Beyond MAP Estimation With the Track-Oriented Multiple Hypothesis Tracker

The track-oriented multiple hypothesis tracker (TOMHT) is a popular algorithm for tracking multiple targets in a cluttered environment. In tracking parlance it is known as a multi-scan, maximum a posteriori (MAP) estimator-multi-scan because it enumerates possible data associations jointly over several scans, and MAP because it seeks the most likely data association conditioned on the observations. This paper extends the TOMHT, building on its internal representation to support probabilistic queries other than MAP estimation. Specifically, by summing over the TOMHT's pruned space of data association hypotheses one can compute marginal probabilities of individual tracks. Since this summation is generally intractable, any practical implementation must replace it with an approximation. We introduce a factor graph representation of the TOMHT's data association posterior and use variational message-passing to approximate track marginals. In an empirical evaluation, we show that marginal estimates computed through message-passing compare favorably to those computed through explicit summation over the k-best hypotheses, especially as the number of possible hypotheses increases. We also show that track marginals enable parameter estimation in the TOMHT via a natural extension of the expectation maximization algorithm used in single-target tracking. In our experiments, online EM updates using approximate marginals significantly increased tracker robustness to poor initial parameter specification.