Particle flow for nonlinear filters, Bayesian decisions and transport

Abstract

We derive a new algorithm for particle flow with non-zero diffusion corresponding to Bayes' rule, and we report the results of Monte Carlo simulations which show that the new filter is an order of magnitude more accurate than the extended Kalman filter for a difficult nonlinear filter problem. Our new algorithm is simple and fast to compute, and it has an especially nice intuitive formula, which is the same as Newton's method to solve the maximum likelihood estimation (MLE) problem (but for each particle rather than only the MLE), and it is also the same as the extended Kalman filter for the special case of Gaussian densities (but for each particle rather than just the point estimate). All of these particle flows apply to arbitrary multimodal densities with smooth nowhere vanishing non-Gaussian densities.