Generalized Two-Stage Particle Filter for High Dimensions

Abstract

The curse of dimensionality has been a long-standing problem in the field of particle filters (PFs), and prevents their use in real complex systems characterized by large number of unknowns. Recently a two-stage PF (TPF) for high dimensions was proposed, showing promising results with modest number of particles. The TPF modifies the proposal distribution by tempering each state dimension towards the most likely particle proposed and carrying out regular filtering using the constructed proposal. However, it is limited to cases where the measurement equations are completely separable. We propose a new filter inspired by the TPF principle as well as multiple PF (MPF), that can be applied to any setup and that provides a posterior distribution of the tempering coefficient that is updated recursively. Simulations show comparable, and in some cases, even better results than those of a recently proposed improved MPF for high dimensions.