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.

[1]  Hans Driessen,et al.  Particle filter based sensor selection in binary sensor networks , 2008, 2008 11th International Conference on Information Fusion.

[2]  Hans Driessen,et al.  MAP estimation in particle filter tracking , 2008 .

[3]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[4]  A. Doucet,et al.  Maximum a Posteriori Sequence Estimation Using Monte Carlo Particle Filters , 2001, Annals of the Institute of Statistical Mathematics.

[5]  Xiao-Li Hu,et al.  A Basic Convergence Result for Particle Filtering , 2008, IEEE Transactions on Signal Processing.

[6]  Hans Driessen,et al.  The mixed labeling problem in multi target particle filtering , 2007, 2007 10th International Conference on Information Fusion.

[7]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[8]  Oliver Stegle,et al.  An Introduction to Probabilistic modeling , 2010 .

[9]  Hans Driessen,et al.  Tracking closely spaced targets: Bayes outperformed by an approximation? , 2008, 2008 11th International Conference on Information Fusion.