Labeling Uncertainty in Multitarget Tracking

In multitarget tracking, the problem of track labeling (assigning labels to tracks) is an ongoing research topic. The existing literature, however, lacks an appropriate measure of uncertainty related to the assigned labels that has a sound mathematical basis as well as clear practical meaning to the user. This is especially important in a situation where well separated targets move in close proximity with each other and thereafter separate again; in such a situation, it is well known that there will be confusion on target identities, also known as mixed labeling. In this paper, we specify comprehensively the necessary assumptions for a Bayesian formulation of the multitarget tracking and labeling (MTTL) problem to be meaningful. We provide a mathematical characterization of the labeling uncertainties with clear physical interpretation. We also propose a novel labeling procedure that can be used in combination with any existing (unlabeled) MTT algorithm to obtain a Bayesian solution to the MTTL problem. One advantage of the resulting solution is that it readily provides the labeling uncertainty measures. Using the mixed labeling phenomenon in the presence of two targets as our test bed, we show with simulation results that an unlabeled multitarget sequential Monte Carlo (M-SMC) algorithm that employs sequential importance resampling (SIR) augmented with our labeling procedure performs much better than its naive extension, the labeled SIR M-SMC filter.