Details

<p>PREFACE xv</p> <p>ACKNOWLEDGMENTS xix</p> <p>ABBREVIATIONS xxi</p> <p><b>1 INTRODUCTION 1</b></p> <p><b>2 LEAST-SQUARES ADJUSTMENTS 11</b></p> <p>2.1 Elementary Considerations 12</p> <p>2.1.1 Statistical Nature of Surveying Measurements 12</p> <p>2.1.2 Observational Errors 13</p> <p>2.1.3 Accuracy and Precision 13</p> <p>2.2 Stochastic and Mathematical Models 14</p> <p>2.3 Mixed Model 17</p> <p>2.3.1 Linearization 18</p> <p>2.3.2 Minimization and Solution 19</p> <p>2.3.3 Cofactor Matrices 20</p> <p>2.3.4 A Posteriori Variance of Unit Weight 21</p> <p>2.3.5 Iterations 22</p> <p>2.4 Sequential Mixed Model 23</p> <p>2.5 Model Specifications 29</p> <p>2.5.1 Observation Equation Model 29</p> <p>2.5.2 Condition Equation Model 30</p> <p>2.5.3 Mixed Model with Observation Equations 30</p> <p>2.5.4 Sequential Observation Equation Model 32</p> <p>2.5.5 Observation Equation Model with Observed Parameters 32</p> <p>2.5.6 Mixed Model with Conditions 34</p> <p>2.5.7 Observation Equation Model with Conditions 35</p> <p>2.6 Minimal and Inner Constraints 37</p> <p>2.7 Statistics in Least-Squares Adjustment 42</p> <p>2.7.1 Fundamental Test 42</p> <p>2.7.2 Testing Sequential Least Squares 48</p> <p>2.7.3 General Linear Hypothesis 49</p> <p>2.7.4 Ellipses as Confidence Regions 52</p> <p>2.7.5 Properties of Standard Ellipses 56</p> <p>2.7.6 Other Measures of Precision 60</p> <p>2.8 Reliability 62</p> <p>2.8.1 Redundancy Numbers 62</p> <p>2.8.2 Controlling Type-II Error for a Single Blunder 64</p> <p>2.8.3 Internal Reliability 67</p> <p>2.8.4 Absorption 67</p> <p>2.8.5 External Reliability 68</p> <p>2.8.6 Correlated Cases 69</p> <p>2.9 Blunder Detection 70</p> <p>2.9.1 Tau Test 71</p> <p>2.9.2 Data Snooping 71</p> <p>2.9.3 Changing Weights of Observations 72</p> <p>2.10 Examples 72</p> <p>2.11 Kalman Filtering 77</p> <p><b>3 RECURSIVE LEAST SQUARES 81</b></p> <p>3.1 Static Parameter 82</p> <p>3.2 Static Parameters and Arbitrary Time-Varying Variables 87</p> <p>3.3 Dynamic Constraints 96</p> <p>3.4 Static Parameters and Dynamic Constraints 112</p> <p>3.5 Static Parameter, Parameters Subject to Dynamic Constraints, and Arbitrary Time-Varying Parameters 125</p> <p><b>4 GEODESY 129</b></p> <p>4.1 International Terrestrial Reference Frame 131</p> <p>4.1.1 Polar Motion 132</p> <p>4.1.2 Tectonic Plate Motion 133</p> <p>4.1.3 Solid Earth Tides 135</p> <p>4.1.4 Ocean Loading 135</p> <p>4.1.5 Relating of Nearly Aligned Frames 136</p> <p>4.1.6 ITRF and NAD83 138</p> <p>4.2 International Celestial Reference System 141</p> <p>4.2.1 Transforming Terrestrial and Celestial Frames 143</p> <p>4.2.2 Time Systems 149</p> <p>4.3 Datum 151</p> <p>4.3.1 Geoid 152</p> <p>4.3.2 Ellipsoid of Rotation 157</p> <p>4.3.3 Geoid Undulations and Deflections of the Vertical 158</p> <p>4.3.4 Reductions to the Ellipsoid 162</p> <p>4.4 3D Geodetic Model 166</p> <p>4.4.1 Partial Derivatives 169</p> <p>4.4.2 Reparameterization 170</p> <p>4.4.3 Implementation Considerations 171</p> <p>4.4.4 GPS Vector Networks 174</p> <p>4.4.5 Transforming Terrestrial and Vector Networks 176</p> <p>4.4.6 GPS Network Examples 178</p> <p>4.5 Ellipsoidal Model 190</p> <p>4.5.1 Reduction of Observations 191</p> <p>4.5.2 Direct and Inverse Solutions on the Ellipsoid 195</p> <p>4.5.3 Network Adjustment on the Ellipsoid 196</p> <p>4.6 Conformal Mapping Model 197</p> <p>4.6.1 Reduction of Observations 198</p> <p>4.6.2 Angular Excess 200</p> <p>4.6.3 Direct and Inverse Solutions on the Map 201</p> <p>4.6.4 Network Adjustment on the Map 201</p> <p>4.6.5 Similarity Revisited 203</p> <p>4.7 Summary 204</p> <p><b>5 SATELLITE SYSTEMS 207</b></p> <p>5.1 Motion of Satellites 207</p> <p>5.1.1 Kepler Elements 208</p> <p>5.1.2 Normal Orbital Theory 210</p> <p>5.1.3 Satellite Visibility and Topocentric Motion 219</p> <p>5.1.4 Perturbed Satellite Motion 219</p> <p>5.2 Global Positioning System 225</p> <p>5.2.1 General Description 226</p> <p>5.2.2 Satellite Transmissions at 2014 228</p> <p>5.2.3 GPS Modernization Comprising Block IIM, Block IIF, and Block III 239</p> <p>5.3 GLONASS 245</p> <p>5.4 Galileo 248</p> <p>5.5 QZSS 250</p> <p>5.6 Beidou 252</p> <p>5.7 IRNSS 254</p> <p>5.8 SBAS: WAAS, EGNOS, GAGAN, MSAS, and SDCM 254</p> <p><b>6 GNSS POSITIONING APPROACHES 257</b></p> <p>6.1 Observables 258</p> <p>6.1.1 Undifferenced Functions 261</p> <p>6.1.2 Single Differences 271</p> <p>6.1.3 Double Differences 273</p> <p>6.1.4 Triple Differences 275</p> <p>6.2 Operational Details 275</p> <p>6.2.1 Computing the Topocentric Range 275</p> <p>6.2.2 Satellite Timing Considerations 276</p> <p>6.2.3 Cycle Slips 282</p> <p>6.2.4 Phase Windup Correction 283</p> <p>6.2.5 Multipath 286</p> <p>6.2.6 Phase Center Offset and Variation 292</p> <p>6.2.7 GNSS Services 295</p> <p>6.3 Navigation Solution 299</p> <p>6.3.1 Linearized Solution 299</p> <p>6.3.2 DOPs and Singularities 301</p> <p>6.3.3 Nonlinear Closed Solution 303</p> <p>6.4 Relative Positioning 304</p> <p>6.4.1 Nonlinear Double-Difference Pseudorange Solution 305</p> <p>6.4.2 Linearized Double- and Triple-Differenced Solutions 306</p> <p>6.4.3 Aspects of Relative Positioning 310</p> <p>6.4.4 Equivalent Undifferenced Formulation 315</p> <p>6.4.5 Ambiguity Function 316</p> <p>6.4.6 GLONASS Carrier Phase 319</p> <p>6.5 Ambiguity Fixing 324</p> <p>6.5.1 The Constraint Solution 324</p> <p>6.5.2 LAMBDA 327</p> <p>6.5.3 Discernibility 334</p> <p>6.5.4 Lattice Reduction and Integer Least Squares 337</p> <p>6.6 Network-Supported Positioning 357</p> <p>6.6.1 PPP 357</p> <p>6.6.2 CORS 363</p> <p>6.6.3 PPP-RTK 367</p> <p>6.7 Triple-Frequency Solutions 382</p> <p>6.7.1 Single-Step Position Solution 382</p> <p>6.7.2 Geometry-Free TCAR 386</p> <p>6.7.3 Geometry-Based TCAR 395</p> <p>6.7.4 Integrated TCAR 396</p> <p>6.7.5 Positioning with Resolved Wide Lanes 397</p> <p>6.8 Summary 398</p> <p><b>7 REAL-TIME KINEMATICS RELATIVE POSITIONING 401</b></p> <p>7.1 Multisystem Considerations 402</p> <p>7.2 Undifferenced and Across-Receiver Difference Observations 403</p> <p>7.3 Linearization and Hardware Bias Parameterization 408</p> <p>7.4 RTK Algorithm for Static and Short Baselines 418</p> <p>7.4.1 Illustrative Example 422</p> <p>7.5 RTK Algorithm for Kinematic Rovers and Short Baselines 429</p> <p>7.5.1 Illustrative Example 431</p> <p>7.6 RTK Algorithm with Dynamic Model and Short Baselines 435</p> <p>7.6.1 Illustrative Example 437</p> <p>7.7 RTK Algorithm with Dynamic Model and Long Baselines 441</p> <p>7.7.1 Illustrative Example 442</p> <p>7.8 RTK Algorithms with Changing Number of Signals 445</p> <p>7.9 Cycle Slip Detection and Isolation 450</p> <p>7.9.1 Solutions Based on Signal Redundancy 455</p> <p>7.10 Across-Receiver Ambiguity Fixing 466</p> <p>7.10.1 Illustrative Example 470</p> <p>7.11 Software Implementation 473</p> <p><b>8 TROPOSPHERE AND IONOSPHERE 475</b></p> <p>8.1 Overview 476</p> <p>8.2 Tropospheric Refraction and Delay 479</p> <p>8.2.1 Zenith Delay Functions 482</p> <p>8.2.2 Mapping Functions 482</p> <p>8.2.3 Precipitable Water Vapor 485</p> <p>8.3 Troposphere Absorption 487</p> <p>8.3.1 The Radiative Transfer Equation 487</p> <p>8.3.2 Absorption Line Profiles 490</p> <p>8.3.3 General Statistical Retrieval 492</p> <p>8.3.4 Calibration of WVR 494</p> <p>8.4 Ionospheric Refraction 496</p> <p>8.4.1 Index of Ionospheric Refraction 499</p> <p>8.4.2 Ionospheric Function and Cycle Slips 504</p> <p>8.4.3 Single-Layer Ionospheric Mapping Function 505</p> <p>8.4.4 VTEC from Ground Observations 507</p> <p>8.4.5 Global Ionospheric Maps 509</p> <p><b>9 GNSS RECEIVER ANTENNAS 513</b></p> <p>9.1 Elements of Electromagnetic Fields and Electromagnetic Waves 515</p> <p>9.1.1 Electromagnetic Field 515</p> <p>9.1.2 Plane Electromagnetic Wave 518</p> <p>9.1.3 Complex Notations and Plane Wave in Lossy Media 525</p> <p>9.1.4 Radiation and Spherical Waves 530</p> <p>9.1.5 Receiving Mode 536</p> <p>9.1.6 Polarization of Electromagnetic Waves 537</p> <p>9.1.7 The dB Scale 544</p> <p>9.2 Antenna Pattern and Gain 546</p> <p>9.2.1 Receiving GNSS Antenna Pattern and Reference Station and Rover Antennas 546</p> <p>9.2.2 Directivity 553</p> <p>9.2.3 Polarization Properties of the Receiving GNSS Antenna 558</p> <p>9.2.4 Antenna Gain 562</p> <p>9.2.5 Antenna Effective Area 564</p> <p>9.3 Phase Center 565</p> <p>9.3.1 Antenna Phase Pattern 566</p> <p>9.3.2 Phase Center Offset and Variations 568</p> <p>9.3.3 Antenna Calibrations 575</p> <p>9.3.4 Group Delay Pattern 577</p> <p>9.4 Diffraction and Multipath 578</p> <p>9.4.1 Diffraction Phenomena 578</p> <p>9.4.2 General Characterization of Carrier Phase Multipath 585</p> <p>9.4.3 Specular Reflections 587</p> <p>9.4.4 Antenna Down-Up Ratio 593</p> <p>9.4.5 PCV and PCO Errors Due to Ground Multipath 597</p> <p>9.5 Transmission Lines 600</p> <p>9.5.1 Transmission Line Basics 600</p> <p>9.5.2 Antenna Frequency Response 606</p> <p>9.5.3 Cable Losses 608</p> <p>9.6 Signal-to-Noise Ratio 609</p> <p>9.6.1 Noise Temperature 609</p> <p>9.6.2 Characterization of Noise Sources 611</p> <p>9.6.3 Signal and Noise Propagation through a Chain of Circuits 615</p> <p>9.6.4 SNR of the GNSS Receiving System 619</p> <p>9.7 Antenna Types 620</p> <p>9.7.1 Patch Antennas 620</p> <p>9.7.2 Other Types of Antennas 629</p> <p>9.7.3 Flat Metal Ground Planes 629</p> <p>9.7.4 Impedance Ground Planes 634</p> <p>9.7.5 Vertical Choke Rings and Compact Rover Antenna 642</p> <p>9.7.6 Semitransparent Ground Planes 644</p> <p>9.7.7 Array Antennas 645</p> <p>9.7.8 Antenna Manufacturing Issues 650</p> <p>APPENDIXES</p> <p>A GENERAL BACKGROUND 653</p> <p>B THE ELLIPSOID 697</p> <p>C CONFORMAL MAPPING 715</p> <p>D VECTOR CALCULUS AND DELTA FUNCTION 741</p> <p>E ELECTROMAGNETIC FIELD GENERATED BY ARBITRARY SOURCES, MAGNETIC CURRENTS, BOUNDARY CONDITIONS, AND IMAGES 747</p> <p>F DIFFRACTION OVER HALF-PLANE 755</p> <p>G SINGLE CAVITY MODE APPROXIMATION WITH PATCH ANTENNA ANALYSIS 759</p> <p>H PATCH ANTENNAS WITH ARTIFICIAL DIELECTRIC SUBSTRATES 763</p> <p>I CONVEX PATCH ARRAY GEODETIC ANTENNA 769</p> <p>REFERENCES 773</p> <p>AUTHOR INDEX 793</p> <p>SUBJECT INDEX 801</p>

<p><b>ALFRED LEICK, P<small>H</small>D,</b> 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 <i>GPS Solutions.</i> <p><b>LEV RAPOPORT, P<small>H</small>D,</b> 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. <p><b>DMITRY TATARNIKOV, P<small>H</small>D,</b> 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.

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