Variable Resolution Particle Filter

Particle filters are used extensively for tracking the state of non-linear dynamic systems. This paper presents a new particle filter that maintains samples in the state space at dynamically varying resolution for computational efficiency. Resolution within statespace varies by region, depending on the belief that the true state lies within each region. Where belief is strong, resolution is fine. Where belief is low, resolution is coarse, abstracting multiple similar states together. The resolution of the statespace is dynamically updated as the belief changes. The proposed algorithm makes an explicit bias-variance tradeoff to select between maintaining samples in a biased generalization of a region of state space versus in a high variance specialization at fine resolution. Samples are maintained at a coarser resolution when the bias introduced by the generalization to a coarse resolution is outweighed by the gain in terms of reduction in variance, and at a finer resolution when it is not. Maintaining samples in abstraction prevents potential hypotheses from being eliminated prematurely for lack of a sufficient number of particles. Empirical results show that our variable resolution particle filter requires significantly lower computation for performance comparable to a classical particle filter.