On the identification of Wiener systems with polynomial nonlinearity

In this paper we introduce a new method for Wiener system identification that relies on the data collected on two separate experiments. In the first experiment, the system is excited with a sine signal at fixed frequency and phase shift. Using the steady state response of the system, we estimate the static nonlinearity, which is assumed to be a polynomial. In the second experiment, the system is fed with a persistently exciting input, which allows to identify the linear time-invariant block composing the Wiener structure. We show that the estimation of the static nonlinearity reduces to the solution of a least squares problem, and we provide an expression for the asymptotic variance of the estimated polynomial coefficients. The effectiveness of the method is demonstrated through numerical experiments.