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 Obse.