on the fly 272 337 search methods 273 success rate 276 291 time to fix TTFA 291 validation 276 Analytical orbit integration 84 Anechoic chamber 321 Anomaly eccentric 73 mean 73 80 true 64 73 Antarctic plate motion 363 Antenna Dorne Margolin 321 calibration 321 choke ring 321 phase center variation 196 320 reference point 321 satellite 323 swapping 276 ANTEX antenna PCV format 322 Anti Spoofing AS 229 APKIM plate model 529 Apocenter 64 APOLLOSOYUZ 477 Apparent forces 106 Area correction parameters 343 Argument of latitude 71 Argument of perigee 71 ARISTOTELES 472 ASIC 237 Atmospheric drag 102 190 194 478 Atomic time 31 Attenuation factor 516 Attitude control 107 153 177 with GPS 377 Augmentation systems 392 Autonav capability GPS 215 Azimuth determination with GPS 373 BakerNunn Camera 158 163 Balloon satellites 162 Bandwidth 221 234 synthesis technique VLBI 488 Baseline concept GPS 266 283 352 error GPS 304 trivial 284 Baseline constellation GPS 216 BC4 Ballistic Camera 163 World Network 3 140 170 507 Beat frequency 184 Bending correction 59 Bias parameter 137 265 576 Index BIH Terrestrial System BTS 531 Binary phase shift keying 221 234 BIPM Bureau International des Poids et Mesures 35 Blinds mobility with GPS 372 BMK Ballistic Camera 163 Boundary value problem 483 Broadcast ephemerides accuracy 306 clock message 306 GPS 218 222 304 TRANSIT 121 188 194 Bruns 3 Bureau International de lHeure BIH 16 35 206 529 CBand Radar 160 CAcode 216 219 Cadastral surveying with GPS 368 Cage of Bruns 3 CanadaWide Differential GPS 333 340 Canadian Active Control System 333 Base Network 333 Canonical orbital elements 82 Capacitive gradiometer 482 Car driven survey system 370 Carrier phase correction 337 Carrier phase observable GPS 253 Carrier smoothed DGPS 327 Carrier smoothed pseudo ranges 249 Cavendish 480 CCD astrometry 174 camera 173 technology 172 Celestial Ephemeris Origin CEO 21 Celestial Ephemeris Pole CEP 21 494 Celestial Intermediate Pole CIP 21 Celestial pole offset 21 494 Cellular radio GPS data link 331 Centerofmass correction 420 Centrifugal force 106 Cesium standard 35 CHAMP mission 476 Chapman profile 49 Chebyshev polynomials 122 Chipset 237 Choke ring antenna 236 CIGNET 190 CIRA reference atmosphere 103 Circular error probable CEP 303 Civil signal GPS 215 Clock 39 synchronization 306 atomic 39 cesium standard 35 41 215 defining equation 44 GPS receiver 307 hydrogen maser 41 ideal 39 quartz crystal 40 191 relativistic effects 300 rubidium standard 41 215 synchronization 381 Code aided squaring 242 Code division multiple access 219 Codeless signal processing 240 499 Collocation sites 534 Commonview technique time transfer 381 Computer algebra 115 Confidence ellipse 302 Conic section 76 78 Constant of gravitation G 67 Constants of motion 77 Continuously Operating Reference Sta tion 247 333 Control segment GPS 217 298 Control survey with GPS 357 CONUS 339 Conventional Inertial System CIS 13 International Origin CIO 16 Terrestrial Pole CTP 16 Terrestrial System CTS 15 Cooperating reference station 339 Coordinate system see Reference system Coordinate time 38 Coordinates absolute 508 Cartesian 10 Index 577 ellipsoidal 23 geographic 23 relative 507 CORE VLBI network 496 Coriolis force 106 Corner cube reflector 406 Correlator VLBI 486 Cosmic geodesy 5 Costas loop 239 COTES 511 530 Cowell 116 Critical inclination 89 95 Cross correlation 242 Crosslink capability GPS 215 Crossover technique 442 460 Crustal deformation 362 431 490 505 527 Cycle slip 277 DÖDOC Doppler network 205 DÖNAV GPS network 361 Dam control with GPS 374 Data frame GPS 228 Data transmission GPS 331 Datum defect 507 geodetic 25 shift parameters 27 transformation 27 Day mean solar 33 of the Year DOY 35 sidereal 33 Decibel 234 Dedicated laser satellites 411 Deflection of the vertical 26 Deformation analysis 375 Delay lock loop 239 Delay VLBI 486 Department of Defense DoD 229 Department of Transportation DOT 229 DHDN Deutsches Hauptdreiecksnetz 361 Differential GPS 325 351 375 Differential radar interferometry 505 Differential refraction 166 Diffraction GPS signals 319 Digital Elevation Model DEM 503 Digital image 172 Dilution of precision 300 DIODE Orbit Determination System 209 454 Direct motion satellite 81 DISCOS 148 152 188 194 478 Dispersion 45 Distance dependent errors 341 Disturbing potential 85 94 DIVA astrometric mission 180 Doppler beacon 208 Christian Doppler 181 count integrated 184 191 253 curve 181 DORIS 207 effect 143 181 equation 183 error budget 193 log 181 marine application 525 method 143 observation equation 199 receivers 190 192 sonar 198 DORIS 144 207 448 454 456 beacon network 208 days 210 International Service IDS 210 ionospheric correction 196 Pilot Experiment 210 satellites with DORIS payload 208 system components 207 Dorne Margolin antenna 321 DOSE NASA program 493 529 Drag see Atmospheric drag Drag free system 152 DREF 358 Dual rate moon camera 5 Dynamical time 31 37 Eötvös 480 tensor 480 unit 481 Earth Gravitational Model 1996 EGM96 29 578 Index Earth model 6 158 519 from SLR 428 pearshape 517 Earth observation satellites 147 Earth Observing System 441 Earth orientation parameters EOP 20 432 491 494 Earth rotation 20 490 529 from LLR 440 from satellite laser ranging 432 Earth rotation angle 34 Earth rotation correction GPS 299 Eccentric anomaly 73 Eccentricity 3D computation 30 angle 64 function 91 linear 64 numerical 64 Echosounding 375 EDOC Doppler network 205 Effective wavelength GPS 275 EGM96 geopotential model 430 455 521 EGNOS see European GPS Navigation Overlay System EGS see Satellites AJISAI El Niño 467 495 Electromagnetic wave see Wave Ellipsoid 23 Ellipsoidal coordinates 23 height 23 reference system 23 Emergency call E911 372 Empirical forces perturbations 107 Encke 116 Encryption Pcode 229 End of Week EOW rollover 225 Energy integral 72 74 Engineering with GPS 372 Ephemerides DE200 DE405 100 Sun Moon 100 Ephemeris computation 110 second 36 time 31 37 Ephemeris representation see orbit representation Equation of equinoxes 33 Equation of motion 66 Equivalence principle 440 Escape velocity 79 ETRF89 358 EUREF 358 Permanent Network 333 European GPS Navigation Overlay System 340 392 European Remote Sensing Satellite see Satellites ERS1 ERS2 Event camera observation 165 Exact Repeat Mission altimetry 445 Exclusive Economic Zone 523 Extra wide lane 264 Extragalactic radio sources see Quasars FAME astrometric mission 15 178 Faraday content 309 Faraday rotation 44 Federal Radio Navigation Plan FRNP 298 Fiducial point 355 510 First point of Aries 13 Flattening of Earth 5 517 Fleet management 371 Flight path angle 75 Float solution see Ambiguity resolution Footprint altimetry 443 452 Force function 85 Framedragging 436 Frequency standard 39 Fringe frequency 487 Fulltensor gradiometer 480 Fundamental catalogue FK5 13 Fundamental station 535 GAIA astrometric mission 15 180 GALILEO 213 325 393 applications 397 ground segment 394 services 395 signal structure 396 space segment 394 user segment 396 Index 579 Gauss 110 GaussJackson orbit integration 119 GEML2 geopotential model 520 GEMT3 geopotential model 429 455 520 General relativity 37 440 Geoceiver 192 Geocenter motion 432 Geocentric gravitational constant from LLR 440 from SLR 430 Goddard Earth Model GEM 520 GRIM Earth Model 521 GRS80 27 overview 522 SAO Standard Earth 519 Geodesic precession 440 Geodetic astronomy 1 Geodetic datum 25 508 Geodetic mission altimetry 445 Geodetic network analysis 360 densification 360 installation 357 Geodetic Reference System 1980 27 517 Geodynamics 8 362 527 GEODYSSEA 364 Geographic Information System GIS 368 Geoid undulation 25 Geoinformatics 2 GEONET GPS network Japan 334 363 Geopotential models 430 455 Geopotential Research Mission 472 477 Geoscience Laser Altimeter 441 Geostationary orbit 132 Geostrophic flow 465 Geosynchronous orbit 132 Glacial geodesy 380 Glaciology 465 GLAS laser altimeter 441 468 Global Differential GPS Service 332 Globalstar 331 GLONASS 213 325 384 IGEX98 391 mavigation message 387 PZ90 datum 388 receivers 390 signal structure 385 system time 389 GM see Geocentric gravitational constant GNSS 213 383 392 GOCE mission 482 Goddard Earth Model GEM 6 519 Geophysical Astronomical Observatory 415 Space Flight Center GSFC 160 GPS 141 211 Accuracy Improvement Initiative 233 306 adjustment strategies 283 almanac data 346 antenna 235 applications 356 array 505 broadcast ephemerides 222 304 clock 306 constellation 213 control segment 217 data format 329 error budget 297 L2C signal 233 L5 signal 233 meteorology 382 Modernization Program 233 314 navigation data 222 227 observable 252 carrier phase 253 double difference 261 extra wide lane 264 interferometric 255 ionospheric free 264 ionospheric signal 264 narrow lane 263 pseudorange 252 pseudorange difference 253 single difference 254 259 271 triple difference 261 undifferenced phase 255 266 wide lane 263 observation planning 346 348 occultation 382 orbit representation 223 580 Index precise ephemerides 307 receivers 234 Ashtech 247 chipset 237 249 concepts 234 geodetic 245 handheld 248 Javad 248 Leica 246 Macrometer 244 Minimac 245 navigation 248 Rogue 248 SERIES 242 software receiver 237 250 TI 4100 243 Trimble 247 WildMagnavox 246 shadow area 347 signal processing 239 software baseline 283 BERNESE 286 commercial 285 concepts 283 GEONAP 286 GIPSYOASIS II 286 308 Precise Point Positioning 288 scientific 285 space segment 213 stochastic model 342 system time 218 time transfer 381 user segment 234 velocity determination 295 week 221 225 GPS Solutions 213 GPS World 213 234 GPSMET 382 GRACE mission 478 Gradiometry 480 GRARR 160 Grasse 438 Gravimetry 1 airborne 380 Gravitation universal constant G 67 Gravity field degree of development 469 missions 471 tailored 455 Greenwich Mean Observatory GMO 16 GRIM Earth model 520 Group delay 46 GPS 309 VLBI 487 Gulf stream 466 Gyro force 106 Hamilton function 82 Hand Over Word HOW 221 228 Height anomaly 26 ellipsoidal 23 normal 26 orthometric 25 Height determination with Doppler 205 with GPS 315 366 Helix antenna 236 Helmert 1 Highlow mode SST 476 Hill canonical elements 86 orbital parameters 81 HIPPARCOS astrometric mission 14 Hohmann 132 Hopfield model 57 Hour angle 32 Hydrogen maser 489 Hydrographic surveys 206 Iceland crustal motion 364 IERS see International Earth Rotation Service IERS IERS Reference Meridian IRM 16 IERS Reference Pole IRP 16 494 IGEX98 campaign 389 IGS see International GPS Service Impulse analysis laser 413 Inclination function 91 Index of refraction 45 Indirect gravitational effect 101 Inductive gradiometer 482 Index 581 Inertial force 483 integration with GPS 379 platform 379 surveying 206 time 37 Integral of energy 74 76 of momentum 76 of the orbit 76 Integrity 324 392 Intensive session VLBI 494 Interrange vector 412 426 Interchannel bias 237 323 Interference GPS signals 320 Interferogram 503 Interferometer repeatpass 503 singlepass 503 Interferometric GPS observable 255 observations 145 Phase 502 SAR 147 151 447 500 502 Intermediate motion 84 International Astronomical Union IAU 13 International Celestial Reference Frame ICRF 14 489 491 International Celestial Reference System ICRS 14 International DORIS Service IDS 210 International Earth Rotation Service IERS 7 16 20 529 532 International Geophysical Year 5 158 International GLONASS Service IGLOS 392 International GPS Service IGS 7 138 190 218 308 332 397 analysis centers 400 data centers 399 global stations 399 global TEC models 52 global time transfer 381 information system CBIS 401 network 399 pilot projects 401 polyhedron 399 International Laser Ranging Service ILRS 425 International Latitude Service ILS 16 529 International Polar Motion Service IPMS 16 529 International Terrestrial Reference Frame ITRF 16 357 491 ITRF2000 16 494 510 International Terrestrial Reference System ITRS 16 International VLBI Service IVS 493 497 Internet DGPS data link 332 GPS information services 401 Inverted barometric effect 452 Ionosphere 49 correction term Doppler 195 dispersion 52 disturbances 51 313 electron density 54 group delay 54 layers 49 mapping function 50 model Klobuchar 311 monitoring system 188 MSTD 314 refraction 54 195 490 scintillation 313 signal propagation 52 142 309 tomography 188 309 Ionospheric analysis center IGS 313 free signal 311 signal GPS 264 IRIS VLBI network 496 JGM3 geopotential model 430 455 Julian century 34 date 34 Kalman filter 119 222 Kaula rule of thumb 194 582 Index Kepler equation 73 first law 63 orbital parameters 68 second law 70 72 term 90 third law 72 Kepler 63 Kinematic GPS see Rapid methods GPS Kinematic survey 276 Kinetic energy orbital motion 75 Klobuchar ionospheric model 311 Lagrange 85 libration points 134 perturbation equations 85 Landers earthquake 505 Laplace 110 condition 480 spherical harmonics 515 Laser altimetry 441 bottom profiling 380 delay 421 jitter 421 oscillators 411 ranging systems 411 satellites 407 site function 421 two color 421 LASSO experiment 436 Latency 328 Law of areas 65 Law of gravitation 66 67 Law of the seas 523 Leap second 36 Legendre polynomials 90 125 514 Length of day LOD 433 LenseThirring Precession 436 LEO orbit determination 382 Libration 134 440 Limb sounding 477 Line of apsides 64 Line of position LOP 303 Linear combinations GPS signals 258 Location Based Services 249 371 Long arc method 4 137 Longitude of ascending node 224 Look angle 503 Love number 435 Lowlow mode SST 477 Lumped coefficients 108 Lunar ephemerides 100 method 5 Lunar laser ranging LLR 436 mdaily terms 96 Macrometer GPS receiver 241 243 244 498 Magnetic field CHAMP 477 Mapping function ionospheric 310 Marine boundaries 523 Marine geodesy 8 206 375 523 Marine positioning 524 Marini and Murray 420 Mark III Mark IV Mark 5 VLBI processing system 491 Master control station GPS 217 Matera 438 Mathematical geodesy 2 Maxwells equation 43 McDonald Observatory 438 Mean anomaly 73 103 orbital elements 85 Mean sea level 451 Measurement domain algorithm DGPS 339 MERIT 434 511 530 campaign 496 Standards 531 Meteorology with GPS 382 Microchannel plate photomultiplier MCP 413 Microstrip antenna 236 Minimac GPS receiver 245 Minitrack 146 MITES 498 MOBLAS laser ranging system 415 Modified Julian Date 34 Monitor station GPS 217 Index 583 Monitoring with GPS 372 Multimission satellite altimetry 454 Multipath 316 at satellites 319 calibration 318 ERS2 solar panel 155 mitigation 317 Multiple reference stations 338 345 361 Multiplex technique 237 Nbody problem 101 Nadir error 457 Narrow correlator 318 Narrow lane 263 NASA Crustal Dynamics Program CDP 492 496 529 National Geodetic Survey NGS 170 National Imagery and Mapping Agency NIMA 29 Nationwide DGPS 333 Navigation 8 523 with GPS 375 Navigation message GPS 222 NAVSAT 182 NAVSTAR Global Positioning System see GPS Navy Ionospheric Monitoring System 188 Navy Navigation Satellite System NNSS 182 NdYAG laser 411 NdYAP laser 416 NEOS VLBI network 496 Network design GPS 350 Networked reference stations 339 Newton 66 Niell model 315 Nonet rotation 16 490 528 Nodal motion 95 precession 89 Node vector 80 Nonconservative force field 115 Nonfiducial orbit 308 Nonrotating origin 21 34 Normal gravity 516 Normal point 123 143 155 422 North American Datum 205 Northern hole 322 347 385 Nuisance parameter 265 Numerical orbit integration 84 Nutation 18 32 489 495 IAU 2000 model 19 Wahr model 19 NUVEL plate motion model 17 210 494 528 Ocean circulation 465 Ocean dynamic topography 452 Ocean seasons 467 Ocean tide model 459 Oceanography 465 Offshore industry 524 Omnistar 333 340 Operational control segment see Control segment OPNET 189 Orbit determination 110 kinematic 120 boundary value problem 110 113 DORIS 209 dynamic 120 from SLR observations 428 initial value problem 110 POD 120 reduceddynamic 120 Orbit integration Cowell 116 Encke 117 RungeKutta method 119 analytical 84 114 multistep method 119 numerical 84 114 116 119 predictorcorrector method 119 singlestep method 119 Orbit representation Chebyshev polynomials 122 GPS 223 navigation satellites 121 polynomial approximation 122 Orbital parameters Hill 81 Keplerian 68 mean 85 584 Index osculating 84 Orbits Geostationary Earth Orbit GEO 129 132 Highly Elliptical Orbit HEO 130 Inclined Geosynchronous Orbit IGSO 130 Intermediate Circular Orbit ICO 129 Low Earth Orbit LEO 129 Medium Earth Orbit MEO 129 sunsynchronous 131 Ordnance Survey National GPS Network 334 Oscillator quality Doppler observations 197 GPS observations 323 Osculating orbital elements 84 118 Pcode 216 219 PW tracking 243 Parallel channel 236 Parameter elimination 265 287 342 Parameterestimation 4 135 265 287 342 Passive satellites 148 Pearshape of Earth 4 517 Pericenter 64 Perifocal system 110 Perigee vector 80 Period satellite motion 79 Perturbations elements 94 longperiod 95 mdaily terms 96 secular 95 shortperiod 96 Perturbed satellite motion 83 Perturbing forces 83 Earths oblateness 96 empirical accelerations 107 Moon 98 nongravitational 115 306 ocean tides 101 relativistic acceleration 107 solar radiation pressure 104 solid Earth tides 101 Sun 98 Phase angle 44 comparison 141 constant 43 interferometric 502 lock loop 239 unwrapping 504 velocity 46 Photogrammetric plate reduction 168 Photogrammetry 378 aircraft navigation 378 ground control points 206 378 sensor orientation 378 Photomultiplier 413 Physical geodesy 2 PIVEX 498 Pixel 172 500 Plasmasphere 309 Plate reduction 167 175 Plate tectonics 464 490 527 Polar geodesy 206 Polar motion 20 206 490 POLARIS VLBI network 496 POSEIDON altimeter 448 Positioning 506 Postglacial rebound 430 PostNewtonian physics 438 Potential centrifugal 514 disturbing 515 gravitational 514 Potential energy orbital motion 75 PRARE 151 154 447 456 Precession 18 489 constant from LLR 440 IAU 2000 model 19 nodal 89 Precise ephemerides 510 NASA JPL 308 GPS 307 IGS 308 NIMA 307 SP3 format 307 TRANSIT 190 Precise Point Positioning 283 288 307 342 Index 585 Precise Positioning Service PPS 229 298 Precision farming 370 Precision Orbit Determination 120 382 Prime Minitrack 160 PRN signal GPS 216 219 Process noise GPS analysis 324 Prograde motion satellite 95 Pseudo Random Noise see PRN signal Pseudokinematic GPS 289 292 Pseudorange 201 211 252 Pseudorange difference 253 Puerto Rico Trench 444 Pulsar 42 Pulse half width laser 413 PZ90 GLONASS datum 388 Qswitch 412 Quasar see Radio source Quasigeoid 26 Radar 500 Radar altimeter 144 443 Radar bands 47 Radio Data System RDS 331 Radio frequency GPS data link 331 Radio occultation 382 Radio source VLBI 14 146 489 Radiobeacon DGPS 333 Radome 323 Rapid methods GPS 289 Rayleigh 46 Retracking altimeter data 454 Real Time Kinematic GPS 327 336 accuracy 338 applications 338 368 Receiver noise 323 Reconnaissance sheet 350 Rectification 118 Reference frame 12 Reference satellite 269 Reference system 10 Cartesian 10 ellipsoidal 23 equatorial 13 local astronomical 22 quasiinertial 13 spacetime 38 Refraction differential 166 index 45 ionospheric 54 tropospheric 56 196 Refractivity 45 Relative GPS 325 Relativistic effects 37 106 193 198 299 440 495 Relaxed orbit 203 Reliability 354 Remote sensing 500 Remote sensing satellites 147 Resonances 107 Retroreflector 404 406 Retrograde motion satellite 81 95 RINEX 281 329 ROCK42 model GPS satellites 105 306 Root mean square error RMS 302 Rotation matrix 11 Rover roving GPS receiver 290 326 RTCM GPS data format 330 Ruby laser 411 RungeKutta see Orbit integration San Andreas Fault 431 SAO Standard Earth 6 115 163 SAPOS 291 335 341 345 361 SAR see Synthetic Apertur Radar Satellite altimetry 144 443 applications 461 multimission 454 observation equation 451 satellites 450 Satellite geodesy applications 7 definition 2 dynamical method 4 137 427 507 514 geometrical method 3 137 159 427 507 orbital method 4 159 Satellite gravity gradiometry 147 471 480 Satellite laser ranging 141 404 applications 424 data processing 418 586 Index parameter estimation 427 ranging systems 411 414 satellites with reflectors 407 spaceborne laser 441 system development trends 416 system performance standards 418 426 tracking priority list 426 transportable systems 415 Satellite pass 191 Satellite refraction 166 Satellitetosatellite tracking 144 471 473 Satellites ÖRSTED 382 AJISAI 140 151 ANNA1B 6 159 ASIJAI 409 ATS6 476 BEACON EXPLORERB 405 CHAMP 120 145 382 473 476 CRYOSAT 451 468 DIVA 180 ECHO1 6 140 162 170 ECHO2 140 162 170 ENVISAT1 208 449 500 ERS1 144 150 446 500 ERS2 144 150 448 500 ETALON 389 410 EXPLORER1 6 EXPLORER19 162 EXPLORER39 162 FAME 178 GAIA 180 GEOS1 159 162 GEOS2 159 160 162 170 GEOS3 144 149 160 444 476 520 GEOSAT 144 445 GEOSAT FOLLOWON GFO 144 449 GFZ1 410 GLONASS 389 GLONASSM 390 GOCE 147 473 482 GPS 214 Block I 214 Block IIIIa 214 Block IIF 215 Block III 231 Block IIR 214 Block IIRM 215 GRACE 382 473 478 GRAVITY PROBE B 149 153 HALCA 499 HIPPARCOS 14 177 ICESAT 144 382 441 468 INMARSAT 325 331 393 JERS1 502 JASON 144 208 449 LAGEOS 162 520 LAGEOS1 142 409 LAGEOS2 142 409 METEOR 154 MICROLAB 382 NOVA 187 195 OSCAR 187 PAGEOS 6 140 162 170 RADARSAT 502 RADIOASTRON 499 SEASAT1 144 150 444 501 SPOT 207 SPUTNIK1 1 158 SPUTNIK2 6 STARLETTE 142 162 408 STELLA 142 409 STEP 153 TDRS 152 499 TIPS 149 436 TOPEXPOSEIDON 120 144 208 382 447 520 TRANSIT1B 6 TRIAD 153 WESTPAC1 410 420 SBG Camera 164 Sea floor mapping 524 Sea floor positioning 526 Sea level monitoring 375 Sea state bias 458 Sea surface topography 451 459 Seamount 464 Search and Rescue function GALILEO 395 Index 587 Second time ephemeris 36 leap second 36 SI 35 Secondtime 31 SECOR 142 159 Selective Availability SA 229 298 Semi kinematic GPS 292 Semi short arc method 137 203 Semilatus rectum 77 Semimajor axis numerical value 171 522 Semicodeless signal processing 240 Semitrain technique laser 414 Sensor orientation with GPS 378 Sequencing channel 236 SERIES GPS receiver 242 498 Session GPS 283 353 Short arc method 4 124 137 159 203 Shuttle Imaging Radar SIR 502 Shuttle Radar Topography Mission SRTM 503 504 Sidereal time 32 Signal in Space Range Error 233 298 Signal processing GPS 239 Signal propagation 42 delay 323 diffraction 319 interference 320 ionosphere 309 laser light 420 multipath 316 receiver delay 196 troposphere 314 SINEX 289 498 Single difference observable 147 254 Single photon avalanche diode SPAD 414 SIRGAS 334 358 364 Skyfix 333 340 SKYLAB 444 SLR2000 laser system 418 Smithsonian Astrophysical Observatory 158 Standard Earth 519 star catalog 166 SNR Signal to noise ratio 234 Software receiver 237 323 Solarradiationpressure 104 190 194 410 Solid Earth tides 435 490 South American Datum 205 SP3 Precise ephemerides data format 307 Space Shuttle 132 SpaceVLBI 499 Spaceborne laser 441 Spacewise approach gradiometry 483 Spatial smoothing orbit 123 Speckle 501 Spherical error probable SEP 304 Spread spectrum technique 221 234 320 Squaring technique 241 242 SQUID 153 Standard Earth 6 519 Standard Positioning Service SPS 229 298 STAR accelerometer 479 Star catalog GSC 175 HIPPARCOS 175 Tycho2 175 UCAC 175 Star tracker 154 177 441 477 State space domain DGPS 326 340 Stellar triangulation 169 STEP 472 Stochastic model GPS 342 Stop and go GPS 292 Streak camera 413 421 Subduction zone 527 Subsatellite track 126 Sunsynchronous orbit 131 Synthetic Aperture Radar SAR 500 T2L2 experiment 436 Tailored gravity model 429 455 Tandem mission ERS12 151 503 Tangential coordinates 167 Telematics 371 Telemetry Word TLM 228 Terrestrial Ephemeris Origin TEO 21 Terrestrial time 31 37 Tesseral coefficients 519 Thrust force 107 588 Index TI 4100 GPS receiver 243 Tidal friction 440 Tidal uplift 435 Tidal upload 324 Tides ocean 101 solid Earth 101 408 435 459 490 TIGO 497 537 laser ranging module 416 Time atomic 35 comparison SLR 435 coordinate 38 DUT1 36 epoch 31 global transfer 381 GLONASS 389 GPS 36 218 inertial 37 mean solar 33 pulsar 42 scales 31 sidereal 32 unit 31 universal 32 UTC 36 Time of closest approach 182 Time to fix ambiguities TTFA 276 291 337 Timewise approach gradiometry 483 Torsion balance 480 Total Electron Content 50 Tracking priority list SLR 426 TRANET 190 445 456 Transfer orbit 132 TRANSIT Improvement Program 187 TRANSIT system 143 182 186 212 ionosphere 53 Translocation 202 Transponder 142 Transportable laser systems 415 Trilateration 159 Trivial baseline GPS 284 Tropical year 37 Troposphere 48 Black approximation 59 Hopfield model 57 mapping function 58 Marini mapping function 58 Niell model 315 refraction 56 314 487 490 signal propagation 52 Tropospheric scale bias 60 315 TSIKADA 186 Tunnel surveying with GPS 374 TurboRogue GPS receiver 248 Turner formula 168 Twobody problem 62 Twowayranging 404 Tycho Brahe 63 Ultrarapid orbits GPS 308 Universal time 31 32 User Range Error 298 Variation of constants 84 Velocity determination GPS 295 Vernal equinox 32 Very Long Baseline Interferometry VLBI 146 266 485 accuracy of products 496 Earth orientation parameters 494 electronic VLBI 491 global network 492 international cooperation 496 list of parameters 488 observation equation 487 observing modes 490 satellitebased 498 Space Observatory Program 499 telescopes 492 Virtual reference station 247 291 340 343 Visviva equations 79 VLBA VLBI network 496 Walker constellation 394 Water vapor radiometer 61 315 490 Wave amplitude 44 dispersion 45 frequency domain 46 modulation 44 periodic 43 polarization 44 Index 589 propagation 43 45 significant height 452 WEGENER 529 WEGENERMEDLAS 362 416 431 Wettzell 438 535 Laser Ranging System 415 VLBI telescope 492 WideAreaAugmentation System 340 392 WideArea Differential GPS 328 333 339 Wide lane 263 World Geodetic System 28 194 WGS 72 28 190 WGS 84 28 190 357 Ybias GPS satellites 306 Ycode GPS 229 Zcount 221 Ztracking 243 Zero antenna 322 ZIMLAT laser telescope 176 Zonal harmonics 96 515