基于DFP的二阶Volterra模型及其对Rossler混沌序列的预测

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

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Rssler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.

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 in-verse autocorrelation matrix estimation ,role of τ（ n ） of DFPSOVF model are studied .Simulations ,which apply DFPSOVF model to single step predictions for R？ssler chaotic time series ,illustrate that the proposed algorithm can guarantee its stability and conver-gence and there haven’t divergence problems using LMS and NLMS algorithms .