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Type II approximate Bayes perspective to multiple hypothesis tracking

Multiple hypothesis tracking (MHT) is a computational procedure for recursively estimating multi-object configurations and states from measurements with association uncertainties, noise, false alarms and less than one probability of detection. From a probabilistic modelling perspective, the complete multi-object tracking (MT) model is intractable to perform statistical inference as the multi-object and measurement association configurations constitute infinite sets. In this article, we provide explicit formulae to demonstrate that MHT is a type II maximum a posteriori (MAP) approximate Bayes inference procedure over the complete MT model. In particular, we introduce a MT model that captures all typical uncertainties and show that the joint density of the global model hypotheses and the other variables involved is well defined. This model allows us to define the MT problem mathematically and contrast MHT and sequential Bayesian filtering. We argue that the computational procedures constituting an MHT algorithm such as model hypothesis pruning can be treated as a second stage of approximation for finding near-optimal solutions to the MAP problem given a computational budget.