Approximate Bayesian approach to non-Gaussian estimation in linear model with dependent state and noise vectors

An approach to the design of non-Gaussian filters which retain the computationally attractive recursive structure of Kalman filters and can approximate exactly a minimum variance estimate was successfully proposed and used by Marsreliez and Martin (1977) to construct different non-Gaussian (and robust) filters under independence of state and noise vectors. In this paper the authors extend the technique to solve the estimation problem with dependent state and noise vectors when both of them may be non-Gaussian simultaneously. Application to design of different optimal (and stable) estimation algorithms is illustrated