Frequency domain subspace system identification using non-parametric noise models

In the general case of non-uniformly spaced frequency domain data and/or arbitrarily colored disturbing noise, the frequency domain subspace identification algorithms described by Mckelvey et al. (1996) and Van et al. (1996), are consistent only if the covariance matrix of the disturbing noise is known. This paper studies the asymptotic properties (strong convergence, convergence rate, asymptotic normality, strong consistency and loss in efficiency) of these algorithms when the true noise covariance matrix is replaced by the sample noise covariance matrix obtained from a small number of independent repeated experiments. As an additional result the strong convergence (in case of model errors), the convergence rate and the asymptotic normality of the subspace algorithms with known noise covariance matrix follows