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). Prior work has been devoted to the blind identification of Wiener and Hammerstein systems in a noiseless situation. Applying these methods to output-noise corrupted data unavoidably results in biased estimates. Fortunately, the bias could be proven to be small for high signal-to-noise ratios. Nevertheless, it is clearly desirable to have a method which is consistent at any noise level. Therefore, this paper extends the existing method, by assuming a second (independent) white Gaussian noise source added to the output before measurement. Due to the presence of an extremely high dimensional integral in the expression of the likelihood function, the problem is very hard in practice. The `curse of dimensionality' is avoided by approximating this integral by Laplace's method for integrals. The paper includes the illustration of the method on a simulation example, showing that the bias is possibly lower than in the method that ignores the presence of noise.