Spatial error analysis: A unified application-oriented treatment

✍ Scribed by Hsu D.Y.

• Publisher: Wiley
• Year: 1998
• Tongue: English
• Leaves: 224
• Category: Library

✦ Synopsis

"SPATIAL ERROR ANALYSIS is an all-in-one sourcebook on error measurements in one-, two-, and three-dimensional spaces. This book features exhaustive, systematic coverage of error measurement relationships, techniques, and solutions used to solve general, correlated cases. It is packed with 62 figures and 24 tables. MATLAB-based M-files for practical applications created especially for this volume are available on the Web at ftp://ftp.mathworks.com/pub/books/hsu.Solutions to two- and three-dimensional problems are presented without relying on equal standard deviations from each channel. They also make no assumption that the random variables of interest are independent or uncorrelated. MATLAB (developed by MathWorks, Inc.) must be purchased separately."Sponsored by:IEEE Aerospace and Electronic Systems Society.

✦ Table of Contents

Cover......Page 1
Spatial Error Analysis: A Unified Application-Oriented Treatment......Page 4
Table of Contents......Page 7
PREFACE......Page 11
LIST OF FIGURES......Page 14
LIST OF TABLES......Page 16
CHAPTER 1 Introduction......Page 17
1.2 Direct Problems......Page 18
1.3 Inverse Problems......Page 19
1.4 Use of Author-Generated M-files......Page 20
1.5 Summary ofM-files......Page 21
CHAPTER 2 Parameter Estimation from Samples......Page 22
2.1 Point Estimate of Population Parameters......Page 23
2.2 Sampling Distribution......Page 26
2.3 Interval Estimate of Population Mean......Page 27
2.4 Interval Estimate of Population Standard Deviation......Page 29
2.5 Summary of M-files......Page 34
3.1 Normal Distribution......Page 37
3.2.3 Mean Absolute Error (MAE)......Page 40
3.2.4 Linear Error Probable (LEP)......Page 41
3.3 Direct Problems......Page 42
3.4 Inverse Problems......Page 43
3.5 Summary of M-files......Page 47
4.1 Two-Dimensional Normal Distribution......Page 48
4.2 Direct and Inverse Problems......Page 50
4.3 Case 1, A == An P == 0, U E [0, 1]......Page 52
4.4 Case 2, A == Ac, P == 0, u == 1......Page 54
4.5.1 Mean Radial Error (MRE)......Page 55
4.5.5 Circular Error Probable (CEP)......Page 56
4.5.6 CEP Rate and RPE Rate......Page 61
4.6 Case 3, A == Ac, P == 0, U E [0, 1]......Page 62
4.6.1 Limiting Situation: u -+ 0......Page 63
4. 7 Case 4, A == Ac, P E [- 1, 1], U E [0, 1]......Page 65
4.7.1 Limiting Situation: Ipi -+ 1......Page 68
4.8 Case 5, A == Ae, P == 0, U E [0, 1]......Page 69
4.9 Case 6, A == A e' P E [- 1, 1], U E [0, 1]......Page 72
4.9.1 Limiting Situation: Ipl -+ 1......Page 73
4.10 PDF of the Angular Position of a Random Point......Page 74
4.11 SummaryofM-files......Page 77
5.1 Three-Dimensional Normal Distribution......Page 78
5.2 Direct and Inverse Problems......Page 79
5.3 Case 1, V == Vb, Pxy == Pyz == Pxz == 0, U, V E [0, 1]......Page 81
5.4 Case 2, V == V s , Pxy == P yz == Pxz == 0, U == v == 1......Page 82
5.5.4 Standard Radial Error (SRE)......Page 84
5.5.5 Spherical Error Probable (SEP)......Page 85
5.6 Case 3, V == V s , Pxy == Pyz == Pxz == 0, U, V E [0, 1]......Page 89
5.7 Case 4, V == V s , Pxy, pyz, P xz E [-1, 1], U, v E [0,1]......Page 93
5.8 Case 5, V == V e , Pxy == Pyz == Pxz == 0, U, V E [0, 1]......Page 95
5.8.1 Limiting Situation: a/(Jx == b/(Jy == c/(Jz......Page 96
5.9 Case 6, A == Ae, PXY' Pyz, Pxz E [-1, 1], U, v E [0, 1]......Page 97
5.10 Summary ofM-files......Page 98
6.1 Basic Assumptions and General Approach......Page 100
6.2 Maximum Likelihood Estimation of n, a......Page 101
6.3 Dependence of GM/RMS on n......Page 102
6.3.3 tjJ(n/2) for 0 < n/2 < 1......Page 103
6.4 Dependency of R(P)/RMS on n......Page 105
6.5 Relationship Between R(p)/RMS and GM/RMS......Page 106
6.6 Summary of M-files......Page 108
CHAPTER 7 Position Location Problems......Page 110
7.1 Single Error-Ellipse Analysis......Page 111
7.1.1 Approach 1. Fictitious Sigma and Cut Angle......Page 114
7.1.2 Approach 2. New Sigmas Along the Major and Minor Axes......Page 117
7.2 Consideration of Geometrical Factors......Page 118
7.3 Analysis of Multiple Error-Ellipses......Page 122
7.3.1 Mutually Parallel Axes......Page 123
7.3.2 Randomly Oriented Axes......Page 125
7.4 Summary of M-files......Page 128
CHAPTER 8 Risk Analysis......Page 129
8.2 Seller's Risk......Page 131
8.3 The Pass/Fail Criterion......Page 133
8.4 Buyer's Risk......Page 134
8.5 A Practical Example......Page 135
8.6 Generalization......Page 137
8.7 Summary of M-files......Page 138
A.2.1 Normal Distribution......Page 140
A.2.4 Rayleigh Distribution......Page 141
A.4 Generation of Standard Normal Random Variable......Page 142
B.1 Confidence Interval and Confidence Limits......Page 144
B.2 Determination of y-Confidence Interval......Page 145
C.1 Linear Combination of N Independent Random Variables......Page 146
C.2 Product of Two Random Variables......Page 147
C.4 Independence and Uncorrelatedness......Page 148
C.5 PDF of z == x + y......Page 149
C.7 PDF of z == x/y......Page 151
APPENDIX D GPS Dilution of Precisions......Page 153
E.1 M-files Used in Chapter 1......Page 155
E.2 M-files Used in Chapter 2......Page 158
E.3 M-files Used in Chapter 3......Page 163
E.4 M-files Used in Chapter 4......Page 168
E.5 M-files Used in Chapter 5......Page 183
E.6 M-files Used in Chapter 6......Page 200
E.7 M-files Used in Chapter 7......Page 210
E.8 M-files Used in Chapter 8......Page 217
BIBLIOGRAPHY......Page 220
INDEX......Page 221
ABOUT THE AUTHOR......Page 224