Consistency analysis of subspace identification methods based on a linear regression approach

Knudsen, Torben

doi:10.1016/s0005-1098(00)00125-4

Cited by 80 publications

(40 citation statements)

References 17 publications

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“…Based on the unifying theorem, all these algorithms can be interpreted as a singular value decomposition of a weighted matrix. The statistical properties such as consistency and efficiency of them have been investigated recently (Bauer, 2003(Bauer, , 2005Bauer & Ljung, 2002;Chiuso & Picci, 2004;Gustafsson, 2002; ଁ A brief version of this paper was presented at the 13th IFAC Symposium on System Identification, August 27, 2003, Rotterdam, Jansson & Wahlberg, 1998;Knudsen, 2001;Larimore, 1996). All these variants are shown to be generically consistent.…”

Section: Introductionmentioning

confidence: 99%

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A novel subspace identification approach with enforced causal models

2005

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Subspace identication methods (SIMs) for estimating state-space models have been proven to be very useful and numerically ecient. They exist in several variants, but have one feature in common: as a rst step, a collection of high-order ARX models are estimated from vectorized inputoutput 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 coecients 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 the 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 poles. AbstractSubspace 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. ᭧

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Section: Introductionmentioning

confidence: 99%

“…First of all, we start with the analysis of existing subspace formulation using the linear regression formulation (Jansson & Wahlberg, 1998;Knudsen, 2001). This means that essentially several ARX models are estimated directly from data with different prediction intervals.…”

Section: Introductionmentioning

confidence: 99%

A novel subspace identification approach with enforced causal models

2005

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“…With the analysis of existing subspace formulation using the linear regression formulation (Jansson and Wahlberg, 1996;Jansson and Wahlberg, 1998;Knudsen, 2001), we reveal that the typical SIM algorithms actually use non-parsimonious model formulation, with extra terms in the model that appear to be non-causal. These terms, although conveniently included for performing subspace projection, are the causes for inflated variance in the estimates and partially responsible for the loss of closed-loop identifiability.…”

Section: Introductionmentioning

confidence: 99%

Closed-loop subspace identification with innovation estimation

Qin

Ljung

2003

IFAC Proceedings Volumes

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Most subspace identification algorithms are not applicable to closedloop identification because they require future input to be uncorrelated with past innovation. In this paper, we propose a new subspace identification method that remove this requirement by using a parsimonious model formulation with innovation estimation. A simulation example is included to show the effectiveness of the proposed method.

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“…It is rather brief, for details and proofs please refer to (Knudsen, 2001). There are different theoretical frameworks for subspace identification.…”

Section: Consistent Estimate Of the Deterministic Partmentioning

confidence: 99%

“…Recently, consistency for the whole deterministic part has been established under weak conditions (Bauer and Jansson, 2000;Knudsen, 2001). Unfortunately, similar good methods for the stochastic part under these weak conditions are still missing.…”

Section: Introductionmentioning

confidence: 99%