A new quasi-Monte Carlo filtering algorithm based on number theoretical method

Abstract

To improve the filtering precision when dealing with the state estimation problem of nonlinear/non-Gaussian systems, we propose a novel sequential quasi-Monte Carlo (SQMC) filtering algorithm which is analogous to the sequential Monte Carlo (SMC) or particle filtering methods. The central idea of the new algorithm is to apply one of the deterministic sampling methods, i.e., number theoretic sampling method to SQMC. The point set of uniform distribution generated by cyclotomic field can construct more uniform scattered points in unit cube. Therefore, random samples generated by the point set of uniform distribution can adequately describe the posterior probability density function (PDF). Simulation results show that the proposed filtering algorithm provides better performance in nonlinear/non-Gaussian state estimation when compared to classical particle filter, SQMC using Halton sequence in presence of severe nonlinearity.