AN EFFICIENT MESH-FREE IMPLICIT FILTER FOR NONLINEAR FILTERING PROBLEMS

摘要

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.