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Fast TheoBR: A method for long data set stability analysis

Published

Author(s)

Jennifer A. Taylor, David A. Howe

Abstract

TheoBR (Theo1 with Bias Removed) is a high-confidence statistic that evaluates frequency stability at long \tau values. However, for real-world data sets that are thousands of points and longer, the calculation of the bias with respect to the Allan Variance is very slow, taking hours, days, or even weeks on a typical personal computer. In order to make TheoBR more accessible for use on these types of data sets, a method of averaging points together within the data set is developed. The error introduced into the bias calculation by this technique is analyzed and compared to the exact bias value and a correction formula developed to minimize this error for FM noise types. Finally, this ''Fast TheoBR" technique is applied to a real data set of 223,120 points and determines stability at the longest \tau values in seconds as opposed to weeks.
Citation
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control
Volume
57
Issue
9

Keywords

Allan variance, flicker noise, frequency, noise, phase, stability, TheoBR, TheoH, time, white noise

Citation

Taylor, J. and Howe, D. (2010), Fast TheoBR: A method for long data set stability analysis, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50609 (Accessed April 16, 2024)
Created August 31, 2010, Updated October 12, 2021