Multi-channel Kalman filters for active noise control

S. van Ophem, Arthur P. Berkhoff

    Research output: Contribution to journalArticleAcademicpeer-review

    10 Citations (Scopus)

    Abstract

    By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm.
    Original languageUndefined
    Pages (from-to)2105-2115
    Number of pages11
    JournalJournal of the Acoustical Society of America
    Volume133
    Issue number4
    DOIs
    Publication statusPublished - Apr 2013

    Keywords

    • EWI-23254
    • METIS-296395
    • IR-85426

    Cite this

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    title = "Multi-channel Kalman filters for active noise control",
    abstract = "By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm.",
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    Multi-channel Kalman filters for active noise control. / van Ophem, S.; Berkhoff, Arthur P.

    In: Journal of the Acoustical Society of America, Vol. 133, No. 4, 04.2013, p. 2105-2115.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Multi-channel Kalman filters for active noise control

    AU - van Ophem, S.

    AU - Berkhoff, Arthur P.

    N1 - 10.1121/1.4792646

    PY - 2013/4

    Y1 - 2013/4

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    AB - By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm.

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