Abstract: Based on the deterministic and nonlinear characterization of the chaotic signals, a new reduced parameter nonlinear adaptive filter is proposed to make adaptive predictions of chaotic time series. The sigmoid function is introduced to nonlinear predictive filter for reducing unknown parameters of the second-order Volterra filters. A reduced parameter nonlinear adaptive filtering prediction schemeis suggested in order to track current chaotic trajectory by using precedent predictive error for adjusting filter parameters rather than approximating global o r local map of chaotic series. Experimental results show that this reduced param eter nonlinear adaptive filter, which is only trained with 50 samples and 20 ite rations, can be successfully used to make one-step and multi-step predictions of chaotic time series.

Keywords: 
• chaos /
• nonlinear adaptive prediction /
• reduced parameter nonlinear filter /
• adapti ve algorithms