Frequency-domain system identification using non-parametric noise models estimated from a small number of data sets (Q1362427)

The paper deals with nonparametric frequency-domain identification of a linear SISO system, where input-output measurements are disturbed with zero-mean Gaussian noise, independently distributed at different frequencies. In the method proposed, the exact weighting covariance matrices in the weighted least squares estimator are replaced by the sample counterparts. It is shown that the system can be identified using the sample means and sample covariance matrices calculated from a small number of independently repeated experiments, i.e. that the resulting parameter estimates are strongly consistent for an increasing number of data points in each experiment. The loss in efficiency, due to the poor quality of the sample variance, relative to the situation where the exact covariances of the disturbing noise are a priori known, is thoroughly examined, and the mean value and variance of the cost function at its global minimum are studied. Some illustrative examples, concerning the open-loop and closed-loop identification problems, are included.