- Title
- Variance error quantifications that are exact for finite-model order
- Creator
- Ninness, Brett; Hjalmarsson, Hakan
- Relation
- IEEE Transactions on Automatic Control Vol. 49, Issue 8, p. 1275-1291
- Publisher Link
- http://dx.doi.org/10.1109/TAC.2004.832202
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2004
- Description
- This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length. They are therefore “exact” for arbitrarily small true model order. Other authors have recognized the importance of such expressions and have derived them for the case of finite-impulse response-like model structures in which denominators are fixed at true values and only numerator terms are estimated. This paper progresses beyond this situation to address the more general output-error and Box–Jenkins structures in which full dynamics models (both numerator and denominator terms) and noise models may be estimated. A key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed.
- Subject
- Terms—Orthonormal bases; parameter estimation; system identification; variance error
- Identifier
- uon:858
- Identifier
- http://hdl.handle.net/1959.13/26401
- Identifier
- ISSN:1053-587x
- Rights
- Copyright © 2004 IEEE. Reprinted from IEEE Transactions on Automatic Control. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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