Accuracy analysis of linear function identification in Wiener system

Abstract

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.