Analysis of the maximum likelihood, total least squares and principal component approaches for frequency response function estimation

This paper considers the problem of estimation frequency response functions (FRFs) for a single-input single-output (SISO) system in the presence of additive noise on both input and output measurements. It demonstrates that principle component analysis (PCA) can be employed to solve such problems and demonstrates that this is equivalent to the methods based on total least squares (TLS). FRF estimation is also cast as a problem in statistical inference and the use of the principle of maximum likelihood (ML) leads to a novel development of a generalised TLS scheme. This analysis also provides a framework within which one can compute asymptotic expressions for the variance of such estimators.