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Related Experiment Video

Updated: May 23, 2026

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

Statistical biases and very-long-term time stability analysis.

François Vernotte¹, Éric Lantz

¹UTINAM, Observatory Terre-Homme-Environnement-Temps-Astronomie (THETA) of Franche-Comté, University of Franche-Comté/Centre National de la Recherche Scientifique (CNRS), Besançon, France. francois.vernotte@obs-besancon.fr

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|April 7, 2012

Summary

Accurately predicting long-term time stability requires addressing log-log bias in variance estimates. This study introduces a method for unbiased logarithmic fitting, improving timekeeping and navigation accuracy.

Related Experiment Videos

Last Updated: May 23, 2026

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

Area of Science:

Metrology and Measurement Science
Timekeeping and Navigation Systems

Background:

Accurate prediction of very-long-term time stability is crucial for timekeeping, navigation, and spatial applications.
Current methods extrapolate measurement data using estimators like Allan variance, often fitted on log-log graphs.

Purpose of the Study:

To theoretically calculate and address the bias present in the logarithmic fitting of variance estimates.
To develop a reliable method for unbiased logarithmic fitting to improve long-term stability predictions.

Main Methods:

Theoretical calculation of log-log bias based on equivalent degrees of freedom.
Simulations over a large number of realizations to validate the bias calculation.
Development and application of an unbiased logarithmic fitting method.

Main Results:

Quantification of the bias between the average log of estimates and the log of the true estimated variance.
Demonstration of the bias through extensive simulations.
Validation of a new method for unbiased logarithmic fitting.

Conclusions:

The proposed method provides a reliable way to perform unbiased logarithmic fits for variance estimates.
This unbiased fitting enhances the confidence in extrapolating stability assessments for very-long-term time prediction.
Improved time stability prediction has significant implications for precision applications.