基于DFP的二阶Volterra滤波器及其在混沌序列预测中的应用

为克服应用Least Mean Square（LMS），Normalized LMS（NLMS）或Recursive Least Square（RLS）算法估计二阶Volterra滤波器系数时参数选择不当引起的问题，提出了基于后验误差假设并具有可变收敛因子的Davidon-Fletcher-Powell（DFP）方法的二阶Volterra自适应滤波器（DFPSOVF）．给出参数估计算法中自相关逆矩阵估计的递归更新公式，并对算法的计算复杂度进行了分析．应用DFPSOVF滤波器对纯净和不同信噪比下的Lorenz混沌时间序列以及实际采集的具有混沌特性的温度时间序列进行单步预测，仿真表明其能够保证算法的稳定性和收敛性，不存在LMS算法和NLMS算法的发散问题．

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

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 haven＇t divergence problems using LMS and NLMS algorithms.