A novel subspace identification approach with enforced causal models

S. Joe QIN*, Weilu LIN, Lennart LJUNG

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

87 Citations (Scopus)


Subspace identification methods (SIMs) for estimating state-space models have been proven to be very useful and numerically efficient. They exist in several variants, but all have one feature in common: as a first step, a collection of high-order ARX models are estimated from vectorized input-output data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coefficients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed-loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices (A, B, C, D) and Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles. © 2005 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)2043-2053
Number of pages11
Issue number12
Early online date29 Sept 2005
Publication statusPublished - Dec 2005
Externally publishedYes

Bibliographical note

Financial support from Natural Science Foundation under CTS-9985074, National Science Foundation of China under an Overseas Young Investigator Award (60228001), a Faculty Research Assignment grant from University of Texas, and Weyerhaeuser Company through sponsorship of the Texas–Wisconsin Modeling and Control Consortium are gratefully acknowledged.


  • Causal model
  • Subspace identification
  • Variance analysis


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