# GPS Satellite Surveying. 4th Edition

• ID: 3024898
• Book
• 840 Pages
• John Wiley and Sons Ltd
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THE MOST COMPREHENSIVE, UP–TO–DATE GUIDE ON GPS TECHNOLOGY FOR SURVEYING

Three previous editions have established GPS Satellite Surveying as the definitive industry reference. Now fully updated and expanded to reflect the newest developments in the field, this Fourth Edition features cutting–edge information on GNSS antennas, precise point positioning, real–time relative positioning, lattice reduction, and much more. Expert authors examine additional tools and applications, offering complete coverage of geodetic surveying using satellite technologies.

The past decade has seen a major evolution in surveying technology. This comprehensive guide covers best practices and preferred methods, helping you:

• Get fully up to speed on the latest GPS/GNSS developments
• Explore the characteristics of satellite systems
• Understand how satellite technology is used in surveying
• Work with real–time kinematics relative positioning
• Examine in–depth information on adjustments and geodesy
• Learn the fundamentals of positioning, lattice adjustment, antennas, and more

GPS Satellite Surveying, Fourth Edition, offers reliable, up–to–date guidance for surveyors, transportation and civil engineers, geologists, geographers, technicians, and students.

Note: Product cover images may vary from those shown
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PREFACE xv

ACKNOWLEDGMENTS xix

ABBREVIATIONS xxi

1 INTRODUCTION 1

2 LEAST–SQUARES ADJUSTMENTS 11

2.1 Elementary Considerations 12

2.1.1 Statistical Nature of Surveying Measurements 12

2.1.2 Observational Errors 13

2.1.3 Accuracy and Precision 13

2.2 Stochastic and Mathematical Models 14

2.3 Mixed Model 17

2.3.1 Linearization 18

2.3.2 Minimization and Solution 19

2.3.3 Cofactor Matrices 20

2.3.4 A Posteriori Variance of Unit Weight 21

2.3.5 Iterations 22

2.4 Sequential Mixed Model 23

2.5 Model Specifications 29

2.5.1 Observation Equation Model 29

2.5.2 Condition Equation Model 30

2.5.3 Mixed Model with Observation Equations 30

2.5.4 Sequential Observation Equation Model 32

2.5.5 Observation Equation Model with Observed Parameters 32

2.5.6 Mixed Model with Conditions 34

2.5.7 Observation Equation Model with Conditions 35

2.6 Minimal and Inner Constraints 37

2.7 Statistics in Least–Squares Adjustment 42

2.7.1 Fundamental Test 42

2.7.2 Testing Sequential Least Squares 48

2.7.3 General Linear Hypothesis 49

2.7.4 Ellipses as Confidence Regions 52

2.7.5 Properties of Standard Ellipses 56

2.7.6 Other Measures of Precision 60

2.8 Reliability 62

2.8.1 Redundancy Numbers 62

2.8.2 Controlling Type–II Error for a Single Blunder 64

2.8.3 Internal Reliability 67

2.8.4 Absorption 67

2.8.5 External Reliability 68

2.8.6 Correlated Cases 69

2.9 Blunder Detection 70

2.9.1 Tau Test 71

2.9.2 Data Snooping 71

2.9.3 Changing Weights of Observations 72

2.10 Examples 72

2.11 Kalman Filtering 77

3 RECURSIVE LEAST SQUARES 81

3.1 Static Parameter 82

3.2 Static Parameters and Arbitrary Time–Varying Variables 87

3.3 Dynamic Constraints 96

3.4 Static Parameters and Dynamic Constraints 112

3.5 Static Parameter, Parameters Subject to Dynamic Constraints, and Arbitrary Time–Varying Parameters 125

4 GEODESY 129

4.1 International Terrestrial Reference Frame 131

4.1.1 Polar Motion 132

4.1.2 Tectonic Plate Motion 133

4.1.3 Solid Earth Tides 135

4.1.5 Relating of Nearly Aligned Frames 136

4.1.6 ITRF and NAD83 138

4.2 International Celestial Reference System 141

4.2.1 Transforming Terrestrial and Celestial Frames 143

4.2.2 Time Systems 149

4.3 Datum 151

4.3.1 Geoid 152

4.3.2 Ellipsoid of Rotation 157

4.3.3 Geoid Undulations and Deflections of the Vertical 158

4.3.4 Reductions to the Ellipsoid 162

4.4 3D Geodetic Model 166

4.4.1 Partial Derivatives 169

4.4.2 Reparameterization 170

4.4.3 Implementation Considerations 171

4.4.4 GPS Vector Networks 174

4.4.5 Transforming Terrestrial and Vector Networks 176

4.4.6 GPS Network Examples 178

4.5 Ellipsoidal Model 190

4.5.1 Reduction of Observations 191

4.5.2 Direct and Inverse Solutions on the Ellipsoid 195

4.5.3 Network Adjustment on the Ellipsoid 196

4.6 Conformal Mapping Model 197

4.6.1 Reduction of Observations 198

4.6.2 Angular Excess 200

4.6.3 Direct and Inverse Solutions on the Map 201

4.6.4 Network Adjustment on the Map 201

4.6.5 Similarity Revisited 203

4.7 Summary 204

5 SATELLITE SYSTEMS 207

5.1 Motion of Satellites 207

5.1.1 Kepler Elements 208

5.1.2 Normal Orbital Theory 210

5.1.3 Satellite Visibility and Topocentric Motion 219

5.1.4 Perturbed Satellite Motion 219

5.2 Global Positioning System 225

5.2.1 General Description 226

5.2.2 Satellite Transmissions at 2014 228

5.2.3 GPS Modernization Comprising Block IIM, Block IIF, and Block III 239

5.3 GLONASS 245

5.4 Galileo 248

5.5 QZSS 250

5.6 Beidou 252

5.7 IRNSS 254

5.8 SBAS: WAAS, EGNOS, GAGAN, MSAS, and SDCM 254

6 GNSS POSITIONING APPROACHES 257

6.1 Observables 258

6.1.1 Undifferenced Functions 261

6.1.2 Single Differences 271

6.1.3 Double Differences 273

6.1.4 Triple Differences 275

6.2 Operational Details 275

6.2.1 Computing the Topocentric Range 275

6.2.2 Satellite Timing Considerations 276

6.2.3 Cycle Slips 282

6.2.4 Phase Windup Correction 283

6.2.5 Multipath 286

6.2.6 Phase Center Offset and Variation 292

6.2.7 GNSS Services 295

6.3 Navigation Solution 299

6.3.1 Linearized Solution 299

6.3.2 DOPs and Singularities 301

6.3.3 Nonlinear Closed Solution 303

6.4 Relative Positioning 304

6.4.1 Nonlinear Double–Difference Pseudorange Solution 305

6.4.2 Linearized Double– and Triple–Differenced Solutions 306

6.4.3 Aspects of Relative Positioning 310

6.4.4 Equivalent Undifferenced Formulation 315

6.4.5 Ambiguity Function 316

6.4.6 GLONASS Carrier Phase 319

6.5 Ambiguity Fixing 324

6.5.1 The Constraint Solution 324

6.5.2 LAMBDA 327

6.5.3 Discernibility 334

6.5.4 Lattice Reduction and Integer Least Squares 337

6.6 Network–Supported Positioning 357

6.6.1 PPP 357

6.6.2 CORS 363

6.6.3 PPP–RTK 367

6.7 Triple–Frequency Solutions 382

6.7.1 Single–Step Position Solution 382

6.7.2 Geometry–Free TCAR 386

6.7.3 Geometry–Based TCAR 395

6.7.4 Integrated TCAR 396

6.7.5 Positioning with Resolved Wide Lanes 397

6.8 Summary 398

7 REAL–TIME KINEMATICS RELATIVE POSITIONING 401

7.1 Multisystem Considerations 402

7.2 Undifferenced and Across–Receiver Difference Observations 403

7.3 Linearization and Hardware Bias Parameterization 408

7.4 RTK Algorithm for Static and Short Baselines 418

7.4.1 Illustrative Example 422

7.5 RTK Algorithm for Kinematic Rovers and Short Baselines 429

7.5.1 Illustrative Example 431

7.6 RTK Algorithm with Dynamic Model and Short Baselines 435

7.6.1 Illustrative Example 437

7.7 RTK Algorithm with Dynamic Model and Long Baselines 441

7.7.1 Illustrative Example 442

7.8 RTK Algorithms with Changing Number of Signals 445

7.9 Cycle Slip Detection and Isolation 450

7.9.1 Solutions Based on Signal Redundancy 455

7.10 Across–Receiver Ambiguity Fixing 466

7.10.1 Illustrative Example 470

7.11 Software Implementation 473

8 TROPOSPHERE AND IONOSPHERE 475

8.1 Overview 476

8.2 Tropospheric Refraction and Delay 479

8.2.1 Zenith Delay Functions 482

8.2.2 Mapping Functions 482

8.2.3 Precipitable Water Vapor 485

8.3 Troposphere Absorption 487

8.3.1 The Radiative Transfer Equation 487

8.3.2 Absorption Line Profiles 490

8.3.3 General Statistical Retrieval 492

8.3.4 Calibration of WVR 494

8.4 Ionospheric Refraction 496

8.4.1 Index of Ionospheric Refraction 499

8.4.2 Ionospheric Function and Cycle Slips 504

8.4.3 Single–Layer Ionospheric Mapping Function 505

8.4.4 VTEC from Ground Observations 507

8.4.5 Global Ionospheric Maps 509

9 GNSS RECEIVER ANTENNAS 513

9.1 Elements of Electromagnetic Fields and Electromagnetic Waves 515

9.1.1 Electromagnetic Field 515

9.1.2 Plane Electromagnetic Wave 518

9.1.3 Complex Notations and Plane Wave in Lossy Media 525

9.1.4 Radiation and Spherical Waves 530

9.1.5 Receiving Mode 536

9.1.6 Polarization of Electromagnetic Waves 537

9.1.7 The dB Scale 544

9.2 Antenna Pattern and Gain 546

9.2.1 Receiving GNSS Antenna Pattern and Reference Station and Rover Antennas 546

9.2.2 Directivity 553

9.2.3 Polarization Properties of the Receiving GNSS Antenna 558

9.2.4 Antenna Gain 562

9.2.5 Antenna Effective Area 564

9.3 Phase Center 565

9.3.1 Antenna Phase Pattern 566

9.3.2 Phase Center Offset and Variations 568

9.3.3 Antenna Calibrations 575

9.3.4 Group Delay Pattern 577

9.4 Diffraction and Multipath 578

9.4.1 Diffraction Phenomena 578

9.4.2 General Characterization of Carrier Phase Multipath 585

9.4.3 Specular Reflections 587

9.4.4 Antenna Down–Up Ratio 593

9.4.5 PCV and PCO Errors Due to Ground Multipath 597

9.5 Transmission Lines 600

9.5.1 Transmission Line Basics 600

9.5.2 Antenna Frequency Response 606

9.5.3 Cable Losses 608

9.6 Signal–to–Noise Ratio 609

9.6.1 Noise Temperature 609

9.6.2 Characterization of Noise Sources 611

9.6.3 Signal and Noise Propagation through a Chain of Circuits 615

9.6.4 SNR of the GNSS Receiving System 619

9.7 Antenna Types 620

9.7.1 Patch Antennas 620

9.7.2 Other Types of Antennas 629

9.7.3 Flat Metal Ground Planes 629

9.7.4 Impedance Ground Planes 634

9.7.5 Vertical Choke Rings and Compact Rover Antenna 642

9.7.6 Semitransparent Ground Planes 644

9.7.7 Array Antennas 645

9.7.8 Antenna Manufacturing Issues 650

APPENDIXES

A GENERAL BACKGROUND 653

B THE ELLIPSOID 697

C CONFORMAL MAPPING 715

D VECTOR CALCULUS AND DELTA FUNCTION 741

E ELECTROMAGNETIC FIELD GENERATED BY ARBITRARY SOURCES, MAGNETIC CURRENTS, BOUNDARY CONDITIONS, AND IMAGES 747

F DIFFRACTION OVER HALF–PLANE 755

G SINGLE CAVITY MODE APPROXIMATION WITH PATCH ANTENNA ANALYSIS 759

H PATCH ANTENNAS WITH ARTIFICIAL DIELECTRIC SUBSTRATES 763

I CONVEX PATCH ARRAY GEODETIC ANTENNA 769

REFERENCES 773

AUTHOR INDEX 793

SUBJECT INDEX 801

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