Computational suboptimal filter for a class of Wiener-Poisson driven stochastic processes

Abstract

The minimum mean square estimate (MMSE) for a stochastic process driven simultaneously by Wiener and Poisson processes is characterized by an infinite number of stochastic differential equations (even in the simplest linear case), and so is not practically implementable. In this article, a practical approximation to the solution is developed in terms of a computationally suboptimal filter for the estimation problem. Basically, it detects and estimates the Poisson driving process using a Maximum A Posteriori (MAP) criterion, and then reconstructs the entire system state using MMSE applied to a system approximating the original one