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

Authors:
D. Bauer;M. Deistler;W. Scherrer
Affiliations:
Institut für Ökonometrie, Operations Research und Systemtheorie, Technische Universität Wien, Argentinierstr. 8/119, A-1040 Vienna, Austria;Institut für Ökonometrie, Operations Research und Systemtheorie, Technische Universität Wien, Argentinierstr. 8/119, A-1040 Vienna, Austria;Institut für Ökonometrie, Operations Research und Systemtheorie, Technische Universität Wien, Argentinierstr. 8/119, A-1040 Vienna, Austria
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

Asymptotic normality for a class of subspace algorithms, which estimate the state in a first step, is derived. Expressions for the asymptotic variance are given. Linear systems with unobserved white noise inputs are considered. A class of subspace estimates for the system matrices obtained by estimating the state in the first step is analyzed. The main result presented here states asymptotic normality of subspace estimates. In addition, a consistency result for the system matrix estimates is given. An algorithm to compute the asymptotic variances of the estimates is presented. In a final section the implications of the result are discussed.