Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs

Linear systems with unobserved white noise inputs are considered. A class o f subspace estimates for the system matrices obtained by estimating the sta te in the first step is analyzed. The main result presented here states asy mptotic normality of subspace estimates. In addition, a consistency result for the system matrix estimates is given. An algorithm to compute the asymp totic variances of the estimates is presented. In a final section the impli cations of the result are discussed. (C) 1999 Elsevier Science Ltd. All rig hts reserved.