Precomputed-gain nonlinear filters for nonlinear systems with state-dependent noise

Two precomputed-gain nonlinear filters are proposed for estimating the states of nonlinear systems corrupted by both external and parametric noises and subjected to linear noisy measurement systems. The exact nonlinear filters are first formulated through the Kolmogorov and Kushner's equations. The concepts of equivalent external excitation combined with statistical linearization or local linearization are then employed to derive two precomputed-gain nonlinear filters. The resulting filters are shown to have the same structure as that of extended Kalman filter but filter-gain histories can be precomputed. Simulation results obtained from the proposed nonlinear filters and the corresponding linear filters for Duffing-type stochastic systems are compared through Monte Carlo techniques.