Point estimation for jump Markov systems: Various MAP estimators

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 values of the stochastic variables. Additionally, we will provide an example based on tracking closely spaced objects in a binary sensor network to illustrate some of the results and show their applicability.