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Efficient Computation of Cramer-Rao Bounds for the Transfer Functions of MIMO State-Space Systems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1998 (English)Report (Other academic)
Abstract [en]

The present contribution deals with the accuracy of the transfer function of state-space parametric models estimated under the prediction error identification framework. More precisely, we intend to propagate the Cramer-Rao bound usually available on the covariance matrix of the state-space parameter estimates to that of the coefficients of the corresponding input-to-output transfer function. A natural way to solve this problem is to take advantage of the Jacobian matrix of the state-space to transfer function transformation while applying Gauss' formula for evaluating the covariance of the transfer function coefficients. Here, we focus on the computational aspects of the evaluation of this Jacobian matrix. In doing so, we show that the most computationally efficient way to access this matrix is to evaluate it as the product of the Jacobian matrices associated to the two following transformations: firstly, from the original state-space model to a state-space representation where the state-feedback matrix is diagonal and, secondly, from this latter state-space representation to the model transfer function. Note that the elements of these two Jacobian matrices are evaluated analytically.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1998. , 16 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2024
Keyword [en]
Prediction error identification, MIMO Systems, Cramer-Rao bound, Matrix perturbation theory
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55640ISRN: LiTH-ISY-R-2024OAI: oai:DiVA.org:liu-55640DiVA: diva2:316434
Funder
Swedish Research Council
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-08

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Ljung, Lennart

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