Theoretical Analysis of the Modified Allan Variance

Bernier, Laurent-Guy

doi:10.1109/freq.1987.201012

Cited by 48 publications

(26 citation statements)

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“…the square root of the time variance (TVAR); the root mean square of time interval error (TIErms); and the maximum time interval error (MTIE). As far as the formal definition of the first three quantities and the relevant theoretical background are concerned, the reader is referred to [14] and [16]- [21]. The last two quantities, on the other hand, have been introduced mainly by telecommunications engineers and may appear somehow "exotic" to the traditional world of time and frequency metrology; a detailed analysis of their properties is available in [36] and [37].…”

Section: B Standard Estimators Of the Time-domain Stability Quantitiesmentioning

confidence: 99%

Clock stability characterization and measurement in telecommunications

Bregni

1997

IEEE Trans. Instrum. Meas.

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Clock stability characterization and measurement for telecommunications pose peculiar issues and requirements. This paper aims to provide an overview on this subject. After briefly recalling the background work, the key features and issues of clock stability characterization and measurement in telecommunications are described. The timing signal reference model and the stability quantities adopted in the new international standards are introduced and the impact of the measurement configuration and of the time error sampling period on their behavior are elucidated. The measurement of clock stability in telecommunications is then addressed, and a standard practical measurement procedure is outlined. Several measurement results are provided to support the concepts expounded with experimental evidence. The results shown have been chosen among those obtained throughout the last three years by testing clocks of digital switching exchanges, clocks for synchronous digital hierarchy (SDH) equipment, and state-of-the-art stand-alone slave clocks for synchronization networks. They thus represent a survey of the actual performance of clocks currently deployed in telecommunications networks.

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Section: B Standard Estimators Of the Time-domain Stability Quantitiesmentioning

confidence: 99%

Clock stability characterization and measurement in telecommunications

Bregni

1997

IEEE Trans. Instrum. Meas.

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“…where E[ · ] is the mean value operator over the signal process X [5]. For p = 1 we recover the well-known Allan variance.…”

Section: The Modified Allan Variancementioning

confidence: 99%

“…In this section we introduce and recall the main properties of the Modified Allan variance (MAVAR) [5,16], and of the log-regression estimator of the Hurst parameter based on it [7,8,9]. …”

Section: The Modified Allan Variancementioning

confidence: 99%

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Analysis of a Hurst parameter estimator based on the modified Allan variance

Bianchi

Bregni

Crimaldi

et al. 2012

2012 IEEE Global Communications Conference (GLOBECOM)

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ABSTRACT. In order to estimate the Hurst parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods of common use. Here we link it to the wavelets setting and provide an asymptotic analysis in the case the signal process is a fractional Brownian motion. In particular we show that the MAVAR log-regression estimator is consistent and asymptotically normal, providing the related confidence intervals for a suitable choice on the regression weights. Finally, we show some numerical examples.

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“…In previous papers [6] [7], the Modified Allan Variance (MAVAR) was introduced as traffic analysis tool for accurate estimation of H and γ. MAVAR is a well-known time-domain quantity, originally conceived in 1981 for frequency stability characterization of precision oscillators [8] [11] by modifying the definition of the Allan Variance (AVAR) recommended by IEEE in 1971 [12]. MAVAR was designed with the goal of discriminating noise types with power-law spectrum (i.e., in broad terms, fractional noise) recognized very commonly in frequency sources.…”

Section: Introductionmentioning

confidence: 99%