Eigenvalue-based time delay estimation of repetitive biomedical signals

Pablo Laguna (Corresponding Author), Ainara Garde, Beatriz F. Giraldo, Olivier Meste, Raimon Jané, Leif Sörnmo

    Research output: Contribution to journalArticleAcademicpeer-review

    12 Downloads (Pure)

    Abstract

    The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5Mwhen using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.
    Original languageEnglish
    Pages (from-to)107-119
    Number of pages13
    JournalDigital Signal Processing: A Review Journal
    Volume75
    DOIs
    Publication statusPublished - 1 Apr 2018

    Fingerprint

    Time Delay Estimation
    Maximum likelihood
    Time delay
    Eigenvalue
    Correlation Matrix
    Ensemble
    Maximum Likelihood Estimator
    White noise
    Jitter
    Eigenvalues and eigenfunctions
    Error analysis
    Estimate
    Unknown
    Particle Swarm
    Eigenvalues
    Gaussian White Noise
    Estimation Error
    Maximum Likelihood Estimate
    Initialization
    Eigenvector

    Keywords

    • Biomedical signals
    • Eigenanalysis
    • Ensemble analysis
    • Time delay estimation

    Cite this

    Laguna, Pablo ; Garde, Ainara ; Giraldo, Beatriz F. ; Meste, Olivier ; Jané, Raimon ; Sörnmo, Leif. / Eigenvalue-based time delay estimation of repetitive biomedical signals. In: Digital Signal Processing: A Review Journal. 2018 ; Vol. 75. pp. 107-119.
    @article{b4883600bb6a41bc865a3e1c42647161,
    title = "Eigenvalue-based time delay estimation of repetitive biomedical signals",
    abstract = "The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5Mwhen using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.",
    keywords = "Biomedical signals, Eigenanalysis, Ensemble analysis, Time delay estimation",
    author = "Pablo Laguna and Ainara Garde and Giraldo, {Beatriz F.} and Olivier Meste and Raimon Jan{\'e} and Leif S{\"o}rnmo",
    year = "2018",
    month = "4",
    day = "1",
    doi = "10.1016/j.dsp.2018.01.007",
    language = "English",
    volume = "75",
    pages = "107--119",
    journal = "Digital Signal Processing: A Review Journal",
    issn = "1051-2004",
    publisher = "Elsevier",

    }

    Eigenvalue-based time delay estimation of repetitive biomedical signals. / Laguna, Pablo (Corresponding Author); Garde, Ainara; Giraldo, Beatriz F.; Meste, Olivier; Jané, Raimon; Sörnmo, Leif.

    In: Digital Signal Processing: A Review Journal, Vol. 75, 01.04.2018, p. 107-119.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Eigenvalue-based time delay estimation of repetitive biomedical signals

    AU - Laguna, Pablo

    AU - Garde, Ainara

    AU - Giraldo, Beatriz F.

    AU - Meste, Olivier

    AU - Jané, Raimon

    AU - Sörnmo, Leif

    PY - 2018/4/1

    Y1 - 2018/4/1

    N2 - The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5Mwhen using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.

    AB - The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5Mwhen using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.

    KW - Biomedical signals

    KW - Eigenanalysis

    KW - Ensemble analysis

    KW - Time delay estimation

    U2 - 10.1016/j.dsp.2018.01.007

    DO - 10.1016/j.dsp.2018.01.007

    M3 - Article

    VL - 75

    SP - 107

    EP - 119

    JO - Digital Signal Processing: A Review Journal

    JF - Digital Signal Processing: A Review Journal

    SN - 1051-2004

    ER -