Errors-in-variables identification using maximum likelihood estimation in the frequency domain

This paper deals with the identification of errors-in-variables (EIV) models corrupted by additive and uncorrelated white Gaussian noises when the noise-free input is an arbitrary signal, not required to be periodic. In particular, a frequency domain maximum likelihood (ML) estimator is proposed and analyzed in some detail. As some other EIV estimators, this method assumes that the ratio of the noise variances is known. The estimation problem is formulated in the frequency domain. It is shown that the parameter estimates are consistent. An explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is derived. The possibility to effectively use lowpass filtered data by using only part of the frequency domain is discussed, analyzed and illustrated.