Prediction of chaotic time series by using adaptive higher-order nonlinear Fourier infrared filter

Based on the Volterra expansion of nonlinear dynamical system functions and the deterministic and nonlinear characterization of the chaotic signals,an adaptive higher-order nonlinear Fourier infrared (HONFIR) filter is proposed to make prediction of chaotic time series. The time domain orthogonal algorithm is taken to update filter's coefficients. A higher order nonlinear adaptive filtering scheme is suggested in order to track current chaotic trajectory by using preceding predictive error for adjustign filter parameters rather than approximating global or local map of chaotic series. Experimental results show that: (1) this adaptive HONFIR filter can be successfully used to predict hyperchaotic time series; (2)the prediction capacities of the HONFIR filter is related to its nonlinear function,but not determined by the HONFIR filter's degree of nonlinearity; (3) the adaptive prediction performance of the HONFIR filter is not confined by the Takens embedding dimension; (4) the proposed HONFIR filter can have some anti-noise ability.