Reconstruction of chaotic dynamic systems using non-linear filters

This article proposes a methodology based on sequential Monte Carlo techniques that permits state estimate of chaotic dynamic systems with Gaussian errors and non-linear dynamics in real time. Such systems arise naturally in many varied applications. We illustrate the methodology through the reconstruction of the states of the chaotic maps of Henon, Ikeda, Tinkerbell and Lorenz, using four different algorithms, namely, generic particle filter (GPF), particle filter with re -sampling (PFR), unscented Kalman filter (UKF) and an unscented particle filter (UPF). The performance of the filters was evaluated in terms of the empirical standard deviation and the computation times showing little variance among the estimated errors and a rapid execution of the algorithms.