Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods

by Zhu; Yunmin

• ISBN13: 9781439874523
• ISBN10: 1439874522
• Format: Hardcover
• Copyright: 2012-07-05
• Publisher: CRC Press

Summary

Multisource information fusion has become a crucial technique in areas such as sensor networks, space technology, air traffic control, military engineering, communications, industrial control, agriculture, and environmental engineering. Exploring recent signficant results, this book presents essential mathematical descriptions and methods for multisensory decision and estimation fusion. It covers general adapted methods and systematic results, includes computer experiments to support the theoretical results, and fixes several popular but incorrect results in the field.

Table of Contents

Preface	p. xiii
Acknowledgment	p. xix
Introduction	p. 1
Fundamental Problems	p. 2
Core of Fundamental Theory and General Mathematical Ideas	p. 3
Classical Statistical Decision	p. 4
Bayes Decision	p. 5
Neyman-Pearson Decision	p. 8
Neyman-Pearson Criterion	p. 8
Minimax Decision	p. 10
Linear Estimation and Kalman Filtering	p. 11
Basics of Convex Optimization	p. 17
Convex Optimization	p. 17
Basic Terminology of Optimization	p. 17
Duality	p. 22
Relaxation	p. 24
S-Procedure Relaxation	p. 24
SDP Relaxation	p. 26
Parallel Statistical Binary Decision Fusion	p. 29
Optimal Sensor Rules for Binary Decision Given Fusion Rule	p. 30
Formulation for Bayes Binary Decision	p. 30
Formulation of Fusion Rules via Polynomials of Sensor Rules	p. 31
Fixed-Point Type Necessary Condition for the Optimal Sensor Rules	p. 33
Finite Convergence of the Discretized Algorithm	p. 37
Unified Fusion Rule	p. 45
Expression of the Unified Fusion Rule	p. 45
Numerical Examples	p. 48
Two Sensors	p. 48
Three Sensors	p. 50
Four Sensors	p. 52
Extension to Neyman-Pearson Decision	p. 53
Algorithm Searching for Optimal Sensor Rules	p. 56
Numerical Examples	p. 57
General Network Statistical Decision Fusion	p. 59
Elementary Network Structures	p. 60
Parallel Network	p. 60
Tandem Network	p. 62
Hybrid (Tree) Network	p. 64
Formulation of Fusion Rule via Polynomials of Sensor Rules	p. 64
Fixed-Point Type Necessary Condition for Optimal Sensor Rules	p. 69
Iterative Algorithm and Convergence	p. 71
Unified Fusion Rule	p. 74
Unified Fusion Rule for Parallel Networks	p. 75
Unified Fusion Rule for Tandem and Hybrid Networks	p. 78
Numerical Examples	p. 79
Three-Sensor System	p. 80
Four-Sensor System	p. 82
Optimal Decision Fusion with Given Sensor Rules	p. 84
Problem Formulation	p. 85
Computation of Likelihood Ratios	p. 87
Locally Optimal Sensor Decision Rules with Communications among Sensors	p. 88
Numerical Examples	p. 90
Two-Sensor Neyman-Pearson Decision System	p. 91
Three-Sensor Bayesian Decision System	p. 91
Simultaneous Search for Optimal Sensor Rules and Fusion Rule	p. 96
Problem Formulation	p. 96
Necessary Conditions for Optimal Sensor Rules and an Optimal Fusion Rule	p. 99
Iterative Algorithm and Its Convergence	p. 103
Extensions to Multiple-Bit Compression and Network Decision Systems	p. 110
Extensions to the Multiple-Bit Compression	p. 110
Extensions to Hybrid Parallel Decision System and Tree Network Decision System	p. 112
Numerical Examples	p. 116
Two Examples for Algorithm 3.2	p. 116
An Example for Algorithm 3.3	p. 119
Performance Analysis of Communication Direction for Two-Sensor Tandem Binary Decision System	p. 120
Problem Formulation	p. 122
System Model	p. 122
Bayes Decision Region of Sensor 2	p. 122
Bayes Decision Region of Sensor 1(Fusion Center)	p. 127
Bayes Cost Function	p. 128
Results	p. 129
Numerical Examples	p. 140
Network Decision Systems with Channel Errors	p. 143
Some Formulations about Channel Error	p. 144
Necessary Condition for Optimal Sensor Rules Given a Fusion Rule	p. 145
Special Case: Mutually Independent Sensor Observations	p. 149
Unified Fusion Rules for Network Decision Systems	p. 151
Network Decision Structures with Channel Errors	p. 151
Unified Fusion Rule in Parallel Bayesian Binary Decision System	p. 154
Unified Fusion rules for General Network Decision Systems with Channel Errors	p. 155
Numerical Examples	p. 157
Parallel Bayesian Binary Decision System	p. 157
Three-Sensor Decision System	p. 159
Some Uncertain Decision Combinations	p. 163
Representation of Uncertainties	p. 164
Dempster Combination Rule Based on Random Set Formulation	p. 165
Dempster's Combination Rule	p. 167
Mutual Conversion of the Basic Probability Assignment and the Random Set	p. 167
Combination Rules of the Dempster-Shafer Evidences via Random Set Formulation	p. 168
All Possible Random Set Combination Rules	p. 169
Correlated Sensor Basic Probabilistic Assignments	p. 171
Optimal Bayesian Combination Rule	p. 172
Examples of Optimal Combination Rule	p. 174
Fuzzy Set Combination Rule Based on Random Set Formulation	p. 177
Mutual Conversion of the Fuzzy Set and the Random Set	p. 178
Some Popular Combination Rules of Fuzzy Sets	p. 179
General Combination Rules	p. 181
Using the Operations of Sets Only	p. 182
Using the More General Correlation of the Random Variables	p. 183
Relationship between the t-Norm and Two-Dimensional Distribution Function	p. 184
Examples	p. 186
Hybrid Combination Rule Based on Random Set Formulation	p. 188
Convex Linear Estimation Fusion	p. 191
LMSE Estimation Fusion	p. 192
Formulation of LMSE Fusion	p. 192
Optimal Fusion Weights	p. 195
Efficient Iterative Algorithm for Optimal Fusion	p. 200
Appropriate Weighting Matrix	p. 201
Iterative Formula of Optimal Weighting Matrix	p. 204
Iterative Algorithm for Optimal Estimation Fusion	p. 205
Examples	p. 210
Recursion of Estimation Error Covariance in Dynamic Systems	p. 212
Optimal Dimensionality Compression for Sensor Data in Estimation Fusion	p. 214
Problem Formulation	p. 215
Preliminary	p. 216
Analytic Solution for Single-Sensor Case	p. 218
Search for Optimal Solution in the Multisensor Case	p. 220
Existence of the Optimal Solution	p. 220
Optimal Solution at a Sensor While Other Sensor Compression Matrices Are Given	p. 221
Numerical Example	p. 223
Quantization of Sensor Data	p. 224
Problem Formulation	p. 227
Necessary Conditions for Optimal Sensor Quantization Rules and Optimal Linear Estimation Fusion	p. 229
Gauss-Seidel Iterative Algorithm for Optimal Sensor Quantization Rules and Linear Estimation Fusion	p. 235
Numerical Examples	p. 237
Kalman Filtering Fusion	p. 241
Distributed Kalman Filtering Fusion with Cross-Correlated Sensor Noises	p. 243
Problem Formulation	p. 244
Distributed Kalman Filtering Fusion without Feedback	p. 246
Optimality of Kalman Filtering Fusion with Feedback	p. 249
Global Optimality of the Feedback Filtering Fusion	p. 250
Local Estimate Errors	p. 251
The Advantages of the Feedback	p. 252
Distributed Kalman Filtering Fusion with Singular Covariances of Filtering Error and Measurement Noises	p. 254
Equivalence Fusion Algorithm	p. 255
LMSE Fusion Algorithm	p. 255
Numerical Examples	p. 257
Optimal Kalman Filtering Trajectory Update with Unideal Sensor Messages	p. 261
Optimal Local-Processor Trajectory Update with Unideal Measurements	p. 262
Optimal Local-Processor Trajectory Update with Addition of OOSMs	p. 263
Optimal Local-Processor Trajectory Update with Removal of Earlier Measurement	p. 267
Optimal Local-Processor Trajectory Update with Sequentially Processing Unideal Measurements	p. 268
Numerical Examples	p. 269
Optimal Distributed Fusion Trajectory Update with Local-Processor Unideal Updates	p. 271
Optimal Distributed Fusion Trajectory Update with Addition of Local OOSM Update	p. 272
Optimal Distributed State Trajectory Update with Removal of Earlier Local Estimate	p. 274
Optimal Distributed Fusion Trajectory Update with Sequential Processing of Local Unideal Updates	p. 275
Random Parameter Matrices Kalman Filtering Fusion	p. 276
Random Parameter Matrices Kalman Filtering	p. 276
Random Parameter Matrices Kalman Filtering with Multisensor Fusion	p. 278
Some Applications	p. 281
Application to Dynamic Process with False Alarm	p. 281
Application to Multiple-Model Dynamic Process	p. 282
Novel Data Association Method Based on the Integrated Random Parameter Matrices Kalman Filtering	p. 285
Some Traditional Data Association Algorithms	p. 285
Single-Sensor DAIRKF	p. 287
Multisensor DAIRKF	p. 292
Numerical Examples	p. 295
Distributed Kalman Filtering Fusion with Packet Loss/Intermittent Communications	p. 303
Traditional Fusion Algorithms with Packet Loss	p. 303
Sensors Send Raw Measurements to Fusion Center	p. 304
Sensors Send Partial Estimates to Fusion Center	p. 304
Sensors Send Optimal Local Estimates to Fusion Center	p. 305
Remodeled Multisensor System	p. 306
Distributed Kalman Filtering Fusion with Sensor Noises Cross-Correlated and Correlated to Process Noise	p. 310
Optimal Distributed Kalman Filtering Fusion with Intermittent Sensor Transmissions or Packet Loss	p. 313
Suboptimal Distributed Kalman Filtering Fusion with Intermittent Sensor Transmissions or Packet Loss	p. 317
Robust Estimation Fusion	p. 323
Robust Linear MSE Estimation Fusion	p. 324
Minimizing Euclidean Error Estimation Fusion for Uncertain Dynamic System	p. 330
Preliminaries	p. 333
Problem Formulation of Centralized Fusion	p. 333
State Bounding Box Estimation Based on Centralized Fusion	p. 335
State Bounding Box Estimation Based on Distributed Fusion	p. 336
Measures of Size of an Ellipsoid or a Box	p. 337
Centralized Fusion	p. 338
Distributed Fusion	p. 351
Fusion of Multiple Algorithms	p. 356
Numerical Examples	p. 357
Figures 7.4 through 7.7 for Comparisons between Algorithms 7.1 and 7.2	p. 358
Figures 7.8 through 7.10 for Fusion of Multiple Algorithms	p. 363
Minimized Euclidean Error Data Association for Uncertain Dynamic System	p. 365
Formulation of Data Association	p. 365
MEEDA Algorithms	p. 368
Numerical Examples	p. 378
References	p. 395
Index	p. 407
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