Combined instrumental variable and subspace fitting approach to parameter estimation of noisy input-output systems

The paper considers the problem of estimating the parameters of linear discrete-time systems from noise-corrupted input-output measurements, under fairly general conditions: the output and input noises may be auto-correlated and they may be cross-correlated as well. By using the instrumental-variable (IV) principle a covariance matrix is obtained, the singular vectors of which bear complete information on the parameters of the system under study. A weighted subspace fitting (WSF) procedure is then employed on the sample singular vectors to derive estimates of the parameters of the system. The combined IV-WSF method proposed in the present paper is noniterative and simple to use. Its large-sample statistical performance is analyzed in detail and the theoretical results so obtained are used to predict the behavior of the method in samples with practical lengths. Several numerical examples are included to show the agreement between the theoretically predicted and the empirically observed performances