GTLS algorithms in the frequency domain system identification using noise information out of a finite number of repeated independent realizations

This paper gives an overview of the stochastic properties of frequency domain total least squares estimators for rational transfer function models of linear time-invariant systems. The generalized total least squares (GTLS) and the bootstrapped total least squares (BTLS) methods require the exact knowledge of the noise covariance matrix. The paper studies the asymptotic behavior for the GTLS and the BTLS estimator when the covariance matrix is replaced by the sample covariance matrix obtained from a small number of independent repeated observations. The GTLS estimates remain consistent and do not loose any asymptotic efficiency when replacing the exact covariance matrix with the sample covariance matrix. The BTLS estimator, whose efficiency approaches the maximum likelihood efficiency, needs to be adapted slightly to produce consistent estimates.