Analysis of powers-of-two calculations of the Allan variance and their relation to the standard variance

Published

May 18, 2019

Author(s)

Noah K. Schlossberger, David A. Howe

Abstract

In this work we show that powers of two multiples of the sampling period are the optimal set of averaging period Allan variance (AVAR) calculations for determining power law noise types present in recorded data. The primary merit of AVAR is that it indicates the slopes associated with each of the power law noise types as well as the level of each type included, even for a mixture of noise types. We show that unlike other arbitrary series, the powers-of- two values are spectrally the closest-to-independent set of AVAR values possible, and thus optimally decompose frequencies in such a way as to have the least uncertainty in estimating slopes. We further demonstrate the unique property of this choice of averaging period series by proving the equivalence between the sums of the powers-of-two values of the non-overlapping Allan variance and twice the value of the standard variance.

Conference Dates

April 14-18, 0019

Conference Location

Orlando, FL, US

Conference Title

2019 IEEE International Frequency Control Symposium IFCS-EFTF

Pub Type

Conferences

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Keywords

Allan Variance, Power Law Noise Determination, Stability Characterization, Standard Variance, Statistical Theory

Citation

Schlossberger, N. and Howe, D. (2019), Analysis of powers-of-two calculations of the Allan variance and their relation to the standard variance, 2019 IEEE International Frequency Control Symposium IFCS-EFTF, Orlando, FL, US, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=927984 (Accessed October 14, 2025)