A type of realizable, nonlinearfiltering algorithm, derived for dynamic systems involving non-white and white processes, is clearly superior to several other nonlinear flters.
Snmmary--This paper presents a modified approach to solve state estimation problems of nonlinear dynamic systems involving noise free, uncorrelated and correlated state and measurement noise processes. The basic approach makes use of the matrix minimum principle together with the Kolmogorov and Kushner's equations to minimize the error-variance, taken to be the estimation criterion. The filtering equations obtained for nonlinear systems with white noise process axe exact, but for non-white noise processes the results obtained are approximate.
For systems with polynomial or product types nonlinearities, the proposed algorithms can be evaluated without the need of approximation under the assumption that the estimator errors are Gaussian. Such an assumption is significantly different from the most commonly used assumption that the state is Ganssian. Simulation results obtained from the proposed filtering algorithms are compared to various other approximate nonlinear filters. The results indicate the superiority of the proposed filter over those of other filters investigated.