Wiener系统中线性函数辨识的渐近性分析

Accuracy Analysis of linear Function Identification in Wiener System

针对Wiener系统中的两类未知参数以相互结合的形式出现在非线性函数中,通过预测误差法辨识此两类未知参数,进而确定Wiener系统中线性部分的系统对象模型的渐近方差矩阵形式。在白噪声激励的作用下,推导出Wiener系统中线性部分的渐近方差表达式。此渐近方差表达式中不包含有模型阶数的存在,其利用某个由正交基构成的生成核函数来替换原模型阶数,使得在已知某些先验信息知识的前提下,该渐近方差式能更精确地接近于各自对应的真实采样值。最后用仿真算例验证本文方法的有效性和可行性。

To two class unknown parameter vectors from Wiener system which were combined in nonlinear function,we can use prediction error method to identify these two class unknown parameter vectors and furthermore determine the asymptotic covariance matrix expressions of the system object model in Wiener system.In this paper,we derive the linear part＇s asymptotic covariance matrix expressions in white noise.The model orders do not exist in these two asymptotic covariance forms.And we use some reproducing kernel function constructed by a group of orthonormal basis functions to replace the model order.So when some priori information about the former system were known,these two asymptotic covariance matrix expressions can appropriate their true sample values accurately.Finally,the efficiency and possibility of the proposed strategy can be confirmed by the simulation example results.