Particle Filter for State and Unknown Input Estimation of Chaotic Systems

Chaotic systems exhibit highly nonlinear, complex and unpredictable behaviors. Thereby, these systems have received much attention in a variety of fields over the past few decades. In this paper we develop a particle filter algorithm to solve the problem of chaotic state and unknown input estimation from arbitrarily nonlinear time series. Thus, even if there exist Gaussian or non-Gaussian noise in chaotic maps, not only the chaotic states can be estimated by the proposed particle filter but also the unknown inputs. A computer simulation is conducted on the famous Holmes map to demonstrate the effectiveness and the high performances of the proposed estimation approach.