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 Optimal Distributed Kalman Filtering Fusion with Intermittent Sensor Transmissions or Packet Loss Suboptimal Distributed Kalman Filtering Fusion with Intermittent Sensor Transmissions or Packet Loss p. 310 p. 313 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 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.