An accessible coverage of random finite set based multi-target filtering algorithms such as the Probability Hypothesis
Table of Contents
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
1.5 Dynamic Models 9
1.6 Measurement Models 14
1.7 Filter Initialization 15
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
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
2.4 Bayesian Filtering 51
2.5 Box Particle Filtering 52
2.6 Box Particle Filtering Derived from the Bayesian Inference Using a Mixture of Uniform Probability Density Functions 56
2.7 Box-PF Illustration over a Target Tracking Example 65
2.8 Application for a Vehicle Dynamic Localization Problem 67
2.9 Conclusions 71
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
3.3 Random Finite Sets 81
3.4 Multiple Target Filtering and Estimation 85
3.5 Multitarget Miss Distances 91
3.6 The Probability Hypothesis Density (PHD) Filter 95
3.7 The Cardinalized PHD Filter 105
3.8 Numerical Examples 111
3.9 MeMBer Filter 117
4. The Continuous Time Roots of the Interacting Multiple Model Filter 127
Henk A.P. Blom
4.1 Introduction 127
4.2 Hidden Markov Model Filter 129
4.3 System with Markovian Coefficients 136
4.4 Markov Jump Linear System 141
4.5 Continuous-Discrete Filtering 149
4.6 Concluding Remarks 154
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
5.3 Track Filtering 170
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
5.8 Summary 189
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
6.3 Bayesian Approach to Ground Moving Target Tracking 209
6.4 Exploitation of Road Network Data 222
6.5 Convoy Track Maintenance Using Random Matrices 234
6.6 Convoy Tracking with the Cardinalized Probability Hypothesis Density Filter 243
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
7.3 PCRLB Formulations in Cluttered Environments 262
7.4 An Approximate PCRLB for Maneuevring Target Tracking 269
7.5 A General Framework for the Deployment of Stationary Sensors 271
7.6 UAV Trajectory Planning 294
7.7 Summary and Conclusions 305
8. Track-Before-Detect Techniques 311
Samuel J. Davey, Mark G. Rutten, and Neil J. Gordon
8.1 Introduction 311
8.2 Models 318
8.3 Baum Welch Algorithm 327
8.4 Dynamic Programming: Viterbi Algorithm 331
8.5 Particle Filter 334
8.6 ML-PDA 337
8.7 H-PMHT 341
8.8 Performance Analysis 347
8.9 Applications: Radar and IRST Fusion 354
8.10 Future Directions 357
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
10. Intent Inference and Detection of Anomalous Trajectories: A Metalevel Tracking Approach 387
Vikram Krishnamurthy
10.1 Introduction 387
10.2 Anomalous Trajectory Classification Framework 393
10.3 Trajectory Modeling and Inference Using Stochastic Context-Free Grammars 395
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
PART III SENSOR MANAGEMENT AND CONTROL
11. Radar Resource Management for Target Tracking—A Stochastic Control Approach 417
Vikram Krishnamurthy
11.1 Introduction 417
11.2 Problem Formulation 422
11.3 Structural Results and Lattice Programming for Micromanagement 431
11.4 Radar Scheduling for Maneuvering Targets Modeled as Jump Markov Linear System 437
11.5 Summary 444
12. Sensor Management for Large-Scale Multisensor-Multitarget Tracking 447
Ratnasingham Tharmarasa and Thia Kirubarajan
12.1 Introduction 447
12.2 Target Tracking Architectures 451
12.3 Posterior Cram´er–Rao Lower Bound 452
12.4 Sensor Array Management for Centralized Tracking 458
12.5 Sensor Array Management for Distributed Tracking 473
12.6 Sensor Array Management for Decentralized Tracking 489
12.7 Conclusions 507
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
13.3 Network Partition and Message Integration for Hybrid Model 532
13.4 Hybrid Message Passing Algorithm for Classification 536
13.5 Numerical Experiments 537
13.6 Concluding Remarks 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
14.3 Multisensor Fusion Systems—Design and Performance Evaluation 560
14.4 Summary and Continuing Questions 564
15. Detection and Estimation of Radiological Sources 579
Mark Morelande and Branko Ristic
15.1 Introduction 579
15.2 Estimation of Point Sources 580
15.3 Estimation of Distributed Sources 590
15.4 Searching for Point Sources 599
15.5 Conclusions 612
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
16.4 Distributed Detection in Wireless Sensor Networks 634
16.5 Copula-Based Fusion of Correlated Decisions 645
16.6 Conclusion 652
17. Evidential Networks for Decision Support in Surveillance Systems 661
Alessio Benavoli and Branko Ristic
17.1 Introduction 661
17.2 Valuation Algebras 662
17.3 Local Computation in a VA 668
17.4 Theory of Evidence as a Valuation Algebra 672
17.5 Examples of Decision Support Systems 685
References 702
Index 705
