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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 Adjustm
Ã¥¼Ò°³
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.
New feature
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¢ç.
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.
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