Optimal state estimation for uncertain, time varying systems with non-Gaussian initial state

The problem of state estimation for partially unknown, time-varying, linear systems with non-Gaussian initial conditions is addressed. It is shown that the optimal estimator for this problem is an adaptive Lainiotis (1989) filter with nonlinear Lainiotis filters for non-Gaussian initial conditions as elemental filters. Closed-form solutions for several explicit cases of the initial state PDFs are given. Simulation experiments show the superiority of the proposed algorithm over an adaptive Lainiotis filter with Kalman filters as elemental filters