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Bayesian Multiple Target Tracking : Radar S. - Lawrence D. Stone

Bayesian Multiple Target Tracking

Radar S.

Hardcover

Published: 31st July 1999
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Using the Bayesian inference framework, this book enables the reader to design and develop mathematically sound algorithms for dealing with tracking problems involving multiple targets, multiple sensors, and multiple platforms. It shows how non-linear Multiple Hypothesis Tracking and the Theory of United Tracking are successful methods when multiple target tracking must be performed without contacts or association. With detailed examples illustrating the developed concepts, algorithms, and approaches, the book helps the reader track when observations are non-linear functions of target site, when the target state distributions or measurements error distributions are not Gaussian, when notions of contact and association are merged or unresolved among more than one target, and in low data rate and low signal to noise ratio situations.

Prefacep. ix
Introductionp. xiii
Acknowledgmentsp. xix
Tracking Problemsp. 1
Tracking a Single Targetp. 1
Tracking a Surface Shipp. 1
Submarine Versus Submarine Trackingp. 7
Periscope Detection and Trackingp. 13
Tracking Multiple Targetsp. 17
Tracking Aircraftp. 17
Underwater Surveillancep. 19
Classification of Tracking Systemsp. 23
Target Assumptionsp. 24
Information Assumptionsp. 25
Emphasisp. 26
Referencesp. 27
Bayesian Inference and Likelihood Functionsp. 29
The Case for Bayesian Inferencep. 29
The Likelihood Function and Bayes' Theoremp. 33
The Likelihood Functionp. 33
Bayes' Theoremp. 33
Examples of Likelihood Functionsp. 35
A Gaussian Contact Modelp. 35
A Gaussian Bearing-Error Modelp. 36
Combining Bearing and Contact Datap. 39
A Signal-Plus-Noise Modelp. 42
Negative Informationp. 46
Positive Informationp. 49
Radar and Infrared Detectionp. 51
Referencesp. 53
Single Target Trackingp. 55
Bayesian Filteringp. 56
Recursive Bayesian Filteringp. 56
Recursive Bayesian Prediction and Smoothingp. 62
Kalman Filteringp. 67
Discrete Kalman Filteringp. 68
Continuous-Discrete Kalman Filteringp. 72
Discrete Bayesian Filteringp. 78
Nodestar Implementationp. 78
Correlated-Bearing Likelihood Functionp. 86
Three-Dimensional Bearing Likelihood Functionp. 93
Detection-No Detection Likelihood Functionp. 95
Land Avoidance Likelihood Functionp. 100
Elliptical Contact Likelihood Functionp. 101
ELINT Likelihood Functionp. 101
Referencesp. 102
Classical Multiple Target Tracking: Multiple Hypothesis Trackingp. 103
Multiple Target Tracking Problemp. 105
Multiple Target Motion Modelp. 105
Multiple Target Likelihood Functionsp. 106
Contacts, Scans, and Association Hypothesesp. 107
Scan and Data Association Likelihood Functionsp. 111
General Multiple Hypothesis Trackingp. 114
Conditional Target Distributionsp. 115
Association Probabilitiesp. 116
General MHT Recursionp. 117
Association Probabilities for Gaussian Distributionsp. 119
Association Probabilities for Non-Gaussian Distributionsp. 122
Joint Association of Multiple Attribute Observationsp. 124
Summary of Assumptions for General MHT Recursionp. 125
Independent Multiple Hypothesis Trackingp. 126
Conditionally Independent Scan Association Likelihood Functionsp. 126
Independent MHT Recursionp. 130
Linear Gaussian Multiple Hypothesis Trackingp. 131
Example of Nonlinear MHTp. 136
Description of Tracking Problemp. 136
Operation of Trackerp. 138
Tracker Outputp. 141
Notesp. 157
Referencesp. 158
Multiple Target Tracking Without Contacts or Associationp. 161
Unified Tracking Modelp. 162
Multiple Target Motion and Likelihood Function Assumptionsp. 162
Posterior Distributionp. 162
Unified Tracking Recursionp. 163
Summary of Assumptions for Unified Tracking Recursionp. 164
Relationship of Unified Tracking to Multiple Hypothesis Trackingp. 165
MHT is a Special Case of Unified Trackingp. 165
Extensions of MHTp. 168
Applications of Unified Trackingp. 169
Examples for Which Association is Meaningfulp. 172
Examples for Which Association is Not Meaningfulp. 178
An Example With an Unknown Number of Targetsp. 180
Relationship of Unified Tracking to Other Tracking Algorithmsp. 204
Referencesp. 206
Likelihood Ratio Detection and Tracking: Theoretical Foundationsp. 209
Basic Definitions and Relationsp. 209
Likelihood Ratiop. 212
Measurement Likelihood Ratiop. 212
Likelihood Ratio Recursionp. 213
Log-Likelihood Ratiosp. 215
Declaring a Target Presentp. 216
Example of Likelihood Ratio Detection and Trackingp. 219
Simulated Detection and Tracking Resultsp. 221
Comparison to Matched Filter Detectionp. 224
Measurement Likelihood Ratiosp. 229
Additive Target Effects in Gaussian Noisep. 230
Modification for Random Target Strengthp. 231
Maximum Likelihood for Unknown Target Strengthp. 233
Designing for a Marginally Detectable Targetp. 234
Additive Target Effects in Multivariate Gaussian Noisep. 236
Targets With Additive Small Signalsp. 236
Additive Target Effects in Complex Gaussian Noisep. 241
Variance Modifying Targets in Gaussian Noisep. 242
Targets Modifying the Mean and Covariance of Gaussian Datap. 243
Exponential Distributionsp. 244
Thresholded Datap. 245
Binomial Distributions: M of N Test Statisticsp. 247
Dealing with Nuisance Parametersp. 248
Models of Likelihood Ratio Propagationp. 248
Transitions to and from the Null Statep. 249
Continuous Transition Models Within the State Spacep. 254
Discrete Transition Models Within the State Spacep. 255
Deterministic Evolutionsp. 257
State Entropy and Information Measuresp. 258
Some Theorems Regarding Measurement Log-Likelihood Ratiosp. 258
Information and Entropy in State Propagationp. 262
Referencesp. 267
Likelihood Ratio Detection and Tracking: Implementation Issuesp. 269
Framework for Limiting False Alarmsp. 269
Measurement Likelihood Ratios in the Presence of Noise Onlyp. 269
False Alarm Rate and Target Detection Rate Relationsp. 271
Likelihood Ratio Density in the Presence of Noise Onlyp. 273
Performance Prediction Methodologyp. 274
Approximate Determination of Detection Performancep. 275
The Role of Motion Updatesp. 276
The Role of the Information Updatesp. 277
The Role of Averaging or Cell Formulationsp. 277
Numerical Implementation of Likelihood Ratio Trackersp. 278
Sampled Field Approachp. 279
Cell-Based Approachp. 283
Kalman-Like Approachp. 284
Appendixp. 291
About the Authorsp. 293
Indexp. 295
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9781580530248
ISBN-10: 1580530249
Series: Radar S.
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 324
Published: 31st July 1999
Publisher: Artech House Publishers
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 2.2
Weight (kg): 0.62