The Pairwise-Markov Bernoulli Filter

The Bernoulli filter is a general, Bayes-optimal solution for tracking a single disappearing and reappearing target, using a sensor whose observations are corrupted by missed detections and a general, known clutter process. Like virtually all target-tracking algorithms it presumes restrictive independence assumptions, namely a hidden Markov model (HMM) structure on the sensor and target. That is, the current state of the target depends only on its previous state, and the measurement collected from it depends only on its current state. Pieczynski's pairwise Markov model (PMM) relaxes these restrictions. In it, the current target state can additionally depend on the previous measurement; and the current measurement can additionally depend on the previous measurement and previous target state. In this paper we show how to correctly generalize the PMM to the multitarget (MPMM) case; and use the MPMM to derive a "PMM Bernoulli filter" that obeys PMM rather than restrictive HMM sensor/target statistics.