Spatial Error Analysis: A Unified Application-Oriented Treatment

✍ Scribed by David Y. Hsu

• Publisher: Wiley-IEEE Press
• Year: 1998
• Tongue: English
• Leaves: 233
• Edition: 1
• 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

Table Of Contents......Page 7
Preface......Page 11
List Of Figures......Page 14
List Of Tables......Page 16
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
2 Parameter Estimation From Samples......Page 23
2.1 Point Estimate Of Population Parameters......Page 24
2.2 Sampling Distribution......Page 27
2.3 Interval Estimate Of Population Mean......Page 28
2.4 Interval Estimate Of Population Standard Deviation......Page 30
2.5 Summary Of M-files......Page 35
3.1 Normal Distribution......Page 39
3.2.3 Mean Absolute Error (mae)......Page 42
3.2.4 Linear Error Probable (lep)......Page 43
3.3 Direct Problems......Page 44
3.4 Inverse Problems......Page 45
3.5 Summary Of M-files......Page 49
4.1 Two-dimensional Normal Distribution......Page 51
4.2 Direct And Inverse Problems......Page 53
4.3 Case 1, A == An P == 0, U E [0, 1]......Page 55
4.4 Case 2, A == Ac, P == 0, U == 1......Page 57
4.5.1 Mean Radial Error (mre)......Page 58
4.5.5 Circular Error Probable (cep)......Page 59
4.5.6 Cep Rate And Rpe Rate......Page 64
4.6 Case 3, A == Ac, P == 0, U E [0, 1]......Page 65
4.6.1 Limiting Situation: U -+ 0......Page 66
4. 7 Case 4, A == Ac, P E [- 1, 1], U E [0, 1]......Page 68
4.7.1 Limiting Situation: Ipi -+ 1......Page 71
4.8 Case 5, A == Ae, P == 0, U E [0, 1]......Page 72
4.9 Case 6, A == A E' P E [- 1, 1], U E [0, 1]......Page 75
4.9.1 Limiting Situation: Ipl -> 1......Page 76
4.10 Pdf Of The Angular Position Of A Random Point......Page 77
4.11 Summaryofm-files......Page 80
5.1 Three-dimensional Normal Distribution......Page 81
5.2 Direct And Inverse Problems......Page 82
5.3 Case 1, V == Vb, Pxy == Pyz == Pxz == 0, U, V E [0, 1]......Page 84
5.4 Case 2, V == V S , Pxy == P Yz == Pxz == 0, U == V == 1......Page 85
5.5.4 Standard Radial Error (sre)......Page 87
5.5.5 Spherical Error Probable (sep)......Page 88
5.6 Case 3, V == V S , Pxy == Pyz == Pxz == 0, U, V E [0, 1]......Page 92
5.7 Case 4, V == V S , Pxy, Pyz, P Xz E [-1, 1], U, V E [0,1]......Page 96
5.8 Case 5, V == V E , Pxy == Pyz == Pxz == 0, U, V E [0, 1]......Page 98
5.8.1 Limiting Situation: A/(jx == B/(jy == C/(jz......Page 99
5.9 Case 6, A == Ae, Pxy' Pyz, Pxz E [-1, 1], U, V E [0, 1]......Page 100
5.10 Summary Ofm-files......Page 101
6.1 Basic Assumptions And General Approach......Page 103
6.2 Maximum Likelihood Estimation Of N, A......Page 104
6.3 Dependence Of Gm/rms On N......Page 105
6.3.3 Tjj(n/2) For 0 < N/2 < 1......Page 106
6.4 Dependency Of R(p)/rms On N......Page 108
6.5 Relationship Between R(p)/rms And Gm/rms......Page 109
6.6 Summary Of M-files......Page 111
7 Position Location Problems......Page 113
7.1 Single Error-ellipse Analysis......Page 114
7.1.1 Approach 1. Fictitious Sigma And Cut Angle......Page 117
7.1.2 Approach 2. New Sigmas Along The Major And Minor Axes......Page 120
7.2 Consideration Of Geometrical Factors......Page 121
7.3 Analysis Of Multiple Error-ellipses......Page 125
7.3.1 Mutually Parallel Axes......Page 126
7.3.2 Randomly Oriented Axes......Page 128
7.4 Summary Of M-files......Page 131
8 Risk Analysis......Page 133
8.2 Seller's Risk......Page 135
8.3 The Pass/fail Criterion......Page 137
8.4 Buyer's Risk......Page 138
8.5 A Practical Example......Page 139
8.6 Generalization......Page 141
8.7 Summary Of M-files......Page 142
A.2.1 Normal Distribution......Page 145
A.2.4 Rayleigh Distribution......Page 146
A.4 Generation Of Standard Normal Random Variable......Page 147
B.1 Confidence Interval And Confidence Limits......Page 149
B.2 Determination Of Y-confidence Interval......Page 150
C.1 Linear Combination Of N Independent Random Variables......Page 151
C.2 Product Of Two Random Variables......Page 152
C.4 Independence And Uncorrelatedness......Page 153
C.5 Pdf Of Z == X + Y......Page 154
C.7 Pdf Of Z == X/y......Page 156
Appendix D Gps Dilution Of Precisions......Page 159
E.1 M-files Used In 1......Page 161
E.2 M-files Used In 2......Page 164
E.3 M-files Used In 3......Page 169
E.4 M-files Used In 4......Page 174
E.5 M-files Used In 5......Page 189
E.6 M-files Used In 6......Page 206
E.7 M-files Used In 7......Page 216
E.8 M-files Used In 8......Page 223
Bibliography......Page 227
Index......Page 229
About The Author......Page 233