A nonlinear filter based on Fokker Planck equation and MCMC measurement updates

This paper presents a nonlinear filter based on the Fokker-Planck equation (FPE) for uncertainty propagation, coupled with a fast measurement update step. The measurement update is implemented as a function approximation performed over a Markov chain Monte Carlo (MCMC) sample of the unnormalized posterior obtained from the Bayes rule. MCMC sampling also results in fast computation of the normalization factor of the posterior, which is typically a computationally heavy step. A previously developed semianalytical meshless tool is employed to solve FPE for high dimensional systems in real time. Performance of the filter is studied for dynamical systems with 2 and 4 dimensional state spaces.