Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs

Matthijs van Berkel, Gerd Vandersteen, Egon Geerardyn, Rik Pintelon, Heiko J. Zwart, Marco de Baar

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)

    Abstract

    The identification of the spatially dependent parameters in Partial Differential Equations (PDEs) is important in both physics and control problems. A methodology is presented to identify spatially dependent parameters from spatio-temporal measurements. Local non-rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters. A sample Maximum Likelihood Estimator (SMLE) in the frequency domain is used, because it takes noise properties into account and allows for high accuracy consistent parameter estimation. Confidence bounds on the parameters are estimated based on the noise properties of the measurements. This method is successfully applied to the simulations of a finite difference model of a parabolic PDE with piecewise constant parameters.
    Original languageUndefined
    Pages (from-to)2113-2119
    Number of pages7
    JournalAutomatica
    Volume50
    Issue number8
    DOIs
    Publication statusPublished - Aug 2014

    Keywords

    • EWI-25236
    • Maximum likelihood estimators
    • Heat flows
    • IR-92442
    • Systems transfer functions
    • METIS-309627
    • Partial differential equations

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