A Maximum Entropy Method for Particle Filtering

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimuminformation models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz. key words: Bayesian estimation, filtering, particle methods, maximumentropy, mixture models, ensemble Kalman filter. *corresponding author: Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD 21218 U.S.A. Email: [email protected], Tel:410-5167201, Fax: 410-516-7459 †Department of Mathematics, University of Arizona, Tucson, AZ 85721 U.S.A. running head: Maximum-Entropy Filter