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基本説明
Updated edition of the classic textbook for adjustment computations and spatial information analysis.
Full Description
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. This Fifth Edition offers new screenshots to guide students through the exercises, more problems, more worked solutions in the solutions manual, as well as PowerPoint slides from the author's lectures.
Contents
PREFACE xvACKNOWLEDGMENTS xix1 Introduction 11.1. Introduction 11.2. Direct and Indirect Measurements 21.3. Measurement Error Sources 21.4. Definitions 31.5. Precision versus Accuracy 41.6. Redundant Observations in Surveying and Their Adjustment 61.7. Advantages of Least Squares Adjustment 81.8. Overview of the Book 9Problems 102 Observations and Their Analysis 122.1. Introduction 122.2. Sample versus Population 122.3. Range and Median 132.4. Graphical Representation of Data 142.5. Numerical Methods of Describing Data 172.6. Measures of Central Tendency 172.7. Additional Definitions 182.8. Alternative Formula for Determining Variance 212.9. Numerical Examples 222.10. Derivation of the Sample Variance (Bessel's Correction) 262.11. Software 28Problems 29Practical Exercises 323 Random Error Theory 333.1. Introduction 333.2. Theory of Probability 333.3. Properties of the Normal Distribution Curve 363.4. Standard Normal Distribution Function 383.5. Probability of the Standard Error 413.6. Uses for Percent Errors 433.7. Practical Examples 44Problems 46Programming Problems 484 Confidence Intervals 494.1. Introduction 494.2. Distributions Used in Sampling Theory 514.3. Confidence Interval for the Mean: t statistic 554.4. Testing the Validity of the Confidence Interval 584.5. Selecting a Sample Size 594.6. Confidence Interval for a Population Variance 604.7. Confidence Interval for the Ratio of Two Population Variances 614.8. Software 64Problems 665 Statistical Testing 705.1. Hypothesis Testing 705.2. Systematic Development of a Test 735.3. Test of Hypothesis for the Population Mean 745.4. Test of Hypothesis for the Population Variance 765.5. Test of Hypothesis for the Ratio of Two Population Variances 795.6. Software 82Problems 836 Propagation of Random Errors in Indirectly Measured Quantities 866.1. Basic Error Propagation Equation 866.2. Frequently Encountered Specific Functions 916.3. Numerical Examples 926.4. Software 966.5. Conclusions 98Problems 98Practical Exercises 1027 Error Propagation in Angle and Distance Observations 1037.1. Introduction 1037.2. Error Sources in Horizontal Angles 1037.3. Reading Errors 1047.4. Pointing Errors 1067.5. Estimated Pointing and Reading Errors with Total Stations 1077.6. Target-Centering Errors 1087.7. Instrument-Centering Errors 1107.8. Effects of Leveling Errors in Angle Observations 1137.9. Numerical Example of Combined Error Propagation in a Single Horizontal Angle 1167.10. Using Estimated Errors to Check Angular Misclosure in a Traverse 1177.11. Errors in Astronomical Observations for Azimuth 1197.12. Errors in Electronic Distance Observations 1247.13. Software 125Problems 126Programming Problems 1308 Error Propagation in Traverse Surveys 1318.1. Introduction 1318.2. Derivation of Estimated Error in Latitude and Departure 1328.3. Derivation of Estimated Standard Errors in Course Azimuths 1348.4. Computing and Analyzing Polygon Traverse Misclosure Errors 1348.5. Computing and Analyzing Link Traverse Misclosure Errors 1408.6. Software 1448.7. Conclusions 145Problems 145Programming Problems 1509 Error Propagation in Elevation Determination 1519.1. Introduction 1519.2. Systematic Errors in Differential Leveling 1519.3. Random Errors in Differential Leveling 1549.4. Error Propagation in Trigonometric Leveling 159Problems 162Programming Problems 16410 Weights of Observations 16510.1. Introduction 16510.2. Weighted Mean 16710.3. Relation between Weights and Standard Errors 16910.4. Statistics of Weighted Observations 16910.5. Weights in Angle Observations 17110.6. Weights in Differential Leveling 17110.7. Practical Examples 173Problems 17511 Principles of Least Squares 17811.1. Introduction 17811.2. Fundamental Principle of Least Squares 17911.3. Fundamental Principle of Weighted Least Squares 18111.4. Stochastic Model 18211.5. Functional Model 18311.6. Observation Equations 18411.7. Systematic Formulation of the Normal Equations 18611.8. Tabular Formation of the Normal Equations 18811.9. Using Matrices to Form Normal Equations 18911.10. Least Squares Solution of Nonlinear Systems 19211.11. Least Squares Fit of Points to a Line or Curve 19511.12. Calibration of an EDM Instrument 19911.13. Least Squares Adjustment Using Conditional Equations 20011.14. The Previous Example Using Observation Equations 20211.15. Software 203Problems 20412 Adjustment of Level Nets 21012.1. Introduction 21012.2. Observation Equation 21012.3. Unweighted Example 21112.4. Weighted Example 21412.5. Reference Standard Deviation 21612.6. Another Weighted Adjustment 21812.7. Software 221Problems 223Programming Problems 22713 Precisions of Indirectly Determined Quantities 22813.1. Introduction 22813.2. Development of the Covariance Matrix 22813.3. Numerical Examples 23213.4. Standard Deviations of Computed Quantities 233Problems 236Programming Problems 23914 Adjustment of Horizontal Surveys: Trilateration 24014.1. Introduction 24014.2. Distance Observation Equation 24214.3. Trilateration Adjustment Example 24414.4. Formulation of a Generalized Coefficient Matrix for a More Complex Network 25014.5. Computer Solution of a Trilaterated Quadrilateral 25114.6. Iteration Termination 25514.7. Software 256Problems 258Programming Problems 26415 Adjustment of Horizontal Surveys: Triangulation 26615.1. Introduction 26615.2. Azimuth Observation Equation 26615.3. Angle Observation Equation 26915.4. Adjustment of Intersections 27115.5. Adjustment of Resections 27615.6. Adjustment of Triangulated Quadrilaterals 282Problems 287Programming Problems 29616 Adjustment of Horizontal Surveys: Traverses and Horizontal Networks 29816.1. Introduction to Traverse Adjustments 29816.2. Observation Equations 29816.3. Redundant Equations 29916.4. Numerical Example 30016.5. Minimum Amount of Control 30616.6. Adjustment of Networks 30716.7. 2 Test: Goodness of Fit 315Problems 316Programming Problems 32617 Adjustment of GNSS Networks 32717.1. Introduction 32717.2. GNSS Observations 32817.3. GNSS Errors and the Need for Adjustment 33017.4. Reference Coordinate Systems for GNSS Observations 33117.5. Converting between the Terrestrial and Geodetic Coordinate Systems 33417.6. Application of Least Squares in Processing GNSS Data 33717.7. Network Preadjustment Data Analysis 34017.8. Least Squares Adjustment of GNSS Networks 346Problems 352Programming Problems 36618 Coordinate Transformations 36818.1. Introduction 36818.2. Two-Dimensional Conformal Coordinate 36818.3. Equation Development 36918.4. Application of Least Squares 37118.5. Two-Dimensional Affine Coordinate Transformation 37418.6. Two-Dimensional Projective Coordinate Transformation 37718.7. Three-Dimensional Conformal Coordinate Transformation 38018.8. Statistically Valid Parameters 386Problems 390Programming Problems 39619 Error Ellipse 39719.1. Introduction 39719.2. Computation of Ellipse Orientation and Semiaxes 39919.3. Example Problem of Standard Error Ellipse Calculations 40419.4. Another Example Problem 40619.5. Error Ellipse Confidence Level 40719.6. Error Ellipse Advantages 40919.7. Other Measures of Station Uncertainty 412Problems 413Programming Problems 41520 Constraint Equations 41620.1. Introduction 41620.2. Adjustment of Control Station Coordinates 41620.3. Holding Control Fixed in a Trilateration Adjustment 42120.4. Helmert's Method 42420.5. Redundancies in a Constrained Adjustment 42920.6. Enforcing Constraints through Weighting 429Problems 431Practical Exercises 43421 Blunder Detection in Horizontal Networks 43521.1. Introduction 43521.2. A Priori Methods for Detecting Blunders in Observations 43621.3. A Posteriori Blunder Detection 43821.4. Development of the Covariance Matrix for the Residuals 43921.5. Detection of Outliers in Observations: Data Snooping 44221.6. Detection of Outliers in Observations: The Tau Criterion 44421.7. Techniques Used In Adjusting Control 44421.8. Data Set with Blunders 44621.9. Further Considerations 45321.10. Survey Design 45521.11. Software 457Problems 458Practical Exercises 46222 General Least Squares Method and Its Application to Curve Fitting and Coordinate Transformations 46422.1. Introduction to General Least Squares 46422.2. General Least Squares Equations for Fitting a Straight Line 46422.3. General Least Squares Solution 46622.4. Two-Dimensional Coordinate Transformation by General Least Squares 47022.5. Three-Dimensional Conformal Coordinate Transformation by General Least Squares 476Problems 478Programming Problems 48223 Three-Dimensional Geodetic Network Adjustment 48323.1. Introduction 48323.2. Linearization of Equations 48523.3. Minimum Number of Constraints 49023.4. Example Adjustment 49023.5. Building an Adjustment 49923.6. Comments on Systematic Errors 49923.7. Software 502Problems 503Programming Problems 50724 Combining GPS and Terrestrial Observations 50824.1. Introduction 50824.2. Helmert's Transformation 51024.3. Rotations between Coordinate Systems 51324.4. Combining GPS Baseline Vectors with Traditional Observations 51424.5. Another Approach to Transforming Coordinates between Reference Frames 51824.6. Other Considerations 521Problems 522Programming Problems 52425 Analysis of Adjustments 52525.1. Introduction 52525.2. Basic Concepts, Residuals, and the Normal Distribution 52525.3. Goodness-of-Fit Test 52825.4. Comparison of Residual Plots 53125.5. Use of Statistical Blunder Detection 533Problems 53426 Computer Optimization 53626.1. Introduction 53626.2. Storage Optimization 53626.3. Direct Formation of the Normal Equations 53926.4. Cholesky Decomposition 54026.5. Forward and Back Solutions 54226.6. Using the Cholesky Factor to Find the Inverse of the Normal Matrix 54326.7. Spareness and Optimization of the Normal Matrix 545Problems 549Programming Problems 549Appendix A Introduction to Matrices 550A.1. Introduction 550A.2. Definition of a Matrix 550A.3. Size or Dimensions of a Matrix 551A.4. Types of Matrices 552A.5. Matrix Equality 553A.6. Addition or Subtraction of Matrices 554A.7. Scalar Multiplication of a Matrix 554A.8. Matrix Multiplication 554A.9. Computer Algorithms for Matrix Operations 557A.10. Use of the MATRIX Software 560Problems 562Programming Problems 564Appendix B Solution of Equations by Matrix Methods 565B-1. Introduction 565B-2. Inverse Matrix 565B-3. Inverse of a 2 x 2 Matrix 566B-4. Inverses by Adjoints 568B-5. Inverses by Elementary Row Transformation 569B-6. Example Problem 573Problems 574Programming Problems 575Appendix C Nonlinear Equations and Taylor's Theorem 576C.1. Introduction 576C.2. Taylor Series Linearization of Nonlinear Equations 576C.3. Numerical Example 577C.4. Using Matrices to Solve Nonlinear Equations 579C.5. Simple Matrix Example 580C.6. Practical Example 581C.7. Concluding Remarks 583Problems 584Programming Problems 585Appendix D Normal Error Distribution Curve and Other Statistical Tables 586D.1. Development of the Normal Distribution Curve Equation 586D.2. Other Statistical Tables 594Appendix E Confidence Intervals for the Mean 606Appendix F Map Projection Coordinate Systems 612F.1. Introduction 612F.2. Mathematics of the Lambert Conformal Conic Map Projection 613F.3. Mathematics from the Transverse Mercator 616F.4. Stereographic Map Projection 619F.5. Reduction of Observations 621Appendix G Companion Web Site 625G.1. Introduction 625G.2. File Formats and Memory Matters 626G.3. Software 626G.4. Using the Software as an Instructional Aid 630Appendix H Solutions to Selected Problems 631BIBLIOGRAPHY 636INDEX 639
