A DFP-method-based second-order Volterra filter and its application to chaotic time series prediction

Abstract

In order to overcome problems caused by improper parameters selection when applying Least Mean Square (LMS), Normalized LMS (NLMS) or Recursive Least Square (RLS) algorithms to estimate coefficients of second-order Volterra filter, a Davidon-Fletcher-Powell (DFP)-method-based second-order Volterra filter (DFPSOVF) has been proposed, which is based on a posteriori error assumption and is characteristic of variable convergence factor. Recursive update formulation of the inverse of auto-correlation matrix and analysis of computational complexity for the DFPSOVF filter are presented. Simulations, which apply DFPSOVF filter to single step predictions for Lorenz chaotic time series in pure and different signal-to-noise ratio (SNR) as well as real measured chaotic temperature series, illustrate that the proposed filter can guarantee its stability and convergence and there havent divergence problems using LMS and NLMS algorithms.