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GPS Satellite Surveying, Fourth Edition.pdf
GPS SATELLITE SURVEYING
1ch1
2ch2
2.1 ELEMENTARY CONSIDERATIONS
2.1.1 Statistical Nature of Surveying Measurements
2.1.2 Observational Errors
2.1.3 Accuracy and Precision
2.2 STOCHASTIC AND MATHEMATICAL MODELS
2.3 MIXED MODEL
2.3.1 Linearization
2.3.2 Minimization and Solution
2.3.3 Cofactor Matrices
2.3.4 A Posteriori Variance of Unit Weight
2.3.5 Iterations
2.4 SEQUENTIAL MIXED MODEL
2.5 MODEL SPECIFICATIONS
2.5.1 Observation Equation Model
2.5.2 Condition Equation Model
2.5.3 Mixed Model with Observation Equations
2.5.4 Sequential Observation Equation Model
2.5.5 Observation Equation Model with Observed Parameters
2.5.6 Mixed Model with Conditions
2.5.7 Observation Equation Model with Conditions
2.6 MINIMAL AND INNER CONSTRAINTS
2.7 STATISTICS IN LEAST-SQUARES ADJUSTMENT
2.7.1 Fundamental Test
2.7.2 Testing Sequential Least Squares
2.7.3 General Linear Hypothesis
2.7.4 Ellipses as Confidence Regions
2.7.5 Properties of Standard Ellipses
2.7.6 Other Measures of Precision
2.8 RELIABILITY
2.8.1 Redundancy Numbers
2.8.2 Controlling Type-II Error for a Single Blunder
2.8.3 Internal Reliability
2.8.4 Absorption
2.8.5 External Reliability
2.8.6 Correlated Cases
2.9 BLUNDER DETECTION
2.9.1 Tau Test
2.9.2 Data Snooping
2.9.3 Changing Weights of Observations
2.10 EXAMPLES
2.11 KALMAN FILTERING
3ch3
3.1 STATIC PARAMETER
3.2 STATIC PARAMETERS AND ARBITRARY TIME-VARYINGVARIABLES
3.3 DYNAMIC CONSTRAINTS
3.4 STATIC PARAMETERS AND DYNAMIC CONSTRAINTS
3.5 STATIC PARAMETER, PARAMETERS SUBJECT TO DYNAMICCONSTRAINTS, AND ARBITRARY TIME-VARYING PARAMETERS
4ch4
4.1 INTERNATIONAL TERRESTRIAL REFERENCE FRAME
4.2 INTERNATIONAL CELESTIAL REFERENCE SYSTEM
4.3 DATUM
4.4 3D GEODETIC MODEL
4.5 ELLIPSOIDAL MODEL
4.6 CONFORMAL MAPPING MODEL
4.7 SUMMARY
5ch5
5.1 MOTION OF SATELLITES
5.2 GLOBAL POSITIONING SYSTEM
5.3 GLONASS
5.4 GALILEO
5.5 QZSS
5.6 BEIDOU
5.7 IRNSS
5.8 SBAS: WAAS, EGNOS, GAGAN, MSAS, AND SDCM
5ch6
6.1 OBSERVABLES
6.1.1 Undifferenced Functions
6.1.2 Single Differences
6.1.3 Double Differences
6.1.4 Triple Differences
6.2 OPERATIONAL DETAILS
6.2.1 Computing the Topocentric Range
6.2.2 Satellite Timing Considerations
6.2.3 Cycle Slips
6.2.4 Phase Windup Correction
6.2.5 Multipath
6.2.6 Phase Center Offset and Variation
6.2.7 GNSS Services
6.3 NAVIGATION SOLUTION
6.3.1 Linearized Solution
6.3.2 DOPs and Singularities
6.3.3 Nonlinear Closed Solution
6.4 RELATIVE POSITIONING
6.4.1 Nonlinear Double-Difference Pseudorange Solution
6.4.2 Linearized Double- and Triple-Differenced Solutions
6.4.3 Aspects of Relative Positioning
6.4.4 Equivalent Undifferenced Formulation
6.4.5 Ambiguity Function
6.4.6 GLONASS Carrier Phase
6.5 AMBIGUITY FIXING
6.5.1 The Constraint Solution
6.5.2 LAMBDA
6.5.3 Discernibility
6.5.4 Lattice Reduction and Integer Least Squares
6.6 NETWORK-SUPPORTED POSITIONING
6.6.1 PPP
6.6.2 CORS
6.6.3 PPP-RTK
6.7 TRIPLE-FREQUENCY SOLUTIONS
6.7.1 Single-Step Position Solution
6.7.2 Geometry-Free TCAR
6.7.3 Geometry-Based TCAR
6.7.4 Integrated TCAR
6.7.5 Positioning with Resolved Wide Lanes
6.8 SUMMARY
6ch7
7.1 MULTISYSTEM CONSIDERATIONS
7.2 UNDIFFERENCED AND ACROSS-RECEIVER DIFFERENCEOBSERVATIONS
7.3 LINEARIZATION AND HARDWARE BIAS PARAMETERIZATION
7.4 RTK ALGORITHM FOR STATIC AND SHORT BASELINES
7.5 RTK ALGORITHM FOR KINEMATIC ROVERS AND SHORTBASELINES
7.6 RTK ALGORITHM WITH DYNAMIC MODEL AND SHORTBASELINES
7.7 RTK ALGORITHM WITH DYNAMIC MODEL AND LONGBASELINES
7.8 RTK ALGORITHMS WITH CHANGING NUMBER OF SIGNALS
7.9 CYCLE SLIP DETECTION AND ISOLATION
7.10 ACROSS-RECEIVER AMBIGUITY FIXING
7.11 SOFTWARE IMPLEMENTATION
7ch8
8.1 OVERVIEW
8.2 TROPOSPHERIC REFRACTION AND DELAY
8.2.1 Zenith Delay Functions
8.2.2 Mapping Functions
8.2.3 Precipitable Water Vapor
8.3 TROPOSPHERE ABSORPTION
8.3.1 The Radiative Transfer Equation
8.3.2 Absorption Line Profiles
8.3.3 General Statistical Retrieval
8.3.4 Calibration of WVR
8.4 IONOSPHERIC REFRACTION
8.4.1 Index of Ionospheric Refraction
8.4.2 Ionospheric Function and Cycle Slips
8.4.3 Single-Layer Ionospheric Mapping Function
8.4.4 VTEC from Ground Observations
8.4.5 Global Ionospheric Maps
8ch9
9.1 ELEMENTS OF ELECTROMAGNETIC FIELDS ANDELECTROMAGNETIC WAVES
9.1.1 Electromagnetic Field
9.1.2 Plane Electromagnetic Wave
9.1.3 Complex Notations and Plane Wave in Lossy Media
9.1.4 Radiation and Spherical Waves
9.1.5 Receiving Mode
9.1.6 Polarization of Electromagnetic Waves
9.1.7 The dB Scale
9.2 ANTENNA PATTERN AND GAIN
9.2.1 Receiving GNSS Antenna Pattern and Reference Stationand Rover Antennas
9.2.2 Directivity
9.2.3 Polarization Properties of the Receiving GNSS Antenna
9.2.4 Antenna Gain
9.2.5 Antenna Effective Area
9.3 PHASE CENTER
9.3.1 Antenna Phase Pattern
9.3.2 Phase Center Offset and Variations
9.3.3 Antenna Calibrations
9.3.4 Group Delay Pattern
9.4 DIFFRACTION AND MULTIPATH
9.4.1 Diffraction Phenomena
9.4.2 General Characterization of Carrier Phase Multipath
9.4.3 Specular Reflections
9.4.4 Antenna Down-Up Ratio
9.4.5 PCV and PCO Errors Due to Ground Multipath
9.5 TRANSMISSION LINES
9.5.1 Transmission Line Basics
9.5.2 Antenna Frequency Response
9.5.3 Cable Losses
9.6 SIGNAL-TO-NOISE RATIO
9.6.1 Noise Temperature
9.6.2 Characterization of Noise Sources
9.6.3 Signal and Noise Propagation through a Chain of Circuits
9.6.4 SNR of the GNSS Receiving System
9.7 ANTENNA TYPES
9.7.1 Patch Antennas
9.7.2 Other Types of Antennas
9.7.3 Flat Metal Ground Planes
9.7.4 Impedance Ground Planes
9.7.5 Vertical Choke Rings and Compact Rover Antenna
9.7.6 Semitransparent Ground Planes
9.7.7 Array Antennas
9.7.8 Antenna Manufacturing Issues
9app1
10app2
11app3
12app4
13app5
14app6
15app7
16app8
17app9
18refs
19indauth
20ndsub
GPS SATELLITE SURVEYING
GPS SATELLITE
SURVEYING
Fourth Edition
ALFRED LEICK
LEV RAPOPORT
DMITRY TATARNIKOV
Cover image: Eric Morrison, UMaine and Wiley
Cover design: Wiley
This book is printed on acid-free paper.
Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data
Leick, Alfred.
GPS satellite surveying / Alfred Leick, Lev Rapoport Dmitry Tatarnikov. – Fourth edition.
pages cm
Includes index.
ISBN 978-1-118-67557-1 (cloth) – 9781119018285 (epdf) – 9781119018261 (epub) 1. Artificial
satellites in surveying. 2. Global Positioning System. I. Rapoport, Lev. II. Tatarnikov, Dmitry. III. Title.
TA595.5.L45 2015
526.9 ′82–dc23
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
2014040585
CONTENTS
PREFACE
ACKNOWLEDGMENTS
ABBREVIATIONS
1 INTRODUCTION
2 LEAST-SQUARES ADJUSTMENTS
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
xv
xix
xxi
1
11
v
vi
CONTENTS
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
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
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
81
129
CONTENTS
vii
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
4.4.6.1 Montgomery County Geodetic Network / 178
4.4.6.2 SLC Engineering Survey / 182
4.4.6.3 Orange County Densification / 183
4.5 Ellipsoidal Model / 190
4.5.1 Reduction of Observations / 191
4.5.1.1 Angular Reduction to Geodesic / 192
4.5.1.2 Distance Reduction to Geodesic / 193
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
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
207
viii
CONTENTS
5.1.4 Perturbed Satellite Motion / 219
5.1.4.1 Gravitational Field of the Earth / 220
5.1.4.2 Acceleration due to the Sun and the Moon / 222
5.1.4.3 Solar Radiation Pressure / 222
5.1.4.4 Eclipse Transits and Yaw Maneuvers / 223
5.2 Global Positioning System / 225
5.2.1 General Description / 226
5.2.2 Satellite Transmissions at 2014 / 228
5.2.2.1 Signal Structure / 229
5.2.2.2 Navigation Message / 237
5.2.3 GPS Modernization Comprising Block IIM, Block IIF, and
Block III / 239
5.2.3.1 Introducing Binary Offset Carrier (BOC)
Modulation / 241
5.2.3.2 Civil L2C Codes / 243
5.2.3.3 Civil L5 Code / 243
5.2.3.4 M-Code / 244
5.2.3.5 Civil L1C Code / 244
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
6.1 Observables / 258
6.1.1 Undifferenced Functions / 261
257
6.1.1.1 Pseudoranges / 261
6.1.1.2 Carrier Phases / 263
6.1.1.3 Range plus Ionosphere / 266
6.1.1.4 Ionospheric-Free Functions / 266
6.1.1.5 Ionospheric Functions / 267
6.1.1.6 Multipath Functions / 267
6.1.1.7 Ambiguity-Corrected Functions / 268
6.1.1.8 Triple-Frequency Subscript Notation / 269
6.1.2 Single Differences / 271
6.1.2.1 Across-Receiver Functions / 271
6.1.2.2 Across-Satellite Functions / 272
6.1.2.3 Across-Time Functions / 272
CONTENTS
ix
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
6.2.2.1 Satellite Clock Correction and Timing Group
Delay / 278
6.2.2.2 Intersignal Correction / 279
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
6.2.6.1 Satellite Phase Center Offset / 292
6.2.6.2 User Antenna Calibration / 293
6.2.7 GNSS Services / 295
6.2.7.1 IGS / 295
6.2.7.2 Online Computing / 298
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
6.4.3.1 Singularities / 310
6.4.3.2 Impact of a Priori Position Error / 311
6.4.3.3 Independent Baselines / 312
6.4.3.4 Antenna Swap Technique / 314
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
6.5.4.1 Branch-and-Bound Approach / 338
6.5.4.2 Finke-Pohst Algorithm / 349
6.5.4.3 Lattice Reduction Algorithms / 351
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