Approximate solution of optimal filtering problem with respect to the MAP estimation using partial sums of the Edgeworth series

Abstract

Based on the continuous-time particle filter and approximation of the probability density by partial sums of the Edgeworth series, a statistical algorithm for the approximate solution of the optimal filtering problem with respect to the MAP estimation is formed. In the proposed algorithm, the mode of the conditional distribution for each unobservable state vector component is expressed in terms of conditional third, fourth, fifth or sixth order central moments. Numerical example is given.