Details

Adjustment Computations


Adjustment Computations

Spatial Data Analysis
6. Aufl.

von: Charles D. Ghilani

168,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 29.09.2017
ISBN/EAN: 9781119390312
Sprache: englisch
Anzahl Seiten: 720

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Beschreibungen

<b>The definitive guide to bringing accuracy to measurement, updated and supplemented</b> <p><i>Adjustment Computations</i> 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. <p>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. <ul> <li>Apply industry-standard methodologies to error analysis and adjustment</li> <li>Translate your skills to the real-world with instruction focused on the practical</li> <li>Master the fundamentals as well as specific computations and analysis</li> <li>Strengthen your understanding of critical topics on the Fundamentals in Surveying Licensing Exam</li> </ul> <p>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; <i>Adjustment Computations</i> provides the real-world training you need to identify, analyze, and correct for potentially crucial errors.
<p>Preface xv</p> <p>Acknowledgments xix</p> <p><b>1 Introduction 1</b></p> <p>1.1 Introduction 1</p> <p>1.2 Direct and Indirect Measurements 2</p> <p>1.3 Measurement Error Sources 2</p> <p>1.4 Definitions 3</p> <p>1.5 Precision versus Accuracy 4</p> <p>1.6 Redundant Observations in Surveying and Their Adjustment 7</p> <p>1.7 Advantages of Least Squares Adjustment 8</p> <p>1.8 Overview of the Book 10</p> <p>Problems 10</p> <p><b>2 Observations and Their Analysis 13</b></p> <p>2.1 Introduction 13</p> <p>2.2 Sample versus Population 13</p> <p>2.3 Range and Median 14</p> <p>2.4 Graphical Representation of Data 15</p> <p>2.5 Numerical Methods of Describing Data 18</p> <p>2.6 Measures of Central Tendency 18</p> <p>2.7 Additional Definitions 19</p> <p>2.8 Alternative Formula for Determining Variance 22</p> <p>2.9 Numerical Examples 24</p> <p>2.10 Root Mean Square Error and Mapping Standards 28</p> <p>2.11 Derivation of the Sample Variance (Bessel’s Correction) 31</p> <p>2.12 Software 32</p> <p>Problems 34</p> <p>Practical Exercises 37</p> <p><b>3 Random Error Theory 39</b></p> <p>3.1 Introduction 39</p> <p>3.2 Theory of Probability 39</p> <p>3.3 Properties of the Normal Distribution Curve 42</p> <p>3.4 Standard Normal Distribution Function 44</p> <p>3.5 Probability of the Standard Error 47</p> <p>3.6 Uses for Percent Errors 50</p> <p>3.7 Practical Examples 50</p> <p>Problems 53</p> <p>Programming Problems 55</p> <p><b>4 Confidence Intervals 57</b></p> <p>4.1 Introduction 57</p> <p>4.2 Distributions Used in Sampling Theory 59</p> <p>4.3 Confidence Interval for the Mean: <i>t </i>Statistic 63</p> <p>4.4 Testing the Validity of the Confidence Interval 66</p> <p>4.5 Selecting a Sample Size 67</p> <p>4.6 Confidence Interval for a Population Variance 68</p> <p>4.7 Confidence Interval for the Ratio of Two Population Variances 70</p> <p>4.8 Software 72</p> <p>Problems 75</p> <p><b>5 Statistical Testing 79</b></p> <p>5.1 Hypothesis Testing 79</p> <p>5.2 Systematic Development of a Test 82</p> <p>5.3 Test of Hypothesis for the Population Mean 84</p> <p>5.4 Test of Hypothesis for the Population Variance 85</p> <p>5.5 Test of Hypothesis for the Ratio of Two Population Variances 89</p> <p>5.6 Software 92</p> <p>Problems 93</p> <p><b>6 Propagation of Random Errors in Indirectly Measured Quantities 97</b></p> <p>6.1 Basic Error Propagation Equation 97</p> <p>6.2 Frequently Encountered Specific Functions 102</p> <p>6.3 Numerical Examples 103</p> <p>6.4 Software 107</p> <p>6.5 Conclusions 109</p> <p>Problems 109</p> <p>Practical Exercises 112</p> <p><b>7 Error Propagation in Angle and Distance Observations 113</b></p> <p>7.1 Introduction 113</p> <p>7.2 Error Sources in Horizontal Angles 113</p> <p>7.3 Reading Errors 114</p> <p>7.4 Pointing Errors 116</p> <p>7.5 Estimated Pointing and Reading Errors with Total Stations 117</p> <p>7.6 Target-Centering Errors 118</p> <p>7.7 Instrument Centering Errors 120</p> <p>7.8 Effects of Leveling Errors in Angle Observations 123</p> <p>7.9 Numerical Example of Combined Error Propagation in a Single Horizontal Angle 126</p> <p>7.10 Using Estimated Errors to Check Angular Misclosure in a Traverse 127</p> <p>7.11 Errors in Astronomical Observations for Azimuth 130</p> <p>7.12 Errors in Electronic Distance Observations 135</p> <p>7.13 Centering Errors When Using Range Poles 136</p> <p>7.14 Software 137</p> <p>Problems 138</p> <p>Programming Problems 141</p> <p><b>8 Error Propagation in Traverse Surveys 143</b></p> <p>8.1 Introduction 143</p> <p>8.2 Derivation of Estimated Error in Latitude and Departure 144</p> <p>8.3 Derivation of Estimated Standard Errors in Course Azimuths 146</p> <p>8.4 Computing and Analyzing Polygon Traverse Misclosure Errors 146</p> <p>8.5 Computing and Analyzing Link Traverse Misclosure Errors 152</p> <p>8.6 Software 156</p> <p>8.7 Conclusions 157</p> <p>Problems 157</p> <p>Programming Problems 161</p> <p><b>9 Error Propagation in Elevation Determination 163</b></p> <p>9.1 Introduction 163</p> <p>9.2 Systematic Errors in Differential Leveling 163</p> <p>9.3 Random Errors in Differential Leveling 166</p> <p>9.4 Error Propagation in Trigonometric Leveling 171</p> <p>Problems 174</p> <p>Programming Problems 177</p> <p><b>10 Weights of Observations 179</b></p> <p>10.1 Introduction 179</p> <p>10.2 Weighted Mean 181</p> <p>10.3 Relationship Between Weights and Standard Errors 183</p> <p>10.4 Statistics of Weighted Observations 184</p> <p>10.5 Weights in Angle Observations 185</p> <p>10.6 Weights in Differential Leveling 186</p> <p>10.7 Practical Examples 187</p> <p>Problems 190</p> <p><b>11 Principles of Least Squares 193</b></p> <p>11.1 Introduction 193</p> <p>11.2 Fundamental Principle of Least Squares 194</p> <p>11.3 The Fundamental Principle of Weighted Least Squares 196</p> <p>11.4 The Stochastic Model 197</p> <p>11.5 Functional Model 197</p> <p>11.6 Observation Equations 199</p> <p>11.7 Systematic Formulation of the Normal Equations 201</p> <p>11.8 Tabular Formation of the Normal Equations 203</p> <p>11.9 Using Matrices to Form the Normal Equations 204</p> <p>11.10 Least Squares Solution of Nonlinear Systems 207</p> <p>11.11 Least Squares Fit of Points to a Line or Curve 211</p> <p>11.12 Calibration of an EDM Instrument 214</p> <p>11.13 Least Squares Adjustment Using Conditional Equations 215</p> <p>11.14 The Previous Example Using Observation Equations 217</p> <p>11.15 Software 219</p> <p>Problems 219</p> <p><b>12 Adjustment of Level Nets 225</b></p> <p>12.1 Introduction 225</p> <p>12.2 Observation Equation 225</p> <p>12.3 Unweighted Example 226</p> <p>12.4 Weighted Example 229</p> <p>12.5 Reference Standard Deviation 231</p> <p>12.6 Another Weighted Adjustment 233</p> <p>12.7 Software 236</p> <p>Problems 238</p> <p>Programming Problems 242</p> <p><b>13 Precisions of Indirectly Determined Quantities 245</b></p> <p>13.1 Introduction 245</p> <p>13.2 Development of the Covariance Matrix 245</p> <p>13.3 Numerical Examples 249</p> <p>13.4 Standard Deviations of Computed Quantities 250</p> <p>Problems 254</p> <p>Programming Problems 256</p> <p><b>14 Adjustment of Horizontal Surveys: Trilateration 257</b></p> <p>14.1 Introduction 257</p> <p>14.2 Distance Observation Equation 259</p> <p>14.3 Trilateration Adjustment Example 261</p> <p>14.4 Formulation of a Generalized Coefficient Matrix for a More Complex Network 268</p> <p>14.5 Computer Solution of a Trilaterated Quadrilateral 269</p> <p>14.6 Iteration Termination 273</p> <p>14.7 Software 274</p> <p>Problems 276</p> <p>Programming Problems 282</p> <p><b>15 Adjustment of Horizontal Surveys: Triangulation 283</b></p> <p>15.1 Introduction 283</p> <p>15.2 Azimuth Observation Equation 284</p> <p>15.3 Angle Observation Equation 286</p> <p>15.4 Adjustment of Intersections 288</p> <p>15.5 Adjustment of Resections 293</p> <p>15.6 Adjustment of Triangulated Quadrilaterals 298</p> <p>Problems 303</p> <p>Programming Problems 312</p> <p><b>16 Adjustment of Horizontal Surveys: Traverses and Horizontal Networks 313</b></p> <p>16.1 Introduction to Traverse Adjustments 313</p> <p>16.2 Observation Equations 313</p> <p>16.3 Redundant Equations 314</p> <p>16.4 Numerical Example 315</p> <p>16.5 Minimum Amount of Control 321</p> <p>16.6 Adjustment of Networks 322</p> <p>16.7 <i>𝜒</i><sup>2 </sup>Test: Goodness of Fit 330</p> <p>Problems 331</p> <p>Programming Problems 342</p> <p><b>17 Adjustment of GNSS Networks 343</b></p> <p>17.1 Introduction 343</p> <p>17.2 GNSS Observations 344</p> <p>17.3 GNSS Errors and the Need for Adjustment 347</p> <p>17.4 Reference Coordinate Systems for GNSS Observations 347</p> <p>17.5 Converting Between the Terrestrial and Geodetic Coordinate Systems 350</p> <p>17.6 Application of Least Squares in Processing GNSS Data 354</p> <p>17.7 Network Preadjustment Data Analysis 356</p> <p>17.8 Least Squares Adjustment of GNSS Networks 363</p> <p>Problems 369</p> <p>Programming Problems 386</p> <p><b>18 Coordinate Transformations 389</b></p> <p>18.1 Introduction 389</p> <p>18.2 The Two-Dimensional Conformal Coordinate 389</p> <p>18.3 Equation Development 390</p> <p>18.4 Application of Least Squares 392</p> <p>18.5 Two-Dimensional Affine Coordinate Transformation 395</p> <p>18.6 The Two-Dimensional Projective Coordinate Transformation 398</p> <p>18.7 Three-Dimensional Conformal Coordinate Transformation 401</p> <p>18.8 Statistically Valid Parameters 407</p> <p>Problems 411</p> <p>Programming Problems 418</p> <p><b>19 Error Ellipse 419</b></p> <p>19.1 Introduction 419</p> <p>19.2 Computation of Ellipse Orientation and Semiaxes 421</p> <p>19.3 Example Problem of Standard Error Ellipse Calculations 426</p> <p>19.4 Another Example Problem 428</p> <p>19.5 The Error Ellipse Confidence Level 429</p> <p>19.6 Error Ellipse Advantages 431</p> <p>19.7 Other Measures of Station Uncertainty 435</p> <p>Problems 441</p> <p>Programming Problems 442</p> <p><b>20 Constraint Equations 443</b></p> <p>20.1 Introduction 443</p> <p>20.2 Adjustment of Control Station Coordinates 443</p> <p>20.3 Holding Control Station Coordinates and Directions of Lines Fixed in a Trilateration Adjustment 449</p> <p>20.4 Helmert’s Method 452</p> <p>20.5 Redundancies in a Constrained Adjustment 458</p> <p>20.6 Enforcing Constraints through Weighting 458</p> <p>Problems 460</p> <p>Practical Problems 463</p> <p><b>21 Blunder Detection in Horizontal Networks 465</b></p> <p>21.1 Introduction 465</p> <p>21.2 A Priori Methods for Detecting Blunders in Observations 466</p> <p>21.3 A Posteriori Blunder Detection 468</p> <p>21.4 Development of the Covariance Matrix for the Residuals 470</p> <p>21.5 Detection of Outliers in Observations: Data Snooping 472</p> <p>21.6 Detection of Outliers in Observations: The Tau Criterion 474</p> <p>21.7 Techniques Used in Adjusting Control 476</p> <p>21.8 A Data Set with Blunders 477</p> <p>21.9 Some Further Considerations 485</p> <p>21.10 Survey Design 487</p> <p>21.11 Software 489</p> <p>Problems 490</p> <p>Practical Problems 496</p> <p><b>22 The General Least Squares Method and Its Application to Curve Fitting and Coordinate Transformations 497</b></p> <p>22.1 Introduction to General Least Squares 497</p> <p>22.2 General Least Squares Equations for Fitting a Straight Line 497</p> <p>22.3 General Least Squares Solution 499</p> <p>22.4 Two-Dimensional Coordinate Transformation by General Least Squares 503</p> <p>22.5 Three-Dimensional Conformal Coordinate Transformation by General Least Squares 509</p> <p>Problems 511</p> <p>Programming Problems 515</p> <p><b>23 Three-Dimensional Geodetic Network Adjustment 517</b></p> <p>23.1 Introduction 517</p> <p>23.2 Linearization of Equations 519</p> <p>23.3 Minimum Number of Constraints 524</p> <p>23.4 Example Adjustment 525</p> <p>23.5 Building an Adjustment 533</p> <p>23.6 Comments on Systematic Errors 534</p> <p>23.7 Software 537</p> <p>Problems 538</p> <p>Programming Problems 543</p> <p><b>24 Combining GNSS and Terrestrial Observations 545</b></p> <p>24.1 Introduction 545</p> <p>24.2 The Helmert Transformation 547</p> <p>24.3 Rotations between Coordinate Systems 551</p> <p>24.4 Combining GNSS Baseline Vectors with Traditional Observations 552</p> <p>24.5 Another Approach to Transforming Coordinates between Reference Frames 556</p> <p>24.6 Other Considerations 559</p> <p>Problems 560</p> <p>Programming Problems 563</p> <p><b>25 Analysis of Adjustments 565</b></p> <p>25.1 Introduction 565</p> <p>25.2 Basic Concepts, Residuals, and the Normal Distribution 565</p> <p>25.3 Goodness of Fit Test 568</p> <p>25.4 Comparison of GNSS Residual Plots 572</p> <p>25.5 Use of Statistical Blunder Detection 574</p> <p>Problems 574</p> <p><b>26 Computer Optimization 577</b></p> <p>26.1 Introduction 577</p> <p>26.2 Storage Optimization 578</p> <p>26.3 Direct Formation of the Normal Equations 580</p> <p>26.4 Cholesky Decomposition 581</p> <p>26.5 Forward and Back Solutions 583</p> <p>26.6 Using the Cholesky Factor to Find the Inverse of the Normal Matrix 584</p> <p>26.7 Spareness and Optimization of the Normal Matrix 586</p> <p>Problems 590</p> <p>Programming Problems 590</p> <p><b>Appendix A Introduction to Matrices 591</b></p> <p>A.1 Introduction 591</p> <p>A.2 Definition of a Matrix 591</p> <p>A.3 Size or Dimensions of a Matrix 592</p> <p>A.4 Types of Matrices 593</p> <p>A.5 Matrix Equality 594</p> <p>A.6 Addition or Subtraction of Matrices 595</p> <p>A.7 Scalar Multiplication of a Matrix 595</p> <p>A.8 Matrix Multiplication 595</p> <p>A.9 Computer Algorithms for Matrix Operations 598</p> <p>A.10 Use of the Matrix Software 601</p> <p>Problems 603</p> <p>Programming Problems 605</p> <p><b>Appendix B Solution of Equations by Matrix Methods 607</b></p> <p>B.1 Introduction 607</p> <p>B.2 Inverse Matrix 607</p> <p>B.3 The Inverse of a 2 × 2 Matrix 608</p> <p>B.4 Inverses by Adjoints 610</p> <p>B.5 Inverses by Elementary Row Transformations 611</p> <p>B.6 Example Problem 616</p> <p>Problems 617</p> <p>Programming Problems 618</p> <p><b>Appendix C Nonlinear Equations and Taylor’s Theorem 619</b></p> <p>C.1 Introduction 619</p> <p>C.2 Taylor Series Linearization of Nonlinear Equations 619</p> <p>C.3 Numerical Example 620</p> <p>C.4 Using Matrices to Solve Nonlinear Equations 622</p> <p>C.5 Simple Matrix Example 623</p> <p>C.6 Practical Example 624</p> <p>C.7 Concluding Remarks 626</p> <p>Problems 627</p> <p>Programming Problems 628</p> <p><b>Appendix D The Normal Error Distribution Curve and Other Statistical Tables 629</b></p> <p>D.1 Development for Normal Distribution Curve Equation 629</p> <p>D.2 Other Statistical Tables 637</p> <p><b>Appendix E Confidence Intervals for the Mean 649</b></p> <p><b>Appendix F Map Projection Coordinate Systems 655</b></p> <p>F.1 Introduction 655</p> <p>F.2 Mathematics of the Lambert Conformal Conic Map Projection 657</p> <p>F.3 Mathematics from the Transverse Mercator 659</p> <p>F.4 Stereographic Map Projection 662</p> <p>F.5 Reduction of Observations 663</p> <p><b>Appendix G Companion Website 669</b></p> <p>G.1 Introduction 669</p> <p>G.2 File Formats and Memory Matters 670</p> <p>G.3 Software 670</p> <p>G.4 Using the Software as an Instructional Aid 674</p> <p><b>Appendix H Answers to Selected Problems 675</b></p> <p>Bibliography 681</p> <p>Index 685</p>
<p><b>D<small>R</small>. CHARLES D. GHILANI</b> is a Professor Emeritus of Engineering. He taught in the B.S. Surveying Engineering and A.S. Surveying Technology programs at Pennsylvania State University. He holds a Ph.D. and M.S. in Civil and Environmental Engineering from the University of Wisconsin-Madison, and a B.S. degree in mathematics and education from the University of Wisconsin-Milwaukee. He is an honorary member of the Pennsylvania Society of Land Surveyors (P.S.L.S.), the president of the American Association for Geodetic Surveying, and the editor of <i>Surveying and Land Information Science</i>. He has received the Milton S. Eisenhower Distinguished Teaching Award in 2013, and the 2017 Surveying and Geomatics Educator's Society Educator Award.
<p><b>The Definitive Guide to Bringing Accuracy to Measurement, Updated and Supplemented</b> <p><i>Adjustment Computations</i> 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<sup>®</sup>. <p>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. <ul> <li>Apply industry-standard methodologies to error analysis and adjustment</li> <li>Translate your skills to the real-world with instruction focused on the practical</li> <li>Master the fundamentals as well as specific computations and analysis</li> <li>Strengthen your understanding of critical topics on the Fundamentals in Surveying Licensing Exam</li> </ul> <p>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; <i>Adjustment Computations</i> provides the real-world training you need to identify, analyze, and correct for potentially crucial errors.

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