Identification of a Wiener System via Semidefinite Programming

Abstract

This paper presents a new method for the identification of Wiener systems in the presence of output noise. The Wiener system identification problem is formulated as a convex Semidefinite Programming (SDP) problem by constraining a finite dimensional time dependency between signals. The main contribution of this paper is that the proposed method is robust to output noise and neither the Gaussian assumption of the input signal nor the invertibility of the static nonlinearity is necessary. The main assumption used in this paper is that static nonlinearity is monotonically non-decreasing. In the proposed identification method, the linear dynamical system is parametrized as a Finite Impulse Response (FIR) model and a nonparametric identification method is used to create the noise free output signal. Because both the intermediate signal and the noise free output signal are unknown, an over-parametrization technique is used. Once parameters are estimated, a Singular Value Decomposition (SVD) is used to separate the linear system parameters and the noise free output signal. The proposed identification method is applied to simulation data from a Wiener system. The effectiveness and accuracy of the proposed method are verified via numerical simulations.