Design of Efficient Point-Mass Filter for Linear and Nonlinear Dynamic Models

This letter deals with the state estimation of nonlinear stochastic dynamic systems in the Bayesian framework. The emphasis is laid on the numerical solution to the Chapman-Kolmogorov equation by the widely-used point-mass method. It is shown, that the standard prediction step of the point-mass filter can be decomposed into two parts;
advection
and
diffusion
solution. This decomposition allows application of the fast Fourier transform, which
speeds up
the prediction step by several orders of magnitude making the point-mass filter attractive even for higher dimensional models. The proposed efficient point-mass filter is illustrated in a numerical simulation with available source codes and is compared with the particle filter.