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  • 1.
    Annergren, Mariette
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Larsson, Christian A.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Bombois, Xavier
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Application-Oriented Input Design in System Identification Optimal input design for control2017In: IEEE CONTROL SYSTEMS MAGAZINE, ISSN 1066-033X, Vol. 37, no 2, p. 31-56Article in journal (Refereed)
  • 2.
    Wahlberg, Bo
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Annergren, Mariette
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On l(1) Mean and Variance Filtering2011In: 2011 CONFERENCE RECORD OF THE FORTY-FIFTH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS & COMPUTERS (ASILOMAR) / [ed] Matthews, M B, IEEE , 2011, p. 1913-1916Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumption is that the mean value is piecewise constant in time, and the task is to estimate the change times and the mean values within the segments. The second case is when the mean value is constant, but the variance can change. The assumption is that the variance is piecewise constant in time, and we want to estimate change times and the variance values within the segments. To find solutions to these problems, we will study an l(1) regularized maximum likelihood method, related to the fused lasso method and l(1) trend filtering, where the parameters to be estimated are free to vary at each sample. To penalize variations in the estimated parameters, the l(1)-norm of the time difference of the parameters is used as a regularization term. This idea is closely related to total variation denoising. The main contribution is that a convex formulation of this variance estimation problem, where the parametrization is based on the inverse of the variance, can be formulated as a certain l(1) mean estimation problem. This implies that results and methods for mean estimation can be applied to the challenging problem of variance segmentation/estimation.

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