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  • 1.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency Domain Identification of Continuous-Time Systems: Reconstruction and Robustness2006Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Approaching parameter estimation from the discrete-time domain is the dominating paradigm in system identification. Identification of continuous-time models on the other hand is motivated by the fact that modelling of physical systems often take place in continuous-time. For many practical applications there is also a genuine interest in the parameters connected to these physical models.

    The most important element of time- and frequency-domain identification from sampled data is the discrete-time system, which is connected to the parameters of the underlying continuous-time system. For input-output models, it governs the frequency response from the sampled input to the sampled output. In case of time series, it models the spectrum of the sampled output.

    As the rate of sampling increase, the relationship between the discrete- and continuous-time parameters can become more or less ill-conditioned. Mainly, because the gathering of the poles of the discrete-time system around the value 1 in the complex plane will produce numerical difficulties while mapping back to the continuous-time parameters. We will therefore investigate robust alternatives to using the exact discrete-time system, which are based on more direct use of the continuous-time system. Another, maybe more important, reason for studying such approximations is that they will provide insight into how one can deal with non-uniformly sampled data.

    An equally important issue in system identification is the effect of model choice. The user might not know a lot about the system to begin with. Often, the model will only capture a particular aspect of the data which the user is interested in. Deviations can, for instance, be due to mis-readings while taking measurements or un-modelled dynamics in the case of dynamical systems. They can also be caused by misunderstandings about the continuous-time signal that underlies sampled data. From a user perspective, it is important to be able to control how and to what extent these un-modelled aspects influence the quality of the intended model.

    The classical way of reducing the effect of modelling errors in statistics, signal processing and identification in the time-domain is to introduce a robust norm into the criterion function of the method. The thesis contains results which quantify the effect of broad-band disturbances on the quality of frequency-domain parameter estimates. It also contains methods to reduce the effect of narrow-band disturbances or frequency domain outliers on frequency-domain parameter estimates by means of methods from robust statistics.

  • 2.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Methods for Frequency Domain Estimation of Continuous-Time Models2004Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Approaching parameter estimation from the discrete-time domain is the dominating paradigm in system identification. Identification of continuous-time models on the other hand is motivated by the fact that modelling of physical systems often take place in continuous-time. For many practical applications there is also a genuine interest in the parameters connected to these physical models. In the black-box discrete-time modelling framework however, the identified parameters often lack a physical interpretation.

    Uniform sampling has also been a standard assumption. A single sensor delivering measurements at a constant rate has been considered as the ideal situation. With the advent of networked asynchronous sensors the validity of this assumption has however changed. In fields such as economics and finance, uniform sampling might not be practically possible. This indicates a need for methods coping with non-uniform sampling.

    In the first part of this thesis the problem of estimation of irregularly sampled continuous-time ARMA models in the frequency domain is treated. In this process, the mode! output is assumed to be piecewise constant or piecewise linear, and an approximation of the continuous-time spectral density is calculated. Maximum Likelihood estimation in the frequency domain is then used to obtain parameter estimates. Rules of thumb concerning the mode! bias and variance are derived and used in order to select the frequencies to be used in estimation. Finally, the methods are applied to a tire pressure estimation problem.

    The second part ofthe thesis treats frequency domain identification of continuoustime ARMA and OE models for uniformly sampled data. Here the end objective is to inspire improved interpolation schemes which excel over the piecewise-linear and piecewise-constant approximations used in the first part. The result is a method which estimates the continuous-time spectrum/Fourier transform from its discretetime counterpart.

  • 3.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Continuous-Time AR Modeling using Non-Uniformly Sampled Measurements2005In: Proceedings of the 2005 IEEE International Conference on Acoustics, Speech and Signal Processing, 2005, Vol. 4, p. 105-108Conference paper (Refereed)
    Abstract [en]

    A frequency domain approach to continuous-time auto regressive (AR) signal modeling is proposed. The algorithm allows for data pre-filtering as opposed to conventional AR modelling in the time domain. We illustrate the method by extracting resonance frequencies from data from a real-life application.

  • 4.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Continuous-Time AR Modeling Using Non-Uniformly Sampled Measurements2004Report (Other academic)
    Abstract [en]

    A frequency domain approach to continuous-time auto regressive (AR) signal modeling is proposed. The algorithm allows for data pre-filtering as opposed to conventional AR modelling in the time domain. We illustrate the method by extracting resonance frequencies from data from a real-life application.

  • 5.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Pintelon, Rik
    Vrije Universiteit Brussel, Belgium.
    Robust Frequency Domain ARMA Modelling2006In: Proceedings of the 14th IFAC Symposium on System Identification, 2006, p. 380-385Conference paper (Refereed)
    Abstract [en]

    In this paper a method for the rejection of frequency domain outliers is proposed. The algorithm is based on the work by Huber on M-estimators and the concept of influence function introduced by Hampel. The estimation takes placein the context of frequency domain continuous-time ARMA modelling, but the method can be also be applied to the discrete time case.

  • 6.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Pintelon, Riki
    Vrije Universiteit Brussel, Belgium.
    Robust Frequency Domain ARMA Modelling2005Report (Other academic)
    Abstract [en]

    In this paper a method for the rejection of frequency domain outliers is proposed. The algorithm is based on the work by Huber on M-estimators and the concept of influence function introduced by Hampel. The estimation takes placein the context of frequency domain continuous-time ARMA modelling, but the method can be also be applied to the discrete time case.

  • 7.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Polynomial Complexity for a Nesterov-Todd Potential-Reduction Method with Inexact Search Directions: Examples related to the KYP Lemma2003Report (Other academic)
    Abstract [en]

    In this paper is discussed how to efficiently solve semidefinite programs related to the Kalman-Yakubovich-Popov lemma. We consider a potential-reduction method where Nesterov-Todd search directions are computed inexactly by applying a preconditioned conjugate gradient method on the Schur complement equations. An efficient preconditioner based on Lyapunov equations is derived. We give a proof of polynomial convergence for this interior point method.

  • 8.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency Domain Identification of Continuous-Time ARMA Models: Interpolation and Non-uniform Sampling2004Report (Other academic)
    Abstract [en]

    In this paper is discussed how to estimate irregularly sampled continuous-time 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 continuous-time Fourier transform is calculated. ML-estimation in the frequency domain is then used to obtain parameter estimates.

  • 9.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. IPCOSAptitude Ltd, United Kingdom.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency Domain Identification of Continuous-Time Output Error Models: Part I: Uniformly Sampled Data and Frequency Function Approximation2010Report (Other academic)
    Abstract [en]

    This paper treats several aspects relevant to identification of continuous-time Output error (OE) models based on sampled data. The exact method for doing this is well known both for data given in the time and frequency domains. This approach becomes somewhat complex, especially for non-uniformly sampled data. We study various ways to approximate the exact method for reasonably fast sampling. While an objective is to gain insights into the non-uniform sampling case, this paper only gives explicit results for uniform sampling.

  • 10.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. IPCOSAptitude Ltd, United Kingdom.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency Domain Identification of Continuous-Time Output Error Models: Part II: Non-Uniformly Sampled Data and B-Spline Output Approximation2010Report (Other academic)
    Abstract [en]

    This paper treats several aspects relevant to the identification of continuous-time output error (OE) models based on non-uniformly sampled output data. The exact method for doing this is well known in the time domain, where the continuous-time system is discretized, simulated and the result is fitted in a mean square sense to measured data. The material presented here is based on a method proposed in a companion paper (Gillberg andamp; Ljung, 2010) which deals with the same topic but for the case of uniformly sampled data. In this text it will be shown how that method suggests that the output should be reconstructed using a B-spline with uniformly distributed knots. This representation can then be used to directly identify the continuous-time system without proceeding via discretization. Only the relative degree of the model is used to choose the order of the spline.

  • 11.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time ARMA Models from Non-Uniformly Sampled Data2005Report (Other academic)
    Abstract [en]

    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.

  • 12.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. IPCOSAptitude Ltd, United Kingdom.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time ARMA Models from Sampled Data2010Report (Other academic)
    Abstract [en]

    The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.

  • 13.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time ARMA Models from Sampled Data2005In: Proceedings of 16th IFAC World Congress, 2005, p. 37-37Conference paper (Refereed)
    Abstract [en]

    This paper treats identification of continuous-time output error (OE) models based on sampled data. The exact method for doing this is well known both for data given in the time and frequency domains. This approach becomes some-what complex, especially for non-uniformly sampled data. We study various ways to approximate the exact method for reasonably fast sampling. While an objective is to gain insights into the non-uniform sampling case, this paper only gives explicit results for uniform sampling.

  • 14.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time ARMA Models from Sampled Data2009Report (Other academic)
    Abstract [en]

    The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.

  • 15.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time ARMA Models from Sampled Data2004Report (Other academic)
    Abstract [en]

    This paper treats identification of continuous-time output error (OE) models based on sampled data. The exact method for doing this is well known both for data given in the time and frequency domains. This approach becomes some-what complex, especially for non-uniformly sampled data. We study various ways to approximate the exact method for reasonably fast sampling. While an objective is to gain insights into the non-uniform sampling case, this paper only gives explicit results for uniform sampling.

  • 16.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time Output Error Models from Non-Uniformly Sampled Data2005Report (Other academic)
    Abstract [en]

    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 from non-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 sample ddata. 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.

  • 17.
    Gillberg, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time Output Error Models from Sampled Data2004Report (Other academic)
    Abstract [en]

    This paper treats identification of continuous-time output error (OE) models based on sampled data. The exact method for doing this is well known both for data given in the time and frequency domains. This approach becomes somewhat complex, especially for non-uniformly sampled data. We study various ways to approximate the exact method for reasonably fast sampling. While an objective is to gain insights into the non-uniform sampling case, this paper only gives explicit results for uniform sampling.

  • 18.
    Hansson, Anders
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Polynomial Complexity for a Nesterov-Todd Potential-Reduction Method with Inexact Search Directions2003In: Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, p. 3824-3829 vol.4Conference paper (Refereed)
    Abstract [en]

    In this paper is discussed how to efficiently solve semidefinite programs related to the Kalman-Yakubovich-Popov lemma. We consider a potential-reduction method where Nesterov-Todd search directions are computed inexactly by applying a preconditioned conjugate gradient method to the Schur complement equation. An efficient preconditioner based on Lyapunov equations is derived. We give a proof of polynomial convergence for this interior point method.

  • 19.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time Output Error Models from Non-Uniformly Sampled Data2006In: Proceedings of the 14th IFAC Symposium on System Identification, 2006, p. 214-218Conference paper (Refereed)
    Abstract [en]

    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 from non-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 sample ddata. 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.

  • 20.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency-Domain Identification of Continuous-Time Output Error Models from Sampled Data2005In: Proceedings of 16th IFAC World Congress, 2005, p. 15-15Conference paper (Refereed)
    Abstract [en]

    This paper treats identification of continuous-time output error (OE) models based on sampled data. The exact method for doing this is well known both for data given in the time and frequency domains. This approach becomes somewhat complex, especially for non-uniformly sampled data. We study various ways to approximate the exact method for reasonably fast sampling. While an objective is to gain insights into the non-uniform sampling case, this paper only gives explicit results for uniform sampling.

  • 21.
    Wallin, Ragnar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gillberg, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A Decomposition Approach for Solving KYP-SDPs2004Report (Other academic)
    Abstract [en]

    Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm is applied to the problem to improve efficiency.

1 - 21 of 21
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