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1.
  • Akçay, Hüseyin, et al. (författare)
  • On the Choice of Norms in System Identification
  • 1994
  • Rapport (övrigt vetenskapligt)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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2.
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3.
  • Enqvist, Martin, 1976-, et al. (författare)
  • Identification of Wiener System with Monotonous Nonlinearity
  • 2006
  • Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 978-3-902661-02-9 ; s. 166-171
  • Konferensbidrag (refereegranskat)abstract
    • A Wiener system is composed of a linear dynamic subsystem followedby a static nonlinearity. It is well known in the literature that the identifcationof the linear subsystem of a Wiener system can be separated from that of theoutput nonlinearity, if the input signal is a Gaussian noise. In order to deal withthe non Gaussian input case, two new algorithms are proposed in this paper fordirect identifcation of the linear subsystem, regardless of any parametrization ofthe output nonlinearity. The essential assumption required in this paper is thestrict monotonousness of the output nonlinearity.
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4.
  • Forsman, Krister, et al. (författare)
  • Merging 'Reasoning' and Filtering in a Bayesian Framework : Some Sensitivity and Optimality Aspects
  • 1989
  • Rapport (övrigt vetenskapligt)abstract
    • An approach is described how to incorporate knowledge of symbolic/logic character 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. This merging of logic and numerics is essential in many problems of adaptation in control and signal processing.
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5.
  • Gillberg, Jonas, et al. (författare)
  • Frequency-Domain Identification of Continuous-Time ARMA Models from Non-Uniformly Sampled Data
  • 2005
  • Rapport (övrigt vetenskapligt)abstract
    • This paper treats direct identification of continuous-time autoregressive moving average (CARMA) time-series models. The main result is a method for estimating the continuous-time power spectral density fromnon-uniformly sampled data. It is based on the interpolation (smoothing) using the Kalman filter. A deeper analysis is also carried out for the case of uniformly sampled data. This analysis provides a basis for proceeding with the non-uniform case. Numerical examples illustrating the performance of the method are also provided both, for spectral and subsequent parameter estimation.
6.
  • Gustafsson, Fredrik, et al. (författare)
  • Signal processing : exercises
  • 2010
  • Bok (övrigt vetenskapligt)abstract
    • This book provides signal processing exercises and can with advantage be used together with the text book Signal Processing by Fredrik Gustafsson, Lennart Ljung and Mille Millnert. The chapters of the books are aligned, which means that there are matching exercises to each theory chapter. The first part of the book treats classical digital signal processing based on transforms and filters, while model based digital processing is in focus in the second part. Some exercises are more theoretical and solved by hand, while others are intended for Matlab on a computer. The book material is inspired by real problems, and so are the exercises. This is emphasized by the use of data sets, both simulated and real. Most exercises have complete solutions, and a section with hints provides guidance to some exercises. Selected exercises also result in a Matlab function corresponding to specific signal processing algorithms. These functions are used to solve other exercises. Thereby, the reader gradually build up a signal processing toolbox during the studies of the material. The book homepage contains more information and links to access the matlab functions, data sets and examples used in the book. Main book Signal Processing
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7.
  • Gustavsson, Ivar, et al. (författare)
  • Identification of Processes in Closed Loop-Identifiability and Accuracy Aspects
  • 1977
  • Ingår i: Automatica. - Elsevier. - 0005-1098. ; 13:1, s. 59-75
  • Tidskriftsartikel (refereegranskat)abstract
    • It is often necessary in practice to perform identification experiments on systems operating in closed loop. There has been some confusion about the possibilities of successful identification in such cases, evidently due to the fact that certain common methods then fail. A rapidly increasing literature on the problem is briefly surveyed in this paper, and an overview of a particular approach is given. It is shown that prediction error identification methods, applied in a direct fashion will given correct estimates in a number of feedback cases. Furthermore, the accuracy is not necessarily worse in the presence of feedback; in fact optimal inputs may very well require feedback terms. Some practical applications are also described.
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8.
  • Hagenblad, Anna, et al. (författare)
  • Maximum Likelihood Identification of Wiener Models
  • 2009
  • Rapport (övrigt vetenskapligt)abstract
    • The Wiener model is a block oriented model, having a linear dynamic system followed by a static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. We show that this will, in general, lead to biased estimates if there are other disturbances present than measurement noise. The implications of Bussgang's theorem in this context are also discussed. For the case with general disturbances, we derive the Maximum Likelihood method and show how it can be efficiently implemented. Comparisons between this new algorithm and the traditional approach, confirm that the new method is unbiased and also has superior accuracy.
9.
  • Hjalmarsson, Håkan, 1962-, et al. (författare)
  • Estimating Model Variance in the Case of Undermodeling
  • 1992
  • Ingår i: IEEE Transactions on Automatic Control. - 0018-9286. ; 37:7, s. 1004-1008
  • Tidskriftsartikel (refereegranskat)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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10.
  • Hjalmarsson, Håkan, et al. (författare)
  • How to estimate model uncertainty in the case of under-modelling
  • 1990
  • Ingår i: Proceedings of the American Control Conference. - San Diego, CA, USA. ; s. 323-324
  • Konferensbidrag (refereegranskat)abstract
    • A method for estimating the parameter avoidance for the least-squares method by exploiting the ergodicity properties exhibited by the weighted least-squares estimate is presented. The method is illustrated by an example of a second-order system corrupted by strongly correlated high-frequency measurement noise.
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