Asymptotic variances of subspace estimates

We provide new expressions for the asymptotic covariance of the estimated parameters (A, B, C, D) of a state space model obtained by some popular subspace identification method. The expressions, similar but simpler than the asymptotic covariance formulas which have so far been published in the literature, involve the inverses of the conditional covariance matrices Σ(xx|u⁺), Σ(u⁺u⁺|x) thus providing a direct link of possible ill-conditioning of the estimation problem with the asymptotic variance of the estimates. A study of ill-conditioning of subspace identification has been presented. The formulas can be applied to several subspace methods including N4SID, MOESP, CVA, etc