Nonlinear Filter Based on the Fokker-Planck Equation

This paper presents a nonlinear filter based on the Fokker-Planck equation for uncertainty propagation coupled with a fast measurement update step. The measurement update is implemented as a function approximation performed on a Markov chain Monte Carlo sample of the unnormalized posterior obtained from the Bayes rule. Markov chain Monte Carlo sampling also results in fast computation of the normalization constant of the posterior, which is typically a computationally heavy step. For the propagation step, a previously developed semianalytical meshless tool is employed to solve the Fokker-Planck equation for high-dimensional systems in real time. Performance of the filter is studied for dynamical systems with two-, three-, and four-dimensional state spaces.