Identification of Wiener Systems With Clipped Observations

In this paper, we consider the parametric version of Wiener systems where both the linear and nonlinear parts are identified with clipped observations in the presence of internal and external noises. Also the static functions are allowed noninvertible. We propose a classification based support vector machine (SVM) and formulate the identification problem as a convex optimization. The solution to the optimization problem converges to the true parameters of the linear system if it is an finite-impulse-response (FIR) system, even though clipping reduces a great deal of information about the system characteristics. In identifying a Wiener system with a stable infinite-impulse-response (IIR) system, an FIR system is used to approximate it and the problem is converted to identifying the FIR system together with solving a set of nonlinear equations. This leads to biased estimates of parameters in the IIR system while the bias can be controlled by choosing the order of the approximated FIR system.