Intro
Preface
Contents
Acronyms
1 Introduction to Analytic Combinatorics and Tracking
1.1 Introduction
1.2 The Benefits of Analytic Combinatorics to Tracking
1.3 Sensor and Object Models in Tracking
1.4 Likelihood Functions and Assignments
1.5 A First Look at Generating Functions for Tracking Problems
1.5.1 Statement A-Object Existence and Detection
1.5.2 Statement B-Gridded Measurements
1.5.3 Statement C-Gridded Object State and the Genesis of Tracking
1.6 Generating Functions for Bayes Theorem
1.6.1 GF of the Bayes Posterior Distribution

1.6.2 Bayes Inference in Statement A
1.6.3 Bayes Inference in Statement B
1.6.4 Bayes Inference in Statement C
1.7 Other Models of Object Existence and Detection
1.7.1 Multiple Object Existence Models
1.7.2 Random Number of Object Existence Models
1.7.3 False Alarms
1.8 Organization of the Book
References
2 Tracking One Object
2.1 Introduction
2.2 AC and Bayes Theorem
2.3 Setting the Stage
2.4 Bayes-Markov Single-Object Filter
2.4.1 BM: Assumptions
2.4.2 BM: Generating Functional
2.4.3 BM: Exact Bayesian Posterior Distribution

2.5 Tracking in Clutter-The PDA Filter
2.5.1 PDA: Assumptions
2.5.2 PDA: Generating Functional
2.5.3 PDA: Exact Bayesian Posterior Distribution
2.5.4 PDA: Closing the Bayesian Recursion
2.5.5 PDA: Gating-Conditioning on Subsets of Measurements
2.6 Object Existence-The IPDA Filter
2.6.1 IPDA: Assumptions
2.6.2 IPDA: Generating Functional
2.6.3 IPDA: Exact Bayesian Posterior Distribution
2.6.4 IPDA: Closing the Bayesian Recursion
2.7 Linear-Gaussian Filters
2.7.1 The Classical Kalman Filter
2.7.2 Linear-Gaussian PDA: Without Gating

2.7.3 Linear-Gaussian PDA: With Gating
2.8 Numerical Example: IPDA
References
3 Tracking a Specified Number of Objects
3.1 Introduction
3.2 Joint Probabilistic Data Association (JPDA) Filter
3.2.1 Multivariate Generating Functional
3.2.2 Exact Bayes Posterior Probability Distribution via AC
3.2.3 Measurement Assignments and Cross-Derivative Terms
3.2.4 Closing the Bayesian Recursion
3.2.5 Number of Assignments
3.2.6 Measurement Gating
3.3 Joint Integrated Probabilistic Data Association (JIPDA) Filter
3.3.1 Integrated State Space

3.3.2 Generating Functional
3.3.3 Exact Bayes Posterior Probability Distribution via AC
3.3.4 Closing the Bayesian Recursion
3.4 Resolution/Merged Measurement Problem-JPDA/Res Filter
3.5 Numerical Examples: Tracking with Unresolved Objects
3.5.1 JPDA/Res Filter with Weak and Strong Crossing Tracks
3.5.2 JPDA/Res with Parallel Object Tracks
3.5.3 Discussion of Results
References
4 Tracking a Variable Number of Objects
4.1 Introduction
4.2 Superposition of Multiple Object States
4.2.1 General Considerations
4.2.2 Superposition with Non-identical Object Models