Prediction of chaotic time series by using adaptive higher-order nonlinearFourier 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 propos ed to make prediction of chaotic time series. The time domain orthogonal al gorithm is taken to update filter's coefficients. A higher order nonlinear adaptive filtering scheme is suggested in order to track current chaotic tr ajectory by using preceding predictive error for adjustign filter parameter s rather than approximating global or local map of chaotic series. Experime ntal 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 b y the HONFIR filter's degree of nonlinearity; (3) the adaptive prediction p erformance of the HONFIR filter is not confined by the Takens embedding dim ension; (4) the proposed HONFIR filter can have some anti-noise ability.