Wiener系统辨识中有限阶次的渐近性分析

在白噪声和有色噪声激励下,分别推导出Wiener系统线性部分的渐近方差式.在有色噪声激励下,添加对噪声模型的渐近分析.利用由正交基构成的生成核函数替换模型阶数,得到的两渐近方差式能更精确地接近于对应的真实采样值.根据渐近方差矩阵,建立以输入功率谱为变量的优化问题.通过求解带约束条件的优化问题得到Wiener系统中最优输入信号的功率谱密度.最后用仿真算例验证本文方法的有效性.

Accuracy Analysis of Finite Model Order Estimation in Wiener System Identification

The linear part's asymptotic covariance matrix expressions of the Wiener system excited by white and colored noise were derived. The asymptotic analysis for noise model, which is excited by colored noise, was added. It is found that, when the model order is replaced by some reproducing kernel function constructed by a group of orthonormal basis functions, above derived two asymptotic covariance matrix expressions could be appropriate to their true sample values, respectively. Thus, the optimization could be considered as the function of input power density. By solving this optimization problem with some constrained conditions, the optimal input signal spectrum for Wiener system could be obtained. Finally, the example simulation confirms the efficiency of proposed strategy.