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Integrated Tracking, Classification, and Sensor Management Theory and Applications

by: Mallick, Mahendra; Krishnamurthy, Vikram; Vo, Ba-Ngu

Integrated Tracking, Classification, and Sensor Management Theory and Applications

by: Mallick, Mahendra; Krishnamurthy, Vikram; Vo, Ba-Ngu

ISBN 13:
9780470639054
ISBN 10:
0470639059
Edition: 1st
Format: Hardcover
Copyright: 12/03/2012
Publisher: Wiley-IEEE Press

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Integrated Tracking, Classification, and Sensor Management Theory and Applications > ISBN13: 9780470639054

Summary

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.

Author Biography

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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