Wiener System Identification using Best Linear Approximation within the LS-SVM framework

Wiener systems represent a linear time invariant (LTI) system followed by a static nonlinearity. The identification of these systems has been a research problem for a long time as it is not a trivial task. A new methodology for identifying Wiener systems is proposed in this paper. The proposed method is a combination of well known techniques, namely the Best Linear Approximation (BLA) from the system identification field and Least Squares Support Vector Machines (LS-SVM). Through the BLA a non-parametric approximation to the LTI block is obtained. Next, the coefficients of the transfer function from the LTI block are estimated. Finally the calculated coefficients are included in an LS-SVM formulation for modeling the system. The results indicate that a good estimation of the underlying linear and nonlinear parts can be obtained up to a scaling factor.