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Eigenvalue-based time delay estimation of repetitive biomedical signals

Laguna, Pablo; Garde, Ainara; Giraldo, Beatriz F.; Meste, Olivier; Jané, Raimon and Sörnmo, Leif LU (2018) In Digital Signal Processing: A Review Journal 75. p.107-119
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... (More)

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 5M when 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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Biomedical signals, Eigenanalysis, Ensemble analysis, Time delay estimation
in
Digital Signal Processing: A Review Journal
volume
75
pages
13 pages
publisher
Elsevier
external identifiers
  • scopus:85041393778
ISSN
1051-2004
DOI
10.1016/j.dsp.2018.01.007
language
English
LU publication?
yes
id
6b42c03b-60ec-4385-ba90-6e4942595d7c
date added to LUP
2018-02-15 12:13:50
date last changed
2018-05-29 09:57:02
@article{6b42c03b-60ec-4385-ba90-6e4942595d7c,
  abstract     = {<p>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 5<sup>M</sup> when 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.</p>},
  author       = {Laguna, Pablo and Garde, Ainara and Giraldo, Beatriz F. and Meste, Olivier and Jané, Raimon and Sörnmo, Leif},
  issn         = {1051-2004},
  keyword      = {Biomedical signals,Eigenanalysis,Ensemble analysis,Time delay estimation},
  language     = {eng},
  month        = {04},
  pages        = {107--119},
  publisher    = {Elsevier},
  series       = {Digital Signal Processing: A Review Journal},
  title        = {Eigenvalue-based time delay estimation of repetitive biomedical signals},
  url          = {http://dx.doi.org/10.1016/j.dsp.2018.01.007},
  volume       = {75},
  year         = {2018},
}