Adjustment Computations: Spatial Data Analysis, 6th EditionISBN: 9781119385981
720 pages
October 2017

Description
Adjustment Computations is the classic textbook for spatial information analysis and adjustment computations, providing clear, easytounderstand instruction backed by realworld practicality. From the basic terms and fundamentals of errors to specific adjustment computations and spatial information analysis, this book covers the methodologies and tools that bring accuracy to surveying, GNSS, GIS, and other spatial technologies. Broad in scope yet rich in detail, the discussion avoids overlycomplex theory in favor of practical techniques for students and professionals. This new sixth edition has been updated to align with the latest developments in this rapidly expanding field, and includes new video lessons and updated problems, including worked problems in STATS, MATRIX, ADJUST, and MathCAD.
All measurement produces some amount of error; whether from human mistakes, instrumentation inaccuracy, or environmental features, these errors must be accounted and adjusted for when accuracy is critical. This book describes how errors are identified, analyzed, measured, and corrected, with a focus on least squares adjustment—the most rigorous methodology available.
 Apply industrystandard methodologies to error analysis and adjustment
 Translate your skills to the realworld with instruction focused on the practical
 Master the fundamentals as well as specific computations and analysis
 Strengthen your understanding of critical topics on the Fundamentals in Surveying Licensing Exam
As spatial technologies expand in both use and capability, so does our need for professionals who understand how to check and adjust for errors in spatial data. Conceptual knowledge is one thing, but practical skills are what counts when accuracy is at stake; Adjustment Computations provides the realworld training you need to identify, analyze, and correct for potentially crucial errors.
Table of Contents
PREFACE xv
ACKNOWLEDGMENTS xix
1 Introduction 1
1.1 Introduction / 1
1.2 Direct and Indirect Measurements / 2
1.3 Measurement Error Sources / 2
1.4 Definitions / 3
1.5 Precision versus Accuracy / 4
1.6 Redundant Observations in Surveying and Their Adjustment / 7
1.7 Advantages of Least Squares Adjustment / 8
1.8 Overview of the Book / 10
Problems / 10
2 Observations and Their Analysis 13
2.1 Introduction / 13
2.2 Sample versus Population / 13
2.3 Range and Median / 14
2.4 Graphical Representation of Data / 15
2.5 Numerical Methods of Describing Data / 18
2.6 Measures of Central Tendency / 18
2.7 Additional Definitions / 19
2.8 Alternative Formula for Determining Variance / 22
2.9 Numerical Examples / 24
2.10 Root Mean Square Error and Mapping Standards / 28
2.11 Derivation of the Sample Variance (Bessel’s Correction) / 31
2.12 Software / 32
Problems / 34
Practical Exercises / 37
3 Random Error Theory 39
3.1 Introduction / 39
3.2 Theory of Probability / 39
3.3 Properties of the Normal Distribution Curve / 42
3.4 Standard Normal Distribution Function / 44
3.5 Probability of the Standard Error / 47
3.6 Uses for Percent Errors / 50
3.7 Practical Examples / 50
Problems / 53
Programming Problems / 55
4 Confidence Intervals 57
4.1 Introduction / 57
4.2 Distributions Used in Sampling Theory / 59
4.3 Confidence Interval for the Mean: t Statistic / 63
4.4 Testing the Validity of the Confidence Interval / 66
4.5 Selecting a Sample Size / 67
4.6 Confidence Interval for a Population Variance / 68
4.7 Confidence Interval for the Ratio of Two Population Variances / 70
4.8 Software / 72
Problems / 75
5 Statistical Testing 79
5.1 Hypothesis Testing / 79
5.2 Systematic Development of a Test / 82
5.3 Test of Hypothesis for the Population Mean / 84
5.4 Test of Hypothesis for the Population Variance / 85
5.5 Test of Hypothesis for the Ratio of Two Population Variances / 89
5.6 Software / 92
Problems / 93
6 Propagation of Random Errors in Indirectly Measured Quantities 97
6.1 Basic Error Propagation Equation / 97
6.2 Frequently Encountered Specific Functions / 102
6.3 Numerical Examples / 103
6.4 Software / 107
6.5 Conclusions / 109
Problems / 109
Practical Exercises / 112
7 Error Propagation in Angle and Distance Observations 113
7.1 Introduction / 113
7.2 Error Sources in Horizontal Angles / 113
7.3 Reading Errors / 114
7.4 Pointing Errors / 116
7.5 Estimated Pointing and Reading Errors with Total Stations / 117
7.6 TargetCentering Errors / 118
7.7 Instrument Centering Errors / 120
7.8 Effects of Leveling Errors in Angle Observations / 123
7.9 Numerical Example of Combined Error Propagation in a Single Horizontal Angle / 126
7.10 Using Estimated Errors to Check Angular Misclosure in a Traverse / 127
7.11 Errors in Astronomical Observations for Azimuth / 130
7.12 Errors in Electronic Distance Observations / 135
7.13 Centering Errors When Using Range Poles / 136
7.14 Software / 137
Problems / 138
Programming Problems / 141
8 Error Propagation in Traverse Surveys 143
8.1 Introduction / 143
8.2 Derivation of Estimated Error in Latitude and Departure / 144
8.3 Derivation of Estimated Standard Errors in Course Azimuths / 146
8.4 Computing and Analyzing Polygon Traverse Misclosure Errors / 146
8.5 Computing and Analyzing Link Traverse Misclosure Errors / 152
8.6 Software / 156
8.7 Conclusions / 157
Problems / 157
Programming Problems / 161
9 Error Propagation in Elevation Determination 163
9.1 Introduction / 163
9.2 Systematic Errors in Differential Leveling / 163
9.3 Random Errors in Differential Leveling / 166
9.4 Error Propagation in Trigonometric Leveling / 171
Problems / 174
Programming Problems / 177
10 Weights of Observations 179
10.1 Introduction / 179
10.2 Weighted Mean / 181
10.3 Relationship Between Weights and Standard Errors / 183
10.4 Statistics of Weighted Observations / 184
10.5 Weights in Angle Observations / 185
10.6 Weights in Differential Leveling / 186
10.7 Practical Examples / 187
Problems / 190
11 Principles of Least Squares 193
11.1 Introduction / 193
11.2 Fundamental Principle of Least Squares / 194
11.3 The Fundamental Principle of Weighted Least Squares / 196
11.4 The Stochastic Model / 197
11.5 Functional Model / 197
11.6 Observation Equations / 199
11.7 Systematic Formulation of the Normal Equations / 201
11.8 Tabular Formation of the Normal Equations / 203
11.9 Using Matrices to Form the Normal Equations / 204
11.10 Least Squares Solution of Nonlinear Systems / 207
11.11 Least Squares Fit of Points to a Line or Curve / 211
11.12 Calibration of an EDM Instrument / 214
11.13 Least Squares Adjustment Using Conditional Equations / 215
11.14 The Previous Example Using Observation Equations / 217
11.15 Software / 219
Problems / 219
12 Adjustment of Level Nets 225
12.1 Introduction / 225
12.2 Observation Equation / 225
12.3 Unweighted Example / 226
12.4 Weighted Example / 229
12.5 Reference Standard Deviation / 231
12.6 Another Weighted Adjustment / 233
12.7 Software / 236
Problems / 238
Programming Problems / 242
13 Precisions of Indirectly Determined Quantities 245
13.1 Introduction / 245
13.2 Development of the Covariance Matrix / 245
13.3 Numerical Examples / 249
13.4 Standard Deviations of Computed Quantities / 250
Problems / 254
Programming Problems / 256
14 Adjustment of Horizontal Surveys: Trilateration 257
14.1 Introduction / 257
14.2 Distance Observation Equation / 259
14.3 Trilateration Adjustment Example / 261
14.4 Formulation of a Generalized Coefficient Matrix for a More Complex Network / 268
14.5 Computer Solution of a Trilaterated Quadrilateral / 269
14.6 Iteration Termination / 273
14.7 Software / 274
Problems / 276
Programming Problems / 282
15 Adjustment of Horizontal Surveys: Triangulation 283
15.1 Introduction / 283
15.2 Azimuth Observation Equation / 284
15.3 Angle Observation Equation / 286
15.4 Adjustment of Intersections / 288
15.5 Adjustment of Resections / 293
15.6 Adjustment of Triangulated Quadrilaterals / 298
Problems / 303
Programming Problems / 312
16 Adjustment of Horizontal Surveys: Traverses and Horizontal Networks 313
16.1 Introduction to Traverse Adjustments / 313
16.2 Observation Equations / 313
16.3 Redundant Equations / 314
16.4 Numerical Example / 315
16.5 Minimum Amount of Control / 321
16.6 Adjustment of Networks / 322
16.7 ��2 Test: Goodness of Fit / 330
Problems / 331
Programming Problems / 342
17 Adjustment of GNSS Networks 343
17.1 Introduction / 343
17.2 GNSS Observations / 344
17.3 GNSS Errors and the Need for Adjustment / 347
17.4 Reference Coordinate Systems for GNSS Observations / 347
17.5 Converting Between the Terrestrial and Geodetic Coordinate Systems / 350
17.6 Application of Least Squares in Processing GNSS Data / 354
17.7 Network Preadjustment Data Analysis / 356
17.8 Least Squares Adjustment of GNSS Networks / 363
Problems / 369
Programming Problems / 386
18 Coordinate Transformations 389
18.1 Introduction / 389
18.2 The TwoDimensional Conformal Coordinate / 389
18.3 Equation Development / 390
18.4 Application of Least Squares / 392
18.5 TwoDimensional Affine Coordinate Transformation / 395
18.6 The TwoDimensional Projective Coordinate Transformation / 398
18.7 ThreeDimensional Conformal Coordinate Transformation / 401
18.8 Statistically Valid Parameters / 407
Problems / 411
Programming Problems / 418
19 Error Ellipse 419
19.1 Introduction / 419
19.2 Computation of Ellipse Orientation and Semiaxes / 421
19.3 Example Problem of Standard Error Ellipse Calculations / 426
19.4 Another Example Problem / 428
19.5 The Error Ellipse Confidence Level / 429
19.6 Error Ellipse Advantages / 431
19.7 Other Measures of Station Uncertainty / 435
Problems / 441
Programming Problems / 442
20 Constraint Equations 443
20.1 Introduction / 443
20.2 Adjustment of Control Station Coordinates / 443
20.3 Holding Control Station Coordinates and Directions of Lines Fixed in a Trilateration Adjustment / 449
20.4 Helmert’s Method / 452
20.5 Redundancies in a Constrained Adjustment / 458
20.6 Enforcing Constraints through Weighting / 458
Problems / 460
Practical Problems / 463
21 Blunder Detection in Horizontal Networks 465
21.1 Introduction / 465
21.2 A Priori Methods for Detecting Blunders in Observations / 466
21.3 A Posteriori Blunder Detection / 468
21.4 Development of the Covariance Matrix for the Residuals / 470
21.5 Detection of Outliers in Observations: Data Snooping / 472
21.6 Detection of Outliers in Observations: The Tau Criterion / 474
21.7 Techniques Used in Adjusting Control / 476
21.8 A Data Set with Blunders / 477
21.9 Some Further Considerations / 485
21.10 Survey Design / 487
21.11 Software / 489
Problems / 490
Practical Problems / 496
22 The General Least Squares Method and Its Application to Curve Fitting and Coordinate Transformations 497
22.1 Introduction to General Least Squares / 497
22.2 General Least Squares Equations for Fitting a Straight Line / 497
22.3 General Least Squares Solution / 499
22.4 TwoDimensional Coordinate Transformation by General Least Squares / 503
22.5 ThreeDimensional Conformal Coordinate Transformation by General Least Squares / 509
Problems / 511
Programming Problems / 515
23 ThreeDimensional Geodetic Network Adjustment 517
23.1 Introduction / 517
23.2 Linearization of Equations / 519
23.3 Minimum Number of Constraints / 524
23.4 Example Adjustment / 525
23.5 Building an Adjustment / 533
23.6 Comments on Systematic Errors / 534
23.7 Software / 537
Problems / 538
Programming Problems / 543
24 Combining GNSS and Terrestrial Observations 545
24.1 Introduction / 545
24.2 The Helmert Transformation / 547
24.3 Rotations between Coordinate Systems / 551
24.4 Combining GNSS Baseline Vectors with Traditional Observations / 552
24.5 Another Approach to Transforming Coordinates between Reference Frames / 556
24.6 Other Considerations / 559
Problems / 560
Programming Problems / 563
25 Analysis of Adjustments 565
25.1 Introduction / 565
25.2 Basic Concepts, Residuals, and the Normal Distribution / 565
25.3 Goodness of Fit Test / 568
25.4 Comparison of GNSS Residual Plots / 572
25.5 Use of Statistical Blunder Detection / 574
Problems / 574
26 Computer Optimization 577
26.1 Introduction / 577
26.2 Storage Optimization / 578
26.3 Direct Formation of the Normal Equations / 580
26.4 Cholesky Decomposition / 581
26.5 Forward and Back Solutions / 583
26.6 Using the Cholesky Factor to Find the Inverse of the Normal Matrix / 584
26.7 Spareness and Optimization of the Normal Matrix / 586
Problems / 590
Programming Problems / 590
Appendix A Introduction to Matrices 591
A.1 Introduction / 591
A.2 Definition of a Matrix / 591
A.3 Size or Dimensions of a Matrix / 592
A.4 Types of Matrices / 593
A.5 Matrix Equality / 594
A.6 Addition or Subtraction of Matrices / 595
A.7 Scalar Multiplication of a Matrix / 595
A.8 Matrix Multiplication / 595
A.9 Computer Algorithms for Matrix Operations / 598
A.10 Use of the Matrix Software / 601
Problems / 603
Programming Problems / 605
Appendix B Solution of Equations by Matrix Methods 607
B.1 Introduction / 607
B.2 Inverse Matrix / 607
B.3 The Inverse of a 2 × 2 Matrix / 608
B.4 Inverses by Adjoints / 610
B.5 Inverses by Elementary Row Transformations / 611
B.6 Example Problem / 616
Problems / 617
Programming Problems / 618
Appendix C Nonlinear Equations and Taylor’s Theorem 619
C.1 Introduction / 619
C.2 Taylor Series Linearization of Nonlinear Equations / 619
C.3 Numerical Example / 620
C.4 Using Matrices to Solve Nonlinear Equations / 622
C.5 Simple Matrix Example / 623
C.6 Practical Example / 624
C.7 Concluding Remarks / 626
Problems / 627
Programming Problems / 628
Appendix D The Normal Error Distribution Curve and Other
Statistical Tables 629
D.1 Development for Normal Distribution Curve Equation / 629
D.2 Other Statistical Tables / 637
Appendix E Confidence Intervals for the Mean 649
Appendix F Map Projection Coordinate Systems 655
F.1 Introduction / 655
F.2 Mathematics of the Lambert Conformal Conic Map Projection / 657
F.3 Mathematics from the Transverse Mercator / 659
F.4 Stereographic Map Projection / 662
F.5 Reduction of Observations / 663
Appendix G Companion Website 669
G.1 Introduction / 669
G.2 File Formats and Memory Matters / 670
G.3 Software / 670
G.4 Using the Software as an Instructional Aid / 674
Appendix H Answers to Selected Problems 675
BIBLIOGRAPHY 681
INDEX 685
Author Information
DR. CHARLES D. GHILANI is a Professor Emeritus of Engineering. He taught in the B.S. Surveying Engineering and A.S. Surveying Technology programs at Pennsylvania State University. He holds a Ph.D. and M.S. in Civil and Environmental Engineering from the University of WisconsinMadison, and a B.S. degree in mathematics and education from the University of WisconsinMilwaukee. He is an honorary member of the Pennsylvania Society of Land Surveyors (P.S.L.S.), the president of the American Association for Geodetic Surveying, and the editor of Surveying and Land Information Science. He has received the Milton S. Eisenhower Distinguished Teaching Award in 2013, and the 2017 Surveying and Geomatics Educator's Society Educator Award.
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 

8  145  Errata in Equation 8.4 of Page 145 of Chapter 8 Equation (8.4), change value 0.9167 to 0.9164 in both the occurrences 
21092017 