Blind Maximum Likelihood identification of Wiener systems with measurement noise

This paper is concerned with the maximum likelihood identification of discrete-time Wiener systems from noisy output measurements only (blind identification). It extends the prior developed methods for the blind identification of Wiener (and Hammerstein) systems in a noiseless situation, which, applied to noise-corrupted (output) data unavoidably results in biased estimates. Due to the presence of an extremely high dimensional integral in the expression of the likelihood function, the problem seems very hard at the first glance. The 'curse of dimensionality' is avoided by approximating this integral by Laplace's method for integrals. It turns out that the method works successfully.