%0 Journal Article
%A Bao, Feng
%A Cao, Yanzhao
%A Webster, Clayton G.
%A Zhang, Guannan
%D 2016
%I Begell House
%K nonlinear filtering, implicit algorithm, mesh-free approximation, Shepard's method
%N 1
%P 19-33
%R 10.1615/Int.J.UncertaintyQuantification.2016013870
%T AN EFFICIENT MESH-FREE IMPLICIT FILTER FOR NONLINEAR FILTERING PROBLEMS
%U http://dl.begellhouse.com/journals/52034eb04b657aea,6695b1fe0a01e538,34cec7c24084be58.html
%V 6
%X 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.
%8 2016-08-16