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GPS Satellite Surveying, 4th Edition

ISBN: 978-1-118-67557-1
840 pages
March 2015
GPS Satellite Surveying, 4th Edition (1118675576) cover image

Description

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.

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Table of Contents

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

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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 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.

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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.

ChapterPageDetailsDatePrint Run
Contents xiii Errata in text
Currently Reads:
B.2 Commutation of the Ellipsoidal Surface
Should Read:
B.2 Commutation on the Ellipsoidal Surface
4/10/2015
Preface xvii Errata in text
Currently Reads:
Rapaport

Should Read:
Rapoport
4/10/2015
Introduction 3 Errata in text
Line 4 bottom

Currently Reads:
deals with navigation solution

Should Read:
deals with the navigation solution
4/10/2015
2 19 Errata in equation
In eqn (2.3.14)

Correction:
Delete -(minus) before B
4/10/2015
2 25 Errata in equation
In equation (2.4.22):

Correction:
Replace - symbol with + symbol before Q22W2
4/10/2015
2 36 Errata in text
Line 6 Top:

Currently Reads:
linear-independent

Should Read:
linearly independent
4/10/2015
2 43 Errata in text
Last Paragraph Line 1:

Currently Reads:
parameters are transformed

Should Read:
observations are transformed
4/10/2015
2 53 Errata in equation
In line above the equation (2.7.71):

Currently Reads:
Q1

Should Read:
Qi
4/10/2015
2 62 Errata in equation
In equation (2.8.1):

Replace v Bar (symbol) with v Carrot (symbol)
4/10/2015
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'
4/10/2015
2 78 Errata in equation
Line 3 top:

Currently Reads:
1≤i≤i-1

Should Read:
1≤i-1
4/10/2015
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)
4/10/2015
3 98 Errata in equation
In Eq.(3.3.9) last line:

Remove (t) after W to the power 0.
4/10/2015
4 139 Errata in text
Line 4 bottom:

Currently Reads:
for the National Geodetic

Should Read:
from the National Geodetic
4/10/2015
4 152 Errata in text
Line below equation (4.3.2):

Currently Reads:
mass as being

Should Read:
mass being
4/10/2015
4 173 Errata in text
Line 10 from top

Currently reads:
determined by objections

Should Read:
determined by
4/10/2015
4 181 Errata in text
Line 4:

Currently Reads:
by not using the geodetic

Should Read:
by using the geodetic
4/10/2015
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
4/10/2015
6 328 Errata in equation
Line below (6.5.15):

Currently reads:
b* (unbold)

Should Read:
b* (in Bold)
4/10/2015
6 332 Errata in equation
In equation (6.5.45):

Currently the entire equation is in bold but it should be unbold.
4/10/2015
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
4/10/2015
6 349 Errata in equation
In Equation 6.5.82:

Currently Reads:
i-1 in lower limit of sum symbol

Should Read:
j-1
4/10/2015
6 349 Errata in equation
Line above (6.5.83):

Currently Reads:
C1/2/lnm (in italics)

Should Read:
C1/2/lnn (in italics)
4/10/2015
6 351 Errata in equation
Bottom of 2nd line:

and b1*,...,bn* (this text should be deleted)
4/10/2015
6 352 Errata in equation
Second line in equation 6.5.98:

Currently Reads:
(at the end of the equation)
, i-1

Should Read:
, l-1

NOTE: 'i' and 'l' should be italicized
4/10/2015
6 354 Errata in equation
In equation 6.5.108:

(G*) should be replaced by (Gn-1)
so that, * is removed and n-1 (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*'
4/10/2015
6 360 Errata in text
2 lines above (6.6.9):

Currently Reads:
(6.6.8)

Should Read:
(6.6.6)
4/10/2015
6 363 Errata in equation
6 lines from Top:

Lower limit for DCB should read: P1Y-C/A
Where, except '1' all characters should be in italic.
4/10/2015
6 365 Errata in text
In Section 6.6.2.2 RTK line 1:

Currently reads:
In real-time positioning

Should read:
In real-time kinematic positioning
4/10/2015
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):
4/10/2015
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
4/10/2015
6 371 Errata in text
2 lines above (6.6.54):

Currently Reads:
parameter

Should Read:
bias
4/10/2015
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)
4/10/2015
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)
4/10/2015
6 375 Errata
3 lines above (6.6.70):

Currently Reads:
biases are applied to the observations

Should Read:
biases
4/10/2015
6 377 Errata in text
2 lines below (6.6.83):

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represents, the

Should Read:
represents the
4/10/2015
6 378 Errata in text
Line below (6.6.87):

Currently Reads:
10.7

Should Read:
10.7 cm
4/10/2015
6 380 Errata in text
In Line 1:

Currently Reads:
across-differencing

Should Read:
across-satellite differencing
4/10/2015
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
4/10/2015
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
4/10/2015
6 394 Errata in text
Line below (6.7.41):

Currently Reads:
identical

Should Read:
similar
4/10/2015
7 425 Errata in figure
In Figure 7.4.2:

Delete Russian figure title on top of the figure.
4/10/2015
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
4/10/2015
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'.
4/10/2015
8 502 Errata in equation
In equation 8.4.18:

Delete 'IF2 ≡'
4/10/2015
9 507 Errata in text
Four lines below 9.1.63:

Currently Reads:
1.5-GHz

Should Read:
1.5 GHz
4/10/2015
9 557 Errata in text
6 lines below 9.2.21:

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12.7-dB

Should Read:
12.7 dB
4/10/2015
9 565 Errata in text
3 lines above 9.2.43:

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1-mW

Should Read:
1 mW
4/10/2015
9 567 Errata in text
Line above 9.3.1:

Currently Reads:
with Figure 9.3.1

Should Read:
of Figure 9.3.1
4/10/2015
9 595 Errata in text
4 lines below 9.4.41:

Currently Reads:
down- up

Should Read:
down-up
4/10/2015
9 597 Errata in text
Line 2, 1st paragraph:

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1-mm

Should Read:
1 mm
4/10/2015
9 609 Errata in text
Second line on top:

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10-dB

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10 dB
4/10/2015
9 647 Errata in text
Line above 9.7.44:

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Van Trees

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van Trees
4/10/2015
9 648 Errata in text
End of 2nd paragraph:

Currently Reads:
Van Trees

Should Read:
van Trees
4/10/2015
9 649 Errata in text
Paragraph above 9.7.48:

Currently Reads:
Van Trees

Should Read:
van Trees
4/10/2015
Appendix A 661 Errata in equation
Line 3 from top: Check font in '0'

Currently Reads:
AG=0 (here '0' is in TimesLTStd-BoldItalic font)

Should Read:
AG=0 (here '0' should be in HelveticaNeueLTStd-BdIt font - Refer font in equation A.3.18)
4/10/2015
Appendix A 696 Errata in text
Line 5 from Top:

Currently Reads:
variances (this is present in bold-italic)

Should Read:
variances (this should be unbold and roman)
4/10/2015
Appendix A 696 Errata in equation
In equation A.5.71:

Currently Reads:
Sigma in upper-case

Should Read:
Sigma in lower-case
4/10/2015
Appendix B 703 Errata in text
B.2 Heading:

Currently Reads:
COMPUTATION OF THE ELLIPSOIDAL SURFACE

Should Read:
COMPUTATION ON THE ELLIPSOIDAL SURFACE
4/10/2015
Appendix B 705 Errata in equation
In equation B.2.15:

Close parenthesis '}' is missing.
4/10/2015
Appendix B 704 Errata in text
In line 2, below B.2.6, the second word'p' (lower case) should be 'P' (upper case)
4/10/2015
Appendix B 707 Errata in equation
In equation B.2.25:

Currently Reads:
The font 'r' in first step is in TimesLTStd-Italic font.

Should Read:
The font 'r' in first step should be in HelveticaNeueLTStd-BdIt
4/10/2015
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
4/10/2015
Appendix B 713 Errata in text
Last line in section B.2.8:

Currently Reads:
k=1

Should Read:
K=1
4/10/2015
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 in-line 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.
4/10/2015
Appendix C 730 Errata in Table
In Table C 4.6 Line 6:

Delete the line:
1:M Scale reduction at central meridian
4/10/2015
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