Variance reduction for particle filters of systems with time scale separation

Authors:
Dror Givan;Panagiotis Stinis;Jonathan Weare
Affiliations:
Program in Applied and Computational Mathematics and the Department of Chemical Engineering, Princeton University, Princeton, NJ and Lawrence Berkeley National Laboratory, Department of Mathematic ...;Mathematics Department, University of Minnesota, Minneapolis, MN and Lawrence Berkeley National Laboratory, Department of Mathematics, University of California, Berkeley, CA;Courant Institute of Mathematical Sciences, New York University, New York, NY and Lawrence Berkeley National Laboratory, Department of Mathematics, University of California, Berkeley, CA
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

We present a particle filter construction for a system that exhibits time-scale separation. The separation of time scales aHows two simplifications that we exploit: 1) the use of the averaging principle for the dimensional reduction of the dynamics for each particle during the prediction step and 2) the factorization of the transition probability for the Rao-Blackwellization of the update step. The resulting particle filter is faster and has smaller variance than the particle filter based on the original system. The method is tested on a multiscaIe stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions.