B. Hofmann-Wellenhof,

H. Lichtenegger, J. Collins

Global Positioning System

Theory and Practice

Fifth, revised edition

Springer-Verlag Wien GmbH

Dr. Bernhard Hofmann-Wellenhof Dr. Herbert Lichtenegger Abteilung für Positionierung und Navigation, Technische Universität Graz Graz, Austria

Dr. J ames Collins GPS Services, lnc. Rockville, Maryland, U.S.A.

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those uf translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machines or similar means, and storage in data banks. © 2001 Springer-Verlag Wien Ursprünglich erschienen bei Springer-Verlag Wien New York 2001

Camera-ready copies provided by the authors Cover illustration: photograph courtesy of RockweIl International Printed by Novographic Druck G.m.b.H., A-1230 Wien Printed on acid-free and chlorine-free bleached paper SPIN 10772968

With 45 Figures

ISBN 978-3-211-83534-0 ISBN 978-3-7091-6199-9 (eBook) DOI 10.1007/978-3-7091-6199-9

We dedicate this book to

Benjamin William Remondi

Foreword

This book is dedicated to Dr. Benjamin William Remondi for many reasons.The project of writing a Global Positioning System (GPS) book was con­ceived in April 1988 at a GPS meeting in Darmstadt, Germany. Dr. Remondidiscussed with me the need for an additional GPS textbook and suggesteda possible joint effort. In 1989, I was willing to commit myself to such aproject. Unfortunately, the timing was less than ideal for Dr. Remondi.Therefore, I decided to st art the project with other coauthors. Dr. Remondiagreed and indicated his willingness to be a reviewer.

I selected Dr. Herbert Lichtenegger, my colleague from the TechnicalUniversity Graz, Austria, and Dr. James Collins from Rockville, Maryland,U.S.A.

In my opinion, the knowledge of the three authors should cover the widespectrum of GPS. Dr. Lichtenegger is a geodesist with broad experience inboth theory and practice. He has specialized his research to geodetic astron­omy including orbital theory and geodynamical phenomena. Since 1986,Dr. Lichtenegger 's main interest is dedicated to GPS. Dr. Collins retiredfrom the U.S. National Geodetic Survey in 1980, where he was the DeputyDirector. For the past ten years, he has been deeply involved in using GPStechnology with an emphasis on surveying. Dr. Collins was the founder andpresident of GeofHydro Inc. My own background is theoretically oriented.My first chief, Prof. Dr. Peter Meissl , was an excellent theoretician; and myformer chief, Prof. Dr.mult. Helmut Moritz, fortunately, still is.

It is appropriate here to say a word of thanks to Prof. Dr.mult. HelmutMoritz , whom I consider my mentor in science. He is - as is probably widelyknown - one of the world 's leading geodesists and is currently president ofthe International Union for Geodesy and Geophysics (IUGG). In the fall of1984, he told me I should go to the U.S.A. to learn about GPS. I certainlyagreed, although I did not even know what GPS meant. On the same day,Helmut Moritz called Admiral Dr. John Bossler, at that time the Director ofthe National Geodetic Survey, and my first stay in the U.S.A. was arranged.Thank you, Helmut! I still remember the flight where I started to readthe first articles on GPS. I found it interesting but I did not understandvery much. Benjamin W. Remondi deserves t he credit for providing myGPS instruction. He was a very patient and excellent teacher. I benefitedenormously, and I accepted his offer to return to the U.S.A. several times.Aside from the scientific aspect, our families have also become friends.

The selection of topics is certainly different from the original book con-

viii Foreword

ceived by Dr. Remondi. The primary selection criteria of the topics were:relevancy, tutorial content, and the interest and expertise ofthe authors. Thebook is intended to be a text on GPS, recognizing the tremendous need fortextual materials for professionals, teachers, and for students. The authorsbelieve that it was not necessary to dwell on the latest technical advances.Instead, concepts and techniques are emphasized.

The book can be employed as a classroom text at the senior or graduatelevels, depending on the level of specialization desired. It can be read, selec­tively, by professional surveyors, navigators, and many others who need toposition with GPS.

May 1992 B. Hofmann-Wellenhof

Preface

The contents of the book are partitioned into 13 chapters, a section of refer­ences, and a detailed index which should immediately help in finding certaintopics of interest.

The first chapter is a historical review. It shows the origins of surveyingand how global surveying techniques have been developed. In addition, ashort history on the Global Positioning System (GPS) is given.

The second chapter is an overview of GPS . The system is explained bymeans of its three segments: the space segment, the control segment, andthe user segment.

The third chapter deals with the reference systems, such as coordinateand time systems. The celestial and the terrestrial reference frames areexplained in the section on coordinate systems, and the transformation be­tween them is shown. The definition of different times is given in the sectionon time systems, together with appropriate conversion formulas .

The fourth chapter is dedicated to satellite orbits. This chapter specif­ically describes GPS orbits and covers the determination of the Keplerianand the perturbed orbit , as well as the dissemination of the orbital data.

The fifth chapter covers the satellite signal. It shows the fundamentalsof the signal structure with its various components and the principles of thesignal processing.

The sixth chapter deals with the observables. The data acquisitioncomprises code and phase pseudoranges and Doppler data. The chapteralso contains the data combinations, both the phase combinations and thephase/code range combinations. Influences affecting the observables are de­scribed: the atmospheric and relativistic effects, the impact of the antennaphase center, and multipath.

The seventh chapter is dedicated to surveying with GPS. This chapterdefines the terminology used and describes the planning of a GPS survey,surveying procedures, and in situ data processing.

The eighth chapter covers mathematical models for positioning. Modelsfor observed data are investigated. Therefore, models for point positioningand relative positioning, based on various data sets, are derived.

The ninth chapter comprises the data processing and deals with cycleslip detection and repair. This chapter also discusses phase ambiguity res­olution. The method of least squares adjustment is assumed to be knownto the reader and, therefore, only a brief review (including the principle ofKalman filtering) is presented. Consequently, no details are given apart from

x Preface

the linearization of the mathematical models, which are the input for theadjustment procedure.

The tenth chapter links the GPS results to a local datum. The necessarytransformations are given. The combination of GPS and terrestrial data isalso considered.

The eleventh chapter treats software modules. The intent of this chapteris not to give a detailed description of existing software and how it works.This chapter should help the reader decide which software would best suithis purposes . The very short sections of this chapter try to cover the varietyof features which could be relevant to the software.

The twelfth chapter des cribes some applications of GPS. Global, regional,and local uses are mentioned, as well as the installation of control networks.The compatibility of GPS with other systems, such as Inertial NavigationSystems (INS) and the Global Navigation Satellite System (GLONASS) , theRussian equivalent to GPS, is shown.

The thirteenth chapter deals with the future of GPS. Both critical as ­pects , such as selective availability and anti-spoofing, are discussed, alongwith positive aspects such as the combination of GPS with GLONASSand the International Maritime Satellite Communication Organization (IN­MARSAT) . Also, some possible improvements in the hardware and softwaretechnology are suggested.

The hyphenation is based on Webster's Dictionary. Therefore, some de­viations may appear for the reader accustomed to another hyphenation sys­tem. For example, the word "measurement", following Webster's Dictionary,is hyphenated mea-sure-ment; whereas, following The American HeritageDictionary, the hyphenation is meas-ure-ment. The Webster's hyphenationsystem also contains hyphenations which are sometimes unusual for wordswith a foreign language origin. An example is the word "parameter". Fol­lowing Webster's Dictionary, the hyphenation is pa-ram-e-ter. The word hasa Greek origin , and one would expect the hyphenation pa-ra-me-ter.

Symbols representing a vector or a matrix are underlined. The innerproduct of two vectors is indicated by a dot "." . The outer product, crossproduct, or vector product is indicated by the symbol " x" . The norm of avector, i.e., its length, is indicated by two double-bars "II" .

Many persons deserve credit and thanks. Dr. Benjamin W. Remondiof the National Geodetic Survey at Rockville, Maryland, was a reviewer ofthe book. He has critically read and corrected the full volume. His manysuggestions and improvements, critical remarks and proposals are gratefullyacknowledged.

A second technical proofreading was performed by Dipl.-Ing. GerhardKienast from the section of Surveying and Landinformation of the Technical

Preface Xl

University Graz. He has helped us with constructive critique and valuablesuggestions.

Nadine Collins kindly read and edited the book in its final form , improv­ing the flow and grammar of the text.

The index of the book was produced using a computer program writtenby Dr. Walter Klostius from the section of Surveying and Landinformationof the Technical University Graz. Also , his program helped in the detectionof spelling errors.

The book is compiled based on the text system Jb.TEX. Some of the figuresincluded were also developed with Jb.TEX. The remaining figures are drawn byusing Autocad 11.0. The section of Physical Geodesy of the Technical Uni­versity Graz deserves the thanks for these figures. Dr. Norbert Kiihtreiberhas drawn two of these figures, and the others were carefully developed byDr. Konrad Rautz. This shows that theoreticians are also well-suited forpractical tasks.

We are also grateful to the Springer Publishing Company for their adviceand cooperation.

Finally, the inclusion by name of a commercial company or product doesnot constitute an endorsement by the authors. In principle, such inclusionswere avoided whenever possible. Only those names which played a funda­mental role in receiver and processing development are included for historicalpurposes.

May 1992 B. Hofmann-Wellenhof H. Lichtenegger J. Collins

Preface to the fifth editionToday, writing a book on GPS is a completely different matter compared tothe task eight years ago when this book was released for the first time. Inthese eight years , a tremendous improvement in GPS knowledge has occurredwhich would impact a conceptually new book. Topics have evolved whichwere not discussed a few years ago, like the third civil frequency, and bycontrast , other topics have lost much of the importance of the earlier GPSyears . The World Wide Web (WWW) is another feature with strong impact .Some GPS information may be more reliably downloaded in updated formfrom the internet than read in a book. Examples are the steadily changingsatellite constellations and the RINEX format .

xu Preface

In the fifth edition, the afore-mentioned aspects have been consideredto some extent. However, the overall structure of the former editions isretained since this was the request of many reviewers. In addition, the mostrecent advances in GPS technology like the decision to switch off SelectiveAvailability (SA) , the GPS modernization covering the new signal structure,improvements in the space and the control segment, and the augmentationof GPS by satellite-based and ground-based systems leading to future GlobalNavigation Satellite Systems (GNSS) are considered.

An exterior restriction was the limited number of pages of the bookto keep a reasonable price. Figuratively, the more recent advances had tobe implemented in exchange against subjects which might be consideredwell known. For this reason, we also had to reduce the list of references.With some exceptions like books and monographs, we treated this subtlematter by omitting all references "older" than 1990. This was relativelyeasy in cases where more recent publications of the authors were availablebut more critical if this was not the case. Thus, to avoid eliminating namesof distinguished GPS pioneers, the person's name in connection with hisfundamental idea is mentioned accordingly.

The authors are very grateful to Steve Nerem from the University ofTexas at Austin for reporting us several errors we were not aware of. Stevewrote us in detail how to implement the corrections.

Similarly, the authors would like to thank the geodetic group of the DelftUniversity of Technology, The Netherlands, headed by Peter Teunissen, forsupporting us with many ideas and publications concerning the ambiguityresolution . Furthermore, Paul de Jonge and Christian Tiberius wrote us onthe rank deficiency problem in some of our models. This letter arrived brieflybefore the release of the fourth edition and could not be implied adequately.The fifth edition fully encompasses this aspect. Thanks also to Kees de Jongfor providing the figure on the SA discontinuity.

The authors would also like to thank Jan Kouba from the Geodetic Sur­vey of Canada at Ottawa, Shin-Chan Han from the Ohio State University,Maria Tsakiri from the Curtin University of Technology at Perth, Australia,and Werner Oberegger, Austria, for some hints and advices. Thanks also toWalter Klostius, Norbert Kiihtreiber, and Klaus Legat , all Graz Universityof Technology, for some help with the subject index and the figures.

The authors consider this edition the final one in the present structure;if another update should be required, the book will be written from thescratch . Your ideas for a future book and your advice is appreciated andencouraged.

August 2000 B. Hofmann-Wellenhof H. Lichtenegger J. Collins

Contents

Abbreviations

Numerical constants

xix

xxiii

1 Introduction 11.1 The origins of surveying 11.2 Development of global surveying techniques 1

1.2 .1 Optical global triangulation 21.2 .2 Electromagnetic global trilateration 2

1.3 History of the Global Positioning System 31.3.1 Nav igating with GPS 41.3 .2 Surveying with GPS 6

2 Overview of G PS 112.1 Basic concept 112.2 Space segment 12

2.2 .1 Constellation 122.2.2 Satellites 122.2.3 Operational capabilities 152.2.4 Denial of accuracy and access 15

2.3 Control segment 182.3.1 Master control station 192.3.2 Monitor stations 192.3 .3 Ground control stations 19

2.4 User segment 202.4.1 User ca tegories 202.4.2 Receiver types 212.4.3 Information services 23

3 Reference systems 253.1 Introduction 253.2 Coordinate syst ems 27

3.2.1 Definitions 273.2.2 Transformations 30

3.3 Time systems 353.3 .1 Definitions 353.3.2 Conversions 363.3 .3 Calendar 37

XlV Contents

4 Satellite orbits 394.1 Introduction 394.2 Orbit description 39

4.2.1 Keplerian motion 394.2 .2 Perturbed motion 474.2.3 Disturbing accelerations 50

4.3 Orbit determination 544.3 .1 Keplerian orbit 554.3 .2 Perturbed orbit 58

4.4 Orbit dissemination 634.4.1 Tracking networks 634.4.2 Ephemerides 65

5 Satellite signal 715.1 Signal structure 71

5.1.1 Physical fundamentals 715.1.2 Components of the signal 73

5.2 Signal processing , . . 775.2.1 Receiver design 785.2.2 Processing techniques 81

6 Observables 876.1 Data acquisition 87

6.1.1 Code pseudoranges 876.1.2 Phase pseudoranges 886.1.3 Doppler data 906.1.4 Biases and noise 91

6.2 Data combinations 926.2.1 Linear phase combinations 936.2 .2 Code pseudorange smoothing 94

6.3 Atmospheric effects 976.3.1 Phase and group velocity 976.3 .2 Ionospheric refraction 996.3.3 Tropospheric refraction 1066.3.4 Atmospheric monitoring 116

6.4 Relativistic effects 1186.4.1 Special relativity 1186.4.2 General relativity 1226.4.3 Relevant relativistic effects for GPS 122

6.5 Antenna phase center offset and variation 124

Contents xv

6.6 Multipath 1256.6 .1 General remarks 1256.6 .2 Mathematical model 1276.6.3 Multipath reduction 129

7 Surveying with GPS 1337.1 Introduction 133

7.1.1 Terminology definitions 1337.1.2 Observation techniques 1357.1.3 Field equipment 144

7.2 Planning a GPS survey 1467.2.1 General remarks 1467.2.2 Presurvey planning 1477.2 .3 Field reconnaissance 1557.2.4 Monumentation 1577.2.5 Organizational design 157

7.3 Surveying procedure 1627.3.1 Preobservation 1627.3.2 Observation 1657.3.3 Postobservation 1667.3.4 Ties to control monuments 167

7.4 In situ data processing 1687.4.1 Data transfer 1687.4.2 Data processing 1697.4.3 Trouble shooting and quality control 1717.4.4 Datum transformations 1757.4.5 Computation of plane coordinates 178

7.5 Survey report 179

8 Mathematical models for positioning 1818.1 Point positioning 181

8.1.1 Point positioning with code ranges 1818.1.2 Point positioning with carrier phases 1838.1.3 Point positioning with Doppler data 185

8.2 Differential positioning 1868.2 .1 Basic concept 1868.2.2 DGPS with code ranges 1868.2.3 DGPS with phase ranges 188

8.3 Relative positioning 1898.3 .1 Phase differences 1908.3.2 Correlations of the phase combinations . . . . . . . . . . . . . .. 1928.3.3 Static relative positioning 198

xvi Contents

8.3 .4 Kinematic relative positioning 2008.3.5 Pseudokinematic relative positioning 202

9 Data processing 2039.1 Data preprocessing 203

9.1.1 Data handling 2039.1.2 Cycle slip detection and repair 205

9.2 Ambiguity resolut ion 2139.2 .1 General aspects 2139.2.2 Basic approaches 2169.2.3 Search techniques 2239.2.4 Ambiguity validat ion 247

9.3 Adjustment , filtering, and smoothing 2489.3.1 Least squares adjustment 2489.3 .2 Kalman filt ering 2529.3.3 Smoothing 255

9.4 Adjustment of mathematical GPS models 2569.4.1 Linearization 2569.4 .2 Linear model for point positioning with code ranges 2579.4 .3 Linear model for point positioning with carrier phases 2609.4.4 Linear model for rela ti ve position ing 262

9.5 Net wor k adj ustment 2649.5 .1 Single baseline solution 2649.5.2 Mu ltipoint solution 2659.5.3 Single baseline versus multipoin t solu t ion 2689.5 .4 Least squares adjustment of baselines 269

9.6 Dilution of precision 2719.7 Accuracy measures 275

9.7.1 In troduction 2759.7.2 Chi-square distribution 2769.7 .3 Specifications 276

10 Transformation of GPS results 27910.1 Introduction 27910.2 Coordinate transformations 279

10.2.1 Cartesian coordinates and ellipsoidal coordinates 27910.2.2 Global coordinates and local level coordinates 28210.2.3 Ellipsoidal coordinates and plane coordinates 28510.2.4 Height transformation 290

10.3 Datum transformations 29210.3 .1 Three-dimensional transformation 29310.3.2 Two-dimensional transformation 29710.3.3 One-dimensional t ransformation 300

Contents xvii

10.4 Combining GPS and terrestrial data ... ... .. . 30210.4.1 Common coordinate system 30210.4.2 Representation of measurement quantities 303

11 Software modules 30911.1 Introduction 30911.2 Planning 30911.3 Data transfer 31011.4 Data processing 31111.5 Quality control 31311.6 Network computations 31411.7 Data base management 31511.8 Utilities 31611.9 Flexibility 317

12 Applications of GPS 31912.1 General uses of GPS 319

12.1.1 Global uses 32012.1.2 Regional uses 32212.1.3 Local uses 324

12.2 Attitude determination 32612.2.1 Theoretical considerat ions 32612.2 .2 Practical considerations 330

12.3 Airborne GPS for photo-control 33012.4 Interoperability of GPS 333

12.4.1 GPS and Inertial Navigation Systems 33312.4 .2 GPS and GLONASS 33412.4.3 GPS and other sensors 33812.4.4 GPS and the Federal Radionavigation Plan 338

12.5 Installation of control networks 33912.5 .1 Passive control networks 33912.5 .2 Active control networks 341

13 Future of GPS 34513.1 New application aspects 34513.2 GPS modernization 346

13.2.1 Future GPS satellites 34613.2.2 Augmented signal structure . . . . . . . . . . . . . . . . . . . . . . . . .. 346

13.3 GPS augmentation 34713.3.1 Ground-based augmentat ion 34813.3.2 Satellite-based augmentation 348

XVlll Contents

13.4 GNSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34813.4.1 GNSS development 34813.4 .2 GNSSjLoran-C integration 349

13.5 Hardware and software improvements 35013.5.1 Hardware 35013.5.2 Software 352

13.6 Conclusion 352

References 355

Subject index 371

Abbreviations

AFBAOCAROFA-SAVLCIACBISCDMACEPCEPCGSICCHAMPCIGNETCIOCODECORSCRFCSOCDARCDGPSDLLDMADMEDoDDOPDOSEDoTDRMSECEFEGMEGNOSEOPERSFAAFDMAFGCCFOC

Air Force BaseAuxiliary Output ChipAmbiguity Resolution On -the-FlyAnti-SpoofingAu tomatic Vehicle LocationCoarse/Acquisi t ionCentral Bureau Information SystemCode Division Multiple Acces sCelestial Ephemeris PoleCircular Error ProbableCivil GPS Service Interface CommitteeChallenging Mini -satellite PayloadCooperative International GPS NetworkConventional International OriginCenter for Orbit Determination in EuropeContinuously Operating Reference StationCelestial Reference FrameConsolidated Space Operations CenterData Radio ChannelDifferential GPSDelay Lock LoopDefense Mapping AgencyDistance Measuring EquipmentDepartment of DefenseDilution of PrecisionDynamics of Solid EarthDepartment of TransportationDistance Root Mean Square (error)Earth-Centered-Earth-FixedEarth Gravitational ModelEuropean Geostationary Navigation Overlay ServiceEarth Orientation ParametersEarth Remote Sensing (satellite)Federal Aviation AdministrationFrequency Division Multiple AccessFederal Geodetic Control CommitteeFull Operational Capability

xx

FRPFTPGBASGDOPGEOGICGIMGISGLONASSGNSSGOTEXGPSGRSHDOPHIRANHOWlAGIATIAUICRFIERSIFIGEBIGEXIGSILSINMARSATINSIOCIONIRMIRPISUITRFITSITUIUGGIVHSIWVJDJPL

Abbreviations

Federal Radionavigation PlanFile Transfer ProtocolGround-Based Augmentation SystemGeometric Dilution of PrecisionGeostationary Orbit (satellite)GPS Integrity ChannelGlobal Ionosphere MapGeographic Information SystemGlobal Navigation Satellite SystemGlobal Navigation Satellite SystemGlobal Orbit Tracking ExperimentGlobal Positioning SystemGeodetic Reference SystemHorizontal Dilution of PrecisionHigh Range Navigation (system)Hand-Over WordInternational Association of GeodesyInternational Atomic TimeInternational Astronomical UnionIERS (or International) Celestial Reference FrameInternational Earth Rotation ServiceIntermediate FrequencyInteragency GPS Executive BoardInternational GLONASS ExperimentInternational GPS Service (for Geodynamics)Instrument Landing SystemInternational Maritime Satellite (organization)Inertial Navigation SystemInitial Operational CapabilityInstitute of NavigationIERS (or International) Reference MeridianIERS (or International) Reference PoleInternational System of UnitsIERS (or International) Terrestrial Reference FrameIntelligent Transportation SystemInternational Telecommunication UnionInternational Union for Geodesy and GeophysicsIntelligent Vehicle/Highway SystemIntegrated Water VaporJulian DateJet Propulsion Laboratory

Abbreviations

JPOLAASLEOLEPLORANMEDLLMEOMITMITESMJDMLSMRSENADNAGUNANUNASANAVSTARNGSNIMANISNMEANNSSNSWCOCSOEMOTFOTRPCMCIAPDDPDOPPLLPPSPRCPRNRAIMRDSRFRINEXRRCRTCMRTK

xxi

Joint Program OfficeLocal Area Augmentation SystemLow Earth Orbit (satellite)Linear Error ProbableLong- Range Navigation (system)Multipath Estimating Delay Lock LoopMean Earth Orbit (satellite)Massachusetts Institute of TechnologyMiniature Interferometer Terminals for Earth SurveyingModified Julian DateMicrowave Landing SystemMean Radial Spherical ErrorNorth American DatumNotice Advisories to GLONASS UsersNotice Advisories to Navstar UsersNational Aeronautics and Space AdministrationNavigation System with Timing and RangingNational Geodetic SurveyNational Imagery and Mapping AgencyNavigation Information ServiceNational Marine Electronics AssociationNavy Navigation Satellite System (or TRANSIT)Naval Surface Warfare CenterOperational Control SystemOriginal Equipment ManufacturerOn-the-FlyOn-the-RunPC Memory Card International AssociationPresidential Decision DirectivePosition Dilution of PrecisionPhase Lock LoopPrecise Positioning ServicePseudorange CorrectionPseudorandom NoiseReceiver Autonomous Integrity MonitoringRadio Data SystemRadio FrequencyReceiver Independent Exchange (format)Range Rate CorrectionRadio Technical Commission for Maritime (services)Real- Time Kinematic

xxii

SASBASSDSEPSERIESSINEXSLRSNRSPOTSPSSVTACANTCARTDOPTECTLMTOPEXTOWTRFTTTVECUEREUHFURLUSCGUSGSUSNOUTUTCUTMVDOPVHFVLBIVORVRSWAASWADGPSWGSWRCWWW

Abbreviations

Selective AvailabilitySatellite-Based Augmentation SystemSelective DenialSpherical Error ProbableSatellite Emission Range Inferred Earth SurveyingSoftware Independent Exchange (format)Satellite Laser RangingSignal-to-Noise RatioSatellite Probatoire d 'Observation de la TerreStandard Positioning ServiceSpace VehicleTactical Air NavigationThree-Carrier Ambiguity ResolutionTime Dilution of PrecisionTotal Electron ContentTelemetry (word)(Ocean) Topography ExperimentTime-of-Week (count)Terrestrial Reference FrameTerrestrial TimeTotal Vertical Electron ContentUser Equivalent Range ErrorUltra High FrequencyUniform Resource LocatorU.S . Coast GuardU.S. Geological SurveyU.S. Naval ObservatoryUniversal TimeUniversal Time CoordinatedUniversal Transverse Mercator (projection)Vertical Dilution of PrecisionVery High FrequencyVery Long Baseline InterferometryVHF Omnidirectional Range (equipment)Virtual Reference StationWide Area Augmentation SystemWide Area Differential GPSWorld Geodetic SystemWorld Radio ConferenceWorld Wide Web

Numerical constants

GPS signal frequencies

fa = 10.23 MHz fundamental frequencyL1 = 1575.42 MHz primary carrier frequencyL2 = 1 227.60 MHz secondary carrier frequency

WGS-84

a = 6378137.0mf = 1/298.257223563WE = 7292115.10-11 rad s"!GM = 3986004.418 · 108 m3 S-2

semimajor axis of ellipsoidflattening of ellipsoidangular velocity of the earthearth 's gravitational constant

b 6356 752.31425 m semiminor axis of ellipsoide2 6.694379990 13 . 10-3 first numerical eccentricitye,2 6.739496 74226 . 10-3 second numerical eccentricity

Various constants

c = 299792458 m s-1WE = 7292115.1467· 10-11 rad 5-

1

CD = January 6.0,1980JD = 2444244.5

velocity of lightuntruncated angular velocityCivil date of GPS standard epochJulian date of GPS standard epoch