Near-Optimal Resampling In Particle Filters Using The Ising Energy Model

Resampling increasing the variance of the tracking algorithm in Particle Filtering (PF). Instead of utilizing resampling procedures that rely on asymptotic convergence properties, we show that intelligently selecting and replicating a set of samples can better represent the posterior approximation and improve the overall performance of the PF. To this end, we formulate the resampling procedure as an integer program that minimizes an upper bound on the Kullback-Leibler divergence (KLD) between the resampled distribution and the posterior approximation. We then transform the problem into an Ising energy minimization problem, which we are able to efficiently solve. Applying our novel paradigm to a challenging sequential importance resampling (SIR) simulation shows faster convergence over the number of resampled particles and a 35% improvement in the median KLD for a fixed number of particles.