ANALYSES, DEVELOPMENT, AND APPLICATIONS OF TLS ALGORITHMS IN FREQUENCY-DOMAIN SYSTEM-IDENTIFICATION

This paper gives an overview of frequency domain total least squares ( TLS) estimators for rational transfer function models of linear time-i nvariant multivariable systems. The statistical performance of the dif ferent approaches are analyzed through their equivalent cost functions . Both generalized and bootstrapped total least squares (GTLS and BTLS ) methods require the exact knowledge of the noise covariance matrix. The paper also studies the asymptotic (the number of data points going to infinity) behavior of the GTLS and BTLS estimators when the exact noise covariance matrix is replaced by the sample noise covariance mat rix obtained from a (small) number of independent data sets. Even if o nly two independent repeated observations are available, it is shown t hat the estimates are still strongly consistent without any increase i n the asymptotic uncertainty.