Integrated Tracking, Classification, and Sensor Management Theory and Applications
, by Mallick, Mahendra; Krishnamurthy, Vikram; Vo, Ba-Ngu
- ISBN: 9780470639054 | 0470639059
- Cover: Hardcover
- Copyright: 12/3/2012
The vital resource contains four inter-related parts: Filtering, Multi-target Multi-sensor Tracking, Sensor Management and Control, and Target Classification. These four areas have seen remarkable progress in algorithmic development and mathematical analysis in recent years. These areas are of importance in statistical signal processing, radar systems, operations research, and control theory. They include the intelligence, surveillance, and reconnaissance (ISR) applications that and the book puts the focus on careful mathematical formulation, clear description of theory, and real-world applications in these areas. Written by experts in the field, this book presents results in a form so that they are readily accessible to researchers and practitioners.
MAHENDRA MALLICK, PhD, is Principal Research Scientist at the Propagation Research Associates, Inc. A senior member of the IEEE, he has served as the associate editor-in-chief of the online journal of the International Society of Information Fusion (ISIF).
VIKRAM KRISHNAMURTHY, PhD, holds the Canada Research Chair in Statistical Signal Processing at The University of British Columbia. He is an IEEE Fellow and Editor-in-Chief of the IEEE Journal of Selected Topics in Signal Processing.
BA-NGU VO, PhD, is Professor and Chair of Signals and Systems in the Department of Electrical and Computer Engineering at Curtin University in Western Australia. He is Associate Editor for IEEE Transactions on Aerospace and Electronic Systems.
PREFACE xvii
CONTRIBUTORS xxiii
PART I FILTERING
1. Angle-Only Filtering in Three Dimensions 3
Mahendra Mallick, Mark Morelande, Lyudmila Mihaylova, Sanjeev Arulampalam, and Yanjun Yan
1.1 Introduction 3
1.2 Statement of Problem 6
1.3 Tracker and Sensor Coordinate Frames 6
1.4 Coordinate Systems for Target and Ownship States 7
1.4.1 Cartesian Coordinates for State Vector and Relative State Vector 7
1.4.2 Modified Spherical Coordinates for Relative State Vector 8
1.5 Dynamic Models 9
1.5.1 Dynamic Model for State Vector and Relative State Vector in Cartesian Coordinates 9
1.5.2 Dynamic Model for Relative State Vector in Modified Spherical Coordinates 11
1.6 Measurement Models 14
1.6.1 Measurement Model for Relative Cartesian State 14
1.6.2 Measurement Model for Modified Spherical Coordinates 15
1.7 Filter Initialization 15
1.7.1 Initialization of Relative Cartesian Coordinates 16
1.7.2 Initialization of Modified Spherical Coordinates 16
1.8 Extended Kalman Filters 17
1.9 Unscented Kalman Filters 19
1.10 Particle Filters 23
1.11 Numerical Simulations and Results 28
1.12 Conclusions 31
Appendix1A Derivations for Stochastic Differential Equations in MSC 32
Appendix1B Transformations Between Relative Cartesian Coordinates and MSC 35
Appendix1C Filter Initialization for Relative Cartesian Coordinates and MSC 35
References 40
2. Particle Filtering Combined with Interval Methods for Tracking Applications 43
Amadou Gning, Lyudmila Mihaylova, Fahed Abdallah, and Branko Ristic
2.1 Introduction 43
2.2 Related Works 44
2.3 Interval Analysis 46
2.3.1 Basic Concepts 46
2.3.2 Inclusion Functions 47
2.3.3 Constraint Satisfaction Problems 48
2.3.4 Contraction Methods 50
2.4 Bayesian Filtering 51
2.5 Box Particle Filtering 52
2.5.1 Main Steps of the Box Particle Filter 52
2.6 Box Particle Filtering Derived from the Bayesian Inference Using a Mixture of Uniform Probability Density Functions 56
2.6.1 Time Update Step 57
2.6.2 Measurement Update Step 63
2.7 Box-PF Illustration over a Target Tracking Example 65
2.7.1 Simulation Set-Up 65
2.8 Application for a Vehicle Dynamic Localization Problem 67
2.9 Conclusions 71
References 72
3. Bayesian Multiple Target Filtering Using Random Finite Sets 75
Ba-Ngu Vo, Ba-Tuong Vo, and Daniel Clark
3.1 Introduction 75
3.2 Overview of the Random Finite Set Approach to Multitarget Filtering 76
3.2.1 Single-Target Filtering 76
3.2.2 Random Finite Set and Multitarget Filtering 77
3.2.3 Why Random Finite Set for Multitarget Filtering? 80
3.3 Random Finite Sets 81
3.3.1 Probability Density 82
3.3.2 Janossy Densities 83
3.3.3 Belief Functional and Density 83
3.3.4 The Probability Hypothesis Density 84
3.3.5 Examples of RFS 84
3.4 Multiple Target Filtering and Estimation 85
3.4.1 Multitarget Dynamical Model 86
3.4.2 Multitarget Observation Model 87
3.4.3 Multitarget Bayes Recursion 88
3.4.4 Multitarget State Estimation 88
3.5 Multitarget Miss Distances 91
3.5.1 Metrics 91
3.5.2 Hausdorff Metric 92
3.5.3 Optimal Mass Transfer (OMAT) Metric 92
3.5.4 Optimal Subpattern Assignment (OSPA) Metric 94
3.6 The Probability Hypothesis Density (PHD) Filter 95
3.6.1 The PHD Recursion for Linear Gaussian Models 97
3.6.2 Implementation Issues 100
3.6.3 Extension to Nonlinear Gaussian Models 101
3.7 The Cardinalized PHD Filter 105
3.7.1 The CPHD Recursion for Linear Gaussian Models 107
3.7.2 Implementation Issues 109
3.7.3 The CPHD Filter for Fixed Number of Targets 110
3.8 Numerical Examples 111
3.9 MeMBer Filter 117
3.9.1 MeMBer Recursion 117
3.9.2 Multitarget State Estimation 118
3.9.3 Extension to Track Propagation 119
3.9.4 MeMBer Filter for Image Data 119
3.9.5 Implementations 122
References 122
4. The Continuous Time Roots of the Interacting Multiple Model Filter 127
Henk A.P. Blom
4.1 Introduction 127
4.1.1 Background and Notation 128
4.2 Hidden Markov Model Filter 129
4.2.1 Finite-State Markov Process 129
4.2.2 SDEs Having a Markov Chain Solution 130
4.2.3 Filtering a Hidden Markov Model (HMM) 131
4.2.4 Robust Versions of the HMM Filter 133
4.3 System with Markovian Coefficients 136
4.3.1 The Filtering Problem Considered 136
4.3.2 Evolution of the Joint Conditional Density 136
4.3.3 Evolution of the Conditional Density of xt Given θt 139
4.3.4 Special Cases 141
4.4 Markov Jump Linear System 141
4.4.1 The Filtering Problem Considered 141
4.4.2 Pre-IMM Filter Equations 142
4.4.3 Continuous-Time IMM Filter 144
4.4.4 Linear Version of the Pre-IMM Equations 145
4.4.5 Relation Between Bjork’s Filter and Continuous-Time IMM 148
4.5 Continuous-Discrete Filtering 149
4.5.1 The Continuous-Discrete Filtering Problem Considered 149
4.5.2 Evolution of the Joint Conditional Density 149
4.5.3 Continuous-Discrete SIR Particle Filtering 150
4.5.4 Markov Jump Linear Case 152
4.5.5 Continuous-Discrete IMM Filter 152
4.6 Concluding Remarks 154
Appendix4A Differentiation Rule for Discontinuous Semimartingales 155
Appendix4B Derivation of Differential for ˆRt (θ) 156
References 159
PART II MULTITARGET MULTISENSOR TRACKING
5. Multitarget Tracking Using Multiple Hypothesis Tracking 165
Mahendra Mallick, Stefano Coraluppi, and Craig Carthel
5.1 Introduction 165
5.2 Tracking Algorithms 166
5.2.1 Tracking with Target Identity (or Track Label) 168
5.2.2 Tracking without Target Identity (or Track Label) 169
5.3 Track Filtering 170
5.3.1 Dynamic Models 171
5.3.2 Measurement Models 172
5.3.3 Single Model Filter for a Nonmaneuvering Target 172
5.3.4 Filtering Algorithms 175
5.3.5 Multiple Switching Model Filter for a Maneuvering Target 178
5.4 MHT Algorithms 179
5.5 Hybrid-State Derivations of MHT Equations 180
5.6 The Target-Death Problem 185
5.7 Examples for MHT 186
5.7.1 Example 1: N-Scan Pruning in Track-Oriented MHT 186
5.7.2 Example 2: Maneuvering Target in Heavy Clutter 187
5.8 Summary 189
References 190
6. Tracking and Data Fusion for Ground Surveillance 203
Michael Mertens, Michael Feldmann, Martin Ulmke, and Wolfgang Koch
6.1 Introduction to Ground Surveillance 203
6.2 GMTI Sensor Model 204
6.2.1 Model of the GMTI Clutter Notch 204
6.2.2 Signal Strength Measurements 206
6.3 Bayesian Approach to Ground Moving Target Tracking 209
6.3.1 Bayesian Tracking Filter 210
6.3.2 Essentials of GMTI Tracking 212
6.3.3 Filter Update with Clutter Notch 214
6.3.4 Target Strength Estimation 217
6.4 Exploitation of Road Network Data 222
6.4.1 Modeling of Road Networks 223
6.4.2 Densities on Roads 225
6.4.3 Application: Precision Targeting 229
6.4.4 Track-Based Road-Map Extraction 229
6.5 Convoy Track Maintenance Using Random Matrices 234
6.5.1 Object Extent Within the Bayesian Framework 235
6.5.2 Road-Map Assisted Convoy Track Maintenance 237
6.5.3 Selected Numerical Examples 242
6.6 Convoy Tracking with the Cardinalized Probability Hypothesis Density Filter 243
6.6.1 Gaussian Mixture CPHD Algorithm 244
6.6.2 Integration of Digital Road Maps 248
6.6.3 Target State Dependent Detection Probability 249
6.6.4 Exemplary Results for Small Convoys 250
References 251
7. Performance Bounds for Target Tracking: Computationally Efficient Formulations and Associated Applications 255
Marcel Hernandez
7.1 Introduction 255
7.2 Bayesian Performance Bounds 258
7.2.1 The Estimation Problem 258
7.2.2 A General Class of Lower Bounds 258
7.2.3 Efficient Fixed Dimensionality Recursions 260
7.3 PCRLB Formulations in Cluttered Environments 262
7.3.1 Measurement Model 262
7.3.2 Information Reduction Factor Approach 263
7.3.3 Measurement Sequence Conditioning Approach 264
7.3.4 Measurement Existence Sequence Conditioning Approach 265
7.3.5 Calculation of the Information Reduction Factors 266
7.3.6 Relationships Between the Various Performance Bounds 268
7.4 An Approximate PCRLB for Maneuevring Target Tracking 269
7.4.1 Motion Model 269
7.4.2 Best-Fitting Gaussian Approach 269
7.4.3 Recursive Computation of Best-Fitting Gaussian Approximation 270
7.5 A General Framework for the Deployment of Stationary Sensors 271
7.5.1 Introduction 271
7.5.2 Interval Between Deployments 273
7.5.3 Use of Existing Sensors 276
7.5.4 Locations and Number of New Sensors 277
7.5.5 Performance Measure 280
7.5.6 Efficient Search Technique 281
7.5.7 Example—Sonobuoy Deployment in Submarine Tracking 282
7.6 UAV Trajectory Planning 294
7.6.1 Scenario Overview 294
7.6.2 Measure of Performance 294
7.6.3 One-Step-Ahead Planning 295
7.6.4 Two-Step-Ahead Planning 295
7.6.5 Adaptive Horizon Planning 296
7.6.6 Simulations 298
7.7 Summary and Conclusions 305
References 307
8. Track-Before-Detect Techniques 311
Samuel J. Davey, Mark G. Rutten, and Neil J. Gordon
8.1 Introduction 311
8.1.1 Historical Review of TBD Approaches 312
8.1.2 Limitations of Conventional Detect-then-Track 315
8.2 Models 318
8.2.1 Target Model 318
8.2.2 Sensor Model 321
8.3 Baum Welch Algorithm 327
8.3.1 Detection 328
8.3.2 Parameter Selection 329
8.3.3 Complexity Analysis 329
8.3.4 Summary 331
8.4 Dynamic Programming: Viterbi Algorithm 331
8.4.1 Parameter Selection 333
8.4.2 Complexity Analysis 333
8.4.3 Summary 333
8.5 Particle Filter 334
8.5.1 Parameter Selection 336
8.5.2 Complexity Analysis 336
8.5.3 Summary 337
8.6 ML-PDA 337
8.6.1 Optimization Methods 340
8.6.2 Validation 340
8.6.3 Summary 341
8.7 H-PMHT 341
8.7.1 Efficient Two-Dimensional Implementation 344
8.7.2 Nonlinear Gaussian Measurement Function 345
8.7.3 Track Management 346
8.7.4 Summary 346
8.8 Performance Analysis 347
8.8.1 Simulation Scenario 348
8.8.2 Measures of Performance 349
8.8.3 Overall ROC 350
8.8.4 Per-Frame ROC 350
8.8.5 Estimation Accuracy 353
8.8.6 Computation Requirements 353
8.9 Applications: Radar and IRST Fusion 354
8.10 Future Directions 357
References 358
9. Advances in Data Fusion Architectures 363
Stefano Coraluppi and Craig Carthel
9.1 Introduction 363
9.2 Dense-Target Scenarios 364
9.3 Multiscale Sensor Scenarios 368
9.4 Tracking in Large Sensor Networks 370
9.5 Multiscale Objects 372
9.6 Measurement Aggregation 378
9.7 Conclusions 383
References 383
10. Intent Inference and Detection of Anomalous Trajectories: A Metalevel Tracking Approach 387
Vikram Krishnamurthy
10.1 Introduction 387
10.1.1 Examples of Metalevel Tracking 388
10.1.2 SCFGs and Reciprocal Markov Chains 390
10.1.3 Literature Survey 391
10.1.4 Main Results 392
10.2 Anomalous Trajectory Classification Framework 393
10.2.1 Trajectory Classification in Radar Tracking 393
10.2.2 Radar Tracking System Overview 394
10.3 Trajectory Modeling and Inference Using Stochastic Context-Free Grammars 395
10.3.1 Review of Stochastic Context-Free Grammars 396
10.3.2 SCFG Models for Anomalous Trajectories 396
10.3.3 Bayesian Signal Processing of SCFG Models 400
10.4 Trajectory Modeling and Inference Using Reciprocal Processes (RP) 403
10.5 Example 1: Metalevel Tracking for GMTI Radar 406
10.6 Example 2: Data Fusion in a Multicamera Network 407
10.7 Conclusion 413
References 413
PART III SENSOR MANAGEMENT AND CONTROL
11. Radar Resource Management for Target Tracking—A Stochastic Control Approach 417
Vikram Krishnamurthy
11.1 Introduction 417
11.1.1 Approaches to Radar Resource Management 419
11.1.2 Architecture of Radar Resource Manager 420
11.1.3 Organization of Chapter 421
11.2 Problem Formulation 422
11.2.1 Macro and Micromanager Architecture 422
11.2.2 Target and Measurement Model 423
11.2.3 Micromanagement to Maximize Mutual Information of Targets 424
11.2.4 Formulation of Micromanagement as a Multivariate POMDP 426
11.3 Structural Results and Lattice Programming for Micromanagement 431
11.3.1 Monotone Policies for Micromanagement with Mutual Information Stopping Cost 432
11.3.2 Monotone POMDP Policies for Micromanagement 433
11.3.3 Radar Macromanagement 436
11.4 Radar Scheduling for Maneuvering Targets Modeled as Jump
Markov Linear System 437
11.4.1 Formulation of Jump Markov Linear System Model 437
11.4.2 Suboptimal Radar Scheduling Algorithms 440
11.5 Summary 444
References 444
12. Sensor Management for Large-Scale Multisensor-Multitarget Tracking 447
Ratnasingham Tharmarasa and Thia Kirubarajan
12.1 Introduction 447
12.1.1 Sensor Management 447
12.1.2 Centralized Tracking 448
12.1.3 Distributed Tracking 449
12.1.4 Decentralized Tracking 450
12.1.5 Organization of the Chapter 451
12.2 Target Tracking Architectures 451
12.2.1 Centralized Tracking 451
12.2.2 Distributed Tracking 452
12.2.3 Decentralized Tracking 452
12.3 Posterior Cram´er–Rao Lower Bound 452
12.3.1 Multitarget PCRLB for Centralized Tracking 453
12.4 Sensor Array Management for Centralized Tracking 458
12.4.1 Problem Description 458
12.4.2 Problem Formulation 458
12.4.3 Solution Technique 465
12.4.4 Simulation 465
12.4.5 Simulation Results 467
12.5 Sensor Array Management for Distributed Tracking 473
12.5.1 Track Fusion 474
12.5.2 Performance of Distributed Tracking with Full Feedback at Every Measurement Step 475
12.5.3 PCRLB for Distributed Tracking 476
12.5.4 Problem Description 476
12.5.5 Problem Formulation 477
12.5.6 Solution Technique 479
12.5.7 Simulation Results 485
12.6 Sensor Array Management for Decentralized Tracking 489
12.6.1 PCRLB for Decentralized Tracking 490
12.6.2 Problem Description 490
12.6.3 Problem Formulation 491
12.6.4 Solution Technique 500
12.6.5 Simulation Results 501
12.7 Conclusions 507
Appendix12A Local Search 510
Appendix 12B Genetic Algorithm 512
Appendix 12C Ant Colony Optimization 514
References 516
PART IV ESTIMATION AND CLASSIFICATION
13. Efficient Inference in General Hybrid Bayesian Networks for Classification 523
Wei Sun and Kuo-Chu Chang
13.1 Introduction 523
13.2 Message Passing: Representation and Propagation 526
13.2.1 Unscented Transformation 528
13.2.2 Unscented Message Passing 530
13.3 Network Partition and Message Integration for Hybrid Model 532
13.3.1 Message Integration for Hybrid Model 533
13.4 Hybrid Message Passing Algorithm for Classification 536
13.5 Numerical Experiments 537
13.5.1 Experiment Method 537
13.5.2 Experiment Results 540
13.5.3 Complexity of HMP-BN 542
13.6 Concluding Remarks 544
References 544
14. Evaluating Multisensor Classification Performance with Bayesian Networks 547
Eswar Sivaraman and Kuo-Chu Chang
14.1 Introduction 547
14.2 Single-Sensor Model 548
14.2.1 A New Approach for Quantifying Classification Performance 548
14.2.2 Efficient Estimation of the Global Classification Matrix 550
14.2.3 The Global Classification Matrix: Some Experiments 554
14.2.4 Sensor Design Quality Metrics 557
14.3 Multisensor Fusion Systems—Design and Performance Evaluation 560
14.3.1 Performance Evaluation of Multisensor Models—Good Sensors 560
14.3.2 Performance Evaluation of Multisensor Fusion Systems—Not-so-Good Sensors 563
14.4 Summary and Continuing Questions 564
Appendix14A Developing a Sensor’s Local Confusion Matrix 565
Appendix 14B Solving for the Off-Diagonal Elements of the Global Classification Matrix 567
Appendix 14C A Graph-Theoretic Representation of the Recursive Approach for Estimating the Diagonal Elements of the GCM 569
Appendix 14C.1 The Binomial Case (n = 2,m = 2) 569
Appendix 14C.2 The Multinomial Case (n,m > 2) 571
Appendix14D Designing Monte Carlo Simulations of the GCM 573
Appendix 14D.1 Single-Sensor GCM 573
Appendix 14D.2 Multisensor GCM 574
Appendix 14E Proof of Approximation 1 574
References 576
15. Detection and Estimation of Radiological Sources 579
Mark Morelande and Branko Ristic
15.1 Introduction 579
15.2 Estimation of Point Sources 580
15.2.1 Model 581
15.2.2 Source Parameter Estimation 581
15.2.3 Simulation Results 585
15.2.4 Experimental Results 587
15.3 Estimation of Distributed Sources 590
15.3.1 Model 591
15.3.2 Estimation 593
15.3.3 Simulation Results 595
15.3.4 Experimental Results 598
15.4 Searching for Point Sources 599
15.4.1 Model 600
15.4.2 Sequential Search Using a POMDP 601
15.4.3 Implementation of the POMDP 603
15.4.4 Simulation Results 608
15.4.5 Experimental Results 611
15.5 Conclusions 612
References 614
PART V DECISION FUSION AND DECISION SUPPORT
16. Distributed Detection and Decision Fusion with Applications to Wireless Sensor Networks 619
Qi Cheng, Ruixin Niu, Ashok Sundaresan, and Pramod K. Varshney
16.1 Introduction 619
16.2 Elements of Detection Theory 620
16.3 Distributed Detection with Multiple Sensors 624
16.3.1 Topology 624
16.3.2 Conditional Independence Assumption 626
16.3.3 Dependent Observations 632
16.3.4 Discussion 634
16.4 Distributed Detection in Wireless Sensor Networks 634
16.4.1 Counting Rule in a Wireless Sensor Network with Signal Decay 636
16.4.2 Performance Analysis: Sensors with Identical Statistics 636
16.4.3 Performance Analysis: Sensors with Nonidentical Statistics 637
16.5 Copula-Based Fusion of Correlated Decisions 645
16.5.1 Copula Theory 645
16.5.2 System Design Using Copulas 646
16.5.3 Illustrative Example: Application to Radiation Detection 648
16.5.4 Remark 650
16.6 Conclusion 652
Appendix16A Performance Analysis of a Network with Nonidentical Sensors via Approximations 653
Appendix 16A.1 Binomial I Approximation 653
Appendix 16A.2 Binomial II Approximation 654
Appendix 16A.3 DeMoivre–Laplace Approximation 654
Appendix 16A.4 Total Variation Distance 655
References 656
17. Evidential Networks for Decision Support in Surveillance Systems 661
Alessio Benavoli and Branko Ristic
17.1 Introduction 661
17.2 Valuation Algebras 662
17.2.1 Mathematical Definitions and Results 664
17.2.2 Axioms 665
17.2.3 Probability Mass Functions as a Valuation Algebra 667
17.3 Local Computation in a VA 668
17.3.1 Fusion Algorithm 668
17.3.2 Construction of a Binary Join Tree 670
17.3.3 Inward Propagation 672
17.4 Theory of Evidence as a Valuation Algebra 672
17.4.1 Combination 676
17.4.2 Marginalization 677
17.4.3 Inferring and Eliciting the Evidential Model 678
17.4.4 Decision Making 681
17.5 Examples of Decision Support Systems 685
17.5.1 Target Identification 685
17.5.2 Threat Assessment 690
Appendix17A Construction of a BJT 699
Appendix 17B Inward Propagation 700
References 702
Index 705
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