On the state estimation of chaotic systems by a particle filter and an extended Kalman filter

This paper addresses a comparison of performances between the particle filter (PF) and the extended Kalman filter (EKF) for the discrete-time state reconstruction of chaotic systems. In fact, the extended Kalman filter and the particle filter are two widely used methods for solving nonlinear state estimation problems. The EKF is a sub-optimal approach, which implements a Kalman filter for a system dynamics that results from the linearization of the original nonlinear filter dynamics around the previous state estimates. However, the aforementioned filter has been defined on the assumption that both the process and sensor noises are Gaussian distributed. On the other hand, the particle filter is a more generalized scheme and does not require either of the noises to be Gaussian, as the posterior probabilities are represented by a set of randomly chosen weighted samples. This work aims to compare the performances of the EKF and the PF for the problem of chaotic state estimation from arbitrarily nonlinear time series. Through computer simulations performed on the Holmes-map nonlinear system, the efficiency of the two filters are tested.