Markov Chain Monte Carlo Data Association for Multi-Target Tracking

TLDR

The authors develop Markov chain Monte Carlo data association (MCMCDA) algorithms to solve data association problems in multitarget tracking, including both single‑scan and multi‑scan variants for scenarios with fixed and varying numbers of targets. MCMCDA approximates joint probabilistic data association via a single‑scan algorithm and the optimal Bayesian filter via a multi‑scan algorithm, and the authors provide theoretical analysis and extensive simulations to support these approximations. They prove the single‑scan MCMCDA is a fully polynomial randomized approximation scheme for JPDA and demonstrate through simulations that MCMCDA outperforms multiple hypothesis tracking in accuracy and efficiency under high clutter, low detection, and many‑target conditions.

Abstract

This paper presents Markov chain Monte Carlo data association (MCMCDA) for solving data association problems arising in multitarget tracking in a cluttered environment. When the number of targets is fixed, the single-scan version of MCMCDA approximates joint probabilistic data association (JPDA). Although the exact computation of association probabilities in JPDA is NP-hard, we prove that the single-scan MCMCDA algorithm provides a fully polynomial randomized approximation scheme for JPDA. For general multitarget tracking problems, in which unknown numbers of targets appear and disappear at random times, we present a multi-scan MCMCDA algorithm that approximates the optimal Bayesian filter. We also present extensive simulation studies supporting theoretical results in this paper. Our simulation results also show that MCMCDA outperforms multiple hypothesis tracking (MHT) by a significant margin in terms of accuracy and efficiency under extreme conditions, such as a large number of targets in a dense environment, low detection probabilities, and high false alarm rates.