Study of the statistical performance of the Pisarenko harmonic decomposition method

Stoica, Petre; Nehorai, Arye

doi:10.1049/ip-f-1.1988.0022

Cited by 20 publications

(10 citation statements)

References 2 publications

(1 reference statement)

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“…Pisarenko's method, for example, returns frequency estimates with O(n-l) variances (Sakai 1984;Stoica and Nehorai 1988;Kahn et al 1992). An exception is the Osborne/Bresler/Macovski algorithm, which Kahn et al (1992) showed to be comparable in efficiency to least squares.…”

Section: Eigenanalysis Methodsmentioning

confidence: 99%

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

Smyth

2000

Technometrics

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The problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered. Eigenanalysis methods, such as Pisarenko's method and the extended Prony method, find the eigenvector with minimum eigenvalue of a suitably chosen matrix, and then obtain the complex sinusoids as the roots of the polynomial which has the components of the eigenvector as coefficients. For the sinusoids to be undamped, it is necessary that the roots lie on the unit circle, and hence that the eigenvector be conjugate symmetric. It is shown how this symmetry constraint can be incorporated into eigenanalysis estimation methods in a routine way. The practical importance of the constraint is investigated by Cramér-Rao variance bound calculations and by simulation. Three data examples are included. The following conclusions are made: (i) The symmetry constraint is straightforward to implement, and reduces the amount of computation required. (iii) The relative reduction in variance of the constrained over the unconstrained frequency estimators is arbitrarily large for frequencies close together or near a multiple of π. However there are also frequency values for which the symmetry constraint gives no reduction in variance at low noise-to-signal ratios. (iv) The relative reduction in variance converges to zero for large sample sizes. (v) The symmetry constraint increases the breakdown noise-to-signal ratios above which the various methods fail to give useful results.

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Section: Eigenanalysis Methodsmentioning

confidence: 99%

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

Smyth

2000

Technometrics

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“…The first of these restrictions can be removed by adopting a two-stage procedure as suggested in Subsection 3.2. The second restriction is more difficult to deal with, and several methods have been suggested to generalize the method to situations where the variance covariance matrix of u(t) need not be an identity matrix (see in particular Sakai (1984), Stoica and Nehorai (1988), Kundu and Kannan (1997) etc. ).…”

Section: Pisarenko's Harmonic Decomposition Methodsmentioning

confidence: 99%

Harmonic Regression Models: A Comparative Review with Applications

et al. 2007

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Strongly periodic series occur frequently in many disciplines. This paper reviews one specific approach to analyzing such series viz. the harmonic regression approach.In this paper the five major methods suggested under this approach are critically reviewed and compared, and their empirical potential highlighted via two applications. The out-of-sample forecast comparisons are made using the Superior Predictive Ability test, which specifically guards against the perils of data snooping. Certain tentative conclusions are drawn regarding the relative forecasting ability of the different methods.

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“…Pisarenko's method, for example, returns frequency estimates with O(n −1 ) variances (Sakai, 1984;Stoica and Nehorai, 1988;Kahn et al, 1992). An exception is the Osborne/Bresler/Macovski algorithm, which Kahn et al (1992) show is comparable in efficiency to least squares.…”

Section: Eigenanalysis Methodsmentioning

confidence: 99%

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

Smyth¹

2000

Technometrics

View full text Add to dashboard Cite

The problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered. Eigenanalysis methods, such as Pisarenko's method and the extended Prony method, find the eigenvector with minimum eigenvalue of a suitably chosen matrix, and then obtain the complex sinusoids as the roots of the polynomial which has the components of the eigenvector as coefficients. For the sinusoids to be undamped, it is necessary that the roots lie on the unit circle, and hence that the eigenvector be conjugate symmetric. It is shown how this symmetry constraint can be incorporated into eigenanalysis estimation methods in a routine way. The practical importance of the constraint is investigated by Cramér-Rao variance bound calculations and by simulation. Three data examples are included. The following conclusions are made: (i) The symmetry constraint is straightforward to implement, and reduces the amount of computation required. (iii) The relative reduction in variance of the constrained over the unconstrained frequency estimators is arbitrarily large for frequencies close together or near a multiple of π. However there are also frequency values for which the symmetry constraint gives no reduction in variance at low noiseto-signal ratios. (iv) The relative reduction in variance converges to zero for large sample sizes. (v) The symmetry constraint increases the breakdown noiseto-signal ratios above which the various methods fail to give useful results.

show abstract

Study of the statistical performance of the Pisarenko harmonic decomposition method

Cited by 20 publications

References 2 publications

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

Harmonic Regression Models: A Comparative Review with Applications

Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanalysis Methods

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