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Particle Filter Based MAP estimation for jump Markov systems

Summary: Particle Filter Based MAP estimation for jump
Markov systems
Yvo Boers
and Hans Driessen
Thales Nederland B.V.
Arunabha Bagchi
Department of Applied Mathematics
University of Twente
In this paper we will provide methods to calculate different types of Maximum A Posteriori (MAP) estimators
for jump Markov systems. The MAP estimators that will be provided are calculated on the basis of a running
Particle Filter (PF). Furthermore, we will provide convergence results for these approximate, or particle based
estimators. We will show that the approximate estimators convergence in distribution to the true MAP estimator
values. Additionally, we will provide an example based on tracking closely spaced objects in a binary sensor
network to illustrate some of the results and their applicability.
1 Introduction
The focus of this paper is point estimators for stochastic dynamical systems. The application area of this topic is
naturally very wide. The scope covers all sorts of fields, such as engineering or finance. In fact, any problem that
can be formulated as a dynamical system on which measurements are performed falls in the application area. The
process of inferring information on the state of such a system based on measurements is called filtering.


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering