Weighting Matrices In Subspace Algorithms
Dietmar Bauer · 1998
In this paper we deal with the estimation of linear, time invariant, discrete time systems using so called subspace algorithms. The asymptotic distribution of the estimates is given for the case, when the subspace algorithm is performed using rather general weighting matrices. This result is an extension of the result obtained in [1]. The presented theory is complemented with a comparison of the asymptotic variance for two different weighting matrices and with a simulation study corresponding to the small sample properties. Keywords: Subspace Methods, Asymptotic Properties, Identification, Linear Systems. 1. INTRODUCTION The traditional approach to estimation of finite dimensional linear time invariant systems is to optimize a criterion function (such as the likelihood) over the set of all transfer functions of given degree. Fully automatic procedures have been derived (see e.g. [2]). These procedures are known to be consistent and asymptotically efficient under mild conditions on th...