基于DFP的二阶Volterra模型及其对Rössler混沌序列的预测

为克服最小二乘法或归一化最小二乘法在二阶Volterra建模时参数选择不当引起的问题，在最小二乘法基础上，应用一种基于后验误差假设的可变收敛因子技术，构建了一种基于Davidon-Fletcher-Powell算法的二阶Volterra模型（DFPSOVF）.给出参数估计中自相关逆矩阵估计的递归更新公式，并对其正定性、有界性和τ（n）的作用进行了研究.将DFPSOVF模型应用于Rössler混沌序列的单步预测，仿真结果表明其能够保证算法的稳定性和收敛性，不存在最小二乘法和归一化最小二乘法的发散问题.

A DFP-Based Second-Order Volterra Model with Applications to Rössler Chaotic Series Prediction

To overcome problems caused by improper parameters selection when least mean square(LMS)or normalized LMS(NLMS)method is apphied to model second-order Volterra,based on the LMS method,a novel Davidon-Fletcher-Powell(DFP)-method-based second-order Volterra filter(DFPSOVF)was proposed,which is based on a posteriori error assumption and is characteristic of a variable convergence factor.Recursive update formulation positive definiteness and bounded property of the inverse autocorrelation matrix estimation,role of τ(n) of DFPSOVF model are studied.Simulations,which apply DFPSOVF model to single step predictions for Rössler chaotic time series,illustrate that the proposed algorithm can guarantee its stability and convergence and there haven't divergence problems using LMS and NLMS algorithms.