The nonlinear MMSE filter for partially observed systems driven by non-Gaussian white noise, with applications to failure estimation

The problem of estimating the state of a system subjected to jump inputs has been used as a model for several practical problems. This paper presents a rigorous derivation of the previously unknown minimum mean square error estimator for the state of such systems. The derivation is general enough to encompass a wide variety of non-Gaussian (as well as Gaussian) statistics for the input stochatic process.