Fixed-Lag Smoothing for Bayes optimal exploitation of external knowledge

Particle Filters (PFs) nowadays represent the state of art in nonlinear filtering. In particular, their high flexibility makes PFs particularly suited for Bayes optimal exploitation of possibly available external knowledge. In this paper we propose a new method for optimal processing of external knowledge that can be formalized in terms of hard constraints on the system dynamics. In particular, we are interested in the tracking performance improvements attainable when forward processing of external knowledge is performed over a moving window at every time step. That is, the one step ahead prediction of each particle is obtained through a Fixed-Lag Smoothing procedure, which uses Pseudo-Measurements to evaluate the level of adherence between each particle trajectory and the knowledge over multiple scans. A proof of improvements is presented by utilizing differential entropy as a measure of uncertainty. That is, we show that the differential entropy of the posterior PDF targeted by the proposed approach is always lower or equal to the differential entropy of the posterior PDF usually targeted in constrained filtering. Thus, for a sufficiently large number of particles, a PF implementation of the proposed Knowledge-Based Fixed-Lag Smoother can only improve the track accuracy upon classical algorithms for constrained filtering. Preliminary simulations show that the proposed approach guarantees substantial improvements when compared to the Standard SISR-PF and to the Pseudo-Measurements PF.