Rank reduction and volume minimization approach to state-space subspace system identification

Authors:
Berkant Savas;David Lindgren
Affiliations:
Department of Mathematics, Linköping University, Linköping, Sweden;Department of Electrical Engineering, Linköping University, Linköping, Sweden
Venue:
Signal Processing - Special section: Distributed source coding
Year:
2006

Citing 7
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Abstract

In this paper we consider the reduced rank regression problem minrank L=n,L3 det(Yα - LPβ - L3Uα)(Yα - LPβ - L3Uα)T solved by maximum-likelihood-inspired state-space subspace system identification algorithms. We conclude that the determinant criterion is, due to potential rank-deficiencies, not general enough to handle all problem instances. The main part of the paper analyzes the structure of the reduced rank minimization problem and identifies signal properties in terms of geometrical concepts. A more general minimization criterion is considered, rank reduction followed by volume minimization. A numerically sound algorithm for minimizing this criterion is presented and validated on both simulated and experimental data.