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... ident for ﬁne-structured gravity ﬁeld models from new and forthcoming satellite missions and for the monitoring of Earth’s 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 material 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, surveying 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 statistics. 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 comprehensive 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 The fundamental structure of the ﬁrst edition has been maintained to facilitate continuity of teaching; however, outdated material has been removed and new material has been included.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 re-written. 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 reference frames [2.2], signal propagation [2.3], directions with CCD technology [5.2], 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 chapter on GPS and GNSS [7] has been almost completely re-written 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 [7.5]. GLONASS and the forthcoming GALILEO are included in a new section on GNSS [7.7]. Gravity ﬁeld missions like CHAMP, GRACE and GOCE, because of their increasing 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 historical 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 [5.2] and DORIS [6.7]. The geodetic history of Transit Doppler techniques, 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 [12.5]. International services of interest to satellite geodesy have been included, namely the IGS [7.8.1], the ILRS [8.5.1], the IVS [11.1.3], and the IERS [12.4]. The bibliography has been updated and expanded considerably by adding an increased 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 Dipl.-Ing. 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 understanding. 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 Abbreviations 1 Introduction 1.1 Subject of Satellite Geodesy . . . . . . . . . . . . . . 1.2 Classiﬁcation and Basic Concepts of Satellite Geodesy 1.3 Historical Development of Satellite Geodesy . . . . . . 1.4 Applications of Satellite Geodesy . . . . . . . . . . . . 1.5 Structure and Objective of the Book . . . . . . . . . . vii xvii 1 1 3 5 7 9 10 10 10 12 13 15 17 21 23 25 28 30 31 31 32 35 37 39 42 43 43 45 46 48 52 54 56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Fundamentals 2.1 Reference Coordinate Systems . . . . . . . . . . . . . . . . . . . . . 2.1.1 Cartesian Coordinate Systems and Coordinate Transformations 2.1.2 Reference Coordinate Systems and Frames in Satellite Geodesy 2.1.2.1 Conventional Inertial Systems and Frames . . . . . 2.1.2.2 Conventional Terrestrial Systems and Frames . . . . 2.1.2.3 Relationship between CIS and CTS . . . . . . . . . 2.1.3 Reference Coordinate Systems in the Gravity Field of Earth . 2.1.4 Ellipsoidal Reference Coordinate Systems . . . . . . . . . . . 2.1.5 Ellipsoid, Geoid and Geodetic Datum . . . . . . . . . . . . . 2.1.6 World Geodetic System 1984 (WGS 84) . . . . . . . . . . . . 2.1.7 Three-dimensional Eccentricity Computation . . . . . . . . . 2.2 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Sidereal Time and Universal Time . . . . . . . . . . . . . . . 2.2.3 Atomic Time . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Ephemeris Time, Dynamical Time, Terrestrial Time . . . . . . 2.2.5 Clocks and Frequency Standards . . . . . . . . . . . . . . . . 2.3 Signal Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Some Fundamentals of Wave Propagation . . . . . . . . . . . 2.3.1.1 Basic Relations and Deﬁnitions . . . . . . . . . . . 2.3.1.2 Dispersion, Phase Velocity and Group Velocity . . . 2.3.1.3 Frequency Domains . . . . . . . . . . . . . . . . . 2.3.2 Structure and Subdivision of the Atmosphere . . . . . . . . . 2.3.3 Signal Propagation through the Ionosphere and the Troposphere 2.3.3.1 Ionospheric Refraction . . . . . . . . . . . . . . . 2.3.3.2 Tropospheric Refraction . . . . . . . . . . . . . . . x 3 Contents Satellite Orbital Motion 3.1 Fundamentals of Celestial Mechanics, Two-Body Problem . . . . . . 3.1.1 Keplerian Motion . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Newtonian Mechanics, Two-Body Problem . . . . . . . . . . 3.1.2.1 Equation of Motion . . . . . . . . . . . . . . . . . 3.1.2.2 Elementary Integration . . . . . . . . . . . . . . . 3.1.2.3 Vectorial Integration . . . . . . . . . . . . . . . . . 3.1.3 Orbit Geometry and Orbital Motion . . . . . . . . . . . . . . 3.2 Perturbed Satellite Motion . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Representation of the Perturbed Orbital Motion . . . . . . . . 3.2.1.1 Osculating and Mean Orbital Elements . . . . . . . 3.2.1.2 Lagrange’s Perturbation Equations . . . . . . . . . 3.2.1.3 Gaussian Form of Perturbation Equation . . . . . . 3.2.2 Disturbed Motion due to Earth’s Anomalous Gravity Field . . 3.2.2.1 Perturbation Equation and Geopotential . . . . . . 3.2.2.2 Perturbations of the Elements . . . . . . . . . . . . 3.2.2.3 Perturbations Caused by the Zonal Coefﬁcients Jn . 3.2.3 Other Perturbations . . . . . . . . . . . . . . . . . . . . . . . 3.2.3.1 Perturbing Forces Caused by the Sun and Moon . . 3.2.3.2 Solid Earth Tides and Ocean Tides . . . . . . . . . 3.2.3.3 Atmospheric Drag . . . . . . . . . . . . . . . . . . 3.2.3.4 Direct and Indirect Solar Radiation Pressure . . . . 3.2.3.5 Further Perturbations . . . . . . . . . . . . . . . . 3.2.3.6 Resonances . . . . . . . . . . . . . . . . . . . . . 3.2.4 Implications of Perturbations on Selected Satellite Orbits . . . 3.3 Orbit Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Integration of the Undisturbed Orbit . . . . . . . . . . . . . . 3.3.2 Integration of the Perturbed Orbit . . . . . . . . . . . . . . . 3.3.2.1 Analytical Methods of Orbit Integration . . . . . . 3.3.2.2 Numerical Methods of Orbit Integration . . . . . . 3.3.2.3 Precise Orbit Determination with Spaceborne GPS . 3.3.3 Orbit Representation . . . . . . . . . . . . . . . . . . . . . . 3.3.3.1 Ephemeris Representation for Navigation Satellites 3.3.3.2 Polynomial Approximation . . . . . . . . . . . . . 3.3.3.3 Simpliﬁed Short Arc Representation . . . . . . . . 3.4 Satellite Orbits and Constellations . . . . . . . . . . . . . . . . . . . 3.4.1 Basic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Orbits and Constellations . . . . . . . . . . . . . . . . . . . . 3.4.3 Sun-synchronous, Geostationary, and Transfer Orbits . . . . . 62 62 63 66 66 69 74 77 82 84 84 85 87 88 89 94 96 98 98 101 102 104 105 107 108 109 110 114 114 116 119 120 121 122 124 126 126 128 131 Contents xi 135 135 139 139 141 143 144 144 145 147 147 147 149 152 152 153 154 156 158 159 160 161 161 162 163 164 169 170 172 172 174 176 176 177 177 178 4 Basic Observation Concepts and Satellites Used in Geodesy 4.1 Satellite Geodesy as a Parameter Estimation Problem . . . . . 4.2 Observables and Basic Concepts . . . . . . . . . . . . . . . . 4.2.1 Determination of Directions . . . . . . . . . . . . . . 4.2.2 Determination of Ranges . . . . . . . . . . . . . . . . 4.2.3 Determination of Range Differences (Doppler method) 4.2.4 Satellite Altimetry . . . . . . . . . . . . . . . . . . . 4.2.5 Determination of Ranges and Range-Rates (Satellite-to-Satellite Tracking) . . . . . . . . . . . . . 4.2.6 Interferometric Measurements . . . . . . . . . . . . . 4.2.7 Further Observation Techniques . . . . . . . . . . . . 4.3 Satellites Used in Geodesy . . . . . . . . . . . . . . . . . . . 4.3.1 Basic Considerations . . . . . . . . . . . . . . . . . . 4.3.2 Some Selected Satellites . . . . . . . . . . . . . . . . 4.3.3 Satellite Subsystems . . . . . . . . . . . . . . . . . . 4.3.3.1 Drag Free Systems . . . . . . . . . . . . . . 4.3.3.2 Attitude Control . . . . . . . . . . . . . . . 4.3.3.3 Navigation Payload, PRARE . . . . . . . . 4.3.4 Planned Satellites and Missions . . . . . . . . . . . . 4.4 Some Early Observation Techniques (Classical Methods) . . . 4.4.1 Electronic Ranging SECOR . . . . . . . . . . . . . . 4.4.2 Other Early Observation Techniques . . . . . . . . . . Optical Methods for the Determination of Directions 5.1 Photographic Determination of Directions . . . . . . . . . . 5.1.1 Satellites used for Camera Observations . . . . . . . 5.1.2 Satellite Cameras . . . . . . . . . . . . . . . . . . . 5.1.3 Observation and Plate Reduction . . . . . . . . . . . 5.1.4 Spatial Triangulation . . . . . . . . . . . . . . . . . 5.1.5 Results . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Directions with CCD Technology . . . . . . . . . . . . . . . 5.2.1 Image Coordinates from CCD Observations . . . . . 5.2.2 Star Catalogs, Star Identiﬁcation and Plate Reduction 5.2.3 Applications, Results and Prospects . . . . . . . . . 5.3 Directions from Space Platforms . . . . . . . . . . . . . . . 5.3.1 Star Tracker . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Astrometric Satellites, HIPPARCOS . . . . . . . . . 5.3.3 Planned Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 Doppler Techniques 181 6.1 Doppler Effect and Basic Positioning Concept . . . . . . . . . . . . . 183 6.2 One Successful Example: The Navy Navigation Satellite System . . 186 6.2.1 System Architecture . . . . . . . . . . . . . . . . . . . . . . 187 6.2.2 Broadcast and Precise Ephemerides . . . . . . . . . . . . . . 188 xii Contents 6.3 6.4 6.5 6.6 6.7 Doppler Receivers . . . . . . . . . . . . . . . . . 6.3.1 Basic concept . . . . . . . . . . . . . . . 6.3.2 Examples of Doppler Survey Sets . . . . Error Budget and Corrections . . . . . . . . . . . 6.4.1 Satellite Orbits . . . . . . . . . . . . . . 6.4.2 Ionospheric and Tropospheric Refraction 6.4.3 Receiver System . . . . . . . . . . . . . 6.4.4 Earth Rotation and Relativistic Effects . . 6.4.5 Motion of the Receiver Antenna . . . . . Observation Strategies and Adjustment Models . 6.5.1 Extended Observation Equation . . . . . 6.5.2 Single Station Positioning . . . . . . . . 6.5.3 Multi-Station Positioning . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . 6.6.1 Applications for Geodetic Control . . . . 6.6.2 Further Applications . . . . . . . . . . . DORIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 190 192 193 194 195 196 197 198 199 199 201 202 203 204 205 207 211 211 211 213 217 218 222 222 223 225 227 229 230 234 234 239 240 243 243 245 248 250 252 7 The Global Positioning System (GPS) 7.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Space Segment . . . . . . . . . . . . . . . . . . . . . 7.1.3 Control Segment . . . . . . . . . . . . . . . . . . . . 7.1.4 Observation Principle and Signal Structure . . . . . . 7.1.5 Orbit Determination and Orbit Representation . . . . . 7.1.5.1 Determination of the Broadcast Ephemerides 7.1.5.2 Orbit Representation . . . . . . . . . . . . . 7.1.5.3 Computation of Satellite Time and Satellite Coordinates . . . . . . . . . . . . . . . . . 7.1.5.4 Structure of the GPS Navigation Data . . . . 7.1.6 Intentional Limitation of the System Accuracy . . . . 7.1.7 System Development . . . . . . . . . . . . . . . . . . 7.2 GPS Receivers (User Segment) . . . . . . . . . . . . . . . . . 7.2.1 Receiver Concepts and Main Receiver Components . . 7.2.2 Code Dependent Signal Processing . . . . . . . . . . 7.2.3 Codeless and Semicodeless Signal Processing . . . . . 7.2.4 Examples of GPS receivers . . . . . . . . . . . . . . . 7.2.4.1 Classical Receivers . . . . . . . . . . . . . 7.2.4.2 Examples of Currently Available Geodetic Receivers . . . . . . . . . . . . . . . . . . 7.2.4.3 Navigation and Handheld Receivers . . . . 7.2.5 Future Developments and Trends . . . . . . . . . . . 7.3 GPS Observables and Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents xiii 252 252 255 258 258 265 269 277 277 281 283 289 289 290 292 294 295 297 297 300 304 304 307 309 309 314 316 319 320 320 323 323 325 326 326 329 332 336 338 339 341 7.3.1 7.4 7.5 Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1.1 Classical View . . . . . . . . . . . . . . . . . . . . 7.3.1.2 Code and Carrier Phases . . . . . . . . . . . . . . . 7.3.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . 7.3.2.1 Linear Combinations and Derived Observables . . . 7.3.2.2 Concepts of Parametrization . . . . . . . . . . . . . 7.3.2.3 Resolution of Ambiguities . . . . . . . . . . . . . . 7.3.3 Data Handling . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3.1 Cycle Slips . . . . . . . . . . . . . . . . . . . . . . 7.3.3.2 The Receiver Independent Data Format RINEX . . 7.3.4 Adjustment Strategies and Software Concepts . . . . . . . . . 7.3.5 Concepts of Rapid Methods with GPS . . . . . . . . . . . . . 7.3.5.1 Basic Considerations . . . . . . . . . . . . . . . . 7.3.5.2 Rapid Static Methods . . . . . . . . . . . . . . . . 7.3.5.3 Semi Kinematic Methods . . . . . . . . . . . . . . 7.3.5.4 Pure Kinematic Method . . . . . . . . . . . . . . . 7.3.6 Navigation with GPS . . . . . . . . . . . . . . . . . . . . . . Error Budget and Corrections . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Satellite Geometry and Accuracy Measures . . . . . . . . . . 7.4.3 Orbits and Clocks . . . . . . . . . . . . . . . . . . . . . . . . 7.4.3.1 Broadcast Ephemerides and Clocks . . . . . . . . . 7.4.3.2 Precise Ephemerides and Clocks, IGS . . . . . . . 7.4.4 Signal Propagation . . . . . . . . . . . . . . . . . . . . . . . 7.4.4.1 Ionospheric Effects on GPS Signals . . . . . . . . . 7.4.4.2 Tropospheric Propagation Effects . . . . . . . . . . 7.4.4.3 Multipath . . . . . . . . . . . . . . . . . . . . . . 7.4.4.4 Further Propagation Effects, Diffraction and Signal Interference . . . . . . . . . . . . . . . . . . . . . 7.4.5 Receiving System . . . . . . . . . . . . . . . . . . . . . . . . 7.4.5.1 Antenna Phase Center Variation . . . . . . . . . . . 7.4.5.2 Other Error Sources Related to the Receiving System . . . . . . . . . . . . . . . . . . . . . . . . 7.4.6 Further Inﬂuences, Summary, the Issue of Integrity . . . . . . Differential GPS and Permanent Reference Networks . . . . . . . . . 7.5.1 Differential GPS (DGPS) . . . . . . . . . . . . . . . . . . . . 7.5.1.1 DGPS Concepts . . . . . . . . . . . . . . . . . . . 7.5.1.2 Data Formats and Data Transmission . . . . . . . . 7.5.1.3 Examples of Services . . . . . . . . . . . . . . . . 7.5.2 Real Time Kinematic GPS . . . . . . . . . . . . . . . . . . . 7.5.3 Multiple Reference Stations . . . . . . . . . . . . . . . . . . 7.5.3.1 Wide Area Differential GPS . . . . . . . . . . . . . 7.5.3.2 High Precision Networked Reference Stations . . . xiv Contents 7.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.1 Planning and Realization of GPS Observation . . . . . . . . 7.6.1.1 Setting Up an Observation Plan . . . . . . . . . . 7.6.1.2 Practical Aspects in Field Observations . . . . . . 7.6.1.3 Observation Strategies and Network Design . . . 7.6.2 Possible Applications and Examples of GPS Observations . 7.6.2.1 Geodetic Control Surveys . . . . . . . . . . . . . 7.6.2.2 Geodynamics . . . . . . . . . . . . . . . . . . . 7.6.2.3 Height Determination . . . . . . . . . . . . . . . 7.6.2.4 Cadastral Surveying, Geographic Information Systems . . . . . . . . . . . . . . . . . . . . . . 7.6.2.5 Fleet Management, Telematics, Location Based Services . . . . . . . . . . . . . . . . . . . . . . 7.6.2.6 Engineering and Monitoring . . . . . . . . . . . . 7.6.2.7 Precise Marine Navigation, Marine Geodesy, and Hydrography . . . . . . . . . . . . . . . . . 7.6.2.8 Photogrammetry, Remote Sensing, Airborne GPS 7.6.2.9 Special Applications of GPS . . . . . . . . . . . 7.7 GNSS – Global Navigation Satellite System . . . . . . . . . . . . . 7.7.1 GLONASS . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7.2 GPS/GLONASS Augmentations . . . . . . . . . . . . . . . 7.7.3 GALILEO . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Services and Organizations Related to GPS . . . . . . . . . . . . . 7.8.1 The International GPS Service (IGS) . . . . . . . . . . . . 7.8.2 Other Services . . . . . . . . . . . . . . . . . . . . . . . . 8 . . . . . . . . . 345 345 346 348 350 356 357 362 366 . 368 . 371 . 372 . . . . . . . . . . 375 378 380 383 384 392 393 397 397 401 404 404 406 411 411 412 414 416 418 418 422 424 424 427 428 431 Laser Ranging 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Satellites Equipped with Laser Reﬂectors . . . . . . . . . . . . . . . 8.3 Laser Ranging Systems and Components . . . . . . . . . . . . . . . . 8.3.1 Laser Oscillators . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Other System Components . . . . . . . . . . . . . . . . . . . 8.3.3 Currently Available Fixed and Transportable Laser Systems . 8.3.4 Trends in SLR System Developments . . . . . . . . . . . . . 8.4 Corrections, Data Processing and Accuracy . . . . . . . . . . . . . . 8.4.1 Extended Ranging Equation . . . . . . . . . . . . . . . . . . 8.4.2 Data Control, Data Compression, and Normal Points . . . . . 8.5 Applications of Satellite Laser Ranging . . . . . . . . . . . . . . . . 8.5.1 Realization of Observation Programs, International Laser Ranging Service (ILRS) . . . . . . . . . . . . . . . . . . . . 8.5.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . 8.5.3 Earth Gravity Field, Precise Orbit Determination (POD) . . . 8.5.4 Positions and Position Changes . . . . . . . . . . . . . . . . Contents xv . . . . 432 435 436 441 443 443 444 451 451 452 454 460 461 462 464 465 469 469 473 473 476 477 480 480 482 485 485 485 491 496 498 500 500 502 505 506 506 506 510 511 8.6 8.7 9 8.5.5 Earth Rotation, Polar Motion 8.5.6 Other applications . . . . . Lunar Laser Ranging . . . . . . . . Spaceborne Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Satellite Altimetry 9.1 Basic Concept . . . . . . . . . . . . . . . . . . 9.2 Satellites and Missions . . . . . . . . . . . . . 9.3 Measurements, Corrections, Accuracy . . . . . 9.3.1 Geometry of Altimeter Observations . . 9.3.2 Data Generation . . . . . . . . . . . . 9.3.3 Corrections and Error Budget . . . . . 9.4 Determination of the Mean Sea Surface . . . . 9.5 Applications of Satellite Altimetry . . . . . . . 9.5.1 Geoid and Gravity Field Determination 9.5.2 Geophysical Interpretation . . . . . . . 9.5.3 Oceanography and Glaciology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Gravity Field Missions 10.1 Basic Considerations . . . . . . . . 10.2 Satellite-to-Satellite Tracking (SST) 10.2.1 Concepts . . . . . . . . . . 10.2.2 High-Low Mode, CHAMP . 10.2.3 Low-Low Mode, GRACE . 10.3 Satellite Gravity Gradiometry . . . . 10.3.1 Concepts . . . . . . . . . . 10.3.2 GOCE mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Related Space Techniques 11.1 Very Long Baseline Interferometry . . . . . . . . . . . . . . . . . . 11.1.1 Basic Concept, Observation Equations, and Error Budget . . 11.1.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3 International Cooperation, International VLBI Service (IVS) 11.1.4 VLBI with Satellites . . . . . . . . . . . . . . . . . . . . . 11.2 Interferometric Synthetic Aperture Radar (InSAR) . . . . . . . . . . 11.2.1 Basic Concepts, Synthetic Aperture Radar (SAR) . . . . . . 11.2.2 Interferometric SAR . . . . . . . . . . . . . . . . . . . . . 11.2.3 Differential Radar Interferometry . . . . . . . . . . . . . . 12 Overview and Applications 12.1 Positioning . . . . . . . . . . . . . . . . . . . . . . 12.1.1 Concepts, Absolute and Relative Positioning 12.1.2 Global and Regional Networks . . . . . . . . 12.1.3 Operational Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Contents 12.2 Gravity Field and Earth Models . . . . . . . . . . . . . . . . . . . . 12.2.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.2 Earth Models . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Navigation and Marine Geodesy . . . . . . . . . . . . . . . . . . . . 12.3.1 Possible Applications and Accuracy Requirements in Marine Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Marine Positioning Techniques . . . . . . . . . . . . . . . . . 12.4 Geodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 Recent Crustal Movements . . . . . . . . . . . . . . . . . . . 12.4.2 Earth Rotation, Reference Frames, IERS . . . . . . . . . . . 12.5 Combination of Geodetic Space Techniques . . . . . . . . . . . . . . 12.5.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . 12.5.2 Fundamental Stations . . . . . . . . . . . . . . . . . . . . . . 12.5.3 Integrated Global Geodetic Observing System (IGGOS) . . . References Index 514 514 519 523 523 524 527 527 529 534 534 535 537 539 575 Abbreviations ACP ADOS AI I APL ARP AS ASIC BCRS BIH BIPM BKG BPS BPSK CACS CAD CBIS CCD CDP CEP CEP CIO CIP CIS CNES CONUS CORS CPU CRF CRS Area Correction Parameter African Doppler Survey Accuracy Improvement Initiative Applied Physics Laboratory Antenna Reference Point Anti Spooﬁng Application-Speciﬁc Integrated Circuit Barycentric Celestial Reference System Bureau International de l’Heure Bureau International des poids et Mésures Bundesamt für Kartographie und Geodäsie Bits Per Second Binary Phase Shift Keying Canadian Active Control System Computer Assisted Design Central Bureau (IGS) Information System Charge Coupled Device Crustal Dynamics Program Celestial Ephemeris Pole Circular Error Probable Conventional International Origin Celestial Intermediate Pole Conventional Inertial (Reference) System Centre National d’Études Spatiales Continental U.S. Continuously Operating Reference Station Central Processing Unit Celestial Reference Frame Celestial Reference System CTP CTS DÖDOC DD DEM DGFI DGPS DOD DOP DOY DRMS EDOC EGM96 EGNOS EOP EOS EPS ERM ERP ESA ESNP EU FAA FAGS FIG FK5 FOC FRNP Conventional Terrestrial Pole Conventional Terrestrial (Reference) System German Austrian Doppler Campaign Double Difference Digital Elevation Model Deutsches Geodätisches Forschungsinstitut Differential GPS Department of Defence Dilution of Precision Day Of the Year Distance Root Mean Square European Doppler Campaign Earth Gravitational Model 1996 European Geostationary Navigation Overlay System Earth Orientation Parameter Earth Observing System Real-Time Positioning Service (SAPOS) Exact Repeat Mission Earth Rotation Parameter European Space Agency European Satellite Navigation Program European Union Federal Aviation Administration Federation of Astronomical and Geophysical Data Analysis Services Fédération Internationale des Géomètres Fifth Fundamental Catalogue Full Operational Capability Federal Radio Navigation Plan xviii GAST GCRS GDR GEM GEO GFO GFZ GIC GIS GLAS GM GMST GNSS GRGS GRS80 GSFC HEPS IAU ICD ICO ICRF ICRS IDS IERS IF IGEB IGN IGS IGSO ILRS ILS INSAR Abbreviations Greenwich Apparent Sidereal Time Geocentric Celestial Reference System Geophysical Data Record Goddard Earth Model Geostationary Orbit GEOSAT Follow On GeoForschungsZentrum Potsdam GPS Integrity Channel Geo Information System Geoscience Laser Altimeter System Geodetic Mission Greenwich Mean Sidereal Time Global Navigation Satellite System Groupe de Recherche de Géodésie Spatiale Geodetic Reference System 1980 Goddard Space Flight Center High Precision Real-Time Positioning Service (SAPOS) International Astronomical Union Interface Control Document Intermediate Circular Orbit International Celestial Reference Frame International Celestial Reference System International DORIS Service International Earth Rotation and Reference Systems Service Intermediate Frequency Interagency GPS Executive Board Institut Géographique National International GPS Service Inclined Geo-synchronous Orbit International Laser Ranging Service International Latitude Service Interferometric SAR Institute of Navigation International Polar Motion Service IRIS International Radio Interferometric Surveying IRM IERS Reference Meridian IRP IERS Reference Pole IRV Inter-Range 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 Satellite-based Augmentation System NAD North American Datum NASA National Aeronautics and Space Administration Nd:YAG 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 ION IPMS Abbreviations NIST NOAA OCS PCV PDA PDGPS PDOP PE POD PPP PPS PRN PTB RA RDS RF RMS RNAAC RTCM RTK SA SAD SAO SAPOS SAR SAR SBAS SEP SGG SI SIR SIS SISRE SLR National Institute of Standards National Oceanic and Atmospheric Administration Operational Control Segment Phase Center Variation Personal Digital Assistant Precise Differential GPS Position Dilution of Precision Precise Ephemerides Precise Orbit Determination Precise Point Positioning Precise Positioning Service Pseudo Random Noise Physikalisch Technische Bundesanstalt Radar Altimeter Radio Data System Radio Frequency Root Mean Square Error Regional Network Associate Analysis Center Radio Technical Commission for Marine Sciences Real Time Kinematic Selective Availability South American Datum Smithsonian Astrophysical Observatory Satellite Positioning Service Search And Rescue Synthetic Aperture Radar Satellite Based Augmentation System Spherical Error Probable Satellite Gravity Gradiometry International System of Units Shuttle Imaging Radar Signal in Space Signal in Space Range Error Satellite Laser Ranging SNR SPAD SPS SST SST SV SVN SWH T/P TAI TCB TCG TDB TDT TEC TECU TID TIGO TRF TT TTFA UEE UERE URE USCG USNO UT UTC VLBA VLBI VRS VSOP VTEC WAAS xix Signal-to-Noise Ratio Single Photon Avalanche Diode Standard Positioning Service Satellite-to-Satellite Tracking Sea Surface Topography Space Vehicle Space Vehicle Number Signiﬁcant Wave Height TOPEX/POSEIDON International Atomic Time Barycentric Coordinate Time Geocentric Coordinate Time Barycentric Dynamical Time Terrestrial Dynamical Time Total Electron Content Total Electron Content Unit Travelling Ionospheric Disturbances Transportable Integrated Geodetic Observatory Terrestrial Reference Frame Terrestrial Time Time To Fix Ambiguities User Equipment Error User Equivalent Range Error User Range Error U.S. Coast Guard U.S. Naval Observatory Universal Time Universal Time Coordinated Very Long Baseline Array Very Long Baseline Interferometry Virtual Reference Station VLBI Space Observatory Program Vertical Electron Content Wide Area Augmentation System WADGPS Wide Area Differential GPS 1 1.1 Introduction Subject of Satellite Geodesy Following the classical deﬁnition of Helmert (1880/1884), geodesy is the science of the measurement and mapping of the Earth’s 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 near-Earth, satellites. Further to Helmert’s 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, time-dependent variations. The basic problems are 1. determination of precise global, regional and local three-dimensional positions (e.g. the establishment of geodetic control) 2. determination of Earth’s gravity ﬁeld and linear functions of this ﬁeld (e.g. a precise geoid) 3. measurement and modeling of geodynamical phenomena (e.g. 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 e.g. geophysics, oceanography and navigation, and they form an integral part of geoinformatics. Since the launch of the ﬁrst artiﬁcial satellite, SPUTNIK-1, on October 4, 1957, satellite geodesy has developed into a self-contained ﬁeld in geodetic teaching and research, with close relations and interactions with adjacent ﬁelds (Fig. 1.1). 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 , geographical latitude ), and the astronomical azimuth A of a terrestrial mark are determined from the observation of natural celestial bodies, particularly ﬁxed stars. By Gravimetry we mean the measurement 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 1.1. 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 range-rates 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 geodetic-astronomic 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. [2.1.5]). The determination of coordinates in ellipsoidal or three-dimensional 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, e.g. 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 together. 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 information on Earth’s 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, e.g. Hein (1983). It 1.2 Classiﬁcation and Basic Concepts of Satellite Geodesy 3 ﬁnds a modern realization in the establishment of integrated geodetic-geodynamic observatories (see [12.5], 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 near-Earth satellites are almost exclusively utilized for the observations which are of interest in applied geodesy. Where necessary, other space techniques are dealt with. 1.2 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. Following the classical concepts of Earth-bound trigonometric networks, the satellites may be regarded as “ﬁxed” control points within large-scale or global threedimensional networks. If the satellites are observed simultaneously from different 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 P2 P1 method of satellite geodesy. The concept is illustrated in Fig. 1.2. It has been realized in its purest form through the N New BC4 World Network (see [5.1.5]). Station P3 Compared with classical techniques, the main advantage of the satellite methods is that they can bridge large distances, and thus establish geodetic ties Figure 1.2. Geometrical method; the satellite is between continents and islands. All a high target ground stations belonging to the network can be determined within a uniform, three-dimensional, 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 [3.1.1]. The essential value of the satellite is that it is a moving body within Earth’s gravity ﬁeld. This view leads to the dynamical method of satellite geodesy. The main advantage of satellite observations, when compared with classical techniques, 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 Earth’s ﬂattening, and the proof that the ﬁgure of Earth is non-symmetrical with respect to the equatorial plane (i.e. the pear-shape of Earth, cf. [12.2], Fig. 12.5, 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 its own coordinates”. The geocentric coordinates of the observing ground stations can be derived from the known satellite orbits. This so-called orbital P2 method of coordinate determination is P1 illustrated in Fig. 1.3. Ne wS N The combined determination of tat ion gravity ﬁeld parameters and geocentric P4 coordinates within the domain of dyP3 namical satellite geodesy leads to the general problem of parameter determination or parameter estimation. This may include the determination of the rotational parameters of Earth (Earth rotation, polar motion) as well as other geo- Figure 1.3. Orbital method; the satellite is a dynamical phenomena (cf. [4.1]). The sensor in Earth’s gravity ﬁeld dynamical method of satellite geodesy is also characterized as the indirect method, because the required parameters are determined implicitly from the orbital behavior of the satellites. The distinction geometric–dynamic has, for many years, characterized the development 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: 1.3 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 − satellite-to-satellite tracking (SST). Earth-bound 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. 1.3 Historical Development of Satellite Geodesy The proper development of satellite geodesy started with the launch of the ﬁrst artiﬁcial satellite, SPUTNIK-1, 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 = 1/303. Other solutions came, for example, from Hansen (1864) with f = 1/296, Helmert (1884) with f = 1/297.8, and Hill (1884) with f = 1/297.2 (see Wolf (1985), Torge (2001)). The geometrical approach in satellite geodesy also has some forerunners in the lunar methods. These methods have undergone comprehensive developments since the beginning of the last century. In this context, the Moon is regarded as a geometric target, where the geocentric coordinates are known from orbital theory. The directions between 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 1957/58 a ﬁrst outcome from a global program was obtained with the Dual Rate Moon Camera, developed by Markovitz (1954). The methods of this so-called 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), King-Hele (1958) and O’Keefe (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 determination of Earth’s ﬂattening as f = 1/298.3 from observations of EXPLORER-1 and SPUTNIK-2 by O’Keefe (1958), King-Hele, Merson (1958). Some signiﬁcant 6 1 Introduction events during the years following 1957 are 1957 1958 1958 1959 1959 1960 1960 1960 1962 1962 Launch of SPUTNIK-1, Earth’s Flattening from Satellite Data (f = 1/298.3), Launch of EXPLORER-1, Third Zonal Harmonic (Pear Shape of Earth), Theory of the Motion of Artiﬁcial Satellites (Brouwer), Launch of TRANSIT-1B, Launch of ECHO-1, Theory of Satellite Orbits (Kaula), Launch of ANNA-1B, and 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 Earth’s 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 optical-photographic 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 (e.g. GEM 10, GRIM). The increased accuracy of the observations made possible the measurement of geodynamical phenomena (Earth rotation, polar motion, crustal deformation). Doppler surveying was used worldwide for the installation and maintenance of geodetic control networks (e.g. 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 1.4 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 International Celestial Reference Frame ICRF, based on interferometric radio observations, and the International Terrestrial Reference Frame ITRF, based on different space techniques. 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, e.g. 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 geodetic space techniques is continuing. We have signiﬁcant improvements in accuracy 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 European Galileo, − reﬁnement in Earth observation, e.g. with high resolution radar sensors like interferometric SAR on various platforms, − further establishment of permanent arrays for disaster prevention and environmental monitoring, and − uniﬁcation of different geodetic space techniques in mobile integrated geodeticgeodynamic monitoring systems. 1.4 Applications of Satellite Geodesy The applications of geodetic satellite methods are determined by the achievable accuracy, 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 real-time or near real-time capabilities. Starting with the three basic tasks in satellite geodesy introduced in [1.1], we can give a short summary of possible applications: 8 1 Introduction Global Geodesy − general shape of Earth’s 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 three-dimensional 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 3D-control 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, agriculture, archaeology, expedition cartography etc. Navigation and Marine Geodesy − precise navigation of land-, sea-, and air-vehicles, − precise positioning for marine mapping, exploration, hydrography, oceanography, 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 possible applications. This aspect will be discussed together with the respective techniques. A summarizing discussion of possible applications is given in chapter [12]. 1.5 Structure and Objective of the Book 9 1.5 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 near-Earth 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 today’s 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 e.g. 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 [4]–[11]. The grouping into currently important observation methods is not without problems, because common aspects have to be taken up in different sections, and because the topical methods develop very quickly. This classiﬁcation is nevertheless preferred because the user is, in general, working with a particular observation technique, 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. Cross-references 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 problem-orientated summary of applications is given. The implications of satellite geodesy affect nearly all parts of geodesy and surveying. 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 2.1 Fundamentals 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 representation 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]. Terrestrial 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 individual methods. These particular systems are not necessarily identical because they may be based on different data and different deﬁnitions. Often the relationship between 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. 2.1.1 Cartesian Coordinate Systems and Coordinate Transformations z=z γ P xP zP γ β yP x x xP y y In a Cartesian coordinate system with the axes x, y, z the position of a point P is determined by its position vector xP x P = yP , (2.1) zP where xP , yP , zP are real numbers (Fig. 2.1). The transformation to a second Cartesian coordinate system with identical origin and the axes x , y , z , which is generated from the ﬁrst one by a rotation around the z-axis by the angle γ , can be realized through the matrix operation x P = R 3 (γ )x P (2.2) 0 α γ Figure 2.1. Cartesian coordinate system 2.1 Reference Coordinate Systems 11 with cos γ R 3 (γ ) = − sin γ 0 sin γ cos γ 0 0 0 . 1 (2.3) Equivalent rotations R 1 around the x-axis and R 2 around the y-axis are 1 0 0 cos β 0 − sin β sin α 1 0 . R 1 (α) = 0 cos α R 2 (β) = 0 0 − sin α cos α sin β 0 cos β The representation is valid for a right-handed coordinate system. When viewed towards the origin, a counter-clockwise rotation is positive. Any coordinate transformation can be realized through a combination of rotations. The complete transformation is x P = R 1 (α)R 2 (β)R 3 (γ )x P . (2.4) 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 R i (µ)Rj (ν) = Rj (ν)R i (µ). (3) Matrix multiplication is associative R i (Rj R k ) = (R i Rj )R k . (4) Rotations around the same axis are additive R i (µ)R i (ν) = R i (µ + ν). (5) Inverse and transpose are related by R −1 (µ) = R T (µ) = R i (−µ). i i (6) The following relationship also holds −1 (R i Rj )−1 = Rj R −1 . i (2.5) (2.6) (2.7) (2.8) (2.9) The polarity of coordinate axes can be changed with reﬂectionmatrices −1 0 0 1 0 0 1 0 0 S 1 = 0 1 0 ; S 2 = 0 −1 0 ; S 3 = 0 1 0 . 0 0 1 0 0 1 0 0 −1 (2.10) 12 2 Fundamentals Finally, the matrix for a general rotation by the angles α, β, γ is R= cos β cos γ sin α sin β cos γ − cos α sin γ cos α sin β cos γ + sin α sin γ cos β sin γ sin α sin β sin γ + cos α cos γ cosα sin β sin γ − sin α cos γ − sin β sin α cos β cos α cos β . (2.11) The relation between the position vectors in two arbitrarily rotated coordinate systems is then (2.12) x P = Rx P ; x P = R T x P . 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 1 R(α, β, γ ) = −γ β γ 1 −α −β α . 1 (2.13) Although matrix multiplication does not commute (cf. 2.5) the inﬁnitesimal rotation matrix (2.13) does commute. 2.1.2 Reference Coordinate Systems and Frames in Satellite Geodesy In modern terminology it is distinguished between − reference systems, − reference frames, and − conventional reference systems and frames. A reference system is the complete conceptual deﬁnition of how a coordinate system is formed. It deﬁnes the origin and the orientation of fundamental planes or axes of the system. It also includes the underlying fundamental mathematical and physical models. A conventional reference system is a reference system where all models, numerical constants and algorithms are explicitly speciﬁed. A reference frame means the practical realization of a reference system through observations. It consists of a set of identiﬁable ﬁducial points on the sky (e.g. stars, quasars) or on Earth’s surface (e.g. 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 space-ﬁxed, conventional inertial reference system (CIS) for the description of satellite motion, and − an Earth-ﬁxed, conventional terrestrial reference system (CTS) for the positions of the observation stations and for the description of results from satellite geodesy. 2.1 Reference Coordinate Systems 13 2.1.2.1 Conventional Inertial Systems and Frames Newton’s laws of motion [3.1.2] are only valid in an inertial reference system, i.e. a coordinate system at rest or in a state of uniform rectilinear motion wi |