Least-squares state estimation of systems with state-dependent observation noise (Q1059039)

The least-squares state estimation problem is considered for continuous- time systems with state-dependent observation noise. The observation is decomposed into two parts, i.e. an additive white Gaussian part and a noise-free part, and it is shown that the conditional state distribution, given the observation, is singular with respect to the a priori state distribution. A Bayes-type formula for the optimal filter and an easily applicable approximate filtering formula are obtained.