TheoH and allan deviation as power-law noise estimators

McGee, Jennifer A.; Howe, David A.

doi:10.1109/tuffc.2007.260

Cited by 12 publications

(14 citation statements)

References 17 publications

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“…The frequency reproducibility between data sets was 2 × 10 -13 . With the 49 day measurement, the clock did not reach a flicker floor nor indicated its onset [9]. An important conclusion is that the stability of a trapped ion system utilizing a highly miniaturized package continues to improve over a 49-day run.…”

Section: Long-term Frequency Instabilitymentioning

confidence: 92%

Miniature trapped-ion frequency standard with 171Yb+

Schwindt

Jau

Partner

et al. 2015

2015 Joint Conference of the IEEE International Frequency Control Symposium &Amp; The European Frequency and Time Forum

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We describe the development and frequency instability measurements of a highly miniaturized, buffer gas cooled, trapped-ion atomic clock. The clock utilizes the 12.6 GHz hyperfine transition of the 171 Yb + ion. A custom-built 3 cm 3 vacuum package containing the ion trap is integrated with other key elements of the atomic frequency standard, including a photo multiplier tube, miniaturized laser sources at 369 nm and 935 nm, a local oscillator, and control electronics. With the clock physics package assembled on a 10 cm x 15 cm breadboard, the long-term fractional frequency instability was measured to be 6 × 10 -14 at 25 days of integration. Later, the clock physics package was further miniaturized, and the frequency instability was measured to be 2 × 10 -11 /τ 1/2 at integration times up to 10,000 s.

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Section: Long-term Frequency Instabilitymentioning

confidence: 92%

Miniature trapped-ion frequency standard with 171Yb+

Schwindt

Jau

Partner

et al. 2015

2015 Joint Conference of the IEEE International Frequency Control Symposium &Amp; The European Frequency and Time Forum

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“…The calculation of T k from the C (n) can be completed in O(N 2 ), so if the C (n) could all be calculated in O(N 2 ) then this would reduce the overall complexity of Thêo1 to O(N 2 ). For C (1,2) the definition is already ≤ O(N 2 ), but it can also be achieved for C (3,4) by using a recurrence relation between consecutive terms to avoid the full sum in (8) and 9:…”

Section: Algorithmmentioning

confidence: 99%

“…Compared to the more commonly used Allan variance, Thêo1 has increased confidence at long averaging times, and can be used to estimate stability up to 50% longer averaging times. Thêo1 is also better able to identify which type of 'power-law' noise is present [2], [3]. These properties have allowed Thêo1 to be used for longrunning experiments where datasets cannot easily be extended [4].…”

Section: Introductionmentioning

confidence: 99%

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A Fast Algorithm for Calculation of Thêo1

Lewis

2020

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

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Thêo1 is a frequency stability statistic which is similar to the Allan variance but can provide stability estimates at longer averaging factors and with higher confidence. However, the calculation of Thêo1 is significantly slower than the Allan variance, particularly for large data sets, due to a worse computational complexity. A faster algorithm for calculating the 'all-τ ' version of Thêo1 is developed by identifying certain repeated sums and removing them with a recurrence relation. The new algorithm has a reduced computational complexity, equal to that of the Allan variance. Computation time is reduced by orders of magnitude for many datasets. The new, faster algorithm does introduce an error due to accumulated floating point errors in very large datasets. The error can be compensated for by increasing the numerical precision used at critical steps. The new algorithm can also be used to increase the speed of ThêoBr and ThêoH which are more sophisticated statistics derived from Thêo1.

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“…Time-to-frequency domain coefficients that have traditionally been used with Avar [1], [2] can continue to be used with ThêoH variance. An important benefit is that, at long term, ThêoH deviation has enough narrowness in its range of noise-slope types as compared to Adev that it enables faster detection of the onset of nonstationary noise types of FLFM or RWFM [28], [29].…”

Section: Beyond Avarmentioning

confidence: 99%

ThêoH Bias-removal Method

Howe

McGee-Taylor

Tassett

2006

2006 IEEE International Frequency Control Symposium and Exposition

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A version of Thêo1 variance, called ThêoBR variance (BR for "bias-removed" relative to the Allan variance), is constructed. This relative bias correction is applied over a range of the longest recommended Allan τ values for a given data run. ThêoH deviation ('H' to indicate a hybrid combination of ThêoBR and Allan deviations) is the Allan deviation in short term and switches to the ThêoBR deviation in long term. In the presence of non-integer-power-law and mixed noise types, the approach is as effective and less cumbersome than past approaches, and requires little, if any, a priori knowledge or human judgment of data being analyzed. The substantially gained properties of Thêo1 at large τ , to 50 % beyond the longest possible τ using the Allan deviation alone, can be obtained without Allan bias. Long-term frequency stability can be obtained in essentially onethird less time. For example, a two-month stability can be obtained with three months of data, rather than the four months of data that are usually required for such a point.

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TheoH and allan deviation as power-law noise estimators

Cited by 12 publications

References 17 publications

Miniature trapped-ion frequency standard with <sup>171</sup>Yb<sup>+</sup>

Miniature trapped-ion frequency standard with <sup>171</sup>Yb<sup>+</sup>

A Fast Algorithm for Calculation of Thêo1

ThêoH Bias-removal Method

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