| |
| |
| Preface | |
| |
| |
| Introduction | |
| |
| |
| Acknowledgments | |
| |
| |
| |
| Tracking Problems | |
| |
| |
| |
| Tracking a Single Target | |
| |
| |
| |
| Tracking a Surface Ship | |
| |
| |
| |
| Submarine Versus Submarine Tracking | |
| |
| |
| |
| Periscope Detection and Tracking | |
| |
| |
| |
| Tracking Multiple Targets | |
| |
| |
| |
| Tracking Aircraft | |
| |
| |
| |
| Underwater Surveillance | |
| |
| |
| |
| Classification of Tracking Systems | |
| |
| |
| |
| Target Assumptions | |
| |
| |
| |
| Information Assumptions | |
| |
| |
| |
| Emphasis | |
| |
| |
| References | |
| |
| |
| |
| Bayesian Inference and Likelihood Functions | |
| |
| |
| |
| The Case for Bayesian Inference | |
| |
| |
| |
| The Likelihood Function and Bayes' Theorem | |
| |
| |
| |
| The Likelihood Function | |
| |
| |
| |
| Bayes' Theorem | |
| |
| |
| |
| Examples of Likelihood Functions | |
| |
| |
| |
| A Gaussian Contact Model | |
| |
| |
| |
| A Gaussian Bearing-Error Model | |
| |
| |
| |
| Combining Bearing and Contact Data | |
| |
| |
| |
| A Signal-Plus-Noise Model | |
| |
| |
| |
| Negative Information | |
| |
| |
| |
| Positive Information | |
| |
| |
| |
| Radar and Infrared Detection | |
| |
| |
| References | |
| |
| |
| |
| Single Target Tracking | |
| |
| |
| |
| Bayesian Filtering | |
| |
| |
| |
| Recursive Bayesian Filtering | |
| |
| |
| |
| Recursive Bayesian Prediction and Smoothing | |
| |
| |
| |
| Kalman Filtering | |
| |
| |
| |
| Discrete Kalman Filtering | |
| |
| |
| |
| Continuous-Discrete Kalman Filtering | |
| |
| |
| |
| Discrete Bayesian Filtering | |
| |
| |
| |
| Nodestar Implementation | |
| |
| |
| |
| Correlated-Bearing Likelihood Function | |
| |
| |
| |
| Three-Dimensional Bearing Likelihood Function | |
| |
| |
| |
| Detection-No Detection Likelihood Function | |
| |
| |
| |
| Land Avoidance Likelihood Function | |
| |
| |
| |
| Elliptical Contact Likelihood Function | |
| |
| |
| |
| ELINT Likelihood Function | |
| |
| |
| References | |
| |
| |
| |
| Classical Multiple Target Tracking: Multiple Hypothesis Tracking | |
| |
| |
| |
| Multiple Target Tracking Problem | |
| |
| |
| |
| Multiple Target Motion Model | |
| |
| |
| |
| Multiple Target Likelihood Functions | |
| |
| |
| |
| Contacts, Scans, and Association Hypotheses | |
| |
| |
| |
| Scan and Data Association Likelihood Functions | |
| |
| |
| |
| General Multiple Hypothesis Tracking | |
| |
| |
| |
| Conditional Target Distributions | |
| |
| |
| |
| Association Probabilities | |
| |
| |
| |
| General MHT Recursion | |
| |
| |
| |
| Association Probabilities for Gaussian Distributions | |
| |
| |
| |
| Association Probabilities for Non-Gaussian Distributions | |
| |
| |
| |
| Joint Association of Multiple Attribute Observations | |
| |
| |
| |
| Summary of Assumptions for General MHT Recursion | |
| |
| |
| |
| Independent Multiple Hypothesis Tracking | |
| |
| |
| |
| Conditionally Independent Scan Association Likelihood Functions | |
| |
| |
| |
| Independent MHT Recursion | |
| |
| |
| |
| Linear Gaussian Multiple Hypothesis Tracking | |
| |
| |
| |
| Example of Nonlinear MHT | |
| |
| |
| |
| Description of Tracking Problem | |
| |
| |
| |
| Operation of Tracker | |
| |
| |
| |
| Tracker Output | |
| |
| |
| |
| Notes | |
| |
| |
| References | |
| |
| |
| |
| Multiple Target Tracking Without Contacts or Association | |
| |
| |
| |
| Unified Tracking Model | |
| |
| |
| |
| Multiple Target Motion and Likelihood Function Assumptions | |
| |
| |
| |
| Posterior Distribution | |
| |
| |
| |
| Unified Tracking Recursion | |
| |
| |
| |
| Summary of Assumptions for Unified Tracking Recursion | |
| |
| |
| |
| Relationship of Unified Tracking to Multiple Hypothesis Tracking | |
| |
| |
| |
| MHT is a Special Case of Unified Tracking | |
| |
| |
| |
| Extensions of MHT | |
| |
| |
| |
| Applications of Unified Tracking | |
| |
| |
| |
| Examples for Which Association is Meaningful | |
| |
| |
| |
| Examples for Which Association is Not Meaningful | |
| |
| |
| |
| An Example With an Unknown Number of Targets | |
| |
| |
| |
| Relationship of Unified Tracking to Other Tracking Algorithms | |
| |
| |
| References | |
| |
| |
| |
| Likelihood Ratio Detection and Tracking: Theoretical Foundations | |
| |
| |
| |
| Basic Definitions and Relations | |
| |
| |
| |
| Likelihood Ratio | |
| |
| |
| |
| Measurement Likelihood Ratio | |
| |
| |
| |
| Likelihood Ratio Recursion | |
| |
| |
| |
| Log-Likelihood Ratios | |
| |
| |
| |
| Declaring a Target Present | |
| |
| |
| |
| Example of Likelihood Ratio Detection and Tracking | |
| |
| |
| |
| Simulated Detection and Tracking Results | |
| |
| |
| |
| Comparison to Matched Filter Detection | |
| |
| |
| |
| Measurement Likelihood Ratios | |
| |
| |
| |
| Additive Target Effects in Gaussian Noise | |
| |
| |
| |
| Modification for Random Target Strength | |
| |
| |
| |
| Maximum Likelihood for Unknown Target Strength | |
| |
| |
| |
| Designing for a Marginally Detectable Target | |
| |
| |
| |
| Additive Target Effects in Multivariate Gaussian Noise | |
| |
| |
| |
| Targets With Additive Small Signals | |
| |
| |
| |
| Additive Target Effects in Complex Gaussian Noise | |
| |
| |
| |
| Variance Modifying Targets in Gaussian Noise | |
| |
| |
| |
| Targets Modifying the Mean and Covariance of Gaussian Data | |
| |
| |
| |
| Exponential Distributions | |
| |
| |
| |
| Thresholded Data | |
| |
| |
| |
| Binomial Distributions: M of N Test Statistics | |
| |
| |
| |
| Dealing with Nuisance Parameters | |
| |
| |
| |
| Models of Likelihood Ratio Propagation | |
| |
| |
| |
| Transitions to and from the Null State | |
| |
| |
| |
| Continuous Transition Models Within the State Space | |
| |
| |
| |
| Discrete Transition Models Within the State Space | |
| |
| |
| |
| Deterministic Evolutions | |
| |
| |
| |
| State Entropy and Information Measures | |
| |
| |
| |
| Some Theorems Regarding Measurement Log-Likelihood Ratios | |
| |
| |
| |
| Information and Entropy in State Propagation | |
| |
| |
| References | |
| |
| |
| |
| Likelihood Ratio Detection and Tracking: Implementation Issues | |
| |
| |
| |
| Framework for Limiting False Alarms | |
| |
| |
| |
| Measurement Likelihood Ratios in the Presence of Noise Only | |
| |
| |
| |
| False Alarm Rate and Target Detection Rate Relations | |
| |
| |
| |
| Likelihood Ratio Density in the Presence of Noise Only | |
| |
| |
| |
| Performance Prediction Methodology | |
| |
| |
| |
| Approximate Determination of Detection Performance | |
| |
| |
| |
| The Role of Motion Updates | |
| |
| |
| |
| The Role of the Information Updates | |
| |
| |
| |
| The Role of Averaging or Cell Formulations | |
| |
| |
| |
| Numerical Implementation of Likelihood Ratio Trackers | |
| |
| |
| |
| Sampled Field Approach | |
| |
| |
| |
| Cell-Based Approach | |
| |
| |
| |
| Kalman-Like Approach | |
| |
| |
| Appendix | |
| |
| |
| About the Authors | |
| |
| |
| Index | |