非白高斯输入下辨识非线性系统的方法探讨

Study on Method for Identifying Nonlinear Systems Under Nonwhite Ganssian Inputs

辨识非线性系统的问题的研究有着重要的理论和实际意义.本文从实际应用的角度出发,发展了M.Sdetzen等的方法,把考虑问题的出发点建立在输入是非白高斯过程的基础之上。文中引入了推广Wiener G-泛函的概念,并推出了非线性系统在高斯输入下的推广Wiener G-泛函表示。从而把辨识非线性系统的问题归结为估计推广Wiener G-泛函的问题.本文又进一步导出了用多重Fourier分析的方法进行推广Wiener G-泛函的辨识公式.

The study on identifying nonlinear systems is of highly theore-tical and practical significance. In this paper, the authors have developed thetmethod by M. Schetzen et al. A new concept-the Extended Wiener G-func-fionals-is established that a nonlinea system can de characterized by thefunotionals in the case of nonwhite Gaussian inputs. Meanwhile, the methodof estimating the Extended Wiener G-functionals is formulated on the basisof Fourier analysis. This method has been verified by simulations.