Table of Contents
Preface
Table of Contents
Introduction 1
1. REFERENCE SYSTEMS Yehuda Bock 3
1.1 Introduction 3
1.1.1 Basic GPS Model 4
1.1.2 The Fundamental Polyhedron 5
1.2 Transformation Between the CRF and TRF 6
1.3 Time Systems 8
1.3.1 Atomic Time 9
1.3.2 Dynamical Time 10
1.3.3 Sidereal and Universal Time 11
1.4 Motion of the Earth's Rotation Axis 12
1.4.1 Motion in Celestial System 13
1.4.2 Motion in Terrestrial System 15
1.5 Earth Deformation 18
1.5.1 Rotation vs. Deformation 18
1.5.2 Global Plate Motion 20
1.5.3 Tidal Effects 21
1.5.4 Regional and Local Effects 24
1.5.5 Non-Physical Effects 24
1.6 Conventional Reference Systems 25
1.6.1 International Earth Rotation Service (IERS) 25
1.6.2 Celestial Reference System 25
1.6.3 Terrestrial Reference System 26
1.6.4 Transformation Between ICRF and ITRF 27
1.6.5 WGS 84 27
1.6.6 Ellipsoidal and Local Frames 28
1.6.7 Similarity Transformation 29
1.7 The IGS 30
1.8 Summary 32
Acknowledgements 32
References 34
2. GPS SATELLITE ORBITS Gerhard Beutler 37
2.1 Introduction 37
2.2 Equations of Motion for GPS 40
2.2.1 The Keplerian Elements 40
2.2.2 Equations of Motion in Rectangular Coordinates 44
2.2.3 The Perturbation Equations in the Elements 51
2.2.4 Mean Elements 59
2.2.5 The Parametrization of Satellite Orbits,
Linearization of the Orbit Determination Problem 68
2.2.6 Numerical Integration 71
2.3 The Perturbing Forces Acting on GPS Satellites 79
2.3.1 Overview 79
2.3.2 The Radiation Pressure Models 79
2.3.3 Resonance Effects in GPS Satellite Orbits 81
2.3.4 Development of the Satellite Orbits Since mid 1992 85
2.4 GPS Orbit Types 92
2.4.1 Broadcast and Precise Orbits 92
2.4.2 The IGS Orbits 93
2.4.3 Propagation of Orbit Errors into Baselines and
Networks 95
2.5 Summary and Conclusions 97
Acknowledgements 99
References 99
3. PROPAGATION OF THE GPS SIGNALS Richard B. Langley 103
3.1 Introduction 103
3.2 Electromagnetic Waves 103
3.3 The GPS Signals 106
3.3.1 The Carriers 107
3.3.2 The Codes 108
3.3.3 The Broadcast Message 110
3.3.4 Binary Biphase Modulation 111
3.3.5 The GPS Satellite Clocks and Time 111
3.3.6 Polarisation 112
3.3.7 Putting it all Together 112
3.4 Propagation of Signals in Refractive Media 114
3.4.1 Refractive Index 114
3.4.2 Phase Delay and Group Delay 116
3.5 Atmospheric Refraction 117
3.5.1 Troposphere 117
3.5.2 Ionosphere 126
3.6 Signal Multipath and Scattering 132
3.6.1 Multipath 132
3.6.2 Scattering 134
3.7 Summary 135
Acknowledgements 135
References 135
4. GPS RECEIVERS AND THE OBSERVABLES Richard B. Langley 141
4.1 Introduction 141
4.2 GPS Receivers 143
4.2.1 The Building Blocks 142
4.3 GPS Observables 151
4.3.1 The Pseudorange 151
4.3.2 The Carrier Phase 154
4.3.3 Data Recording 155
4.4 Observation Measurement Errors 156
4.4.1 Thermal Noise 166
4.4.2 Other Measurement Errors 171
4.5 Summary 172
References 172
5. GPS OBSERVATION EQUATIONS AND POSITIONING CONCEPTS
Peter J. G. Teunissen and Alfred Kleusberg 176
5.1 Introduction 176
5.2 GPS Observables 176
5.2.1 The Pseudorange 177
5.2.2 The Carrier Phase 180
5.3 Linear Combinations 182
5.3.1 Single Receiver, Single Satellite, Single Epoch
Linear Combinations 182
5.3.2 Phase Difference Over Time 186
5.3.3 Measurement Difference Between Receivers 187
5.3.4 Measurement Difference Between Satellites 189
5.3.5 Measurement Difference Between Satellites and
Receivers 190
5.4 Single Receiver Nonpositioning Models 191
5.4.1 The Simplified Observation Equations 191
5.4.2 On Single and Dual Frequency Pseudoranges and
Carrier Phases 193
5.5 The Linearized Observation Equations for Positioning 199
5.5.1 The Linearization 199
5.5.2 Single-Point Positioning 201
5.5.3 Relative Positioning 203
5.6 Relative Positioning Models 205
5.6.1 Relative Positioning Using Pseudoranges 205
5.6.2 Relative Positioning Using Carrier Phases 207
5.6.3 On the Slowly Changing Receiver-Satellite Geometry 210
5.7 Summary 216
References 216
6. SINGLE-SITE GPS MODELS Clyde C. Goad 219
6.1 Introduction 219
6.2 Pseudorange Relation 219
6.2.1 Calculation of the Distance Term when Using ECF
Coordinates 220
6.2.2 Linearization 222
6.2.3 Equivalence of the Linear Gauss-Markov Models with
and Without Nuisance Parameters 224
6.2.4 Searching 225
6.3 Direct Solution of Position and Receiver Clock Offset -
Bancroft's Solution (No a Priori Information Regarding
Position) 227
6.3.1 The Solution 228
6.4 Dilution of Precision 231
6.5 Combining Phase and Pseudorange for Single-Site
Determinations 233
6.5.1 Single Frequency Smoothing 234
6.5.2 Dual Frequency Smoothing 234
6.5.3 Discussion 235
6.6 Summary 237
References 237
7. SHORT DISTANCE GPS MODELS Clyde C. Goad 239
7.1 Introduction 239
7.2 Short Distance GPS Models 239
7.2.1 Double Difference Schemes 240
7.2.2 Dynamic Ranges of Double Differences 243
7.2.3 Use of Pseudoranges 244
7.2.4 Dual-Frequency Solutions 245
7.2.5 Other Combinations of Dual-Frequency Phases 246
7.2.6 Effect of the Ionosphere and Troposphere on Short
Baselines 246
7.3 Use of Both Pseudoranges and Phases 247
7.3.1 A Review 248
7.3.2 The Three-Measurement Combinations 251
7.3.3 Anti-Spoofing? 254
7.3.4 Ambiguity Search 254
7.3.5 Nonstatic / Quasi-Static Situation 256
7.3.6 Fast Ambiguity Resolution 256
7.4 Disadvantages of Double Differences 257
7.4.1 Single Differences 258
7.5 Sequential Versus Batch Processing 258
7.6 Network Adjustment - The Final Step 259
7.7 Summary 261
References 261
8. GPS CARRIER PHASE AMBIGUITY FIXING CONCEPTS
Peter J. G. Teunissen 263
8.1 Introduction 263
8.2 Integer Least-Squares Adjustment and Testing 265
8.2.1 The Double-Differenced Carrier Phase Observation
Equations 265
8.2.2 The Float and Fixed Least-Squares Solution 268
8.2.3 Validating the Float and Fixed Solution 271
8.3 Search for the Integer Least-Squares Ambiguities 278
8.3.1 The Ambiguity Search Space and its Planes of
Support 278
8.3.2 Sequential Conditional Least-Squares Ambiguities 282
8.3.3 On the DD Ambiguity Precision and Correlation 288
8.4 The Invertible Ambiguity Transformations 295
8.4.1 The DD Ambiguities are not Unique 295
8.4.2 Linear Combinations of the L1 and L2 DD Carrier
Phases 297
8.4.3 Single-Channel Ambiguity Transformations 302
8.4.4 Multi-Channel Ambiguity Transformations 305
8.5 The LSQ Ambiguity Decorrelation Adjustment 308
8.5.1 The Reparametrized Integer Least-Squares Problem 308
8.5.2 A 2-D Decorrelating Ambiguity Transformation 310
8.5.3 The Decorrelated Least-Squares Ambiguities 316
8.5.4 On the GPS Spectra of Ambiguity Conditional
Variances 326
8.6 Summary 330
Acknowledgement 332
References 333
9. MEDIUM DISTANCE GPS MEASUREMENTS Yehuda Bock 337
9.1 Introduction 337
9.1.1 Definition of Medium Distance 337
9.1.2 Unique Aspects of Medium Distance Measurements 338
9.1.3 Types of Medium Distance Measurements 339
9.2 GPS Models at Medium Distances 340
9.2.1 Mathematical and Stochastic Models 340
9.2.2 Estimated Parameters 347
9.3 Analysis Modes 349
9.3.1 Baseline Mode 350
9.3.2 Session Mode 350
9.3.3 Distributed Session Mode 351
9.3.4 Point Positioning Mode 352
9.3.5 Kinematic and Rapid Static Modes 353
9.3.6 Dynamic Mode 354
9.4 Network Adjustment 354
9.4.1 Free-Network Quasi-Observation Approach 354
9.4.2 Integration with other Geodetic Measurements 358
9.4.3 Software Independent Exchange Format (SINEX) 358
9.4.4 Estimation Procedures 359
9.4.5 Common-Mode Analysis of Adjusted Positions 363
9.5 Case Studies 364
9.5.1 Southern California Permanent GPS Geodetic Array 364
9.5.2 GPS STORM Experiment for Mapping Atmospheric Water
Vapor 370
9.6 Summary 372
Acknowledgements 374
References 375
10. THE GPS AS A TOOL IN GLOBAL GEODYNAMICS Gerhard Beutler 379
10.1 Introduction 379
10.2 The Partial Derivatives of the GPS Observable with
Respect to the Parameters of Global Geodynamics 380
10.3 Geodynamical Parameters not Accessible to the GPS 383
10.4 Estimating Tropospheric Refraction 385
10.5 Miscellaneous Orbit Modeling 388
10.6 Satellite- and Receiver- Clock Estimation 392
10.7 Producing Annual Solutions 393
10.8 Results 394
10.8.1 Earth Rotation Parameters 394
10.8.2 Troposphere Parameters 400
10.8.3 Station Coordinates and Velocities 400
10.8.4 The Impact of Ambiguity Resolution on Global GPS
Analyses 404
10.9 Summary 405
Acknowledgements 406
References 407
