This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers.
The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target’s behavior in a natural fashion rather than assumptions made for mathematical convenience.
The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.
Author(s): Lawrence D. Stone, Roy L. Streit, Stephen L. Anderson
Series: Studies in Big Data, 126
Publisher: Springer
Year: 2023
Language: English
Pages: 123
City: Cham
Contents
1 Introduction
2 Bayesian Single Target Tracking
2.1 Bayesian Inference
2.1.1 Prior Distribution
2.1.2 Likelihood Function
2.1.3 Posterior Distribution
2.1.4 Basic Bayesian Recursion
2.1.5 Examples of Priors, Posteriors, and Likelihood Functions
2.2 Tracking a Moving Target
2.2.1 Prior Distribution on Target Motion
2.2.2 Single Target Tracking Problem
2.2.3 Bayes-Markov Recursion
2.3 Kalman Filtering
2.3.1 Discrete Time Kalman Filtering Equations
2.3.2 Examples of Discrete-Time Gaussian Motion Models
2.3.3 Continuous-Discrete Kalman Filtering Equations
2.3.4 Kalman Filtering Examples
2.3.5 Nonlinear Extensions of Kalman Filtering
References
3 Bayesian Particle Filtering
3.1 Introduction
3.2 Particle Filter Tracking
3.2.1 Motion Model
3.2.2 Bayesian Recursion
3.2.3 Bayesian Particle Filter Recursion
3.2.4 Additional Considerations
3.2.5 Tracking Examples
3.3 Bayesian Particle Filtering Applied to Other Nonlinear Estimation Problems
3.3.1 Nonlinear Time Series Example
3.4 Smoothing Particle Filters
3.4.1 Repeated Filtering
3.4.2 Smoothing Examples
3.5 Notes
References
4 Simple Multiple Target Tracking
4.1 Introduction
4.2 Association Probabilities
4.3 Soft Association
4.4 Simplified JPDA
4.4.1 Particle Filter Implementation of Simplified Nonlinear JPDA
4.4.2 Crossing Targets Example
4.4.3 Feature-Aided Tracking
4.5 More Complex Multiple Target Tracking Problems
References
5 Intensity Filters
5.1 Introduction
5.2 Point Process Model of Multitarget State
5.2.1 Basic Properties of PPPs
5.2.2 Probability Distribution Function for a PPP
5.2.3 Superposition of Point Processes
5.2.4 Target Motion Process
5.2.5 Sensor Measurement Process
5.2.6 Thinning a Process
5.2.7 Augmented Spaces
5.3 iFilter
5.3.1 Augmented State Space Modeling
5.3.2 Predicted Detected and Undetected Target Processes
5.3.3 Measurement Process
5.3.4 Bayes Posterior Point Process (Information Update)
5.3.5 PPP Approximation
5.3.6 Correlation Losses in the PPP Approximation
5.3.7 The iFilter Recursion
5.4 Example
5.5 Notes
References
