| 1. |
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| 2. |
- Akçay, Hüseyin, et al.
(author)
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On the Choice of Norms in System Identification
- 1994
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In: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 103-108
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Reports (other academic/artistic)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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| 3. |
- Forsman, Krister, et al.
(author)
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Merging 'Reasoning' and Filtering in a Bayesian Framework : Some Sensitivity and Optimality Aspects
- 1989
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In: Proceedings of the 28th Conference on Decision and Control. - Linköping : Linköping University. ; , s. 1427-1429
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Conference paper (peer-reviewed)abstract
- It is shown how to incorporate symbolic or logical knowledge into a conventional framework of noisy observations in dynamical systems. The idea is based on approximating the optimal solution that could, theoretically, be computed if a complete Bayesian framework were known (and infinite computational power were available). The nature of the approximations, the deviations from optimality and the sensitivity to ad hoc parameters are specifically addressed.
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| 4. |
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| 5. |
- Hjalmarsson, Håkan, 1962-, et al.
(author)
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A Unifying View of Disturbances in Identification
- 1994
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In: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 73-78
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Conference paper (peer-reviewed)
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| 6. |
- Hjalmarsson, Håkan, 1962-, et al.
(author)
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Discussion of `unknown-but-bounded' disturbances in system identification
- 1993
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In: Proceedings of the IEEE Conference on Decision and Control. - San Antonio, TX, USA : Linköping University. - 0780312988 ; , s. 535-536
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Conference paper (peer-reviewed)abstract
- In this contribution we point out that a fundamental property of a disturbance is that it is independent of the input - otherwise it is rather part of the system. Based on this characterization we show that parameter convergence can be obtained not only for stochastic but also for unknown-but-bounded disturbances if the input is at our disposal.
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| 7. |
- Hjalmarsson, Håkan, 1962-, et al.
(author)
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Estimating model variance in the case of undermodeling
- 1992
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In: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 37:7, s. 1004-1008
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Journal article (peer-reviewed)abstract
- A reliable quality estimate of a given model is a prerequisite for any reasonable use of the model. The model error consists of two different contributions: the bias error and the random error. In this contribution, it is shown that the size (variance) of the random error can be reliably estimated in the case where a true system description cannot be achieved in the model structure used. This consistent error estimate can differ considerably from the conventionally used variance estimate, which could thus be misleading.
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| 8. |
- Hu, Xiao-Li, et al.
(author)
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A Basic Convergence Result for Particle Filtering
- 2007
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In: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems. - Linköping : Linköping University Electronic Press. - 9783902661289 ; , s. 288-293
-
Conference paper (peer-reviewed)abstract
- The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still, a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.
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| 9. |
- Juditsky, A., et al.
(author)
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Nonlinear black-box models in system identification: Mathematical foundations
- 1995
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In: Automatica. - Linköping : Elsevier BV. - 0005-1098 .- 1873-2836. ; 31:12, s. 1725-1750
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Journal article (peer-reviewed)abstract
- We discuss several aspects of the mathematical foundations of the nonlinear black-box identification problem. We shall see that the quality of the identification procedure is always a result of a certain trade-off between the expressive power of the model we try to identify (the larger the number of parameters used to describe the model, the more flexible is the approximation), and the stochastic error (which is proportional to the number of parameters). A consequence of this trade-off is the simple fact that a good approximation technique can be the basis of a good identification algorithm. From this point of view, we consider different approximation methods, and pay special attention to spatially adaptive approximants. We introduce wavelet and 'neuron' approximations, and show that they are spatially adaptive. Then we apply the acquired approximation experience to estimation problems. Finally, we consider some implications of these theoretical developments for the practically implemented versions of the 'spatially adaptive' algorithms. Copyright © 1995 Elsevier Science Ltd All rights reserved.
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| 10. |
- Ljung, Lennart, 1946-, et al.
(author)
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Adaptation and Tracking in System Identification
- 1988
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In: Proceedings of the 8th IFAC Symposium on Identification and System Parameter Estimation. - Linköping : Linköping University. ; , s. 1-10
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Reports (other academic/artistic)abstract
- This article gives a survey of basic techniques to derive and analyse algorithms for tracking time-varying systems. Special attention is paid to how different assumptions about the true system affect the algorithms. Explicit and semi-explicit expressions for the means square errors are derived, which clearly demonstrate the character of the trade-off between tracking ability and noise sensitivity.
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