Adaptive higher-order nonlinear FIR filter prediction of spatiotemporal chaotic time series

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 FIR (HONFIR) filter is proposed to perform prediction of spatiotemporal chaotic time series. The TDO algorithm is used to update the filter´s coefficients. A higher-order nonlinear adaptive filtering scheme is suggested in order to track the current chaotic trajectory by using the preceding predictive error for adjusting filter parameters rather than approximating the global or local map of the chaotic series. Experimental results show that this adaptive HONFIR filter can be successfully used to predict spatiotemporal chaotic time series generated by a globally coupled map (GCM), a two-way coupled map (TCM) and a single-way coupled map (SCM)