| Preface | p. ix |
| Introduction | p. xiii |
| Acknowledgments | p. xix |
| Tracking Problems | p. 1 |
| Tracking a Single Target | p. 1 |
| Tracking a Surface Ship | p. 1 |
| Submarine Versus Submarine Tracking | p. 7 |
| Periscope Detection and Tracking | p. 13 |
| Tracking Multiple Targets | p. 17 |
| Tracking Aircraft | p. 17 |
| Underwater Surveillance | p. 19 |
| Classification of Tracking Systems | p. 23 |
| Target Assumptions | p. 24 |
| Information Assumptions | p. 25 |
| Emphasis | p. 26 |
| References | p. 27 |
| Bayesian Inference and Likelihood Functions | p. 29 |
| The Case for Bayesian Inference | p. 29 |
| The Likelihood Function and Bayes' Theorem | p. 33 |
| The Likelihood Function | p. 33 |
| Bayes' Theorem | p. 33 |
| Examples of Likelihood Functions | p. 35 |
| A Gaussian Contact Model | p. 35 |
| A Gaussian Bearing-Error Model | p. 36 |
| Combining Bearing and Contact Data | p. 39 |
| A Signal-Plus-Noise Model | p. 42 |
| Negative Information | p. 46 |
| Positive Information | p. 49 |
| Radar and Infrared Detection | p. 51 |
| References | p. 53 |
| Single Target Tracking | p. 55 |
| Bayesian Filtering | p. 56 |
| Recursive Bayesian Filtering | p. 56 |
| Recursive Bayesian Prediction and Smoothing | p. 62 |
| Kalman Filtering | p. 67 |
| Discrete Kalman Filtering | p. 68 |
| Continuous-Discrete Kalman Filtering | p. 72 |
| Discrete Bayesian Filtering | p. 78 |
| Nodestar Implementation | p. 78 |
| Correlated-Bearing Likelihood Function | p. 86 |
| Three-Dimensional Bearing Likelihood Function | p. 93 |
| Detection-No Detection Likelihood Function | p. 95 |
| Land Avoidance Likelihood Function | p. 100 |
| Elliptical Contact Likelihood Function | p. 101 |
| ELINT Likelihood Function | p. 101 |
| References | p. 102 |
| Classical Multiple Target Tracking: Multiple Hypothesis Tracking | p. 103 |
| Multiple Target Tracking Problem | p. 105 |
| Multiple Target Motion Model | p. 105 |
| Multiple Target Likelihood Functions | p. 106 |
| Contacts, Scans, and Association Hypotheses | p. 107 |
| Scan and Data Association Likelihood Functions | p. 111 |
| General Multiple Hypothesis Tracking | p. 114 |
| Conditional Target Distributions | p. 115 |
| Association Probabilities | p. 116 |
| General MHT Recursion | p. 117 |
| Association Probabilities for Gaussian Distributions | p. 119 |
| Association Probabilities for Non-Gaussian Distributions | p. 122 |
| Joint Association of Multiple Attribute Observations | p. 124 |
| Summary of Assumptions for General MHT Recursion | p. 125 |
| Independent Multiple Hypothesis Tracking | p. 126 |
| Conditionally Independent Scan Association Likelihood Functions | p. 126 |
| Independent MHT Recursion | p. 130 |
| Linear Gaussian Multiple Hypothesis Tracking | p. 131 |
| Example of Nonlinear MHT | p. 136 |
| Description of Tracking Problem | p. 136 |
| Operation of Tracker | p. 138 |
| Tracker Output | p. 141 |
| Notes | p. 157 |
| References | p. 158 |
| Multiple Target Tracking Without Contacts or Association | p. 161 |
| Unified Tracking Model | p. 162 |
| Multiple Target Motion and Likelihood Function Assumptions | p. 162 |
| Posterior Distribution | p. 162 |
| Unified Tracking Recursion | p. 163 |
| Summary of Assumptions for Unified Tracking Recursion | p. 164 |
| Relationship of Unified Tracking to Multiple Hypothesis Tracking | p. 165 |
| MHT is a Special Case of Unified Tracking | p. 165 |
| Extensions of MHT | p. 168 |
| Applications of Unified Tracking | p. 169 |
| Examples for Which Association is Meaningful | p. 172 |
| Examples for Which Association is Not Meaningful | p. 178 |
| An Example With an Unknown Number of Targets | p. 180 |
| Relationship of Unified Tracking to Other Tracking Algorithms | p. 204 |
| References | p. 206 |
| Likelihood Ratio Detection and Tracking: Theoretical Foundations | p. 209 |
| Basic Definitions and Relations | p. 209 |
| Likelihood Ratio | p. 212 |
| Measurement Likelihood Ratio | p. 212 |
| Likelihood Ratio Recursion | p. 213 |
| Log-Likelihood Ratios | p. 215 |
| Declaring a Target Present | p. 216 |
| Example of Likelihood Ratio Detection and Tracking | p. 219 |
| Simulated Detection and Tracking Results | p. 221 |
| Comparison to Matched Filter Detection | p. 224 |
| Measurement Likelihood Ratios | p. 229 |
| Additive Target Effects in Gaussian Noise | p. 230 |
| Modification for Random Target Strength | p. 231 |
| Maximum Likelihood for Unknown Target Strength | p. 233 |
| Designing for a Marginally Detectable Target | p. 234 |
| Additive Target Effects in Multivariate Gaussian Noise | p. 236 |
| Targets With Additive Small Signals | p. 236 |
| Additive Target Effects in Complex Gaussian Noise | p. 241 |
| Variance Modifying Targets in Gaussian Noise | p. 242 |
| Targets Modifying the Mean and Covariance of Gaussian Data | p. 243 |
| Exponential Distributions | p. 244 |
| Thresholded Data | p. 245 |
| Binomial Distributions: M of N Test Statistics | p. 247 |
| Dealing with Nuisance Parameters | p. 248 |
| Models of Likelihood Ratio Propagation | p. 248 |
| Transitions to and from the Null State | p. 249 |
| Continuous Transition Models Within the State Space | p. 254 |
| Discrete Transition Models Within the State Space | p. 255 |
| Deterministic Evolutions | p. 257 |
| State Entropy and Information Measures | p. 258 |
| Some Theorems Regarding Measurement Log-Likelihood Ratios | p. 258 |
| Information and Entropy in State Propagation | p. 262 |
| References | p. 267 |
| Likelihood Ratio Detection and Tracking: Implementation Issues | p. 269 |
| Framework for Limiting False Alarms | p. 269 |
| Measurement Likelihood Ratios in the Presence of Noise Only | p. 269 |
| False Alarm Rate and Target Detection Rate Relations | p. 271 |
| Likelihood Ratio Density in the Presence of Noise Only | p. 273 |
| Performance Prediction Methodology | p. 274 |
| Approximate Determination of Detection Performance | p. 275 |
| The Role of Motion Updates | p. 276 |
| The Role of the Information Updates | p. 277 |
| The Role of Averaging or Cell Formulations | p. 277 |
| Numerical Implementation of Likelihood Ratio Trackers | p. 278 |
| Sampled Field Approach | p. 279 |
| Cell-Based Approach | p. 283 |
| Kalman-Like Approach | p. 284 |
| Appendix | p. 291 |
| About the Authors | p. 293 |
| Index | p. 295 |
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