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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…mehr
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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.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 840
- Erscheinungstermin: 1. April 2015
- Englisch
- ISBN-13: 9781119018285
- Artikelnr.: 42739366
- Verlag: John Wiley & Sons
- Seitenzahl: 840
- Erscheinungstermin: 1. April 2015
- Englisch
- ISBN-13: 9781119018285
- Artikelnr.: 42739366
ALFRED LEICK, PHD, has served on the Board of Directors of the American Association of Geodetic Surveying. He currently lectures at Michigan Technological University and is the Editor-in-Chief of scholarly journal GPS Solutions. LEV RAPOPORT, PHD, received Russia's highest scientific degree, Doctor of Science, from the Institute of Control Sciences of the Russian Academy of Science, where he is now head of laboratory. He is also a professor at the Moscow Institute of Physics and Technology. DMITRY TATARNIKOV, PHD, received the Doctor of Science degree from Moscow Aviation Institute, where he is currently a professor. He is also the Chief of GNSS Antenna Design and Development for Topcon Technology Center.
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 4.1.4 Ocean Loading 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
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 4.1.4 Ocean Loading 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
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 4.1.4 Ocean Loading 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
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 4.1.4 Ocean Loading 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