Robust and Bayesian Subspace Identification

• Published in: IEEE transactions on automatic control Vol. 70; no. 2; pp. 1395 - 1401
• Main Author: Mesquita, Alexandre R.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bayes methods; Bayesian analysis; Bayesian estimation; Estimation; Estimators; Identification methods; Matrix decomposition; Noise; Noise level; Noise levels; Noise measurement; shrinkage estimators; Singular value decomposition; Subspace methods; subspace system identification; Subspaces; Variance
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3465560

Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of high-dimensional models, limited sample size, or high noise level. Common solutions in statistics to reduce the effect of variance are regularized estimators, shrinkage estimators, and Bayesian estimation. In the current work, we investigate the latter two solutions, which are relatively unexplored in subspace identification methods. Our experimental results, from a large random sample of system models, show that our proposed estimators reduce the median of estimation risks by 10% compared with traditional subspace methods. In the case of large measurement noise, this median estimation risk was reduced by 34%.