GPS Satellite Surveying

Employ the latest satellite positioning tech with this extensive guide GPS Satellite Surveying is the classic text on the subject, providing the most comprehensive coverage of global navigation satellite systems applications for surveying. Fully updated and expanded to reflect the field's latest developments, this new edition contains new information on GNSS antennas, Precise Point Positioning, Real-time Relative Positioning, Lattice Reduction, and much more. New contributors offer additional insight that greatly expands the book's reach, providing readers with complete, in-depth coverage of geodetic surveying using satellite technologies. The newest, most cutting-edge tools, technologies, and applications are explored in-depth to help readers stay up to date on best practices and preferred methods, giving them the understanding they need to consistently produce more reliable measurement. Global navigation satellite systems have an array of uses in military, civilian, and commercial applications. In surveying, GNSS receivers are used to position survey markers, buildings, and road construction as accurately as possible with less room for human error. GPS Satellite Surveying provides complete guidance toward the practical aspects of the field, helping readers to: Get up to speed on the latest GPS/GNSS developments Understand how satellite technology is applied to surveying Examine in-depth information on adjustments and geodesy Learn the fundamentals of positioning, lattice adjustment, antennas, and more The surveying field has seen quite an evolution of technology in the decade since the last edition's publication. This new edition covers it all, bringing the reader deep inside the latest tools and techniques being used on the job. Surveyors, engineers, geologists, and anyone looking to employ satellite positioning will find GPS Satellite Surveying to be of significant assistance. Cover 1 Title Page 5 Copyright 6 Contents 7 Preface 17 Acknowledgments 21 Abbreviations 23 Chapter 1 Introduction 29 Chapter 2 Least-Squares Adjustments 39 2.1 Elementary Considerations 40 2.1.1 Statistical Nature of Surveying Measurements 40 2.1.2 Observational Errors 41 2.1.3 Accuracy and Precision 41 2.2 Stochastic and Mathematical Models 42 2.3 Mixed Model 45 2.3.1 Linearization 46 2.3.2 Minimization and Solution 47 2.3.3 Cofactor Matrices 48 2.3.4 A Posteriori Variance of Unit Weight 49 2.3.5 Iterations 50 2.4 Sequential Mixed Model 51 2.5 Model Specifications 57 2.5.1 Observation Equation Model 57 2.5.2 Condition Equation Model 58 2.5.3 Mixed Model with Observation Equations 58 2.5.4 Sequential Observation Equation Model 60 2.5.5 Observation Equation Model with Observed Parameters 60 2.5.6 Mixed Model with Conditions 62 2.5.7 Observation Equation Model with Conditions 63 2.6 Minimal and Inner Constraints 65 2.7 Statistics in Least-Squares Adjustment 70 2.7.1 Fundamental Test 70 2.7.2 Testing Sequential Least Squares 76 2.7.3 General Linear Hypothesis 77 2.7.4 Ellipses as Confidence Regions 80 2.7.5 Properties of Standard Ellipses 84 2.7.6 Other Measures of Precision 88 2.8 Reliability 90 2.8.1 Redundancy Numbers 90 2.8.2 Controlling Type-II Error for a Single Blunder 92 2.8.3 Internal Reliability 95 2.8.4 Absorption 95 2.8.5 External Reliability 96 2.8.6 Correlated Cases 97 2.9 Blunder Detection 98 2.9.1 Tau Test 99 2.9.2 Data Snooping 99 2.9.3 Changing Weights of Observations 100 2.10 Examples 100 2.11 Kalman Filtering 105 Chapter 3 Recursive Least Squares 109 3.1 Static Parameter 110 3.2 Static Parameters and Arbitrary Time-Varying Variables 115 3.3 Dynamic Constraints 124 3.4 Static Parameters and Dynamic Constraints 140 3.5 Static Parameter, Parameters Subject to Dynamic Constraints, and Arbitrary Time-Varying Parameters 153 Chapter 4 Geodesy 157 4.1 International Terrestrial Reference Frame 159 4.1.1 Polar Motion 160 4.1.2 Tectonic Plate Motion 161 4.1.3 Solid Earth Tides 163 4.1.4 Ocean Loading 163 4.1.5 Relating of Nearly Aligned Frames 164 4.1.6 ITRF and NAD83 166 4.2 International Celestial Reference System 169 4.2.1 Transforming Terrestrial and Celestial Frames 171 4.2.2 Time Systems 177 4.3 Datum 179 4.3.1 Geoid 180 4.3.2 Ellipsoid of Rotation 185 4.3.3 Geoid Undulations and Deflections of the Vertical 186 4.3.4 Reductions to the Ellipsoid 190 4.4 3D Geodetic Model 194 4.4.1 Partial Derivatives 197 4.4.2 Reparameterization 198 4.4.3 Implementation Considerations 199 4.4.4 GPS Vector Networks 202 4.4.5 Transforming Terrestrial and Vector Networks 204 4.4.6 GPS Network Examples 206 4.4.6.1 Montgomery County Geodetic Network 206 4.4.6.2 SLC Engineering Survey 210 4.4.6.3 Orange County Densification 211 4.5 Ellipsoidal Model 218 4.5.1 Reduction of Observations 219 4.5.1.1 Angular Reduction to Geodesic 220 4.5.1.2 Distance Reduction to Geodesic 221 4.5.2 Direct and Inverse Solutions on the Ellipsoid 223 4.5.3 Network Adjustment on the Ellipsoid 224 4.6 Conformal Mapping Model 225 4.6.1 Reduction of Observations 226 4.6.2 Angular Excess 228 4.6.3 Direct and Inverse Solutions on the Map 229 4.6.4 Network Adjustment on the Map 229 4.6.5 Similarity Revisited 231 4.7 Summary 232 Chapter 5 Satellite Systems 235 5.1 Motion of Satellites 235 5.1.1 Kepler Elements 236 5.1.2 Normal Orbital Theory 238 5.1.3 Satellite Visibility and Topocentric Motion 247 5.1.4 Perturbed Satellite Motion 247 5.1.4.1 Gravitational Field of the Earth 248 5.1.4.2 Acceleration due to the Sun and the Moon 250 5.1.4.3 Solar Radiation Pressure 250 5.1.4.4 Eclipse Transits and Yaw Maneuvers 251 5.2 Global Positioning System 253 5.2.1 General Description 254 5.2.2 Satellite Transmissions at 2014 256 5.2.2.1 Signal Structure 257 5.2.2.2 Navigation Message 265 5.2.3 GPS Modernization Comprising Block IIM, Block IIF, and Block III 267 5.2.3.1 Introducing Binary Offset Carrier (BOC) Modulation 269 5.2.3.2 Civil L2C Codes 271 5.2.3.3 Civil L5 Code 271 5.2.3.4 M-Code 272 5.2.3.5 Civil L1C Code 272 5.3 GLONASS 273 5.4 Galileo 276 5.5 QZSS 278 5.6 Beidou 280 5.7 IRNSS 282 5.8 SBAS: WAAS, EGNOS, GAGAN, MSAS, and SDCM 282 Chapter 6 GNSS Positioning Approaches 285 6.1 Observables 286 6.1.1 Undifferenced Functions 289 6.1.1.1 Pseudoranges 289 6.1.1.2 Carrier Phases 291 6.1.1.3 Range plus Ionosphere 294 6.1.1.4 Ionospheric-Free Functions 294 6.1.1.5 Ionospheric Functions 295 6.1.1.6 Multipath Functions 295 6.1.1.7 Ambiguity-Corrected Functions 296 6.1.1.8 Triple-Frequency Subscript Notation 297 6.1.2 Single Differences 299 6.1.2.1 Across-Receiver Functions 299 6.1.2.2 Across-Satellite Functions 300 6.1.2.3 Across-Time Functions 300 6.1.3 Double Differences 301 6.1.4 Triple Differences 303 6.2 Operational Details 303 6.2.1 Computing the Topocentric Range 303 6.2.2 Satellite Timing Considerations 304 6.2.2.1 Satellite Clock Correction and Timing Group Delay 306 6.2.2.2 Intersignal Correction 307 6.2.3 Cycle Slips 310 6.2.4 Phase Windup Correction 311 6.2.5 Multipath 314 6.2.6 Phase Center Offset and Variation 320 6.2.6.1 Satellite Phase Center Offset 320 6.2.6.2 User Antenna Calibration 321 6.2.7 GNSS Services 323 6.2.7.1 IGS 323 6.2.7.2 Online Computing 326 6.3 Navigation Solution 327 6.3.1 Linearized Solution 327 6.3.2 DOPs and Singularities 329 6.3.3 Nonlinear Closed Solution 331 6.4 Relative Positioning 332 6.4.1 Nonlinear Double-Difference Pseudorange Solution 333 6.4.2 Linearized Double- and Triple-Differenced Solutions 334 6.4.3 Aspects of Relative Positioning 338 6.4.3.1 Singularities 338 6.4.3.2 Impact of a Priori Position Error 339 6.4.3.3 Independent Baselines 340 6.4.3.4 Antenna Swap Technique 342 6.4.4 Equivalent Undifferenced Formulation 343 6.4.5 Ambiguity Function 344 6.4.6 GLONASS Carrier Phase 347 6.5 Ambiguity Fixing 352 6.5.1 The Constraint Solution 352 6.5.2 LAMBDA 355 6.5.3 Discernibility 362 6.5.4 Lattice Reduction and Integer Least Squares 365 6.5.4.1 Branch-and-Bound Approach 366 6.5.4.2 Finke-Pohst Algorithm 377 6.5.4.3 Lattice Reduction Algorithms 379 6.5.4.4 Other Searching Strategies 382 6.5.4.5 Connection Between LAMBDA and LLL Methods 384 6.6 Network-Supported Positioning 385 6.6.1 PPP 385 6.6.2 CORS 391 6.6.2.1 Differential Phase and Pseudorange Corrections 391 6.6.2.2 RTK 393 6.6.3 PPP-RTK 395 6.6.3.1 Single-Frequency Solution 395 6.6.3.2 Dual-Frequency Solutions 400 6.6.3.3 Across-Satellite Differencing 407 6.7 Triple-Frequency Solutions 410 6.7.1 Single-Step Position Solution 410 6.7.2 Geometry-Free TCAR 414 6.7.2.1 Resolving EWL Ambiguity 417 6.7.2.2 Resolving the WL Ambiguity 419 6.7.2.3 Resolving the NL Ambiguity 421 6.7.3 Geometry-Based TCAR 423 6.7.4 Integrated TCAR 424 6.7.5 Positioning with Resolved Wide Lanes 425 6.8 Summary 426 Chapter 7 Real-Time Kinematics Relative Positioning 429 7.1 Multisystem Considerations 430 7.2 Undifferenced and Across-Receiver Difference Observations 431 7.3 Linearization and Hardware Bias Parameterization 436 7.4 RTK Algorithm for Static and Short Baselines 446 7.4.1 Illustrative Example 450 7.5 RTK Algorithm for Kinematic Rovers and Short Baselines 457 7.5.1 Illustrative Example 459 7.6 RTK Algorithm with Dynamic Model and Short Baselines 463 7.6.1 Illustrative Example 465 7.7 RTK Algorithm with Dynamic Model and Long Baselines 469 7.7.1 Illustrative Example 470 7.8 RTK Algorithms with Changing Number of Signals 473 7.9 Cycle Slip Detection and Isolation 478 7.9.1 Solutions Based on Signal Redundancy 483 7.10 Across-Receiver Ambiguity Fixing 494 7.10.1 Illustrative Example 498 7.11 Software Implementation 501 Chapter 8 Troposphere and Ionosphere 503 8.1 Overview 504 8.2 Tropospheric Refraction and Delay 507 8.2.1 Zenith Delay Functions 510 8.2.2 Mapping Functions 510 8.2.3 Precipitable Water Vapor 513 8.3 Troposphere Absorption 515 8.3.1 The Radiative Transfer Equation 515 8.3.2 Absorption Line Profiles 518 8.3.3 General Statistical Retrieval 520 8.3.4 Calibration of WVR 522 8.4 Ionospheric Refraction 524 8.4.1 Index of Ionospheric Refraction 527 8.4.2 Ionospheric Function and Cycle Slips 532 8.4.3 Single-Layer Ionospheric Mapping Function 533 8.4.4 VTEC from Ground Observations 535 8.4.5 Global Ionospheric Maps 537 8.4.5.1 IGS GIMs 537 8.4.5.2 International Reference Ionosphere 537 8.4.5.3 GPS Broadcast Ionospheric Model 538 8.4.5.4 NeQuick Model 538 8.4.5.5 Transmission to the User 539 Chapter 9 GNSS Receiver Antennas 541 9.1 Elements of Electromagnetic Fields and Electromagnetic Waves 543 9.1.1 Electromagnetic Field 543 9.1.2 Plane Electromagnetic Wave 546 9.1.3 Complex Notations and Plane Wave in Lossy Media 553 9.1.4 Radiation and Spherical Waves 558 9.1.5 Receiving Mode 564 9.1.6 Polarization of Electromagnetic Waves 565 9.1.7 The dB Scale 572 9.2 Antenna Pattern and Gain 574 9.2.1 Receiving GNSS Antenna Pattern and Reference Station and Rover Antennas 574 9.2.2 Directivity 581 9.2.3 Polarization Properties of the Receiving GNSS Antenna 586 9.2.4 Antenna Gain 590 9.2.5 Antenna Effective Area 592 9.3 Phase Center 593 9.3.1 Antenna Phase Pattern 594 9.3.2 Phase Center Offset and Variations 596 9.3.3 Antenna Calibrations 603 9.3.4 Group Delay Pattern 605 9.4 Diffraction and Multipath 606 9.4.1 Diffraction Phenomena 606 9.4.2 General Characterization of Carrier Phase Multipath 613 9.4.3 Specular Reflections 615 9.4.4 Antenna Down-Up Ratio 621 9.4.5 PCV and PCO Errors Due to Ground Multipath 625 9.5 Transmission Lines 628 9.5.1 Transmission Line Basics 628 9.5.2 Antenna Frequency Response 634 9.5.3 Cable Losses 636 9.6 Signal-to-Noise Ratio 637 9.6.1 Noise Temperature 637 9.6.2 Characterization of Noise Sources 639 9.6.3 Signal and Noise Propagation through a Chain of Circuits 643 9.6.4 SNR of the GNSS Receiving System 647 9.7 Antenna Types 648 9.7.1 Patch Antennas 648 9.7.2 Other Types of Antennas 657 9.7.3 Flat Metal Ground Planes 657 9.7.4 Impedance Ground Planes 662 9.7.5 Vertical Choke Rings and Compact Rover Antenna 670 9.7.6 Semitransparent Ground Planes 672 9.7.7 Array Antennas 673 9.7.8 Antenna Manufacturing Issues 678 Appendix A General Background 681 A.1 Spherical Trigonometry 681 A.2 Rotation Matrices 685 A.3 Linear Algebra 685 A.3.1 Determinants and Matrix Inverse 686 A.3.2 Eigenvalues and Eigenvectors 687 A.3.3 Eigenvalue Decomposition 688 A.3.4 Quadratic Forms 689 A.3.5 Matrix Partitioning 692 A.3.6 Cholesky Decomposition 694 A.3.7 Partial Minimization of Quadratic Functions 697 A.3.8 QR Decomposition 701 A.3.9 Rank One Update of Cholesky Decomposition 704 A.4 Linearization 709 A.5 Statistics 711 A.5.1 One-Dimensional Distributions 711 A.5.2 Distribution of Simple Functions 716 A.5.3 Hypothesis Tests 717 A.5.4 Multivariate Distributions 719 A.5.5 Variance-Covariance Propagation 721 A.5.6 Multivariate Normal Distribution 723 Appendix B The Ellipsoid 725 B.1 Geodetic Latitude, Longitude, and Height 726 B.2 Computation on the Ellipsoidal Surface 731 B.2.1 Fundamental Coefficients 731 B.2.2 Gauss Curvature 733 B.2.3 Elliptic Arc 734 B.2.4 Angle 734 B.2.5 Isometric Latitude 735 B.2.6 Differential Equation of the Geodesic 736 B.2.7 The Gauss Midlatitude Solution 739 B.2.8 Angular Excess 741 B.2.9 Transformation in a Small Region 741 Appendix C Conformal Mapping 743 C.1 Conformal Mapping of Planes 744 C.2 Conformal Mapping of General Surfaces 747 C.3 Isometric Plane 749 C.4 Popular Conformal Mappings 750 C.4.1 Equatorial Mercator 751 C.4.2 Transverse Mercator 752 C.4.3 Lambert Conformal 754 C.4.4 SPC and UTM 766 Appendix D Vector Calculus and Delta Function 769 Appendix E Electromagnetic Field Generated by Arbitrary Sources, Magnetic Currents, Boundary Conditions, and Images 775 Appendix F Diffraction over Half-Plane 783 Appendix G Single Cavity Mode Approximation with Patch Antenna Analysis 787 Appendix H Patch Antennas with Artificial Dielectric Substrates 791 Appendix I Convex Patch Array Geodetic Antenna 797 References 801 Author Index 821 Subject Index 829 EULA 836

Employ the latest satellite positioning tech with this extensive guide

GPS Satellite Surveying is the classic text on the subject, providing the most comprehensive coverage of global navigation satellite systems applications for surveying. Fully updated and expanded to reflect the field's latest developments, this new edition contains new information on GNSS antennas, Precise Point Positioning, Real-time Relative Positioning, Lattice Reduction, and much more. New contributors offer additional insight that greatly expands the book's reach, providing readers with complete, in-depth coverage of geodetic surveying using satellite technologies. The newest, most cutting-edge tools, technologies, and applications are explored in-depth to help readers stay up to date on best practices and preferred methods, giving them the understanding they need to consistently produce more reliable measurement.

Global navigation satellite systems have an array of uses in military, civilian, and commercial applications. In surveying, GNSS receivers are used to position survey markers, buildings, and road construction as accurately as possible with less room for human error. GPS Satellite Surveying provides complete guidance toward the practical aspects of the field, helping readers to:

• Get up to speed on the latest GPS/GNSS developments
• Understand how satellite technology is applied to surveying
• Examine in-depth information on adjustments and geodesy
• Learn the fundamentals of positioning, lattice adjustment, antennas, and more

The surveying field has seen quite an evolution of technology in the decade since the last edition's publication. This new edition covers it all, bringing the reader deep inside the latest tools and techniques being used on the job. Surveyors, engineers, geologists, and anyone looking to employ satellite positioning will find GPS Satellite Surveying to be of significant assistance.

GPS Satellite Surveying is a pioneering book in its field and was at one time the only source on GNSS applications for surveying. The market is now fairly competitive with smaller publishing houses specializing in books on this and related subjects. None of the competing books however has this books emphasis on adjustments and geodesy, which are foundational to satellite surveying are mostly up-to-date. The new edition will offer a substantial and much needed revision on the GPS and GNSS sections, as the technology has evolved greatly over the last ten years. Dr. Leick has recruited two specialists in the field to expand this material to make it comprehensive, complete and representative of the cutting edge of GPS/GNSS technology. A new chapter on GPS antennas will be the only extensive treatment of this topic in print. 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 evolut