Bayes optimal knowledge exploitation for target tracking with hard constraints

Nonlinear target tracking is a well known problem and its Bayes optimal solution, based on particle filtering techniques, is nowadays applied in high performance surveillance systems. Oftentimes, additional information about the environment and the target is available, and can be formalized in terms of constraints on target dynamics. Hence, a Constrained version of the Bayesian Filtering problem has to be solved to achieve optimal tracking performance. In this paper we consider the Constrained Filtering problem for the case of perfectly known hard constraints. We clarify that in such a case the Particle Filter (PF) is still Bayes optimal if we can correctly model the constraints. We then show that from a Bayesian viewpoint, exploitation of the available knowledge in the prediction or in the update step are equivalent. Finally, we consider simple techniques to exploit constraints in the prediction and update steps of a PF, and use the Kullback-Leibler divergence to illustrate their equivalence through simulations.