Asymptotic variance expressions for a frequency domain subspace based system identification algorithm

A frequency domain identification algorithm is analyzed. The algorithm identifies state-space models given samples of the frequency response function given at equidistant frequencies. A first order perturbation analysis is performed revealing an explicit expression of the resulting transfer function perturbation. Stochastic analysis show that the estimate is asymptotically (in data) normal distributed and an expression of the resulting variance is derived. Monte Carlo simulations illustrates the validity of the derived variance also for the nonasymptotic case and a comparison with the Cramer-Rao lower bound shows that the algorithm is suboptimal