On constraints exploitation for particle filtering based target tracking

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. Nonetheless, the practical application of Particle Filters (PFs) may still be difficult, so that possibly available external knowledge can be exploited to increase the tracking performance. In this paper we assume such knowledge be formalized in terms of constraints on target dynamics. Hence, a Constrained version of the Filtering problem has to be solved. We first treat the case of perfectly known hard constraints, and show that exploitation of knowledge in the prediction or in the update step of the Bayesian filtering recursion are equivalent. We then focus on the case of soft constraints. Here, the lack of information on when and how the target violates the constraints makes the filtering problem much more difficult. Simulation results show that a straightforward extension of the Pseudo-Measurements approach is not sufficient. However, detecting the violation of constraints is possible if the knowledge is processed using an Interactive Multiple Models (IMM) scheme.