A Polytopic Box Particle Filter for state estimation of Non Linear Discrete-Time Systems

Abstract

The development of Particle Filters has made possible state estimation of dynamic systems presenting non-linear dynamics and potential multi-modalities. However, the efficiency of these approaches depends tightly of the required number of particles which may prove very high to approximate large range of uncertainty on the process or the measurements. To overcome this issue, the Box-Particle Filter (BPF) combines the versatility of the Particle Filter and the robustness of set-membership algorithms. The particles are replaced by boxes which represent in a compact way large variations of the estimates. Although this filter presents various advantages and requires a small number of boxes to estimate the state, the resulting estimates may prove pessimistic, as the uncertainty description as unions of axis-aligned intervals can be rather rough and doesn’t account for potential dependencies between the resulting estimate components. In the proposed paper, a new version of the BPF is proposed. Boxes are replaced by polytopes (multidimensional polygons) in the filter algorithm, so that they can adapt to represent state components dependency. This modification tends to ameliorate the estimation precision (i.e. the size of the final set that includes the true state decreases) while keeping the number of required polyhedrons small. Several examples illustrate the benefits of such an approach.