GPS Satellite Surveying, 4th EditionISBN: 9781118675571
840 pages
March 2015

Description
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, Realtime Relative Positioning, Lattice Reduction, and much more. New contributors offer additional insight that greatly expands the book's reach, providing readers with complete, indepth coverage of geodetic surveying using satellite technologies. The newest, most cuttingedge tools, technologies, and applications are explored indepth 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 indepth 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.
Table of Contents
PREFACE xv
ACKNOWLEDGMENTS xix
ABBREVIATIONS xxi
1 INTRODUCTION 1
2 LEASTSQUARES 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 LeastSquares 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 TypeII 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 TimeVarying 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 TimeVarying 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 DoubleDifference Pseudorange Solution 305
6.4.2 Linearized Double and TripleDifferenced 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 NetworkSupported Positioning 357
6.6.1 PPP 357
6.6.2 CORS 363
6.6.3 PPPRTK 367
6.7 TripleFrequency Solutions 382
6.7.1 SingleStep Position Solution 382
6.7.2 GeometryFree TCAR 386
6.7.3 GeometryBased TCAR 395
6.7.4 Integrated TCAR 396
6.7.5 Positioning with Resolved Wide Lanes 397
6.8 Summary 398
7 REALTIME KINEMATICS RELATIVE POSITIONING 401
7.1 Multisystem Considerations 402
7.2 Undifferenced and AcrossReceiver 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 AcrossReceiver 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 SingleLayer 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 DownUp 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 SignaltoNoise 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 HALFPLANE 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
Author Information
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 EditorinChief 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.
Errata
Do you think you've discovered an error in this book? Please check the list of errata below to see if we've already addressed the error. If not, please submit the error via our Errata Form. We will attempt to verify your error; if you're right, we will post a correction below.
Chapter  Page  Details  Date  Print Run 

Contents  xiii  Errata in text Currently Reads: B.2 Commutation of the Ellipsoidal Surface Should Read: B.2 Commutation on the Ellipsoidal Surface 
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Preface  xvii  Errata in text Currently Reads: Rapaport Should Read: Rapoport 
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Introduction  3  Errata in text Line 4 bottom Currently Reads: deals with navigation solution Should Read: deals with the navigation solution 
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2  19  Errata in equation In eqn (2.3.14) Correction: Delete (minus) before B 
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2  25  Errata in equation In equation (2.4.22): Correction: Replace  symbol with + symbol before Q22W2 
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2  36  Errata in text Line 6 Top: Currently Reads: linearindependent Should Read: linearly independent 
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2  43  Errata in text Last Paragraph Line 1: Currently Reads: parameters are transformed Should Read: observations are transformed 
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2  53  Errata in equation In line above the equation (2.7.71): Currently Reads: Q1 Should Read: Qi 
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2  62  Errata in equation In equation (2.8.1): Replace v Bar (symbol) with v Carrot (symbol) 
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2  66  Errata in equation In equation (2.8.26): Remove modulus symbol for w alpha Replace the lower limit as minus infinity In line below equation (2.8.26): Replace 'If' as 'if' 
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2  78  Errata in equation Line 3 top: Currently Reads: 1≤i≤i1 Should Read: 1≤i1 
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3  92  Errata in Table TABLE 3.2.1: Row 5 first column Currently Reads: Cholesky decomposition of D caret (t) Should Read: Cholesky decomposition of D caret (t+1) 
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3  98  Errata in equation In Eq.(3.3.9) last line: Remove (t) after W to the power 0. 
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4  139  Errata in text Line 4 bottom: Currently Reads: for the National Geodetic Should Read: from the National Geodetic 
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4  152  Errata in text Line below equation (4.3.2): Currently Reads: mass as being Should Read: mass being 
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4  173  Errata in text Line 10 from top Currently reads: determined by objections Should Read: determined by 
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4  181  Errata in text Line 4: Currently Reads: by not using the geodetic Should Read: by using the geodetic 
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4  203  Errata in equation Middle of 2nd paragraph 8th line: Currently Reads: di = (v2xi + v2xi )1∕2 Should Read: di = (v2xi + v2yi )1∕2 
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6  328  Errata in equation Line below (6.5.15): Currently reads: b* (unbold) Should Read: b* (in Bold) 
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6  332  Errata in equation In equation (6.5.45): Currently the entire equation is in bold but it should be unbold. 
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6  347  Errata in text Line below (6.5.80) Currently Reads: Excluding the slice, we have...+1, which means Should Read: Exclude the slice...+1 means 
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6  349  Errata in equation In Equation 6.5.82: Currently Reads: i1 in lower limit of sum symbol Should Read: j1 
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6  349  Errata in equation Line above (6.5.83): Currently Reads: C1/2/lnm (in italics) Should Read: C1/2/lnn (in italics) 
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6  351  Errata in equation Bottom of 2nd line: and b1*,...,bn* (this text should be deleted) 
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6  352  Errata in equation Second line in equation 6.5.98: Currently Reads: (at the end of the equation) , i1 Should Read: , l1 NOTE: 'i' and 'l' should be italicized 
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6  354  Errata in equation In equation 6.5.108: (G*) should be replaced by (Gn1) so that, * is removed and n1 (in subscript) is included for G. Follow the same in the line below equation 6.5.109 
4/10/2015  
6  355  Errata in equation 2 lines above Equation 6.5.111: Remove caret above 'z' and replace with 'z*' 
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6  360  Errata in text 2 lines above (6.6.9): Currently Reads: (6.6.8) Should Read: (6.6.6) 
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6  363  Errata in equation 6 lines from Top: Lower limit for DCB should read: P1YC/A Where, except '1' all characters should be in italic. 
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6  365  Errata in text In Section 6.6.2.2 RTK line 1: Currently reads: In realtime positioning Should read: In realtime kinematic positioning 
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6  367  Errata in text Line above (6.6.37): Currently Reads: (6.1.31) and (6.1.27) are Should Read: (6.1.32) and (6.1.28) are (frequency identifier omitted): 
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6  370  Errata in text In line below (6.6.47): Currently Reads: The combined Should Read: The correctness of the above solution can be verified by substitution. The combined 
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6  371  Errata in text 2 lines above (6.6.54): Currently Reads: parameter Should Read: bias 
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6  372  Errata in text 2 lines above (6.6.57): Currently Reads: (6.6.51), (6.6.53) , and (6.6.56) Should Read: (6.6.51) to (6.6.56) 
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6  373  Errata 2 lines below (6.6.58): Currently Reads: the satellite hardware Should Read: satellite hardware 2 lines above (6.6.59): Currently Reads: (6.6.38) Should Read: (6.6.37) 
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6  375  Errata 3 lines above (6.6.70): Currently Reads: biases are applied to the observations Should Read: biases 
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6  377  Errata in text 2 lines below (6.6.83): Currently Reads: represents, the Should Read: represents the 
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6  378  Errata in text Line below (6.6.87): Currently Reads: 10.7 Should Read: 10.7 cm 
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6  380  Errata in text In Line 1: Currently Reads: acrossdifferencing Should Read: acrosssatellite differencing 
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6  385  Errata in text 8 lines above (6.7.2): Currently Reads: longer baselines. However, their variance Should Read: longer baselines. In some cases the variance 
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6  386  Errata in values Line below (6.7.6): Currently Reads: a = 2.3269, b = 0.3596 Should Read: a = 0.3596, b = 2.3269 
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6  394  Errata in text Line below (6.7.41): Currently Reads: identical Should Read: similar 
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7  425  Errata in figure In Figure 7.4.2: Delete Russian figure title on top of the figure. 
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7  431  Errata in text Line 12 in 7.5.1: Currently Reads: present section) i and kinematic (Example 7.5.2) cases in comparison Should Read: present section) in comparison 
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8  480  Errata in equation In equation (8.2.4): Currently Reads: Partial pressure is denoted by Capital 'P'. Should Read: Partial pressure should be Lower case 'p'. 
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8  502  Errata in equation In equation 8.4.18: Delete 'IF2 ≡' 
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9  507  Errata in text Four lines below 9.1.63: Currently Reads: 1.5GHz Should Read: 1.5 GHz 
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9  557  Errata in text 6 lines below 9.2.21: Currently Reads: 12.7dB Should Read: 12.7 dB 
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9  565  Errata in text 3 lines above 9.2.43: Currently Reads: 1mW Should Read: 1 mW 
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9  567  Errata in text Line above 9.3.1: Currently Reads: with Figure 9.3.1 Should Read: of Figure 9.3.1 
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9  595  Errata in text 4 lines below 9.4.41: Currently Reads: down up Should Read: downup 
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9  597  Errata in text Line 2, 1st paragraph: Currently Reads: 1mm Should Read: 1 mm 
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9  609  Errata in text Second line on top: Currently Reads: 10dB Should Read: 10 dB 
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9  647  Errata in text Line above 9.7.44: Currently Reads: Van Trees Should Read: van Trees 
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9  648  Errata in text End of 2nd paragraph: Currently Reads: Van Trees Should Read: van Trees 
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9  649  Errata in text Paragraph above 9.7.48: Currently Reads: Van Trees Should Read: van Trees 
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Appendix A  661  Errata in equation Line 3 from top: Check font in '0' Currently Reads: AG=0 (here '0' is in TimesLTStdBoldItalic font) Should Read: AG=0 (here '0' should be in HelveticaNeueLTStdBdIt font  Refer font in equation A.3.18) 
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Appendix A  696  Errata in text Line 5 from Top: Currently Reads: variances (this is present in bolditalic) Should Read: variances (this should be unbold and roman) 
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Appendix A  696  Errata in equation In equation A.5.71: Currently Reads: Sigma in uppercase Should Read: Sigma in lowercase 
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Appendix B  703  Errata in text B.2 Heading: Currently Reads: COMPUTATION OF THE ELLIPSOIDAL SURFACE Should Read: COMPUTATION ON THE ELLIPSOIDAL SURFACE 
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Appendix B  705  Errata in equation In equation B.2.15: Close parenthesis '}' is missing. 
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Appendix B  704  Errata in text In line 2, below B.2.6, the second word'p' (lower case) should be 'P' (upper case) 
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Appendix B  707  Errata in equation In equation B.2.25: Currently Reads: The font 'r' in first step is in TimesLTStdItalic font. Should Read: The font 'r' in first step should be in HelveticaNeueLTStdBdIt 
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Appendix B  710  Errata in text Line 4 above the equation B.2.32: Currently Reads: Figure B.2.7 Should Read: Figure B.2.4 
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Appendix B  713  Errata in text Last line in section B.2.8: Currently Reads: k=1 Should Read: K=1 
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Appendix B  714  Errata in equation In Equations B.2.48, B.2.49 and B.2.50, align all operators i.e.,  (minus symbols) and their respective equations inline with the column heads. Also, in equation B.2.50 delete blank space in the middle of each line i.e., remove space before the  (minus) symbols. 
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Appendix C  730  Errata in Table In Table C 4.6 Line 6: Delete the line: 1:M Scale reduction at central meridian 
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