Estimating the Asymptotic Variance of Closed Loop Subspace Estimators

Subspace identification for closed loop systems has been recently studied by several authors. Recent results are available which express the asymptotic variance of the estimated parameters (and hence of any system invariant) as a function of the “true” underlying system parameters and of certain conditional covariance matrices. When it comes to using these formulas in practice one is faced with the problem of computing an estimator for the variance from input-output data alone. In this paper we discuss this problem, we propose an algorithm which computes an estimate of the variance from data alone and we show, through some simple simulation examples, how this estimate behaves as compared both to the “true” asymptotic variance and to its Monte Carlo estimate.