Robust recursive estimation for linear systems with non-Gaussian state and measurement noises

In many applications we have to deal with densities which are highly non-Gaussian or which may have Gaussian shape in the middle but have potent deviations in the tails. To fight against this deviation, we consider Bayesian estimation in the case of non-Gaussian state and measurement noises. The robust estimation problem for linear discrete-time systems is considered here. The non-Gaussian noises are modeled as a mixture. We present a robust recursive estimation model that is an approximate minimum variance estimator with a maximum a posteriori (MAP) decision rule for determining the noise sequence distribution.<>