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Rank reduction and volume minimization approach to state-space subspace system identification. (English) Zbl 1172.93400
Summary: We consider the reduced rank regression problem
\[ \underset {\text{rank}\bar L = n, L_3} \min \det (Y_{\alpha} - \bar LP_{\beta} - L_3 U_{\alpha})(Y_{\alpha} - \bar L P_{\beta} - L_3 U_{\alpha})^T \]
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.

MSC:
93E10 Estimation and detection in stochastic control theory
62G08 Nonparametric regression and quantile regression
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