Wiener system identification by weighted principal component analysis

International audienceWiener 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

Single minimum nonlinearity Wiener system identification by weighted principal component analysis

International audienceWiener system identification with a finite impulse response (FIR) model is investigated in this paper, focusing on the challenging case of non Gaussian input distribution and non monotonic nonlinearity. The proposed method assumes that the static nonlinear function of the Wiener system has a single minimum (or maximum), but does not assume any parametrization of the nonlinear function. Based on a modified principal component analysis (PCA), referred to as weighted PCA, the FIR coefficients of the Wiener system are estimated without estimating the nonlinear function of the Wiener system. The numerical computation cost is essentially equivalent to those of two standard PCA. Numerical examples in harsh practical conditions, with data generated by Wiener systems involving a discontinuous nonlinear function or an infinite impulse response, are presented to illustrate the robustness and effectiveness of the proposed method