Beyond the Kalman filter : particle filters for tracking applications / Branko Ristic, Sanjeev Arulampalam, Neil Gordon.

Format:

Book

Author/Creator:

Ristic, Branko.

Contributor:

Arulampalam, Sanjeev.

Gordon, Neil, 1967-

Anne and Joseph Trachtman Memorial Book Fund.

Rosengarten Family Fund.

Series:

Artech House radar library

Language:

English

Subjects (All):

Tracking radar--Mathematics.

Tracking radar.

Kalman filtering.

Radar defense networks--United States.

Radar defense networks.

United States.

Physical Description:

xiii, 299 pages : illustrations ; 24 cm.

Place of Publication:

Boston : Artech House, [2004]

Contents:

I Theoretical Concepts 1

1.1 Nonlinear Filtering 3

1.2 The Problem and Its Conceptual Solution 4

1.3 Optimal Algorithms 7

1.3.1 The Kalman Filter 7

1.3.2 Grid-Based Methods 9

1.3.3 Benes and Daum Filters 10

1.4 Multiple Switching Dynamic Models 11

1.5 Basics of Target Tracking 14

Chapter 2 Suboptimal Nonlinear Filters 19

2.1 Analytic Approximations 19

2.2 Numerical Methods 22

2.3 Gaussian Sum Filters 24

2.3.1 Static MM Estimator 25

2.3.2 Dynamic MM Filter 26

2.4 Unscented Kalman Filter 28

2.4.1 Filtering Equations 29

2.4.2 The Unscented Transform 30

Chapter 3 A Tutorial on Particle Filters 35

3.1 Monte Carlo Integration 35

3.2 Sequential Importance Sampling 37

3.3 Resampling 41

3.4 Selection of Importance Density 45

3.4.1 The Optimal Choice 45

3.4.2 Suboptimal Choices 47

3.5 Versions of Particle Filters 48

3.5.1 SIR Filter 48

3.5.2 Auxiliary SIR Filter 49

3.5.3 Particle Filters with an Improved Sample Diversity 52

3.5.4 Local Linearization Particle Filters 55

3.5.5 Multiple-Model Particle Filter 57

3.6 Computational Aspects 58

3.8 Appendix: Combination of Quadratic Terms 61

Chapter 4 Cramer-Rao Bounds for Nonlinear Filtering 67

4.2 Recursive Computation of the Filtering Information Matrix 71

4.3 Special Cases 73

4.3.1 Additive Gaussian Noise 73

4.3.2 Linear/Gaussian Case 75

4.3.3 Zero Process Noise 76

4.4 Multiple-Switching Dynamic Models 76

4.4.1 Enumeration Method 77

4.4.2 Deterministic Trajectory 79

II Tracking Applications 83

Chapter 5 Tracking a Ballistic Object on Reentry 85

5.2 Target Dynamics and Measurements 86

5.3 Cramer-Rao Bound 88

5.4 Tracking Filters 93

5.5 Numerical Results 94

Chapter 6 Bearings-Only Tracking 103

6.2 Problem Formulation 104

6.2.1 Nonmaneuvering Case 104

6.2.2 Maneuvering Case 106

6.2.3 Multiple Sensor Case 108

6.2.4 Tracking with Constraints 108

6.3 Cramer-Rao Lower Bounds 109

6.3.1 Nonmaneuvering Case 109

6.3.2 Maneuvering Case 110

6.3.3 Multiple Sensor Case 112

6.4 Tracking Algorithms 113

6.4.1 Nonmaneuvering Case 113

6.4.2 Maneuvering Target Case 121

6.4.3 Multiple Sensor Case 127

6.4.4 Tracking with Hard Constraints 127

6.5 Simulation Results 129

6.5.1 Nonmaneuvering Case 130

6.5.2 Maneuvering Case 138

6.5.3 Multiple Sensor Case 145

6.5.4 Tracking with Hard Constraints 147

6.7 Appendix: Linearized Transition Matrix for MP-EKF 148

Chapter 7 Range-Only Tracking 153

7.2 Problem Description 154

7.3 Cramer-Rao Bounds 157

7.3.1 Derivations 157

7.3.2 Analysis 158

7.4 Tracking Algorithms 164

7.5 Algorithm Performance and Comparison 168

7.6 Application to Ingara ISAR Data 173

Chapter 8 Bistatic Radar Tracking 179

8.2 Problem Formulation 180

8.3 Cramer-Rao Bounds 183

8.3.1 Derivations 183

8.3.2 Analysis 185

8.4 Tracking Algorithms 189

8.4.1 Stage 1 of Tracker 191

8.4.2 Stage 2 of Tracker 196

8.5 Algorithm Performance 196

Chapter 9 Tracking Targets Through the Blind Doppler 203

9.2 Problem Formulation 204

9.3 EKF-Based Track Maintenance 206

9.4 Particle Filter-Based Solution 208

9.5 Simulation Results 210

Chapter 10 Terrain-Aided Tracking 215

10.2 Problem Description and Formulation 216

10.2.1 Problem Description 216

10.2.2 Dynamics and Measurement Models for VS-IMM 219

10.2.3 Dynamic Models for VS-MMPF 221

10.3 Variable Structure IMM 227

10.3.1 Model Set Update 229

10.4 Variable Structure Multiple-Model Particle Filter 229

10.4.1 Prediction Step 230

10.4.2 Update Step 230

10.5 Simulation Results 231

Chapter 11 Detection and Tracking of Stealthy Targets 239

11.2 Target and Sensor Models 240

11.2.1 Target Model 240

11.2.2 Sensor Model 241

11.3 Conceptual Solution in the Bayesian Framework 242

11.4 A Particle Filter for Track-Before-Detect 244

11.5 A Numerical Example 247

11.6 Performance Analysis 251

11.6.1 Tracking Error Performance 251

11.6.2 Detection Performance 254

11.7 Summary and Extensions 257

Chapter 12 Group and Extended Object Tracking 261

12.2 Tracking Model 263

12.3 Formal Bayesian Solution 265

12.4 Affine Model 268

12.5 Particle Filters 269

12.5.1 SIR Particle Filter 270

12.5.2 Rao-Blackwellized Particle Filter 271

12.6 Simulation Example 273

Appendix Coordinate Transformations for Tracking 289

A.1 Geodetic to ECEF and Vice Versa 290

A.2 ECEF to Tangential Plane and Vice Versa 290.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

158053631X

OCLC:

54079653