  In this paper, we propose a meshfree approximation method for the implicit
filter developed in [2], 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 meshfree 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 meshfree interpolation method. Numerical experiments show the
effectiveness and efficiency of our algorithm.
