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- Gustafsson, Fredrik, et al.
(författare)
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Twenty-one ML estimators for model selection
- 1995
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 31:10, s. 1377-1392
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Tidskriftsartikel (refereegranskat)abstract
- Classical approaches to determine a suitable model structure from observed input-output data are based on hypothesis tests and information-based criteria. Recently, the model structure has been considered as a stochastic variable, and standard estimation techniques have been proposed. The resulting estimators are closely related to the aforementioned methods. However, it turns out that there are a number of prior choices in the problem formulation, which are crucial for the estimators' behavior. The contribution of this paper is to clarify the role of the prior choices, to examine a number of possibilities and to show which estimators are consistent. This is done in a linear regression framework. For autoregressive models, we also investigate a novel prior assumption on stability, and give the estimator for the model order and the parameters themselves. Copyright © 1995 Elsevier Science Ltd All rights reserved.
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| 4. |
- Gustafsson, Fredrik, et al.
(författare)
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Twenty-One ML Estimators for Model Selection
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Classical approaches to determine a suitable model structure from observed input-output data are based on hypothesis tests and information-based criteria. Recently, the model structure has been considered as a stochastic variable, and standard estimation techniques have been proposed. The resulting estimators are closely related to the aforementioned methods. However, it turns out that there are a number of prior choices in the problem formulation, which are crucial for the estimators' behavior. The contribution of this paper is to clarify the role of the prior choices, to examine a number of possibilities and to show which estimators are consistent. This is done in a linear regression framework. For autoregressive models, we also investigate a novel prior assumption on stability, and give the estimator for the model order and the parameters themselves.
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| 5. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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Composite modeling of transfer functions
- 1995
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - New Orleans, LA, USA : Institute of Electrical and Electronics Engineers (IEEE). - 0780326857 ; 40:5, s. 820-832
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Konferensbidrag (refereegranskat)abstract
- The problem under consideration is how to estimate the frequency function of a system and the associated estimation error when a set of possible model structures is given and when one of them is known to contain the true system. The 'classical' solution to this problem is to, firstly, use a consistent model structure selection criterium to discard all but one single structure. Secondly, estimate a model in this structure and, thirdly, conditioned on the assumption that the chosen structure contains the true system, compute an estimate of the estimation error. However, for a finite data set one cannot guarantee that the correct structure is chosen and this 'structural' uncertainty is lost in the previously mentioned approach. In this contribution a method is developed that combines the frequency function estimates and the estimation errors from all possible structures into a joint estimate and estimation error. Hence, this approach by-passes the structure selection problem. This is accomplished by employing a Bayesian setting.
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- Malmström, Magnus, 1994-
(författare)
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Uncertainties in Neural Networks : A System Identification Approach
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In science, technology, and engineering, creating models of the environment to predict future events has always been a key component. The models could be everything from how the friction of a tire depends on the wheels slip to how a pathogen is spread throughout society. As more data becomes available, the use of data-driven black-box models becomes more attractive. In many areas they have shown promising results, but for them to be used widespread in safety-critical applications such as autonomous driving some notion of uncertainty in the prediction is required.An example of such a black-box model is neural networks (NNs). This thesis aims to increase the usefulness of NNs by presenting an method where uncertainty in the prediction is obtained by linearization of the model. In system identification and sensor fusion, under the condition that the model structure is identifiable, this is a commonly used approach to get uncertainty in the prediction from a nonlinear model. If the model structure is not identifiable, such as for NNs, the ambiguities that cause this have to be taken care of in order to make the approach applicable. This is handled in the first part of the thesis where NNs are analyzed from a system identification perspective, and sources of uncertainty are discussed.Another problem with data-driven black-box models is that it is difficult to know how flexible the model needs to be in order to correctly model the true system. One solution to this problem is to use a model that is more flexible than necessary to make sure that the model is flexible enough. But how would that extra flexibility affect the uncertainty in the prediction? This is handled in the later part of the thesis where it is shown that the uncertainty in the prediction is bounded from below by the uncertainty in the prediction of the model with lowest flexibility required for representing true system accurately. In the literature, many other approaches to handle the uncertainty in predictions by NNs have been suggested, of which some are summarized in this work. Furthermore, a simulation and an experimental studies inspired by autonomous driving are conducted. In the simulation study, different sources of uncertainty are investigated, as well as how large the uncertainty in the predictions by NNs are in areas without training data. In the experimental study, the uncertainty in predictions done by different models are investigated. The results show that, compared to existing methods, the linearization method produces similar results for the uncertainty in predictions by NNs.An introduction video is available at https://youtu.be/O4ZcUTGXFN0
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| 9. |
- Ninness, Brett, et al.
(författare)
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Generalized Fourier and Toeplitz results for rational orthonormal bases
- 1998
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Ingår i: SIAM Journal on Control and Optimization. - 0363-0129 .- 1095-7138. ; 37:2, s. 429-460
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a generalization of certain classical Fourier convergence and asymptotic Toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one but rather a rational generalization which encompasses the trigonometric one as a special case. These generalized Fourier and Toeplitz results have particular application in dynamic system estimation theory. Specifically, the results allow a unified treatment of the accuracy of least-squares system estimation using a range of model structures, including those that allow the inclusion of prior knowledge of system dynamics via the specification of fixed pole or zero locations.
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| 10. |
- Ninness, Brett, et al.
(författare)
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The fundamental role of general orthonormal bases in system identification
- 1999
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 44:7, s. 1384-1406
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well-known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros. This is achieved by employing certain new results on generalized Fourier series and the asymptotic properties of Toeplitz-like matrices in such a way that the new variance expressions presented here encompass pre-existing ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved numerical properties. In fact, they are an intrinsic part of estimation since, as shown here, orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them.
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