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Adjustment Computations, 6th Edition

Book Description

The definitive guide to bringing accuracy to measurement, updated and supplemented

Adjustment Computations is the classic textbook for spatial information analysis and adjustment computations, providing clear, easy-to-understand instruction backed by real-world 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 overly-complex 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 industry-standard methodologies to error analysis and adjustment
  • Translate your skills to the real-world 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 real-world training you need to identify, analyze, and correct for potentially crucial errors.

Table of Contents

  1. COVER
  2. TITLE PAGE
  3. PREFACE
  4. ACKNOWLEDGMENTS
  5. CHAPTER 1: INTRODUCTION
    1. 1.1 INTRODUCTION
    2. 1.2 DIRECT AND INDIRECT MEASUREMENTS
    3. 1.3 MEASUREMENT ERROR SOURCES
    4. 1.4 DEFINITIONS
    5. 1.5 PRECISION VERSUS ACCURACY
    6. 1.6 REDUNDANT OBSERVATIONS IN SURVEYING AND THEIR ADJUSTMENT
    7. 1.7 ADVANTAGES OF LEAST SQUARES ADJUSTMENT
    8. 1.8 OVERVIEW OF THE BOOK
    9. PROBLEMS
  6. CHAPTER 2: OBSERVATIONS AND THEIR ANALYSIS
    1. 2.1 INTRODUCTION
    2. 2.2 SAMPLE VERSUS POPULATION
    3. 2.3 RANGE AND MEDIAN
    4. 2.4 GRAPHICAL REPRESENTATION OF DATA
    5. 2.5 NUMERICAL METHODS OF DESCRIBING DATA
    6. 2.6 MEASURES OF CENTRAL TENDENCY
    7. 2.7 ADDITIONAL DEFINITIONS
    8. 2.8 ALTERNATIVE FORMULA FOR DETERMINING VARIANCE
    9. 2.9 NUMERICAL EXAMPLES
    10. 2.10 ROOT MEAN SQUARE ERROR AND MAPPING STANDARDS
    11. 2.11 DERIVATION OF THE SAMPLE VARIANCE (BESSEL'S CORRECTION)
    12. 2.12 SOFTWARE
    13. PROBLEMS
    14. PRACTICAL EXERCISES
  7. CHAPTER 3: RANDOM ERROR THEORY
    1. 3.1 INTRODUCTION
    2. 3.2 THEORY OF PROBABILITY
    3. 3.3 PROPERTIES OF THE NORMAL DISTRIBUTION CURVE
    4. 3.4 STANDARD NORMAL DISTRIBUTION FUNCTION
    5. 3.5 PROBABILITY OF THE STANDARD ERROR
    6. 3.6 USES FOR PERCENT ERRORS
    7. 3.7 PRACTICAL EXAMPLES
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTE
  8. CHAPTER 4: CONFIDENCE INTERVALS
    1. 4.1 INTRODUCTION
    2. 4.2 DISTRIBUTIONS USED IN SAMPLING THEORY
    3. 4.3 CONFIDENCE INTERVAL FOR THE MEAN: T STATISTIC
    4. 4.4 TESTING THE VALIDITY OF THE CONFIDENCE INTERVAL
    5. 4.5 SELECTING A SAMPLE SIZE
    6. 4.6 CONFIDENCE INTERVAL FOR A POPULATION VARIANCE
    7. 4.7 CONFIDENCE INTERVAL FOR THE RATIO OF TWO POPULATION VARIANCES
    8. 4.8 SOFTWARE
    9. PROBLEMS
    10. NOTES
  9. CHAPTER 5: STATISTICAL TESTING
    1. 5.1 HYPOTHESIS TESTING
    2. 5.2 SYSTEMATIC DEVELOPMENT OF A TEST
    3. 5.3 TEST OF HYPOTHESIS FOR THE POPULATION MEAN
    4. 5.4 TEST OF HYPOTHESIS FOR THE POPULATION VARIANCE
    5. 5.5 TEST OF HYPOTHESIS FOR THE RATIO OF TWO POPULATION VARIANCES
    6. 5.6 SOFTWARE
    7. PROBLEMS
    8. NOTES
  10. CHAPTER 6: PROPAGATION OF RANDOM ERRORS IN INDIRECTLY MEASURED QUANTITIES
    1. 6.1 BASIC ERROR PROPAGATION EQUATION
    2. 6.2 FREQUENTLY ENCOUNTERED SPECIFIC FUNCTIONS
    3. 6.3 NUMERICAL EXAMPLES
    4. 6.4 SOFTWARE
    5. 6.5 CONCLUSIONS
    6. PROBLEMS
    7. PRACTICAL EXERCISES
    8. NOTE
  11. CHAPTER 7: ERROR PROPAGATION IN ANGLE AND DISTANCE OBSERVATIONS
    1. 7.1 INTRODUCTION
    2. 7.2 ERROR SOURCES IN HORIZONTAL ANGLES
    3. 7.3 READING ERRORS
    4. 7.4 POINTING ERRORS
    5. 7.5 ESTIMATED POINTING AND READING ERRORS WITH TOTAL STATIONS
    6. 7.6 TARGET-CENTERING ERRORS
    7. 7.7 INSTRUMENT CENTERING ERRORS
    8. 7.8 EFFECTS OF LEVELING ERRORS IN ANGLE OBSERVATIONS
    9. 7.9 NUMERICAL EXAMPLE OF COMBINED ERROR PROPAGATION IN A SINGLE HORIZONTAL ANGLE
    10. 7.10 USING ESTIMATED ERRORS TO CHECK ANGULAR MISCLOSURE IN A TRAVERSE
    11. 7.11 ERRORS IN ASTRONOMICAL OBSERVATIONS FOR AZIMUTH
    12. 7.12 ERRORS IN ELECTRONIC DISTANCE OBSERVATIONS
    13. 7.13 CENTERING ERRORS WHEN USING RANGE POLES
    14. 7.14 SOFTWARE
    15. PROBLEMS
    16. PROGRAMMING PROBLEMS
    17. NOTES
  12. CHAPTER 8: ERROR PROPAGATION IN TRAVERSE SURVEYS
    1. 8.1 INTRODUCTION
    2. 8.2 DERIVATION OF ESTIMATED ERROR IN LATITUDE AND DEPARTURE
    3. 8.3 DERIVATION OF ESTIMATED STANDARD ERRORS IN COURSE AZIMUTHS
    4. 8.4 COMPUTING AND ANALYZING POLYGON TRAVERSE MISCLOSURE ERRORS
    5. 8.5 COMPUTING AND ANALYZING LINK TRAVERSE MISCLOSURE ERRORS
    6. 8.6 SOFTWARE
    7. 8.7 CONCLUSIONS
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTES
  13. CHAPTER 9: ERROR PROPAGATION IN ELEVATION DETERMINATION
    1. 9.1 INTRODUCTION
    2. 9.2 SYSTEMATIC ERRORS IN DIFFERENTIAL LEVELING
    3. 9.3 RANDOM ERRORS IN DIFFERENTIAL LEVELING
    4. 9.4 ERROR PROPAGATION IN TRIGONOMETRIC LEVELING
    5. PROBLEMS
    6. PROGRAMMING PROBLEMS
  14. CHAPTER 10: WEIGHTS OF OBSERVATIONS
    1. 10.1 INTRODUCTION
    2. 10.2 WEIGHTED MEAN
    3. 10.3 RELATIONSHIP BETWEEN WEIGHTS AND STANDARD ERRORS
    4. 10.4 STATISTICS OF WEIGHTED OBSERVATIONS
    5. 10.5 WEIGHTS IN ANGLE OBSERVATIONS
    6. 10.6 WEIGHTS IN DIFFERENTIAL LEVELING
    7. 10.7 PRACTICAL EXAMPLES
    8. PROBLEMS
  15. CHAPTER 11: PRINCIPLES OF LEAST SQUARES
    1. 11.1 INTRODUCTION
    2. 11.2 FUNDAMENTAL PRINCIPLE OF LEAST SQUARES
    3. 11.3 THE FUNDAMENTAL PRINCIPLE OF WEIGHTED LEAST SQUARES
    4. 11.4 THE STOCHASTIC MODEL
    5. 11.5 FUNCTIONAL MODEL
    6. 11.6 OBSERVATION EQUATIONS
    7. 11.7 SYSTEMATIC FORMULATION OF THE NORMAL EQUATIONS
    8. 11.8 TABULAR FORMATION OF THE NORMAL EQUATIONS
    9. 11.9 USING MATRICES TO FORM THE NORMAL EQUATIONS
    10. 11.10 LEAST SQUARES SOLUTION OF NONLINEAR SYSTEMS
    11. 11.11 LEAST SQUARES FIT OF POINTS TO A LINE OR CURVE
    12. 11.12 CALIBRATION OF AN EDM INSTRUMENT
    13. 11.13 LEAST SQUARES ADJUSTMENT USING CONDITIONAL EQUATIONS
    14. 11.14 THE PREVIOUS EXAMPLE USING OBSERVATION EQUATIONS
    15. 11.15 SOFTWARE
    16. PROBLEMS
    17. NOTES
  16. CHAPTER 12: ADJUSTMENT OF LEVEL NETS
    1. 12.1 INTRODUCTION
    2. 12.2 OBSERVATION EQUATION
    3. 12.3 UNWEIGHTED EXAMPLE
    4. 12.4 WEIGHTED EXAMPLE
    5. 12.5 REFERENCE STANDARD DEVIATION
    6. 12.6 ANOTHER WEIGHTED ADJUSTMENT
    7. 12.7 SOFTWARE
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
  17. CHAPTER 13: PRECISIONS OF INDIRECTLY DETERMINED QUANTITIES
    1. 13.1 INTRODUCTION
    2. 13.2 DEVELOPMENT OF THE COVARIANCE MATRIX
    3. 13.3 NUMERICAL EXAMPLES
    4. 13.4 STANDARD DEVIATIONS OF COMPUTED QUANTITIES
    5. PROBLEMS
    6. PROGRAMMING PROBLEMS
    7. NOTE
  18. CHAPTER 14: ADJUSTMENT OF HORIZONTAL SURVEYS: TRILATERATION
    1. 14.1 INTRODUCTION
    2. 14.2 DISTANCE OBSERVATION EQUATION
    3. 14.3 TRILATERATION ADJUSTMENT EXAMPLE
    4. 14.4 FORMULATION OF A GENERALIZED COEFFICIENT MATRIX FOR A MORE COMPLEX NETWORK
    5. 14.5 COMPUTER SOLUTION OF A TRILATERATED QUADRILATERAL
    6. 14.6 ITERATION TERMINATION
    7. 14.7 SOFTWARE
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTES
  19. CHAPTER 15: ADJUSTMENT OF HORIZONTAL SURVEYS: TRIANGULATION
    1. 15.1 INTRODUCTION
    2. 15.2 AZIMUTH OBSERVATION EQUATION
    3. 15.3 ANGLE OBSERVATION EQUATION
    4. 15.4 ADJUSTMENT OF INTERSECTIONS
    5. 15.5 ADJUSTMENT OF RESECTIONS
    6. 15.6 ADJUSTMENT OF TRIANGULATED QUADRILATERALS
    7. PROBLEMS
    8. PROGRAMMING PROBLEMS
    9. NOTE
  20. CHAPTER 16: ADJUSTMENT OF HORIZONTAL SURVEYS: TRAVERSES AND HORIZONTAL NETWORKS
    1. 16.1 INTRODUCTION TO TRAVERSE ADJUSTMENTS
    2. 16.2 OBSERVATION EQUATIONS
    3. 16.3 REDUNDANT EQUATIONS
    4. 16.4 NUMERICAL EXAMPLE
    5. 16.5 MINIMUM AMOUNT OF CONTROL
    6. 16.6 ADJUSTMENT OF NETWORKS
    7. 16.7 χ2 TEST: GOODNESS OF FIT
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTE
  21. CHAPTER 17: ADJUSTMENT OF GNSS NETWORKS
    1. 17.1 INTRODUCTION
    2. 17.2 GNSS OBSERVATIONS
    3. 17.3 GNSS ERRORS AND THE NEED FOR ADJUSTMENT
    4. 17.4 REFERENCE COORDINATE SYSTEMS FOR GNSS OBSERVATIONS
    5. 17.5 CONVERTING BETWEEN THE TERRESTRIAL AND GEODETIC COORDINATE SYSTEMS
    6. 17.6 APPLICATION OF LEAST SQUARES IN PROCESSING GNSS DATA
    7. 17.7 NETWORK PREADJUSTMENT DATA ANALYSIS
    8. 17.8 LEAST SQUARES ADJUSTMENT OF GNSS NETWORKS
    9. PROBLEMS
    10. PROGRAMMING PROBLEMS
    11. NOTES
  22. CHAPTER 18: COORDINATE TRANSFORMATIONS
    1. 18.1 INTRODUCTION
    2. 18.2 THE TWO-DIMENSIONAL CONFORMAL COORDINATE
    3. 18.3 EQUATION DEVELOPMENT
    4. 18.4 APPLICATION OF LEAST SQUARES
    5. 18.5 TWO-DIMENSIONAL AFFINE COORDINATE TRANSFORMATION
    6. 18.6 THE TWO-DIMENSIONAL PROJECTIVE COORDINATE TRANSFORMATION
    7. 18.7 THREE-DIMENSIONAL CONFORMAL COORDINATE TRANSFORMATION
    8. 18.8 STATISTICALLY VALID PARAMETERS
    9. PROBLEMS
    10. PROGRAMMING PROBLEMS
  23. CHAPTER 19: ERROR ELLIPSE
    1. 19.1 INTRODUCTION
    2. 19.2 COMPUTATION OF ELLIPSE ORIENTATION AND SEMIAXES
    3. 19.3 EXAMPLE PROBLEM OF STANDARD ERROR ELLIPSE CALCULATIONS
    4. 19.4 ANOTHER EXAMPLE PROBLEM
    5. 19.5 THE ERROR ELLIPSE CONFIDENCE LEVEL
    6. 19.6 ERROR ELLIPSE ADVANTAGES
    7. 19.7 OTHER MEASURES OF STATION UNCERTAINTY
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTES
  24. CHAPTER 20: CONSTRAINT EQUATIONS
    1. 20.1 INTRODUCTION
    2. 20.2 ADJUSTMENT OF CONTROL STATION COORDINATES
    3. 20.3 HOLDING CONTROL STATION COORDINATES AND DIRECTIONS OF LINES FIXED IN A TRILATERATION ADJUSTMENT
    4. 20.4 HELMERT'S METHOD
    5. 20.5 REDUNDANCIES IN A CONSTRAINED ADJUSTMENT
    6. 20.6 ENFORCING CONSTRAINTS THROUGH WEIGHTING
    7. PROBLEMS
    8. PRACTICAL PROBLEMS
  25. CHAPTER 21: BLUNDER DETECTION IN HORIZONTAL NETWORKS
    1. 21.1 INTRODUCTION
    2. 21.2 A PRIORI METHODS FOR DETECTING BLUNDERS IN OBSERVATIONS
    3. 21.3 A POSTERIORI BLUNDER DETECTION
    4. 21.4 DEVELOPMENT OF THE COVARIANCE MATRIX FOR THE RESIDUALS
    5. 21.5 DETECTION OF OUTLIERS IN OBSERVATIONS: DATA SNOOPING
    6. 21.6 DETECTION OF OUTLIERS IN OBSERVATIONS: THE TAU CRITERION
    7. 21.7 TECHNIQUES USED IN ADJUSTING CONTROL
    8. 21.8 A DATA SET WITH BLUNDERS
    9. 21.9 SOME FURTHER CONSIDERATIONS
    10. 21.10 SURVEY DESIGN
    11. 21.11 SOFTWARE
    12. PROBLEMS
    13. PRACTICAL PROBLEMS
    14. NOTES
  26. CHAPTER 22: THE GENERAL LEAST SQUARES METHOD AND ITS APPLICATION TO CURVE FITTING AND COORDINATE TRANSFORMATIONS
    1. 22.1 INTRODUCTION TO GENERAL LEAST SQUARES
    2. 22.2 GENERAL LEAST SQUARES EQUATIONS FOR FITTING A STRAIGHT LINE
    3. 22.3 GENERAL LEAST SQUARES SOLUTION
    4. 22.4 TWO-DIMENSIONAL COORDINATE TRANSFORMATION BY GENERAL LEAST SQUARES
    5. 22.5 THREE-DIMENSIONAL CONFORMAL COORDINATE TRANSFORMATION BY GENERAL LEAST SQUARES
    6. PROBLEMS
    7. PROGRAMMING PROBLEMS
  27. CHAPTER 23: THREE-DIMENSIONAL GEODETIC NETWORK ADJUSTMENT
    1. 23.1 INTRODUCTION
    2. 23.2 LINEARIZATION OF EQUATIONS
    3. 23.3 MINIMUM NUMBER OF CONSTRAINTS
    4. 23.4 EXAMPLE ADJUSTMENT
    5. 23.5 BUILDING AN ADJUSTMENT
    6. 23.6 COMMENTS ON SYSTEMATIC ERRORS
    7. 23.7 SOFTWARE
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTES
  28. CHAPTER 24: COMBINING GNSS AND TERRESTRIAL OBSERVATIONS
    1. 24.1 INTRODUCTION
    2. 24.2 THE HELMERT TRANSFORMATION
    3. 24.3 ROTATIONS BETWEEN COORDINATE SYSTEMS
    4. 24.4 COMBINING GNSS BASELINE VECTORS WITH TRADITIONAL OBSERVATIONS
    5. 24.5 ANOTHER APPROACH TO TRANSFORMING COORDINATES BETWEEN REFERENCE FRAMES
    6. 24.6 OTHER CONSIDERATIONS
    7. PROBLEMS
    8. PROGRAMMING PROBLEMS
    9. NOTES
  29. CHAPTER 25: ANALYSIS OF ADJUSTMENTS
    1. 25.1 INTRODUCTION
    2. 25.2 BASIC CONCEPTS, RESIDUALS, AND THE NORMAL DISTRIBUTION
    3. 25.3 GOODNESS OF FIT TEST
    4. 25.4 COMPARISON OF GNSS RESIDUAL PLOTS
    5. 25.5 USE OF STATISTICAL BLUNDER DETECTION
    6. PROBLEMS
    7. NOTES
  30. CHAPTER 26: COMPUTER OPTIMIZATION
    1. 26.1 INTRODUCTION
    2. 26.2 STORAGE OPTIMIZATION
    3. 26.3 DIRECT FORMATION OF THE NORMAL EQUATIONS
    4. 26.4 CHOLESKY DECOMPOSITION
    5. 26.5 FORWARD AND BACK SOLUTIONS
    6. 26.6 USING THE CHOLESKY FACTOR TO FIND THE INVERSE OF THE NORMAL MATRIX
    7. 26.7 SPARENESS AND OPTIMIZATION OF THE NORMAL MATRIX
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
    10. NOTES
  31. APPENDIX A: INTRODUCTION TO MATRICES
    1. A.1 INTRODUCTION
    2. A.2 DEFINITION OF A MATRIX
    3. A.3 SIZE OR DIMENSIONS OF A MATRIX
    4. A.4 TYPES OF MATRICES
    5. A.5 MATRIX EQUALITY
    6. A.6 ADDITION OR SUBTRACTION OF MATRICES
    7. A.7 SCALAR MULTIPLICATION OF A MATRIX
    8. A.8 MATRIX MULTIPLICATION
    9. A.9 COMPUTER ALGORITHMS FOR MATRIX OPERATIONS
    10. A.10 USE OF THE MATRIX SOFTWARE
    11. PROBLEMS
    12. PROGRAMMING PROBLEMS
    13. NOTE
  32. APPENDIX B: SOLUTION OF EQUATIONS BY MATRIX METHODS
    1. B.1 INTRODUCTION
    2. B.2 INVERSE MATRIX
    3. B.3 THE INVERSE OF A 2 × 2 MATRIX
    4. B.4 INVERSES BY ADJOINTS
    5. B.5 INVERSES BY ELEMENTARY ROW TRANSFORMATIONS
    6. B.6 EXAMPLE PROBLEM
    7. PROBLEMS
    8. PROGRAMMING PROBLEMS
  33. APPENDIX C: NONLINEAR EQUATIONS AND TAYLOR'S THEOREM
    1. C.1 INTRODUCTION
    2. C.2 TAYLOR SERIES LINEARIZATION OF NONLINEAR EQUATIONS
    3. C.3 NUMERICAL EXAMPLE
    4. C.4 USING MATRICES TO SOLVE NONLINEAR EQUATIONS
    5. C.5 SIMPLE MATRIX EXAMPLE
    6. C.6 PRACTICAL EXAMPLE
    7. C.7 CONCLUDING REMARKS
    8. PROBLEMS
    9. PROGRAMMING PROBLEMS
  34. APPENDIX D: THE NORMAL ERROR DISTRIBUTION CURVE AND OTHER STATISTICAL TABLES
    1. D.1 DEVELOPMENT FOR NORMAL DISTRIBUTION CURVE EQUATION
    2. D.2 OTHER STATISTICAL TABLES
    3. NOTE
  35. APPENDIX E: CONFIDENCE INTERVALS FOR THE MEAN
  36. APPENDIX F: MAP PROJECTION COORDINATE SYSTEMS
    1. F.1 INTRODUCTION
    2. F.2 MATHEMATICS OF THE LAMBERT CONFORMAL CONIC MAP PROJECTION
    3. F.3 MATHEMATICS FROM THE TRANSVERSE MERCATOR
    4. F.4 STEREOGRAPHIC MAP PROJECTION
    5. F.5 REDUCTION OF OBSERVATIONS
    6. NOTES
  37. APPENDIX G: COMPANION WEBSITE
    1. G.1 INTRODUCTION
    2. G.2 FILE FORMATS AND MEMORY MATTERS
    3. G.3 SOFTWARE
    4. G.4 USING THE SOFTWARE AS AN INSTRUCTIONAL AID
  38. APPENDIX H: ANSWERS TO SELECTED PROBLEMS
  39. BIBLIOGRAPHY
  40. INDEX
  41. END USER LICENSE AGREEMENT