Abstract: 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 predic tion of chaotic time series.The time domain orthogonal algorithm is taken to upd ate filter's coefficients.A higher-order nonlinear adaptive filtering scheme is suggested in order to track current chaotic trajectory by using preceding predic tive error for adjustign filter parameters rather than approximating global or l ocal map of chaotic series.Experimental results show that:(1)this adaptive HONFI R filter can be successfully used to predict hyperchaotic time series;(2)the pre diction 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 pr ediction performance of the HONFIR filter is not confined by the Takens embeddin g dimension;(4)the proposed HONFIR filter can have some anti-noise ability.

Keywords: 
• chaos /
• nonlinear model /
• filter