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· 분류 : 외국도서 > 기술공학 > 기술공학 > 토목 > 토목일반
· ISBN : 9781119385981
· 쪽수 : 720쪽
목차
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 Target-Centering 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 Two-Dimensional Conformal Coordinate / 389
18.3 Equation Development / 390
18.4 Application of Least Squares / 392
18.5 Two-Dimensional Affine Coordinate Transformation / 395
18.6 The Two-Dimensional Projective Coordinate Transformation / 398
18.7 Three-Dimensional 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 Two-Dimensional Coordinate Transformation by General Least Squares / 503
22.5 Three-Dimensional Conformal Coordinate Transformation by General Least Squares / 509
Problems / 511
Programming Problems / 515
23 Three-Dimensional 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
