A novel second-order DFP-based volterra filter and its applications to chaotic time series prediction

A novel adaptive second-order Volterra filter based on Davidon-Fletcher-Powell (DFPSOVF) technique has been proposed. Recursive update formula of the inverse estimate of auto-correlation matrix in the DFPSOVF filter is presented. In order to avoid some problems caused by using LMS, NLMS or RLS algorithms, a variable convergence factor based on a posteriori error assumption, which can change with input signal changes in real time, is employed. Simulations, which apply the DFPSOVF filter to single step predictions for Rössler chaotic series and compare its results with those using LMS and NLMS algorithms to SOVF filter, respectively, illustrate that the proposed filter can always guarantee its stability and convergence and there haven´t divergence problems caused by selecting inappropriate parameters with LMS and NLMS algorithms. Key Words: Volterra filter, Davidon-Fletcher-Powell, chaotic time series, prediction, variable convergence factor.