Adjustment Computations : Spatial Data Analysis

**the complete guide to adjusting for measurement error—expanded and updated**no measurement is ever exact. __Adjustment Computations__ updates a classic, definitive text on surveying with the latest methodologies and tools for analyzing and adjusting errors with a focus on least squares adjustments, the most rigorous methodology available and the one on which accuracy standards for surveys are based. This extensively updated __Fifth Edition__ shares new information on advances in modern software and GNSS-acquired data. Expanded sections offer a greater amount of computable problems and their worked solutions, while new screenshots guide readers through the exercises. Continuing its legacy as a reliable primer, __Adjustment Computations__ covers the basic terms and fundamentals of errors and methods of analyzing them and progresses to specific adjustment computations and spatial information analysis. Current and comprehensive, the book features: * Easy-to-understand language and an emphasis on real-world applications * Analyzing data in three dimensions, confidence intervals, statistical testing, and more * An updated support web page containing a 150-page solutions manual, software (STATS, ADJUST, and MATRIX for Windows computers), MathCAD worksheets, and more at http://www.wiley.com/college/ghilani * The latest information on advanced topics such as the tau criterion used in post-adjustment statistical blunder detection __Adjustment Computations, Fifth Edition__ is an invaluable reference and self-study resource for working surveyors, photogrammetrists, and professionals who use GNSS and GIS for data collection and analysis, including oceanographers, urban planners, foresters, geographers, and transportation planners. It's also an indispensable resource for students preparing for licensing exams and the ideal textbook for courses in surveying, civil engineering, forestry, cartography, and geology. Adjustment Computations......Page 3 Contents......Page 7 Preface......Page 17 Acknowledgments......Page 21 1.1. Introduction......Page 25 1.3. Measurement Error Sources......Page 26 1.4. Definitions......Page 27 1.5. Precision versus Accuracy......Page 28 1.6. Redundant Observations in Surveying and Their Adjustment......Page 30 1.7. Advantages of Least Squares Adjustment......Page 32 1.8. Overview of the Book......Page 33 Problems......Page 34 2.2. Sample versus Population......Page 36 2.3. Range and Median......Page 37 2.4. Graphical Representation of Data......Page 38 2.6. Measures of Central Tendency......Page 41 2.7. Additional Definitions......Page 42 2.8. Alternative Formula for Determining Variance......Page 45 2.9. Numerical Examples......Page 46 2.10. Derivation of the Sample Variance (Bessel’s Correction)......Page 50 2.11. Software......Page 52 Problems......Page 53 Practical Exercises......Page 56 3.2. Theory of Probability......Page 57 3.3. Properties of the Normal Distribution Curve......Page 60 3.4. Standard Normal Distribution Function......Page 62 3.5. Probability of the Standard Error......Page 65 3.6. Uses for Percent Errors......Page 67 3.7. Practical Examples......Page 68 Problems......Page 70 Programming Problems......Page 72 4.1. Introduction......Page 73 4.2. Distributions Used in Sampling Theory......Page 75 4.3. Confidence Interval for the Mean: t statistic......Page 79 4.4. Testing the Validity of the Confidence Interval......Page 82 4.5. Selecting a Sample Size......Page 83 4.6. Confidence Interval for a Population Variance......Page 84 4.7. Confidence Interval for the Ratio of Two Population Variances......Page 85 4.8. Software......Page 88 Problems......Page 90 5.1. Hypothesis Testing......Page 94 5.2. Systematic Development of a Test......Page 97 5.3. Test of Hypothesis for the Population Mean......Page 98 5.4. Test of Hypothesis for the Population Variance......Page 100 5.5. Test of Hypothesis for the Ratio of Two Population Variances......Page 103 5.6. Software......Page 106 Problems......Page 107 6.1. Basic Error Propagation Equation......Page 110 6.2. Frequently Encountered Specific Functions......Page 115 6.3. Numerical Examples......Page 116 6.4. Software......Page 120 Problems......Page 122 Practical Exercises......Page 126 7.2. Error Sources in Horizontal Angles......Page 127 7.3. Reading Errors......Page 128 7.4. Pointing Errors......Page 130 7.5. Estimated Pointing and Reading Errors with Total Stations......Page 131 7.6. Target-Centering Errors......Page 132 7.7. Instrument-Centering Errors......Page 134 7.8. Effects of Leveling Errors in Angle Observations......Page 137 7.9. Numerical Example of Combined Error Propagation in a Single Horizontal Angle......Page 140 7.10. Using Estimated Errors to Check Angular Misclosure in a Traverse......Page 141 7.11. Errors in Astronomical Observations for Azimuth......Page 143 7.12. Errors in Electronic Distance Observations......Page 148 7.13. Software......Page 149 Problems......Page 150 Programming Problems......Page 154 8.1. Introduction......Page 155 8.2. Derivation of Estimated Error in Latitude and Departure......Page 156 8.4. Computing and Analyzing Polygon Traverse Misclosure Errors......Page 158 8.5. Computing and Analyzing Link Traverse Misclosure Errors......Page 164 8.6. Software......Page 168 Problems......Page 169 Programming Problems......Page 174 9.2. Systematic Errors in Differential Leveling......Page 175 9.3. Random Errors in Differential Leveling......Page 178 9.4. Error Propagation in Trigonometric Leveling......Page 183 Problems......Page 186 Programming Problems......Page 188 10.1. Introduction......Page 189 10.2. Weighted Mean......Page 191 10.4. Statistics of Weighted Observations......Page 193 10.6. Weights in Differential Leveling......Page 195 10.7. Practical Examples......Page 197 Problems......Page 199 11.1. Introduction......Page 202 11.2. Fundamental Principle of Least Squares......Page 203 11.3. Fundamental Principle of Weighted Least Squares......Page 205 11.4. Stochastic Model......Page 206 11.5. Functional Model......Page 207 11.6. Observation Equations......Page 208 11.7. Systematic Formulation of the Normal Equations......Page 210 11.8. Tabular Formation of the Normal Equations......Page 212 11.9. Using Matrices to Form Normal Equations......Page 213 11.10. Least Squares Solution of Nonlinear Systems......Page 216 11.11. Least Squares Fit of Points to a Line or Curve......Page 219 11.12. Calibration of an EDM Instrument......Page 223 11.13. Least Squares Adjustment Using Conditional Equations......Page 224 11.14. The Previous Example Using Observation Equations......Page 226 11.15. Software......Page 227 Problems......Page 228 12.2. Observation Equation......Page 234 12.3. Unweighted Example......Page 235 12.4. Weighted Example......Page 238 12.5. Reference Standard Deviation......Page 240 12.6. Another Weighted Adjustment......Page 242 12.7. Software......Page 245 Problems......Page 247 Programming Problems......Page 251 13.2. Development of the Covariance Matrix......Page 252 13.3. Numerical Examples......Page 256 13.4. Standard Deviations of Computed Quantities......Page 257 Problems......Page 260 Programming Problems......Page 263 14.1. Introduction......Page 264 14.2. Distance Observation Equation......Page 266 14.3. Trilateration Adjustment Example......Page 268 14.4. Formulation of a Generalized Coefficient Matrix for a More Complex Network......Page 274 14.5. Computer Solution of a Trilaterated Quadrilateral......Page 275 14.6. Iteration Termination......Page 279 14.7. Software......Page 280 Problems......Page 282 Programming Problems......Page 288 15.2. Azimuth Observation Equation......Page 290 15.3. Angle Observation Equation......Page 293 15.4. Adjustment of Intersections......Page 295 15.5. Adjustment of Resections......Page 300 15.6. Adjustment of Triangulated Quadrilaterals......Page 306 Problems......Page 311 Programming Problems......Page 320 16.2. Observation Equations......Page 322 16.3. Redundant Equations......Page 323 16.4. Numerical Example......Page 324 16.5. Minimum Amount of Control......Page 330 16.6. Adjustment of Networks......Page 331 16.7. χ2 Test: Goodness of Fit......Page 339 Problems......Page 340 Programming Problems......Page 350 17.1. Introduction......Page 351 17.2. GNSS Observations......Page 352 17.3. GNSS Errors and the Need for Adjustment......Page 354 17.4. Reference Coordinate Systems for GNSS Observations......Page 355 17.5. Converting between the Terrestrial and Geodetic Coordinate Systems......Page 358 17.6. Application of Least Squares in Processing GNSS Data......Page 361 17.7. Network Preadjustment Data Analysis......Page 364 17.8. Least Squares Adjustment of GNSS Networks......Page 370 Problems......Page 376 Programming Problems......Page 390 18.2. Two-Dimensional Conformal Coordinate......Page 392 18.3. Equation Development......Page 393 18.4. Application of Least Squares......Page 395 18.5. Two-Dimensional Affine Coordinate Transformation......Page 398 18.6. Two-Dimensional Projective Coordinate Transformation......Page 401 18.7. Three-Dimensional Conformal Coordinate Transformation......Page 404 18.8. Statistically Valid Parameters......Page 410 Problems......Page 414 Programming Problems......Page 420 19.1. Introduction......Page 421 19.2. Computation of Ellipse Orientation and Semiaxes......Page 423 19.3. Example Problem of Standard Error Ellipse Calculations......Page 428 19.4. Another Example Problem......Page 430 19.5. Error Ellipse Confidence Level......Page 431 19.6. Error Ellipse Advantages......Page 433 19.7. Other Measures of Station Uncertainty......Page 436 Problems......Page 437 Programming Problems......Page 439 20.2. Adjustment of Control Station Coordinates......Page 440 20.3. Holding Control Fixed in a Trilateration Adjustment......Page 445 20.4. Helmert’s Method......Page 448 20.6. Enforcing Constraints through Weighting......Page 453 Problems......Page 455 Practical Exercises......Page 458 21.1. Introduction......Page 459 21.2. A Priori Methods for Detecting Blunders in Observations......Page 460 21.3. A Posteriori Blunder Detection......Page 462 21.4. Development of the Covariance Matrix for the Residuals......Page 463 21.5. Detection of Outliers in Observations: Data Snooping......Page 466 21.7. Techniques Used In Adjusting Control......Page 468 21.8. Data Set with Blunders......Page 470 21.9. Further Considerations......Page 477 21.10. Survey Design......Page 479 21.11. Software......Page 481 Problems......Page 482 Practical Exercises......Page 486 22.2. General Least Squares Equations for Fitting a Straight Line......Page 488 22.3. General Least Squares Solution......Page 490 22.4. Two-Dimensional Coordinate Transformation by General Least Squares......Page 494 22.5. Three-Dimensional Conformal Coordinate Transformation by General Least Squares......Page 500 Problems......Page 502 Programming Problems......Page 506 23.1. Introduction......Page 507 23.2. Linearization of Equations......Page 509 23.4. Example Adjustment......Page 514 23.6. Comments on Systematic Errors......Page 523 23.7. Software......Page 526 Problems......Page 527 Programming Problems......Page 531 24.1. Introduction......Page 532 24.2. Helmert’s Transformation......Page 534 24.3. Rotations between Coordinate Systems......Page 537 24.4. Combining GPS Baseline Vectors with Traditional Observations......Page 538 24.5. Another Approach to Transforming Coordinates between Reference Frames......Page 542 24.6. Other Considerations......Page 545 Problems......Page 546 Programming Problems......Page 548 25.2. Basic Concepts, Residuals, and the Normal Distribution......Page 549 25.3. Goodness-of-Fit Test......Page 552 25.4. Comparison of Residual Plots......Page 555 25.5. Use of Statistical Blunder Detection......Page 557 Problems......Page 558 26.2. Storage Optimization......Page 560 26.3. Direct Formation of the Normal Equations......Page 563 26.4. Cholesky Decomposition......Page 564 26.5. Forward and Back Solutions......Page 566 26.6. Using the Cholesky Factor to Find the Inverse of the Normal Matrix......Page 567 26.7. Spareness and Optimization of the Normal Matrix......Page 569 Programming Problems......Page 573 A.2. Definition of a Matrix......Page 574 A.3. Size or Dimensions of a Matrix......Page 575 A.4. Types of Matrices......Page 576 A.5. Matrix Equality......Page 577 A.8. Matrix Multiplication......Page 578 A.9. Computer Algorithms for Matrix Operations......Page 581 A.10. Use of the MATRIX Software......Page 584 Problems......Page 586 Programming Problems......Page 588 B-2. Inverse Matrix......Page 589 B-3. Inverse of a 2 × 2 Matrix......Page 590 B-4. Inverses by Adjoints......Page 592 B-5. Inverses by Elementary Row Transformations......Page 593 B-6. Example Problem......Page 597 Problems......Page 598 Programming Problems......Page 599 C.2. Taylor Series Linearization of Nonlinear Equations......Page 600 C.3. Numerical Example......Page 601 C.4. Using Matrices to Solve Nonlinear Equations......Page 603 C.5. Simple Matrix Example......Page 604 C.6. Practical Example......Page 605 C.7. Concluding Remarks......Page 607 Problems......Page 608 Programming Problems......Page 609 D.1. Development of the Normal Distribution Curve Equation......Page 610 D.2. Other Statistical Tables......Page 618 Appendix E Confidence Intervals for the Mean......Page 630 F.1. Introduction......Page 636 F.2. Mathematics of the Lambert Conformal Conic Map Projection......Page 637 F.3. Mathematics from the Transverse Mercator......Page 640 F.4. Stereographic Map Projection......Page 643 F.5. Reduction of Observations......Page 645 G.1. Introduction......Page 649 G.3. Software......Page 650 G.4. Using the Software as an Instructional Aid......Page 654 Appendix H Solutions to Selected Problems......Page 655 Bibliography......Page 660 Index......Page 663

the complete guide to adjusting for measurement error—expanded and updated

no measurement is ever exact. Adjustment Computations updates a classic, definitive text on surveying with the latest methodologies and tools for analyzing and adjusting errors with a focus on least squares adjustments, the most rigorous methodology available and the one on which accuracy standards for surveys are based.

This extensively updated Fifth Edition shares new information on advances in modern software and GNSS-acquired data. Expanded sections offer a greater amount of computable problems and their worked solutions, while new screenshots guide readers through the exercises. Continuing its legacy as a reliable primer, Adjustment Computations covers the basic terms and fundamentals of errors and methods of analyzing them and progresses to specific adjustment computations and spatial information analysis. Current and comprehensive, the book features:

• Easy-to-understand language and an emphasis on real-world applications
• Analyzing data in three dimensions, confidence intervals, statistical testing, and more
• An updated support web page containing a 150-page solutions manual, software (STATS, ADJUST, and MATRIX for Windows computers), MathCAD worksheets, and more at http://www.wiley.com/college/ghilani
• The latest information on advanced topics such as the tau criterion used in post-adjustment statistical blunder detection

Adjustment Computations, Fifth Edition is an invaluable reference and self-study resource for working surveyors, photogrammetrists, and professionals who use GNSS and GIS for data collection and analysis, including oceanographers, urban planners, foresters, geographers, and transportation planners. It's also an indispensable resource for students preparing for licensing exams and the ideal textbook for courses in surveying, civil engineering, forestry, cartography, and geology.

An update to a classic in the field of surveying, this is one of the few books that deals with the important issue of error in spatial data. Originally written for surveyors, it has expanded over the years to encompass the needs of new spatial technologies as they've been introduced (GPS, GIS) and new analytical techniques as they find acceptance.