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 lpnorms, p⩽2<∞ for F(C).


2. 


3. 
 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.


4. 
 Gillberg, Jonas, et al.
(författare)

Frequency Domain Identification of ContinuousTime ARMA Models Interpolation and Nonuniform Sampling
 2004

Rapport (övrigt vetenskapligt)abstract
 In this paper is discussed how to estimate irregularly sampled continuoustime ARMA models in the frequency domain. In the process, the model output signal is assumed to be piecewise constant or piecewise linear, and an approximation of the continuoustime Fourier transform is calculated. MLestimation in the frequency domain is then used to obtain parameter estimates.


5. 
 Gunnarsson, 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


6. 
 Gustavsson, Ivar, et al.
(författare)

Identification of Processes in Closed LoopIdentifiability and Accuracy Aspects
 1977

Ingår i: Automatica.  Elsevier.  00051098. ; 13:1, s. 5975

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.


7. 
 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.


8. 
 Hjalmarsson, Håkan, 1962, et al.
(författare)

Estimating Model Variance in the Case of Undermodeling
 1992

Ingår i: IEEE Transactions on Automatic Control.  00189286. ; 37:7, s. 10041008

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.


9. 
 Hu, XiaoLi, et al.
(författare)

A Basic Convergence Result for Particle Filtering
 2007

Rapport (övrigt vetenskapligt)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 for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.


10. 
 Juditsky, A., et al.
(författare)

Nonlinear blackbox models in system identification: : Mathematical foundations
 1995

Ingår i: Automatica.  00051098 (ISSN). ; 31:12, s. 17251750

Tidskriftsartikel (refereegranskat)abstract
 We discuss several aspects of the mathematical foundations of the nonlinear blackbox identification problem. We shall see that the quality of the identification procedure is always a result of a certain tradeoff 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 tradeoff 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 Â© 1995 Elsevier Science Ltd All rights reserved.

