Wiener system identification by weighted principal component analysis

Wiener system identification is investigated in this paper with a finite impulse response (FIR) model of the linear subsystem. Under the assumption of Gaussian input distribution, this paper mainly aims at addressing a deficiency of the well-known correlation-based method for Wiener system identification: it fails when the nonlinearity of the Wiener system is an even function. This method is, in the considered Gaussian input case, equivalent to the best linear approximation (BLA), which exhibits the same deficiency. The method proposed in this paper is based on a weighted principal component analysis (wPCA). Its consistency is proved in this paper for Wiener systems with either even or non even nonlinearities. Its computational cost is almost the same as that of a standard PCA. Numerical examples are presented to compare the proposed wPCA-based method with the correlation-based method for different Wiener systems with nonlinearities more or less close to an even function.