Asymptotic Variance Analysis of Subspace Identification Methods

Abstract¶

The class of subspace algorithms for system identification is an interesting complement to the maximum likelihood or prediction error methods, especially for multivariable systems. The statistical analysis of the subspace methods is difficult since the estimates depend on the data in a rather complicated manner. Previous results include proofs of generic consistency and asymptotic normality of the estimates. However, no explicit transparent expression for the covariance matrix of the limiting distribution has so far been reported because of the aforementioned difficulties. The main objective of this paper is to provide a methodology that simplifies the asymptotic analysis of subspace based estimation algorithms. The basic idea is illustrated by deriving the asymptotic covariance matrix corresponding to the estimates of the state-space matrices or the transfer function estimate of a quite general subspace algorithm.

Summary¶

Provides a methodology for deriving explicit asymptotic covariance expressions for estimates produced by subspace identification algorithms. The paper helps bridge practical subspace methods and statistical efficiency analysis, especially for multivariable state-space and transfer-function estimation.

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