Adjustment Computations : Spatial Data Analysis (4th Ed., with CD-Rom)

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. Extensively updated, this Fourth Edition covers basic terms and fundamentals of errors and methods of analyzing them and progresses to specific adjustment computations and spatial information analysis. Each chapter includes practical examples, illustrations, and sample practice problems. Current and comprehensive, the book features: Easy-to-understand language and an emphasis on real-world applications. Extensive coverage of the treatment of GPS-acquired data. New chapters on analyzing data in three dimensions, confidence intervals, statistical testing, and more. Extensively updated STATS, ADJUST, and MATRIX software packages. A new companion CD & web site with a 150-page solutions manual, software, MathCAD worksheets, and view graphs. The latest information on advanced topics such as blunder detection and the method of general least squares. Adjustment Computations, Fourth Edition is an invaluable reference and self-study resource for working surveyors, photogrammetrists, and professionals who use GPS 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.

PREFACE. ACKNOWLEDGMENTS. 1 INTRODUCTION. 1.1 Introduction. 1.2 Direct and Indirect Measurements. 1.3 Measurement Error Sources. 1.4 Definitions. 1.5 Precision versus Accuracy. 1.6 Redundant Measurements in Surveying and Their Adjustment. 1.7 Advantages of Least Squares Adjustment. 1.8 Overview of the Book. Problems. 2 OBSERVATIONS AND THEIR ANALYSIS. 2.1 Introduction. 2.2 Sample versus Population. 2.3 Range and Median. 2.4 Graphical Representation of Data. 2.5 Numerical Methods of Describing Data. 2.6 Measures of Central Tendency. 2.7 Additional Definitions. 2.8 Alternative Formula for Determining Variance. 2.9 Numerical Examples. 2.10 Derivation of the Sample Variance (Bessels Correction). 2.11 Programming. Problems. 3 RANDOM ERROR THEORY. 3.1 Introduction. 3.2 Theory of Probability. 3.3 Properties of the Normal Distribution Curve. 3.4 Standard Normal Distribution Function. 3.5 Probability of the Standard Error. 3.6 Uses for Percent Errors. 3.7 Practical Examples. Problems. 4 CONFIDENCE INTERVALS. 4.1 Introduction. 4.2 Distributions Used in Sampling Theory. 4.3 Confidence Interval for the Mean: t Statistic. 4.4 Testing the Validity of the Confidence Interval. 4.5 Selecting a Sample Size. 4.6 Confidence Interval for a Population Variance. 4.7 Confidence Interval for the Ratio of Two Population Variances. Problems. 5 STATISTICAL TESTING. 5.1 Hypothesis Testing. 5.2 Systematic Development of a Test. 5.3 Test of Hypothesis for the Population Mean. 5.4 Test of Hypothesis for the Population Variance. 5.5 Test of Hypothesis for the Ratio of Two Population Variances. Problems. 6 PROPAGATION OF RANDOM ERRORS IN INDIRECTLY MEASURED QUANTITIES. 6.1 Basic Error Propagation Equation. 6.2 Frequently Encountered Specific Functions. 6.3 Numerical Examples. 6.4 Conclusions. Problems. 7 ERROR PROPAGATION IN ANGLE AND DISTANCE OBSERVATIONS. 7.1 Introduction. 7.2 Error Sources in Horizontal Angles. 7.3 Reading Errors. 7.4 Pointing Errors. 7.5 Estimated Pointing and Reading Errors with Total Stations. 7.6 Target Centering Errors. 7.7 Instrument Centering Errors. 7.8 Effects of Leveling Errors in Angle Observations. 7.9 Numerical Example of Combined Error Propagation in a Single Horizontal Angle. 7.10 Use of Estimated Errors to Check Angular Misclosure in a Traverse. 7.11 Errors in Astronomical Observations for an Azimuth. 7.12 Errors in Electronic Distance Observations. 7.13 Use of Computational Software. Problems. 8 ERROR PROPAGATION IN TRAVERSE SURVEYS. 8.1 Introduction. 8.2 Derivation of Estimated Error in Latitude and Departure. 8.3 Derivation of Estimated Standard Errors in Course Azimuths. 8.4 Computing and Analyzing Polygon Traverse Misclosure Errors. 8.5 Computing and Analyzing Link Traverse Misclosure Errors. 8.6 Conclusions. Problems. 9 ERROR PROPAGATION IN ELEVATION DETERMINATION. 9.1 Introduction. 9.2 Systematic Errors in Differential Leveling. 9.3 Random Errors in Differential Leveling. 9.4 Error Propagation in Trigonometric Leveling. Problems. 10 WEIGHTS OF OBSERVATIONS. 10.1 Introduction. 10.2 Weighted Mean. 10.3 Relation between Weights and Standard Errors. 10.4 Statistics of Weighted Observations. 10.5 Weights in Angle Observations. 10.6 Weights in Differential Leveling. 10.7 Practical Examples. Problems. 11 PRINCIPLES OF LEAST SQUARES. 11.1 Introduction. 11.2 Fundamental Principle of Least Squares. 11.3 Fundamental Principle of Weighted Least Squares. 11.4 Stochastic Model. 11.5 Functional Model. 11.6 Observation Equations. 11.6.1 Elementary Example of Observation Equation Adjustment. 11.7 Systematic Formulation of the Normal Equations. 11.8 Tabular Formation of the Normal Equations. 11.9 Using Matrices to Form the Normal Equations. 11.10 Least Squares Solution of Nonlinear Systems. 11.11 Least Squares Fit of Points to a Line or Curve. 11.12 Calibration of an EDM Instrument. 11.13 Least Squares Adjustment Using Conditional Equations. 11.14 Example 11.5 Using Observation Equations. Problems. 12 ADJUSTMENT OF LEVEL NETS. 12.1 Introduction. 12.2 Observation Equation. 12.3 Unweighted Example. 12.4 Weighted Example. 12.5 Reference Standard Deviation. 12.6 Another Weighted Adjustment. Problems. 13 PRECISION OF INDIRECTLY DETERMINED QUANTITIES. 13.1 Introduction. 13.2 Development of the Covariance Matrix. 13.3 Numerical Examples. 13.4 Standard Deviations of Computed Quantities. Problems. 14 ADJUSTMENT OF HORIZONTAL SURVEYS: TRILATERATION. 14.1 Introduction. 14.2 Distance Observation Equation. 14.3 Trilateration Adjustment Example. 14.4 Formulation of a Generalized Coefficient Matrix for a More Complex Network. 14.5 Computer Solution of a Trilaterated Quadrilateral. 14.6 Iteration Termination. Problems. 15 ADJUSTMENT OF HORIZONTAL SURVEYS: TRIANGULATION. 15.1 Introduction. 15.2 Azimuth Observation Equation. 15.3 Angle Observation Equation. 15.4 Adjustment of Intersections. 15.5 Adjustment of Resections. 15.6 Adjustment of Triangulated Quadrilaterals. Problems. 16 ADJUSTMENT OF HORIZONTAL SURVEYS: TRAVERSES AND NETWORKS. 16.1 Introduction to Traverse Adjustments. 16.2 Observation Equations. 16.3 Redundant Equations. 16.4 Numerical Example. 16.5 Minimum Amount of Control. 16.6 Adjustment of Networks. 16.7 x2 Test: Goodness of Fit. Problems. 17 ADJUSTMENT OF GPS NETWORKS, 17.1 Introduction, 17.2 GPS Observations, 17.3 GPS Errors and the Need for Adjustment, 17.4 Reference Coordinate Systems for GPS Observations. 17.5 Converting between the Terrestrial and Geodetic Coordinate Systems. 17.6 Application of Least Squares in Processing GPS Data. 17.7 Network Preadjustment Data Analysis. 17.8 Least Squares Adjustment of GPS Networks. Problems. 18 COORDINATE TRANSFORMATIONS. 18.1 Introduction. 18.2 Two-Dimensional Conformal Coordinate Transformation. 18.3 Equation Development. 18.4 Application of Least Squares. 18.5 Two-Dimensional Affine Coordinate Transformation. 18.6 Two-Dimensional Projective Coordinate Transformation. 18.7 Three-Dimensional Conformal Coordinate Transformation. 18.8 Statistically Valid Parameters. Problems.. 19 ERROR ELLIPSE 369 19.1 Introduction. 19.2 Computation of Ellipse Orientation and Semiaxes. 19.3 Example Problem of Standard Error Ellipse Calculations. 19.4 Another Example Problem. 19.5 Error Ellipse Confidence Level. 19.6 Error Ellipse Advantages. 19.7 Other Measures of Station Uncertainty. Problems. 20 CONSTRAINT EQUATIONS. 20.1 Introduction. 20.2 Adjustment of Contro