Numerical conditioning and asymptotic variance of subspace estimates

Abstract

New formulas for the asymptotic variance of the parameter estimates in subspace identification, show that the accuracy of the parameter estimates depends on certain indices of ‘near collinearity’ of the state and future input subspaces of the system to be identified. This complements the numerical conditioning analysis of subspace methods presented in the companion paper (On the ill-conditioning of subspace identification with inputs, Automatica, doi: 10.1016/j.automatica.2003.11.009).