含过程噪声Wiener系统的递推两阶段参数估计

Recursive Two-stage Parameter Estimation for a Wiener System with a Process Noise

Wiener系统属模块化非线性系统,由一个线性动态模块串联一个非线性静态模块组成,因其结构简单、实用性强,在非线性系统建模中得到广泛应用.最小二乘算法估计过程噪声扰动的Wiener系统时会带有偏估计.为了获得无偏估计,本文提出了一种递推两阶段参数估计算法.首先用FIR函数和多项式函数分别逼近系统的动态传递函数和静态反函数,随后运用递推最小二乘算法和递推辅助变量算法进行参数估计,其中的辅助变量由第一阶段的辨识结果计算得到.研究结果表明,提出的递推两阶段参数估计算法可以得到待辨识Wiener系统的无偏估计,数值仿真验证了该算法的有效性.

For the Wiener system with process noise,the estimate obtained by least-squares algorithm was biased.To obtain unbiased estimation,a recursive two-stage parameter estimation algorithm was proposed.Firstly,the FIR function and the polynomial function were used to approximate the dynamic transfer function and the static inverse function of the Wiener system respectively.Then,the recursive least squares algorithm and the recursive instrumental variable algorithm are used to estimate the parameters.The instrumental variables were calculated from the identification results of the first stage.The theoretical analysis shows that the proposed recursive two-stage parameter estimation algorithm can give unbiased estimate.The algorithm was verified by a numerical example.