References

Code, Programs

Papers

[Barnes1974]

Barnes, 1974, Tables of bias functions https://tf.nist.gov/general/pdf/11.pdf

[Benkler2015]

Benkler, Lisdat, Sterr, On the relation between uncertainties of weighted frequency averages and the various types of Allan deviations. Metrologia, Volume 52, Number 4, 2015. https://doi.org/10.1088/0026-1394/52/4/565 or https://arxiv.org/abs/1504.00466

[Bregni2001]

S. BREGNI, Fast Algorithms for TVAR and MTIE Computation in Characterization of Network Synchronization Performance. http://home.deib.polimi.it/bregni/papers/cscc2001_fastalgo.pdf

[Danielson2016]

Least square estimation of phase, frequency and PDEV https://arxiv.org/abs/1604.01004

[Dawkins2007]

S. T. Dawkins, J. J. McFerran and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 54, no. 5, pp. 918-925, May 2007. https://doi.org/10.1109/TUFFC.2007.337

[Dobrogowski2007]

Dobrogowski & Kasznia Real-time Assessment of Allan Deviation and Time Deviation 2007 IEEE International Frequency Control Symposium Joint with the 21st European Frequency and Time Forum https://doi.org/10.1109/FREQ.2007.4319204

[Greenhall2004]

Greenhall & Riley, “UNCERTAINTY OF STABILITY VARIANCES BASED ON FINITE DIFFERENCES” 35th Annual Precise Time and Time Interval (PTTI) Meeting https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050061319.pdf

[Howe_theo1]

D.A. Howe and T.N. Tasset THEO1: CHARACTERIZATION OF VERY LONG-TERM FREQUENCY STABILITY http://tf.nist.gov/general/pdf/1990.pdf

[Howe2000a]

Howe, Beard, Greenhall, Riley, A TOTAL ESTIMATOR OF THE HADAMARD FUNCTION USED FOR GPS OPERATIONS 32nd PTTI, 2000 https://apps.dtic.mil/dtic/tr/fulltext/u2/a484835.pdf

[Howe1999]

D.A. Howe and F. Vernotte, “Generalization of the Total Variance Approach to the Modified Allan Variance,” Proc. 31 st PTTI Meeting, pp. 267-276, Dec. 1999. https://tycho.usno.navy.mil/ptti/1999papers/paper22.pdf

[Howe2000b]

David A. Howe, The total deviation approach to long-term characterization of frequency stability, IEEE tr. UFFC vol 47 no 5 (2000) http://dx.doi.org/10.1109/58.869040

[Kasdin1992]

Kasdin, N.J., Walter, T., “Discrete simulation of power law noise [for oscillator stability evaluation],” Frequency Control Symposium, 1992. 46th., Proceedings of the 1992 IEEE, pp.274,283, 27-29 May 1992 http://dx.doi.org/10.1109/FREQ.1992.270003

[SP1065]

NIST Special Publication 1065 https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50505

[IEEE1139-2008]

1139-2008 - IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology - Random Instabilities http://dx.doi.org/10.1109/IEEESTD.2008.4797525

[Lantz2019]

KLTS: A rigorous method to compute the confidence intervals for the Three-Cornered Hat and for Groslambert Covariance https://arxiv.org/abs/1904.05849

[Riley_CI]

Confidence Intervals and Bias Corrections for the Stable32 Variance Functions W.J. Riley, Hamilton Technical Services http://www.wriley.com/CI2.pdf

[Riley2004]

Riley,W.J. et al., Power law noise identification using the lag 1 autocorrelation 18th European Frequency and Time Forum (EFTF 2004) https://ieeexplore.ieee.org/document/5075021

[Riley_1]

W.J.Riley, “THE CALCULATION OF TIME DOMAIN FREQUENCY STABILITY” http://www.wriley.com/paper1ht.htm

[Rubiola2015]

The Omega Counter, a Frequency Counter Based on the Linear Regression https://arxiv.org/abs/1506.05009

[Rubiola2022]

The Companion of Enrico’s Chart for Phase Noise and Two-Sample Variances https://arxiv.org/abs/2201.07109

[Rubiola_chart]

The Enrico’s Chart for Phase Noise and Two-Sample Variances https://zenodo.org/records/7691686

[Stein1985]

S. Stein, Frequency and Time - Their Measurement and Characterization. Precision Frequency Control Vol 2, 1985, pp 191-416. http://tf.boulder.nist.gov/general/pdf/666.pdf

[Sesia2011]

SESIA I., GALLEANI L., TAVELLA P., Application of the Dynamic Allan Variance for the Characterization of Space Clock Behavior, http://dx.doi.org/10.1109/TAES.2011.5751232

[Sesia2008]

Ilaria Sesia and Patrizia Tavella, Estimating the Allan variance in the presence of long periods of missing data and outliers. 2008 Metrologia 45 S134 http://dx.doi.org/10.1088/0026-1394/45/6/S19

[Vernotte2011]

F. Vernotte, “Variance Measurements”, 2011 IFCS & EFTF http://www.ieee-uffc.org/frequency-control/learning/pdf/Vernotte-Varience_Measurements.pdf

[Vernotte2015]

The Parabolic Variance (PVAR): A Wavelet Variance Based on the Least-Square Fit https://ieeexplore.ieee.org/document/7323846 or https://arxiv.org/abs/1506.00687

[Vernotte2016]

Three-Cornered Hat versus Allan Covariance http://rubiola.org/pdf-articles/conference/2016-IFCS-Three-cornered.pdf

[Vernotte2018]

Three-Cornered Hat and Groslambert Covariance: A first attempt to assess the uncertainty domains https://arxiv.org/abs/1810.01530

[Vernotte2020]

Response and Uncertainty of the Parabolic Variance PVAR to Non-Integer Exponents of the Power Law https://arxiv.org/pdf/2005.13631.pdf