Total variance, an estimator of long-term frequency stability [standards]

Greenhall, C. A.; Howe, David A.; Percival, Donald B.

doi:10.1109/58.796124

Cited by 82 publications

(49 citation statements)

References 12 publications

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“…The Total Deviation is similar to the better-known Allan deviation, but is a better predictor of long-term fractional frequency instability. 31 The inset is a histogram of the optical frequency measurements, together with a fitted Gaussian function. A recent evaluation of all measurements gives the value of the Hg + frequency f (Hg + ) = 1 064 721 609 899 145.30 ± 0.69 Hz.…”

Section: -18mentioning

confidence: 99%

Optical frequency standards based on mercury and aluminum ions

et al. 2007

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Single-trapped-ion frequency standards based on a 282 nm transition in 199 Hg + and on a 267 nm transition in 27 Al + have been developed at NIST over the past several years. Their frequencies are measured relative to each other and to the NIST primary frequency standard, the NIST-F1 cesium fountain, by means of a self-referenced femtosecond laser frequency comb. Both ion standards have demonstrated instabilities and inaccuracies of less than 1 × 10 −16 .

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Section: -18mentioning

confidence: 99%

Optical frequency standards based on mercury and aluminum ions

et al. 2007

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“…The final and most compelling reason for consideringν 2 X (τ j ) is that its mean square error can be smaller thanν 2 X (τ j ); i.e., since the mean square error of an estimator is equal to the sum of its variance and its squared bias, the bias inν 2 X (τ j ) is compensated for by a decrease in its variability due to the use of the additional MODWT wavelet coefficients. For details, see Greenhall et al [13], where it is noted that the improvement in mean square error comes about only if, instead of analyzing {X t } itself, we apply the MODWT to a series of length 2N formed by extending {X t } with a reflected (i.e., time reversed) version of itself; i.e., we analyze…”

Section: The Wavelet Variancementioning

confidence: 99%

Stochastic models and statistical analysis for clock noise

Percival

2003

Metrologia

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In this primer we first give an overview of stochastic models that can be used to interpret clock noise. Because of their statistical tractability, we concentrate on fractionally differenced (FD) processes, which we relate to fractional Brownian motion, discrete fractional Brownian motion, fractional Gaussian noise and discrete pure power-law processes. We discuss several useful extensions to FD processes, namely, composite FD processes, autoregressive fractionally integrated moving average (ARFIMA) processes and time-varying FD processes. We then consider the statistical analysis of clock noise in terms of how these models are manifested via the spectral density function (SDF) and the wavelet variance (WV), the latter being a generalization of the well-known Allan variance. Both the SDF and the WV decompose the process variance with respect to an independent variable (Fourier frequency for the SDF, and scale for the WV); similarly, judiciously chosen estimators of the SDF and WV decompose the sample variance of clock noise. We give an overview of the statistical properties of estimators of the SDF and the WV and show how these estimators can be used to deduce the parameters of stochastic models for clock noise.

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“…Our decision to avoid the Allan variance is deliberate, as its form -effectively a moving average -specifically masks the effect of LO noise components with long correlation times. In fact the Allan variance is employed by the community in part because it does not diverge at long integration times τ due to LO drifts, as would the sample or true variance [26,[28][29][30]. In the limit where the stability of a frequency reference is dominated by LO noise (and the reference can be treated as perfect) this approach gives physically meaningful results.…”

Section: B Measures Of Frequency Standard Stability For Unlocked Andmentioning

confidence: 99%

Analytically exploiting noise correlations inside the feedback loop to improve locked-oscillator performance

et al. 2016

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We introduce concepts from optimal estimation to the stabilization of precision frequency standards limited by noisy local oscillators. We develop a theoretical framework casting various measures for frequency standard variance in terms of frequency-domain transfer functions, capturing the effects of feedback stabilization via a time-series of Ramsey measurements. Using this framework we introduce a novel optimized hybrid predictive feedforward measurement protocol which employs results from multiple past measurements and transfer-function-based calculations of measurement covariance to improve the accuracy of corrections within the feedback loop. In the presence of common non-Markovian noise processes these measurements will be correlated in a calculable manner, providing a means to capture the stochastic evolution of the LO frequency during the measurement cycle. We present analytic calculations and numerical simulations of oscillator performance under competing feedback schemes and demonstrate benefits in both correction accuracy and long-term oscillator stability using hybrid feedforward. Simulations verify that in the presence of uncompensated dead time and noise with significant spectral weight near the inverse cycle time predictive feedforward outperforms traditional feedback, providing a path towards developing a new class of stabilization "software" routines for frequency standards limited by noisy local oscillators.High-performance passive frequency standards play a major role in technological applications such as network synchronization and GPS [1] as well as many fields of physical inquiry, including radioastronomy (very-longbaseline interferometry) [2], tests of general relativity [3], and particle physics [4]. Atomic clocks exploiting the stability of Cs [5][6][7][8] or other atomic references [9-13] to stabilize an oscillator are known as the most precise timekeeping devices available, but constant performance gains are sought for technical and scientific applications.In many settings, such as miniaturized deployable frequency standards or in GPS-denied environments, a major performance limitation aries from the quality of the local oscillator (LO) that probes and is locked to the atomic transition. The LO frequency may evolve randomly in time due to intrinsic noise processes in the underlying hardware [10,11], leading to time-varying deviations of the LO frequency from that of the stable atomic reference. These instabilities are partially compensated through use of a feedback protocol designed to transfer the stability of the reference to the LO, but their effects cannot be mitigated completely.Early work characterizing the so-called Dick effect [14] demonstrated that no matter how good the reference becomes, LO noise will still produce residual instabilities in the locked LO (LLO) through the feedback protocol itself. The dominant mechanism for this is evolution of the LO's frequency on timescales rapid compared with the shortest measurement and feedback cycle. Major contributors to this phenome...

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Total variance, an estimator of long-term frequency stability [standards]

Cited by 82 publications

References 12 publications

Optical frequency standards based on mercury and aluminum ions

Optical frequency standards based on mercury and aluminum ions

Stochastic models and statistical analysis for clock noise

Analytically exploiting noise correlations inside the feedback loop to improve locked-oscillator performance

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