On instrumental variable and total least squares approaches for identification of noisy systems

Many practical system identification problems can be formulated as linear regression problems. The parameter estimates can be computed using instrumental variables (IV) or total least squares (TLS) estimators, both of which have moderate computational complexity. In this work, explicit expressions for the asymptotic covariance matrix of the TLS estimates is derived and is shown to be same as that of the IV method. The accuracy of the parameter estimates for an errors-in-variables model using the above methods has been treated in particular, as standard analysis does not apply. The results obtained from the numerical simulations show that the practical behaviour of the estimators is well predicted by the theoretical results. We provide an explanation why for finite samples, the IV approach is found to be somewhat more robust than the TLS approach. On the other hand, the TLS approach has lower computational load than the IV method.