Nonlinear adaptive prediction of chaotic time series with a reduced parameter nonlinear adaptive filter

Based on the deterministic and nonlinear characterization of the chaotic si gnals, a new reduced parameter nonlinear adaptive filter is proposed to mak e adaptive predictions of chaotic time series. The sigmoid function is intr oduced to nonlinear predictive filter for reducing unknown parameters of th e second-order Volterra filters. A reduced parameter nonlinear adaptive fil tering prediction scheme is suggested in order to track current chaotic tra jectory by using precedent predictive error for adjusting filter parameters rather than approximating global or local map of chaotic series. Experimen tal results show that this reduced parameter nonlinear adaptive filter, whi ch is only trained with 50 samples and 20 iterations, can be successfully u sed to make one-step and multi-step predictions of chaotic time series.