KLTS: A Rigorous Method to Compute the Confidence Intervals for the Three-Cornered Hat and for Groslambert Covariance

Lantz, E.; Calosso, Claudio; Rubiola, Enrico; Giordano, V.; Fluhr, Christophe; Dubois, Benoît; Vernotte, F.

doi:10.1109/tuffc.2019.2931911

Cited by 7 publications

(7 citation statements)

References 8 publications

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“…The KLT method stands for "Karhunen-Loève Tranform" and was developed in our previous paper [27]. In that paper, KLT has proved to be as efficient as well as rigorous method, making the most of the property of "sufficient statistics".…”

Section: Klt Methodsmentioning

confidence: 99%

“…In that paper, KLT has proved to be as efficient as well as rigorous method, making the most of the property of "sufficient statistics". However the difference with [27] is that we don't have the "sufficient statistics" property (see [34]). It means that KLT method will not give the same result as the cross-sprectrum method whereas it should have in the case of "sufficient statistics".…”

Section: Klt Methodsmentioning

confidence: 99%

“…"inverse problem"). The result obtained are compared to an another method using the Karhunen-Loève transform developed in [27] and the conclusions are presented in Section V.…”

Section: Introductionmentioning

confidence: 99%

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Cross-Spectrum Measurement Statistics: Uncertainties and Detection Limit

Baudiquez

Lantz

Rubiola

et al. 2020

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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The cross-spectrum method consists in measuring a signal c(t) simultaneously with two independent instruments. Each of these instruments contributes to the global noise by its intrinsec (white) noise, whereas the signal c(t) that we want to characterize could be a (red) noise. We first define the real part of the cross-spectrum as a relevant estimator. Then, we characterize the probability density function (PDF) of this estimator knowing the noise level (direct problem) as a Variance-Gamma (VG) distribution. Next, we solve the "inverse problem" thanks to Bayes' theorem to obtain an upper limit of the noise level knowing the estimate. Checked by massive Monte Carlo simulations, VG proves to be perfectly reliable to any number of degrees of freedom (dof). Finally we compare this method with an other method using the Karhunen-Loève transfrom (KLT). We find an upper limit of the signal level slightly different as the one of VG since KLT better takes into account the available informations.

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Section: Klt Methodsmentioning

confidence: 99%

Section: Klt Methodsmentioning

confidence: 99%

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Cross-Spectrum Measurement Statistics: Uncertainties and Detection Limit

Baudiquez

Lantz

Rubiola

et al. 2020

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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“…The KLT method, denoting to the Karhunen-Loève transform, has been developed in [14]. It uses the statistics of the data themselves instead of the statistics of the estimates.…”

Section: B Karhunen-loève Transformmentioning

confidence: 99%

The Statistics of the Cross-Spectrum and the Spectrum Average: Generalization to Multiple Instruments

Baudiquez,

Lantz,

Rubiola

et al. 2022

Preprint

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This article addresses the measurement of the power spectrum of red noise processes at the lowest frequencies, where the minimum acquisition time is so long that it is impossible to average on a sequence of data record. Therefore, averaging is possible only on simultaneous observation of multiple instruments. This is the case of radio astronomy, which we take as the paradigm, but examples may be found in other fields such as climatology and geodesy. We compare the Bayesian confidence interval of the red-noise parameter using two estimators, the spectrum average and the cross-spectrum. While the spectrum average is widely used, the cross-spectrum using multiple instruments is rather uncommon. With two instruments, the cross-spectrum estimator leads to the Variance-Gamma distribution. A generalization to q devices is provided, with the example of the observation of millisecond pulsars with 5 radio telescopes.

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“…The parabolic variance (PVAR) (Benkler et al 2015;Vernotte et al 2016) extends this concept, and exhibits (i) the highest rejection of white noise, and (ii) the efficient detection red noise underneath background with the shortest data record. Moreover, the wavelet covariance (Fest et al 1983;Lantz et al 2019), i.e., Allan covariance (ACOV) or parabolic covariance (PCOV), enables the rejection of the background using two (or more) uncorrelated instruments.…”

Section: Introductionmentioning

confidence: 99%

Applying clock comparison methods to pulsar timing observations

Chen,

Vernotte,

Rubiola

2020

Preprint

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Frequency metrology outperforms any other branch of metrology in accuracy (parts in 10 −16 ) and small fluctuations (< 10 −17 ). In turn, among celestial bodies, the rotation speed of millisecond pulsars (MSP) is by far the most stable (< 10 −18 ). Therefore, the precise measurement of the time of arrival (TOA) of pulsar signals is expected to disclose information about cosmological phenomena, and to enlarge our astrophysical knowledge. Related to this topic, Pulsar Timing Array (PTA) projects have been developed and operated for the last decades. The TOAs from a pulsar can be affected by local emission and environmental effects, in the direction of the propagation through the interstellar medium or universally by gravitational waves from super massive black hole binaries. These effects (signals) can manifest as a low-frequency fluctuation over time, phenomenologically similar to a red noise. While the remaining pulsar intrinsic and instrumental background (noise) are white. This article focuses on the frequency metrology of pulsars. From our standpoint, the pulsar is an accurate clock, to be measured simultaneously with several telescopes in order to reject the uncorrelated white noise. We apply the modern statistical methods of time-and-frequency metrology to simulated pulsar data, and we show the detection limit of the correlated red noise signal between telescopes.

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KLTS: A Rigorous Method to Compute the Confidence Intervals for the Three-Cornered Hat and for Groslambert Covariance

Cited by 7 publications

References 8 publications

Cross-Spectrum Measurement Statistics: Uncertainties and Detection Limit

Cross-Spectrum Measurement Statistics: Uncertainties and Detection Limit

The Statistics of the Cross-Spectrum and the Spectrum Average: Generalization to Multiple Instruments

Applying clock comparison methods to pulsar timing observations

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