A fast algorithm for calculation of Thêo1

Lewis, Ben (2020) A fast algorithm for calculation of Thêo1. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 67 (10). pp. 2187-2190. ISSN 0885-3010 (https://doi.org/10.1109/TUFFC.2020.2996313)

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Abstract

Thêo1 is a frequency stability statistic that 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 that of 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, which is equal to that of the Allan variance. Computation time is reduced by orders of magnitude for many data sets. The new, faster algorithm does introduce an error due to accumulated floating-point errors in very large data sets. 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 that are more sophisticated statistics derived from Thêo1.

  • Item type:Article
    ID code:72475
    Dates:
    Date
    Event
    1 October 2020
    Published
    21 May 2020
    Published Online
    16 May 2020
    Accepted
    Notes:© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:27 May 2020 10:50
    Last modified:22 Apr 2024 00:44
    URI:https://strathprints.strath.ac.uk/id/eprint/72475
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