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    Accurate frequency stability computations require handling data gaps. A new algorithm extends preceding data to fill gaps, preserving noise characteristics and Allan deviation (ADEV) estimates within 90% confidence.

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    Area of Science:

    • Metrology
    • Signal Processing
    • Data Science

    Background:

    • Time series data with gaps pose challenges for frequency stability analysis.
    • Standard Allan variance (AVAR) and Allan deviation (ADEV) calculations require continuous, equally spaced data.
    • Existing gap-filling methods like interpolation or zero-padding yield unreliable ADEV estimates.

    Purpose of the Study:

    • To develop and validate a novel algorithm for imputing data gaps in time series measurements.
    • To ensure accurate computation of frequency stability metrics, specifically Allan deviation (ADEV).
    • To overcome limitations of traditional gap-filling techniques.

    Main Methods:

    • A new algorithm was devised to fill data gaps by extending preceding live data segments.
    • The algorithm was tested on datasets with 30% of values removed (150 out of 513).
    • Imputed data was compared against original data using noise characteristics, data distribution, and ADEV levels/slopes.

    Main Results:

    • The developed algorithm successfully imputed data gaps without compromising data integrity.
    • Imputed datasets showed consistency with original data in noise characteristics and distribution.
    • ADEV measurements on imputed data remained within 90% confidence intervals of the original data's ADEV.

    Conclusions:

    • The proposed gap-filling algorithm provides a reliable method for handling dead times in time series measurements.
    • This approach enables accurate frequency stability variance computations, particularly Allan deviation (ADEV), even with significant data gaps.
    • The algorithm offers a robust solution for metrology and signal processing applications dealing with incomplete time series data.