Adjustment Computations : Statistics and Least Squares in Surveying and GIS,9780471168331

Adjustment Computations : Statistics and Least Squares in Surveying and GIS

by ;
Edition: 3rd
ISBN13: 9780471168331
ISBN10: 0471168335
Format: Hardcover
Pub. Date: 1997-02-01
Publisher(s): Wiley-Interscience
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Summary

This book examines every aspect of least square adjustment. It defines terms and introduces readers to the fundamentals of errors and describes methods for analyzing them. It also illustrates the application of least squares in adjusting a wide range of survey types and provides detailed coverage of applications of least squares to GPSs and GISs.

Author Biography

PAUL R. WOLF, PhD, Emeritus Professor, Department of Civil and Environmental Engineering, University of Wisconsin, is the author of Elements of Photogrammetry and the bestselling Elementary Surveying, now in its ninth edition. CHARLES D. GHILANI, PhD, is Associate Professor in the College of Engineering and Chair of the Surveying Program at Pennsylvania State University.

Table of Contents

Preface xiii(4)
Acknowledgments xvii
1 Introduction
1(12)
1.1 Introduction
1(1)
1.2 Direct and Indirect Measurements
2(1)
1.3 Measurement Error Sources
2(1)
1.4 Definitions
3(1)
1.5 Precision Versus Accuracy
4(3)
1.6 Redundant Measurements in Surveying and Their Adjustment
7(1)
1.7 Advantages of Least-Squares Adjustment
8(2)
1.8 Overview of the Book
10(1)
Problems
10(3)
2 Measurements and Their Analysis
13(22)
2.1 Introduction
13(1)
2.2 Sample Versus Population
13(1)
2.3 Range and Median
14(1)
2.4 Graphical Representation of Data
15(3)
2.5 Numerical Methods of Describing Data
18(1)
2.6 Measures of Central Tendency
19(1)
2.7 Additional Definitions
19(3)
2.8 Alternative Formula for Determining Variance
22(2)
2.9 Numerical Examples
24(6)
2.10 Derivation of the Sample Variance (Bessel's Correction)
30(1)
2.11 STATS Program
31(1)
Problems
31(4)
3 Random Error Theory
35(18)
3.1 Introduction
35(1)
3.2 Theory of Probability
35(3)
3.3 Properties of the Normal Distribution Curve
38(2)
3.4 Standard Normal Distribution Function
40(3)
3.5 Probability of the Standard Error
43(3)
3.6 Uses for Percent Errors
46(1)
3.7 Practical Examples
46(3)
Problems
49(4)
4 Confidence Intervals and Statistical Testing
53(28)
4.1 Introduction
53(2)
4.2 Distributions Used in Sampling Theory
55(4)
4.3 Confidence Interval for the Mean: t Statistic
59(3)
4.4 Testing the Validity of the Confidence Interval
62(1)
4.5 Selecting a Sample Size
62(1)
4.6 Confidence Interval for a Population Variance
63(2)
4.7 Confidence Interval for the Ratio of Two Population Variances
65(2)
4.8 Hypothesis Testing
67(3)
4.9 Test of Hypothesis for the Population Mean
70(3)
4.10 Test of Hypothesis for the Population Variance: o2
73(2)
4.11 Test of Hypothesis for the Ratio of Two Population Variances
75(4)
Problems
79(3)
5 Propagation of Random Errors in Indirectly Measured Quantities
81(16)
5.1 Basic Error Propagation Equation
81(5)
5.2 Frequently Encountered Specific Functions
86(1)
5.3 Numerical Examples
87(4)
5.4 Conclusions
91(1)
Problems
92(5)
6 Error Propagation in Angle and Distance Measurements
97(26)
6.1 Introduction
97(1)
6.2 Error Sources in Horizontal Angles
97(1)
6.3 Reading Errors
98(2)
6.4 Pointing Errors
100(1)
6.5 Estimated Pointing and Reading Errors with Total Stations
101(1)
6.6 Target-Centering Errors
101(3)
6.7 Instrument Centering Errors
104(4)
6.8 Effects of Leveling Error in Angle Measurement
108(2)
6.9 Numerical Example of Combined Error Propagation in a Single Horizontal Angle
110(1)
6.10 Use of Estimated Standard Error to Check Angular Misclosure in a Traverse
111(1)
6.11 Errors in Astronomical Observations for Azimuth
112(5)
6.12 Errors in Electronic Distance Measurements
117(1)
6.13 Use of Spreadsheets
118(1)
Problems
119(4)
7 Error Propagation in Traverse Surveys
123(18)
7.1 Introduction
123(1)
7.2 Derivation of Estimated Error in Latitude and Departure
124(1)
7.3 Derivation of Estimated Standard Errors in Course Azimuths
125(1)
7.4 Computing and Analyzing Polygon Traverse Misclosure Errors
126(6)
7.5 Computing and Analyzing Link Traverse Misclosure Errors
132(4)
7.6 Conclusions
136(1)
Problems
136(5)
8 Error Propagation in Elevation Determination
141(14)
8.1 Introduction
141(1)
8.2 Systematic Errors in Differential Leveling
141(3)
8.3 Random Errors in Differential Leveling
144(5)
8.4 Error Propagation in Trigonometric Leveling
149(4)
Problems
153(2)
9 Weights of Observations
155(14)
9.1 Introduction
155(2)
9.2 Weighted Mean
157(2)
9.3 Relation Between Weights and Standard Errors
159(1)
9.4 Statistics of Weighted Observations
160(2)
9.5 Weights in Angle Measurements
162(1)
9.6 Weights in Differential Leveling
163(1)
9.7 Practical Examples
164(3)
Problems
167(2)
10 Principles of Least Squares
169(32)
10.1 Introduction
169(1)
10.2 Fundamentals Principle of Least Squares
170(2)
10.3 Fundamentals Principle of Weighted Least Squares
172(1)
10.4 Stochastic Model
173(1)
10.5 Mathematical Model
173(1)
10.6 Observation Equations
174(2)
10.7 Systematic Formulation of the Normal Equations
176(4)
10.8 Tabular Formation of the Normal Equations
180(1)
10.9 Using Matrices to Form the Normal Equations
180(4)
10.10 Least-Squares Solution of Nonlinear Systems
184(3)
10.11 Least-Squares Fit of Points to a Line or Curve
187(3)
10.12 Calibration of an EDM Instrument
190(1)
10.13 Least-Squares Adjustment Using Conditional Equations
191(3)
10.14 Example Using Observation Equations
194(1)
Problems
195(6)
11 Adjustment of Level Nets
201(16)
11.1 Introduction
201(1)
11.2 Observation Equation
201(1)
11.3 Unweighted Example
202(2)
11.4 Weighted Example
204(3)
11.5 Reference Standard Deviation
207(2)
11.6 Another Weighted Adjustment
209(3)
Problems
212(5)
12 Precisions of Indirectly Determined Quantities
217(12)
12.1 Introduction
217(1)
12.2 Development of the Covariance Matrix
217(4)
12.3 Numerical Examples
221(1)
12.4 Standard Deviations of Computed Quantities
222(3)
Problems
225(4)
13 Adjustment of Horizontal Surveys: Trilateration
229(20)
13.1 Introduction
229(2)
13.2 Distance Observation Equation
231(2)
13.3 Trilateration Adjustment Example
233(6)
13.4 Formulation of a Generalized Coefficient Matrix for a More Complex Network
239(1)
13.5 Computer Solution of a Trilaterated Quadrilateral
239(4)
13.6 Iteration Termination
243(2)
Problems
245(4)
14 Adjustment of Horizontal Surveys: Triangulation
249(26)
14.1 Introduction
249(1)
14.2 Azimuth Observation Equation
249(3)
14.3 Angle Observation Equation
252(2)
14.4 Adjustment of Intersections
254(5)
14.5 Adjustment of Resections
259(6)
14.6 Adjustment of Triangulated Quadrilaterals
265(4)
Problems
269(6)
15 Adjustment of Horizontal Surveys: Traverses and Networks
275(22)
15.1 Introduction to Traverse Adjustments
275(1)
15.2 The Observation Equations
275(1)
15.3 Redundant Equations
276(1)
15.4 Numerical Example
277(5)
15.5 Minimum Amount of Control
282(1)
15.6 Adjustment of Networks
283(7)
15.7 X2 Test: Goodness of Fit
290(1)
Problems
291(6)
16 Adjustment of GPS Networks
297(38)
16.1 Introduction
297(1)
16.2 GPS Measurements
298(3)
16.3 GPS Errors and the Need for Adjustment
301(1)
16.4 Reference Coordinate Systems for GPS Measurements
301(2)
16.5 Converting Between the Terrestrial and Geodetic Coordinate Systems
303(5)
16.6 Application of Least Squares in Processing GPS Data
308(1)
16.7 Network Preadjustment Data Analysis
309(5)
16.8 Least-Squares Adjustment of GPS Networks
314(7)
Problems
321(14)
17 Coordinate Transformations
335(22)
17.1 Introduction
335(1)
17.2 Two-Dimensional Conformal Coordinate Transformation
335(1)
17.3 Equation Development
336(2)
17.4 Application of Least Squares
338(3)
17.5 Two-Dimensional Affine Coordinate Transformation
341(2)
17.6 Two-Dimensional Projective Coordinate Transformation
343(4)
17.7 Three-Dimensional Conformal coordinate Transformation
347(6)
17.8 Statistically Valid Parameters
353(1)
Problems
354(2)
18 Error Ellipse
357(18)
18.1 Introduction
357(2)
18.2 Computation of Ellipse Orientation and Semiaxes
359(4)
18.3 Example of Standard Error Ellipse Calculations
363(2)
18.4 Another Example
365(2)
18.5 Error Ellipse Confidence Level
367(2)
18.6 Error Ellipse Advantages
369(3)
Problems
372(3)
19 Constraint Equations
375(22)
19.1 Introduction
375(1)
19.2 Adjustment of Control Station Coordinates
375(6)
19.3 Holding Control Station Coordinates and Directions of Lines Fixed in a Trilateration Adjustment
381(4)
19.4 Helmert's Method
385(5)
19.5 Redundancies in a Constrained Adjustment
390(1)
19.6 Enforcing Constraints Through Weighting
390(3)
Problems
393(4)
20 Blunder Detection in Horizontal Survey Networks
397(26)
20.1 Introduction
397(1)
20.2 A Priori Methods for Detecting Blunders in Measurements
398(2)
20.3 A Posteriori Blunder Direction
400(2)
20.4 Development of the Covariance Matrix for the Residuals
402(2)
20.5 Detection of Outliers in Observations
404(2)
20.6 Techniques Used in Adjusting Control
406(1)
20.7 Data Set with Blunders
407(9)
20.8 Some Further Considerations
416(2)
20.9 Survey Design
418(2)
Problems
420(3)
21 General Least-Squares Method and Its Application to Curve Fitting and Coordinate Transformations
423(18)
21.1 Introduction to General Least Squares
423(1)
21.2 General Least-Squares Equations for Fitting a Straight Line
423(2)
21.3 General Least-Squares Solution
425(5)
21.4 Two-Dimensional Coordinate Transformation by General Least Squares
430(5)
21.5 Three-Dimensional Conformal Coordinate Transformation by General Least Squares
435(3)
Problems 453
438(3)
22 Computer Optimization
441(18)
22.1 Introduction
441(1)
22.2 Storage Optimization
441(3)
22.3 Direct Formation of the Normal Equations
444(1)
22.4 Cholesky Decomposition
445(2)
22.5 Forward and Back Solutions
447(3)
22.6 Using the Cholesky Factor to Find the Inverse of the Normal Matrix
450(1)
22.7 Sparseness and Optimization of the Normal Matrix
451(5)
Problems
456(3)
A Introduction to Matrices
459(14)
A.1 Introduction
459(1)
A.2 Definition of a Matrix
459(1)
A.3 Size or Dimensions of a Matrix
460(1)
A.4 Types of Matrices
461(1)
A.5 Matrix Equality
462(1)
A.6 Addition or Subtraction of Matrices
463(1)
A.7 Scalar Multiplication of a Matrix
463(1)
A.8 Matrix Multiplication
464(3)
A.9 Computer Algorithms for Matrix Operations
467(3)
A.10 Use of the Program MATRIX
470(1)
Problems
470(3)
B Solution of Equations by Matrix Methods
473(12)
B.1 Introduction
473(1)
B.2 Inverse Matrix
473(1)
B.3 Inverse of a 2 * 2 Matrix
474(2)
B.4 Inverse by Adjoints
476(2)
B.5 Inverses by Row Transformations
478(2)
B.6 Numerical Example
480(3)
Problems
483(2)
C Nonlinear Equations and Taylor's Theorem
485(10)
C.1 Introduction
485(1)
C.2 Taylor Series Linearization of Nonlinear Equations
485(1)
C.3 Numerical Example
486(2)
C.4 Using Matrices to Solve Nonlinear Equations
488(1)
C.5 Simple Matrix Example
489(1)
C.6 Practical Example
490(3)
Problems
493(2)
D Normal Error Distribution Curve and Other Statistical Tables
495(22)
D.1 Development for the Normal Distribution Curve Equation
495(8)
D.2 Other Statistical Tables
503(14)
E Confidence Intervals for the Mean
517(6)
F Documentation for Software
523(30)
F.1 Introduction
523(1)
F.2 Similarities in the Programs STATS and ADJUST
524(7)
F.3 STATS
531(1)
F.4 ADJUST
532(16)
F.5 MATRIX
548(5)
Bibliography 553(4)
Index 557

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