Analyses, Development, and Applications of TLS Algorithms in Frequency Domain System Identification

Abstract

This paper gives an overview of frequency domain total least squares (TLS) estimators for rational transfer function models of linear time-invariant multivariable systems. The statistical performance of the different 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 matrix obtained from a (small) number of independent data sets. Even if only two independent repeated observations are available, it is shown that the estimates are still strongly consistent without any increase in the asymptotic uncertainty.