A novel two-stage estimation algorithm for nonlinear Hammerstein-Wiener systems from noisy input and output data

This paper investigates the identification problem of Hammerstein-Wiener errors-in-variable systems where the measurement errors of the system input and output are either temporally white or have relatively short memory size compared to the data length, but the corresponding variances are unknown. A two-stage algorithm is developed to estimate the unknown parameters with the first stage employing a modified bias-eliminating least squares algorithm, followed by a singular value decomposition in the second stage. Our proposed estimator is shown to be asymptotically unbiased. The simulation result shows the effectiveness of the proposed algorithm.