Direct identification of the linear block in Wiener system

In the paper, the linear component of the Wiener system is identified under poor knowledge about the static subsystem nonlinearity. Unlike most of other identification methods, the proposed approach allows to decompose the problem of the Wiener system identification into two simpler subproblems. The considered methodology is based on the observation that the impulse response of the dynamic subsystem is proportional to the multiple input single output mapping, directly related to the considered system. Although derivation of the method involves gradient and kernel least squares techniques, the resulting algorithm possesses explicit form and does not utilize any difficult computational procedures. The consistency of the method is proved, and sufficient conditions for algorithm's bandwidth selection are formulated. Practical aspects of the approach are discussed, and applicability of the method for small and moderate number of observations is examined numerically. Copyright (c) 2015 John Wiley & Sons, Ltd.