A nonlinear filter based on Fokker-Planck equation

In this paper, a nonlinear filter based on Fokker-Planck equation (FPE) is presented for applications involving long time durations in between measurement updates. A previously developed semianalytical meshless algorithm is used to obtain the transient FPE response of nonlinear systems in near real time. Use of eigenfunctions of the discretized FP operator as basis functions causes equation error in FPE to reduce with time, implying that the algorithm is especially suited to problems with sparse measurements. The measurement update is implemented via weak form of the Bayes rule. An alternative based on function approximation of the posterior density is suggested to speed up this process. Filtering examples for up to 4-state systems are considered and compared with the extended Kalman filter (EKF).