Beyond The Kalman Filter

by Branko Ristic

Overview

The fundamental building block of a target tracking radar system is the filter for recursive target state estimation, with the Kalman filter being the best-known example. The authors of this work (all of Australia's Defense Science and Technology Organization) believe that particle filters relying on sequential Monte Carlo estimation and non-Gaussian dynamic estimation are growing to be more useful than Kalman filters. Writing for engineers, they review the current status of nonlinear/non-Gaussian filtering and describe common techniques. They then turn their attention to an array of target tracking applications, most of which rely on particle filters. Annotation ©2004 Book News, Inc., Portland, OR

Product Details

ISBN-13:	9781580536318
Publisher:	Artech House, Incorporated
Publication date:	01/31/2004
Series:	Artech House Radar Library
Pages:	318
Sales rank:	686,732
Product dimensions:	6.14(w) x 9.21(h) x 0.75(d)

Table of Contents

	Preface	xi
	Acknowledgments	xiii
I	Theoretical Concepts	1
Chapter 1	Introduction	3
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
1.6	Summary	16
	References	16
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
2.5	Summary	32
	References	32
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
3.7	Summary	61
3.8	Appendix: Combination of Quadratic Terms	61
	References	62
Chapter 4	Cramer-Rao Bounds for Nonlinear Filtering	67
4.1	Background	68
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
4.5	Summary and Further Reading	80
	References	80
II	Tracking Applications	83
Chapter 5	Tracking a Ballistic Object on Reentry	85
5.1	Introduction	85
5.2	Target Dynamics and Measurements	86
5.3	Cramer-Rao Bound	88
5.4	Tracking Filters	93
5.5	Numerical Results	94
5.6	Concluding Remarks	98
	References	101
Chapter 6	Bearings-Only Tracking	103
6.1	Introduction	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
6.6	Summary	148
6.7	Appendix: Linearized Transition Matrix for MP-EKF	148
	References	150
Chapter 7	Range-Only Tracking	153
7.1	Introduction	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
7.7	Summary	176
	References	178
Chapter 8	Bistatic Radar Tracking	179
8.1	Introduction	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
8.6	Summary	199
	References	201
Chapter 9	Tracking Targets Through the Blind Doppler	203
9.1	Introduction	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
9.6	Summary	213
	References	214
Chapter 10	Terrain-Aided Tracking	215
10.1	Introduction	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
10.6	Conclusions	236
	References	237
Chapter 11	Detection and Tracking of Stealthy Targets	239
11.1	Introduction	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
	References	258
Chapter 12	Group and Extended Object Tracking	261
12.1	Introduction	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
12.7	Concluding Remarks	277
	References	284
	Epilogue	287
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
	References	292
	List of Acronyms	293
	About the Authors	295
	Index	297