System identification: theory for the user
System identification: theory for the user
IEEE Transactions on Signal Processing
Identification of systems containing linear dynamic and static nonlinear elements
Automatica (Journal of IFAC)
Least-squares LTI approximation of nonlinear systems and quasistationarity analysis
Automatica (Journal of IFAC)
Linear approximations of nonlinear FIR systems for separable input processes
Automatica (Journal of IFAC)
Identification of linear systems with nonlinear distortions
Automatica (Journal of IFAC)
Initial estimates of the linear subsystems of Wiener-Hammerstein models
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
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This paper consists of two parts. In the first, more theoretic part, two Wiener systems driven by the same Gaussian noise excitation are considered. For each of these systems, the best linear approximation (BLA) of the output (in mean square sense) is calculated, and the residuals, defined as the difference between the actual output and the linearly simulated output is considered for both outputs. The paper is focused on the study of the linear relations that exist between these residuals. Explicit expressions are given as a function of the dynamic blocks of both systems, generalizing earlier results obtained by Brillinger [Brillinger, D. R. (1977). The identification of a particular nonlinear time series system. Biometrika, 64(3), 509-515] and Billings and Fakhouri [Billings, S. A., & Fakhouri, S. Y. (1982). Identification of systems containing linear dynamic and static nonlinear elements. Automatica, 18(1), 15-26]. Compared to these earlier results, a much wider class of static nonlinear blocks is allowed, and the efficiency of the estimate of the linear approximation between the residuals is considerably improved. In the second, more practical, part of the paper, this new theoretical result is used to generate initial estimates for the transfer function of the dynamic blocks of a Wiener-Hammerstein system. This method is illustrated on experimental data.