A Bayesian solution to multi-target tracking problems with mixed labelling

In Multi-Target Tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature and has been previously formulated using Bayesian recursion. However, the existing literature lacks an appropriate measure of uncertainty related to the assigned labels which has sound mathematical basis and clear practical meaning (to the user). This is especially important in a situation where targets move in close proximity with each other and thereafter separate again. Because, in such a situation it is well-known that there will be confusion on target identities, also known as “mixed labelling‿. In this paper, we provide a mathematical characterization of the labelling uncertainties present in Bayesian multi-target tracking and labelling (MTTL) problems and define measures of labelling uncertainties with clear physical interpretation. The introduced uncertainty measures can be used to find the optimal track label assignment, and evaluate track labelling performance. We also analyze in details the mixed labelling phenomenon in the presence of two targets. In addition, we propose a new Sequential Monte Carlo (SMC) algorithm, the Labelling Uncertainty Aware Particle Filter (LUA-PF), for the multi target tracking and labelling problem that can provide good estimates of the uncertainty measures. We validate this using simulation and show that the proposed method performs much better when compared with the performance of the SIR multi-target SMC filter.