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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016013870
pages 19-33

AN EFFICIENT MESH-FREE IMPLICIT FILTER FOR NONLINEAR FILTERING PROBLEMS

Feng Bao
Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, One Bethel Valley Road, P.O. Box 2008, MS-6164, Oak Ridge, Tennessee 37831-6164, USA
Yanzhao Cao
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849; School of Mathematics, Sun Yat Sun University, China
Clayton G. Webster
Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, One Bethel Valley Road, P.O. Box 2008, MS-6164, Oak Ridge, Tennessee 37831-6164, USA
Guannan Zhang
Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, One Bethel Valley Road, P.O. Box 2008, MS-6164, Oak Ridge, Tennessee 37831-6164, USA

ABSTRACT

In this paper, we propose a mesh-free approximation method for the implicit filter developed in Bao et al., Commun. Comput. Phys., 16(2):382-402, 2014, which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the optimal filter over a deterministic state space grid and is developed from samples of the current state obtained by solving the state equation implicitly. The purpose of the mesh-free approximation is to improve the efficiency of the implicit filter in moderately high-dimensional problems. The construction of the algorithm includes generation of random state space points and a mesh-free interpolation method. Numerical experiments show the effectiveness and efficiency of our algorithm.