A unifying framework for multi-target tracking and existence

Most target tracking approaches either assume that the number of targets is constant throughout the time horizon of interest, or that information about target existence (birth and death) is provided by some external source. Here we show how target existence can be integrated within the tracking framework in a rigorous way. The notion of existence is not new, and has been considered before in e.g. [D. Musicki et al., (1994), (2002)]. We provide here a general probabilistic treatment that impacts as little as possible on existing tracking algorithms so that legacy tracking software (and more generally target tracking architectures) can be reused. We first show how the notion of existence can be incorporated into a single target tracking framework (retaining algorithmic invariance). To place the probabilistic recursions into context we relate this single target tracking architecture to the probabilistic data association filter. We then extend the single target results to incorporate existence for multi-target tracking and relate this to an importance sampling implementation of the joint probabilistic data association (JPDA) framework. The treatment presented is entirely general and so facilitates implementation with Kalman filters, extended/unscented Kalman filters, particle filters, etc, i.e. the approach developed is invariant to the filtering and data association mechanisms used, and therein lies the novelty. We apply the proposed framework to the difficult problem of tracking football players in video sequences, where we adopt a mixture Kalman filter implementation.