Filtering, Prediction and Smoothing with Gaussian Sum Representation

Abstract The paper deals with the state estimation problem for discrete-time nonlinear non-Gaussian stochastic dynamic systems. A description of all random variables of the system by the Gaussian sum probability density functions is considered. This assumption enables to obtain an explicit exact or approximate solution of the three basic types of state estimation, i.e. prediction, filtering, and smoothing. Multi-step prediction and smoothing for nonlinear and/or non-Gaussian systems are newly presented. The stress is laid also on systematic presentation of the new and current results of an application of the Gaussian sums in the nonlinear state estimation problem.