{"product_id":"adjustment-computations-isbn-9781119385981","title":"Adjustment Computations","description":"\u003cb\u003eThe definitive guide to bringing accuracy to measurement, updated and supplemented\u003c\/b\u003e \u003cp\u003e\u003ci\u003eAdjustment Computations\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eAll 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. \u003c\/p\u003e\u003cul\u003e \u003cli\u003eApply industry-standard methodologies to error analysis and adjustment\u003c\/li\u003e \u003cli\u003eTranslate your skills to the real-world with instruction focused on the practical\u003c\/li\u003e \u003cli\u003eMaster the fundamentals as well as specific computations and analysis\u003c\/li\u003e \u003cli\u003eStrengthen your understanding of critical topics on the Fundamentals in Surveying Licensing Exam\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eAs 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; \u003ci\u003eAdjustment Computations\u003c\/i\u003e provides the real-world training you need to identify, analyze, and correct for potentially crucial errors. \u003c\/p\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgments xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Direct and Indirect Measurements 2\u003c\/p\u003e \u003cp\u003e1.3 Measurement Error Sources 2\u003c\/p\u003e \u003cp\u003e1.4 Definitions 3\u003c\/p\u003e \u003cp\u003e1.5 Precision versus Accuracy 4\u003c\/p\u003e \u003cp\u003e1.6 Redundant Observations in Surveying and Their Adjustment 7\u003c\/p\u003e \u003cp\u003e1.7 Advantages of Least Squares Adjustment 8\u003c\/p\u003e \u003cp\u003e1.8 Overview of the Book 10\u003c\/p\u003e \u003cp\u003eProblems 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Observations and Their Analysis 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 13\u003c\/p\u003e \u003cp\u003e2.2 Sample versus Population 13\u003c\/p\u003e \u003cp\u003e2.3 Range and Median 14\u003c\/p\u003e \u003cp\u003e2.4 Graphical Representation of Data 15\u003c\/p\u003e \u003cp\u003e2.5 Numerical Methods of Describing Data 18\u003c\/p\u003e \u003cp\u003e2.6 Measures of Central Tendency 18\u003c\/p\u003e \u003cp\u003e2.7 Additional Definitions 19\u003c\/p\u003e \u003cp\u003e2.8 Alternative Formula for Determining Variance 22\u003c\/p\u003e \u003cp\u003e2.9 Numerical Examples 24\u003c\/p\u003e \u003cp\u003e2.10 Root Mean Square Error and Mapping Standards 28\u003c\/p\u003e \u003cp\u003e2.11 Derivation of the Sample Variance (Bessel’s Correction) 31\u003c\/p\u003e \u003cp\u003e2.12 Software 32\u003c\/p\u003e \u003cp\u003eProblems 34\u003c\/p\u003e \u003cp\u003ePractical Exercises 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Random Error Theory 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 39\u003c\/p\u003e \u003cp\u003e3.2 Theory of Probability 39\u003c\/p\u003e \u003cp\u003e3.3 Properties of the Normal Distribution Curve 42\u003c\/p\u003e \u003cp\u003e3.4 Standard Normal Distribution Function 44\u003c\/p\u003e \u003cp\u003e3.5 Probability of the Standard Error 47\u003c\/p\u003e \u003cp\u003e3.6 Uses for Percent Errors 50\u003c\/p\u003e \u003cp\u003e3.7 Practical Examples 50\u003c\/p\u003e \u003cp\u003eProblems 53\u003c\/p\u003e \u003cp\u003eProgramming Problems 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Confidence Intervals 57\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 57\u003c\/p\u003e \u003cp\u003e4.2 Distributions Used in Sampling Theory 59\u003c\/p\u003e \u003cp\u003e4.3 Confidence Interval for the Mean: \u003ci\u003et \u003c\/i\u003eStatistic 63\u003c\/p\u003e \u003cp\u003e4.4 Testing the Validity of the Confidence Interval 66\u003c\/p\u003e \u003cp\u003e4.5 Selecting a Sample Size 67\u003c\/p\u003e \u003cp\u003e4.6 Confidence Interval for a Population Variance 68\u003c\/p\u003e \u003cp\u003e4.7 Confidence Interval for the Ratio of Two Population Variances 70\u003c\/p\u003e \u003cp\u003e4.8 Software 72\u003c\/p\u003e \u003cp\u003eProblems 75\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Statistical Testing 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Hypothesis Testing 79\u003c\/p\u003e \u003cp\u003e5.2 Systematic Development of a Test 82\u003c\/p\u003e \u003cp\u003e5.3 Test of Hypothesis for the Population Mean 84\u003c\/p\u003e \u003cp\u003e5.4 Test of Hypothesis for the Population Variance 85\u003c\/p\u003e \u003cp\u003e5.5 Test of Hypothesis for the Ratio of Two Population Variances 89\u003c\/p\u003e \u003cp\u003e5.6 Software 92\u003c\/p\u003e \u003cp\u003eProblems 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Propagation of Random Errors in Indirectly Measured Quantities 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Basic Error Propagation Equation 97\u003c\/p\u003e \u003cp\u003e6.2 Frequently Encountered Specific Functions 102\u003c\/p\u003e \u003cp\u003e6.3 Numerical Examples 103\u003c\/p\u003e \u003cp\u003e6.4 Software 107\u003c\/p\u003e \u003cp\u003e6.5 Conclusions 109\u003c\/p\u003e \u003cp\u003eProblems 109\u003c\/p\u003e \u003cp\u003ePractical Exercises 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Error Propagation in Angle and Distance Observations 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 113\u003c\/p\u003e \u003cp\u003e7.2 Error Sources in Horizontal Angles 113\u003c\/p\u003e \u003cp\u003e7.3 Reading Errors 114\u003c\/p\u003e \u003cp\u003e7.4 Pointing Errors 116\u003c\/p\u003e \u003cp\u003e7.5 Estimated Pointing and Reading Errors with Total Stations 117\u003c\/p\u003e \u003cp\u003e7.6 Target-Centering Errors 118\u003c\/p\u003e \u003cp\u003e7.7 Instrument Centering Errors 120\u003c\/p\u003e \u003cp\u003e7.8 Effects of Leveling Errors in Angle Observations 123\u003c\/p\u003e \u003cp\u003e7.9 Numerical Example of Combined Error Propagation in a Single Horizontal Angle 126\u003c\/p\u003e \u003cp\u003e7.10 Using Estimated Errors to Check Angular Misclosure in a Traverse 127\u003c\/p\u003e \u003cp\u003e7.11 Errors in Astronomical Observations for Azimuth 130\u003c\/p\u003e \u003cp\u003e7.12 Errors in Electronic Distance Observations 135\u003c\/p\u003e \u003cp\u003e7.13 Centering Errors When Using Range Poles 136\u003c\/p\u003e \u003cp\u003e7.14 Software 137\u003c\/p\u003e \u003cp\u003eProblems 138\u003c\/p\u003e \u003cp\u003eProgramming Problems 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Error Propagation in Traverse Surveys 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 143\u003c\/p\u003e \u003cp\u003e8.2 Derivation of Estimated Error in Latitude and Departure 144\u003c\/p\u003e \u003cp\u003e8.3 Derivation of Estimated Standard Errors in Course Azimuths 146\u003c\/p\u003e \u003cp\u003e8.4 Computing and Analyzing Polygon Traverse Misclosure Errors 146\u003c\/p\u003e \u003cp\u003e8.5 Computing and Analyzing Link Traverse Misclosure Errors 152\u003c\/p\u003e \u003cp\u003e8.6 Software 156\u003c\/p\u003e \u003cp\u003e8.7 Conclusions 157\u003c\/p\u003e \u003cp\u003eProblems 157\u003c\/p\u003e \u003cp\u003eProgramming Problems 161\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Error Propagation in Elevation Determination 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 163\u003c\/p\u003e \u003cp\u003e9.2 Systematic Errors in Differential Leveling 163\u003c\/p\u003e \u003cp\u003e9.3 Random Errors in Differential Leveling 166\u003c\/p\u003e \u003cp\u003e9.4 Error Propagation in Trigonometric Leveling 171\u003c\/p\u003e \u003cp\u003eProblems 174\u003c\/p\u003e \u003cp\u003eProgramming Problems 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Weights of Observations 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 179\u003c\/p\u003e \u003cp\u003e10.2 Weighted Mean 181\u003c\/p\u003e \u003cp\u003e10.3 Relationship Between Weights and Standard Errors 183\u003c\/p\u003e \u003cp\u003e10.4 Statistics of Weighted Observations 184\u003c\/p\u003e \u003cp\u003e10.5 Weights in Angle Observations 185\u003c\/p\u003e \u003cp\u003e10.6 Weights in Differential Leveling 186\u003c\/p\u003e \u003cp\u003e10.7 Practical Examples 187\u003c\/p\u003e \u003cp\u003eProblems 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Principles of Least Squares 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 193\u003c\/p\u003e \u003cp\u003e11.2 Fundamental Principle of Least Squares 194\u003c\/p\u003e \u003cp\u003e11.3 The Fundamental Principle of Weighted Least Squares 196\u003c\/p\u003e \u003cp\u003e11.4 The Stochastic Model 197\u003c\/p\u003e \u003cp\u003e11.5 Functional Model 197\u003c\/p\u003e \u003cp\u003e11.6 Observation Equations 199\u003c\/p\u003e \u003cp\u003e11.7 Systematic Formulation of the Normal Equations 201\u003c\/p\u003e \u003cp\u003e11.8 Tabular Formation of the Normal Equations 203\u003c\/p\u003e \u003cp\u003e11.9 Using Matrices to Form the Normal Equations 204\u003c\/p\u003e \u003cp\u003e11.10 Least Squares Solution of Nonlinear Systems 207\u003c\/p\u003e \u003cp\u003e11.11 Least Squares Fit of Points to a Line or Curve 211\u003c\/p\u003e \u003cp\u003e11.12 Calibration of an EDM Instrument 214\u003c\/p\u003e \u003cp\u003e11.13 Least Squares Adjustment Using Conditional Equations 215\u003c\/p\u003e \u003cp\u003e11.14 The Previous Example Using Observation Equations 217\u003c\/p\u003e \u003cp\u003e11.15 Software 219\u003c\/p\u003e \u003cp\u003eProblems 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Adjustment of Level Nets 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 225\u003c\/p\u003e \u003cp\u003e12.2 Observation Equation 225\u003c\/p\u003e \u003cp\u003e12.3 Unweighted Example 226\u003c\/p\u003e \u003cp\u003e12.4 Weighted Example 229\u003c\/p\u003e \u003cp\u003e12.5 Reference Standard Deviation 231\u003c\/p\u003e \u003cp\u003e12.6 Another Weighted Adjustment 233\u003c\/p\u003e \u003cp\u003e12.7 Software 236\u003c\/p\u003e \u003cp\u003eProblems 238\u003c\/p\u003e \u003cp\u003eProgramming Problems 242\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Precisions of Indirectly Determined Quantities 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 245\u003c\/p\u003e \u003cp\u003e13.2 Development of the Covariance Matrix 245\u003c\/p\u003e \u003cp\u003e13.3 Numerical Examples 249\u003c\/p\u003e \u003cp\u003e13.4 Standard Deviations of Computed Quantities 250\u003c\/p\u003e \u003cp\u003eProblems 254\u003c\/p\u003e \u003cp\u003eProgramming Problems 256\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Adjustment of Horizontal Surveys: Trilateration 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 257\u003c\/p\u003e \u003cp\u003e14.2 Distance Observation Equation 259\u003c\/p\u003e \u003cp\u003e14.3 Trilateration Adjustment Example 261\u003c\/p\u003e \u003cp\u003e14.4 Formulation of a Generalized Coefficient Matrix for a More Complex Network 268\u003c\/p\u003e \u003cp\u003e14.5 Computer Solution of a Trilaterated Quadrilateral 269\u003c\/p\u003e \u003cp\u003e14.6 Iteration Termination 273\u003c\/p\u003e \u003cp\u003e14.7 Software 274\u003c\/p\u003e \u003cp\u003eProblems 276\u003c\/p\u003e \u003cp\u003eProgramming Problems 282\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Adjustment of Horizontal Surveys: Triangulation 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 283\u003c\/p\u003e \u003cp\u003e15.2 Azimuth Observation Equation 284\u003c\/p\u003e \u003cp\u003e15.3 Angle Observation Equation 286\u003c\/p\u003e \u003cp\u003e15.4 Adjustment of Intersections 288\u003c\/p\u003e \u003cp\u003e15.5 Adjustment of Resections 293\u003c\/p\u003e \u003cp\u003e15.6 Adjustment of Triangulated Quadrilaterals 298\u003c\/p\u003e \u003cp\u003eProblems 303\u003c\/p\u003e \u003cp\u003eProgramming Problems 312\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Adjustment of Horizontal Surveys: Traverses and Horizontal Networks 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction to Traverse Adjustments 313\u003c\/p\u003e \u003cp\u003e16.2 Observation Equations 313\u003c\/p\u003e \u003cp\u003e16.3 Redundant Equations 314\u003c\/p\u003e \u003cp\u003e16.4 Numerical Example 315\u003c\/p\u003e \u003cp\u003e16.5 Minimum Amount of Control 321\u003c\/p\u003e \u003cp\u003e16.6 Adjustment of Networks 322\u003c\/p\u003e \u003cp\u003e16.7 \u003ci\u003e𝜒\u003c\/i\u003e\u003csup\u003e2 \u003c\/sup\u003eTest: Goodness of Fit 330\u003c\/p\u003e \u003cp\u003eProblems 331\u003c\/p\u003e \u003cp\u003eProgramming Problems 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Adjustment of GNSS Networks 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 343\u003c\/p\u003e \u003cp\u003e17.2 GNSS Observations 344\u003c\/p\u003e \u003cp\u003e17.3 GNSS Errors and the Need for Adjustment 347\u003c\/p\u003e \u003cp\u003e17.4 Reference Coordinate Systems for GNSS Observations 347\u003c\/p\u003e \u003cp\u003e17.5 Converting Between the Terrestrial and Geodetic Coordinate Systems 350\u003c\/p\u003e \u003cp\u003e17.6 Application of Least Squares in Processing GNSS Data 354\u003c\/p\u003e \u003cp\u003e17.7 Network Preadjustment Data Analysis 356\u003c\/p\u003e \u003cp\u003e17.8 Least Squares Adjustment of GNSS Networks 363\u003c\/p\u003e \u003cp\u003eProblems 369\u003c\/p\u003e \u003cp\u003eProgramming Problems 386\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Coordinate Transformations 389\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 389\u003c\/p\u003e \u003cp\u003e18.2 The Two-Dimensional Conformal Coordinate 389\u003c\/p\u003e \u003cp\u003e18.3 Equation Development 390\u003c\/p\u003e \u003cp\u003e18.4 Application of Least Squares 392\u003c\/p\u003e \u003cp\u003e18.5 Two-Dimensional Affine Coordinate Transformation 395\u003c\/p\u003e \u003cp\u003e18.6 The Two-Dimensional Projective Coordinate Transformation 398\u003c\/p\u003e \u003cp\u003e18.7 Three-Dimensional Conformal Coordinate Transformation 401\u003c\/p\u003e \u003cp\u003e18.8 Statistically Valid Parameters 407\u003c\/p\u003e \u003cp\u003eProblems 411\u003c\/p\u003e \u003cp\u003eProgramming Problems 418\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Error Ellipse 419\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 419\u003c\/p\u003e \u003cp\u003e19.2 Computation of Ellipse Orientation and Semiaxes 421\u003c\/p\u003e \u003cp\u003e19.3 Example Problem of Standard Error Ellipse Calculations 426\u003c\/p\u003e \u003cp\u003e19.4 Another Example Problem 428\u003c\/p\u003e \u003cp\u003e19.5 The Error Ellipse Confidence Level 429\u003c\/p\u003e \u003cp\u003e19.6 Error Ellipse Advantages 431\u003c\/p\u003e \u003cp\u003e19.7 Other Measures of Station Uncertainty 435\u003c\/p\u003e \u003cp\u003eProblems 441\u003c\/p\u003e \u003cp\u003eProgramming Problems 442\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Constraint Equations 443\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 443\u003c\/p\u003e \u003cp\u003e20.2 Adjustment of Control Station Coordinates 443\u003c\/p\u003e \u003cp\u003e20.3 Holding Control Station Coordinates and Directions of Lines Fixed in a Trilateration Adjustment 449\u003c\/p\u003e \u003cp\u003e20.4 Helmert’s Method 452\u003c\/p\u003e \u003cp\u003e20.5 Redundancies in a Constrained Adjustment 458\u003c\/p\u003e \u003cp\u003e20.6 Enforcing Constraints through Weighting 458\u003c\/p\u003e \u003cp\u003eProblems 460\u003c\/p\u003e \u003cp\u003ePractical Problems 463\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Blunder Detection in Horizontal Networks 465\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 465\u003c\/p\u003e \u003cp\u003e21.2 A Priori Methods for Detecting Blunders in Observations 466\u003c\/p\u003e \u003cp\u003e21.3 A Posteriori Blunder Detection 468\u003c\/p\u003e \u003cp\u003e21.4 Development of the Covariance Matrix for the Residuals 470\u003c\/p\u003e \u003cp\u003e21.5 Detection of Outliers in Observations: Data Snooping 472\u003c\/p\u003e \u003cp\u003e21.6 Detection of Outliers in Observations: The Tau Criterion 474\u003c\/p\u003e \u003cp\u003e21.7 Techniques Used in Adjusting Control 476\u003c\/p\u003e \u003cp\u003e21.8 A Data Set with Blunders 477\u003c\/p\u003e \u003cp\u003e21.9 Some Further Considerations 485\u003c\/p\u003e \u003cp\u003e21.10 Survey Design 487\u003c\/p\u003e \u003cp\u003e21.11 Software 489\u003c\/p\u003e \u003cp\u003eProblems 490\u003c\/p\u003e \u003cp\u003ePractical Problems 496\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 The General Least Squares Method and Its Application to Curve Fitting and Coordinate Transformations 497\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction to General Least Squares 497\u003c\/p\u003e \u003cp\u003e22.2 General Least Squares Equations for Fitting a Straight Line 497\u003c\/p\u003e \u003cp\u003e22.3 General Least Squares Solution 499\u003c\/p\u003e \u003cp\u003e22.4 Two-Dimensional Coordinate Transformation by General Least Squares 503\u003c\/p\u003e \u003cp\u003e22.5 Three-Dimensional Conformal Coordinate Transformation by General Least Squares 509\u003c\/p\u003e \u003cp\u003eProblems 511\u003c\/p\u003e \u003cp\u003eProgramming Problems 515\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Three-Dimensional Geodetic Network Adjustment 517\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 517\u003c\/p\u003e \u003cp\u003e23.2 Linearization of Equations 519\u003c\/p\u003e \u003cp\u003e23.3 Minimum Number of Constraints 524\u003c\/p\u003e \u003cp\u003e23.4 Example Adjustment 525\u003c\/p\u003e \u003cp\u003e23.5 Building an Adjustment 533\u003c\/p\u003e \u003cp\u003e23.6 Comments on Systematic Errors 534\u003c\/p\u003e \u003cp\u003e23.7 Software 537\u003c\/p\u003e \u003cp\u003eProblems 538\u003c\/p\u003e \u003cp\u003eProgramming Problems 543\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Combining GNSS and Terrestrial Observations 545\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 545\u003c\/p\u003e \u003cp\u003e24.2 The Helmert Transformation 547\u003c\/p\u003e \u003cp\u003e24.3 Rotations between Coordinate Systems 551\u003c\/p\u003e \u003cp\u003e24.4 Combining GNSS Baseline Vectors with Traditional Observations 552\u003c\/p\u003e \u003cp\u003e24.5 Another Approach to Transforming Coordinates between Reference Frames 556\u003c\/p\u003e \u003cp\u003e24.6 Other Considerations 559\u003c\/p\u003e \u003cp\u003eProblems 560\u003c\/p\u003e \u003cp\u003eProgramming Problems 563\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Analysis of Adjustments 565\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Introduction 565\u003c\/p\u003e \u003cp\u003e25.2 Basic Concepts, Residuals, and the Normal Distribution 565\u003c\/p\u003e \u003cp\u003e25.3 Goodness of Fit Test 568\u003c\/p\u003e \u003cp\u003e25.4 Comparison of GNSS Residual Plots 572\u003c\/p\u003e \u003cp\u003e25.5 Use of Statistical Blunder Detection 574\u003c\/p\u003e \u003cp\u003eProblems 574\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Computer Optimization 577\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e26.1 Introduction 577\u003c\/p\u003e \u003cp\u003e26.2 Storage Optimization 578\u003c\/p\u003e \u003cp\u003e26.3 Direct Formation of the Normal Equations 580\u003c\/p\u003e \u003cp\u003e26.4 Cholesky Decomposition 581\u003c\/p\u003e \u003cp\u003e26.5 Forward and Back Solutions 583\u003c\/p\u003e \u003cp\u003e26.6 Using the Cholesky Factor to Find the Inverse of the Normal Matrix 584\u003c\/p\u003e \u003cp\u003e26.7 Spareness and Optimization of the Normal Matrix 586\u003c\/p\u003e \u003cp\u003eProblems 590\u003c\/p\u003e \u003cp\u003eProgramming Problems 590\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Introduction to Matrices 591\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Introduction 591\u003c\/p\u003e \u003cp\u003eA.2 Definition of a Matrix 591\u003c\/p\u003e \u003cp\u003eA.3 Size or Dimensions of a Matrix 592\u003c\/p\u003e \u003cp\u003eA.4 Types of Matrices 593\u003c\/p\u003e \u003cp\u003eA.5 Matrix Equality 594\u003c\/p\u003e \u003cp\u003eA.6 Addition or Subtraction of Matrices 595\u003c\/p\u003e \u003cp\u003eA.7 Scalar Multiplication of a Matrix 595\u003c\/p\u003e \u003cp\u003eA.8 Matrix Multiplication 595\u003c\/p\u003e \u003cp\u003eA.9 Computer Algorithms for Matrix Operations 598\u003c\/p\u003e \u003cp\u003eA.10 Use of the Matrix Software 601\u003c\/p\u003e \u003cp\u003eProblems 603\u003c\/p\u003e \u003cp\u003eProgramming Problems 605\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Solution of Equations by Matrix Methods 607\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Introduction 607\u003c\/p\u003e \u003cp\u003eB.2 Inverse Matrix 607\u003c\/p\u003e \u003cp\u003eB.3 The Inverse of a 2 × 2 Matrix 608\u003c\/p\u003e \u003cp\u003eB.4 Inverses by Adjoints 610\u003c\/p\u003e \u003cp\u003eB.5 Inverses by Elementary Row Transformations 611\u003c\/p\u003e \u003cp\u003eB.6 Example Problem 616\u003c\/p\u003e \u003cp\u003eProblems 617\u003c\/p\u003e \u003cp\u003eProgramming Problems 618\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Nonlinear Equations and Taylor’s Theorem 619\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Introduction 619\u003c\/p\u003e \u003cp\u003eC.2 Taylor Series Linearization of Nonlinear Equations 619\u003c\/p\u003e \u003cp\u003eC.3 Numerical Example 620\u003c\/p\u003e \u003cp\u003eC.4 Using Matrices to Solve Nonlinear Equations 622\u003c\/p\u003e \u003cp\u003eC.5 Simple Matrix Example 623\u003c\/p\u003e \u003cp\u003eC.6 Practical Example 624\u003c\/p\u003e \u003cp\u003eC.7 Concluding Remarks 626\u003c\/p\u003e \u003cp\u003eProblems 627\u003c\/p\u003e \u003cp\u003eProgramming Problems 628\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D The Normal Error Distribution Curve and Other Statistical Tables 629\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Development for Normal Distribution Curve Equation 629\u003c\/p\u003e \u003cp\u003eD.2 Other Statistical Tables 637\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E Confidence Intervals for the Mean 649\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix F Map Projection Coordinate Systems 655\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eF.1 Introduction 655\u003c\/p\u003e \u003cp\u003eF.2 Mathematics of the Lambert Conformal Conic Map Projection 657\u003c\/p\u003e \u003cp\u003eF.3 Mathematics from the Transverse Mercator 659\u003c\/p\u003e \u003cp\u003eF.4 Stereographic Map Projection 662\u003c\/p\u003e \u003cp\u003eF.5 Reduction of Observations 663\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix G Companion Website 669\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eG.1 Introduction 669\u003c\/p\u003e \u003cp\u003eG.2 File Formats and Memory Matters 670\u003c\/p\u003e \u003cp\u003eG.3 Software 670\u003c\/p\u003e \u003cp\u003eG.4 Using the Software as an Instructional Aid 674\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix H Answers to Selected Problems 675\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography 681\u003c\/p\u003e \u003cp\u003eIndex 685\u003c\/p\u003e   \u003cp\u003e\u003cb\u003eD\u003csmall\u003eR\u003c\/small\u003e. CHARLES D. GHILANI\u003c\/b\u003e 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 \u003ci\u003eSurveying and Land Information Science\u003c\/i\u003e. He has received the Milton S. Eisenhower Distinguished Teaching Award in 2013, and the 2017 Surveying and Geomatics Educator's Society Educator Award.    \u003c\/p\u003e\u003cp\u003e\u003cb\u003eThe Definitive Guide to Bringing Accuracy to Measurement, Updated and Supplemented\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eAdjustment Computations\u003c\/i\u003e 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\u003csup\u003e®\u003c\/sup\u003e. \u003c\/p\u003e\u003cp\u003eAll 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. \u003c\/p\u003e\u003cul\u003e \u003cli\u003eApply industry-standard methodologies to error analysis and adjustment\u003c\/li\u003e \u003cli\u003eTranslate your skills to the real-world with instruction focused on the practical\u003c\/li\u003e \u003cli\u003eMaster the fundamentals as well as specific computations and analysis\u003c\/li\u003e \u003cli\u003eStrengthen your understanding of critical topics on the Fundamentals in Surveying Licensing Exam\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eAs 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; \u003ci\u003eAdjustment Computations\u003c\/i\u003e provides the real-world training you need to identify, analyze, and correct for potentially crucial errors.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988661649637,"sku":"NP9781119385981","price":201.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119385981.jpg?v=1761781162","url":"https:\/\/k12savings.com\/products\/adjustment-computations-isbn-9781119385981","provider":"K12savings","version":"1.0","type":"link"}