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Computational Suboptimal Filter for a Class of Wiener-Poisson Driven Stochastic Processes

Research paper by Raghib M. abu-Saris, Floyd B. Hanson

Indexed on: 01 Jul '97Published on: 01 Jul '97Published in: Dynamics and Control



Abstract

The minimum mean square estimate (MMSE) for a stochastic process drivensimultaneously by Wiener and Poisson processes is characterized by aninfinite number of stochastic differential equations (even in the simplestlinear case), and so is not practically implementable. In this article, apractical approximation to the solution is developed in terms of acomputationally suboptimal filter for the estimation problem. Basically, itdetects and estimates the Poisson driving process using a Maximum APosteriori (MAP) criterion, and then reconstructs the entire system stateusing MMSE applied to a system approximating the original one.