Incorporating Best Linear Approximation within LS-SVM-Based Hammerstein System Identification

Hammerstein systems represent the coupling of a static nonlinearity and a linear time invariant (LTI) system. The identification problem of such systems has been a focus of research during a long time as it is not a trivial task. In this paper a methodology for identifying Hammerstein systems is proposed. To achieve this, a combination of two powerful techniques is used, namely, we combine Least Squares Support Vector Machines (LS-SVM) and the Best Linear Approximation (BLA). First, an approximation to the LTI block is obtained through the BLA method. Then, the estimated coefficients of the transfer function from the LTI block are included in a LS-SVM formulation for modeling the system. The results indicate that a good estimation of the underlying nonlinear system can be obtained up to a scaling factor.