Abstract
Time series measurements with data gaps (dead times) prevent accurate computations of frequency stability variances such as the Allan variance (AVAR) and its square-root the Allan deviation (ADEV). To extract frequency distributions, time-series data must be sequentially ordered and equally spaced. Data gaps, particularly large ones, make ADEV estimates unreliable. Gap imputation by interpolation, zero-padding, or adjoining live segments, all fail in various ways. We have devised an algorithm that fills gaps by imputing an extension of preceding live data and explaining its advantages. To demonstrate the effectiveness of the algorithm, we have implemented it on 513-length original datasets and have removed 30% (150 values). The resulting data is consistent with the original in all three major criteria: the noise characteristic, the distribution, and the ADEV levels and slopes. Of special importance is that all ADEV measurements on the imputed dataset lie within 90% confidence of the statistic for the original dataset.
Highlights
Time series measurements of clocks and oscillators must be spaced to characterize noise models using Allan deviation (ADEV)
Frequency stability is characterized by the Allan deviation, designated as σy(τ), ADEV or sq-rt Allan variance (AVAR) and its related statistical estimators include the modified-Allan deviation (MDEV), THEO, TDEV, TOTDEV, etc
These estimators are in the class of “frequency-time” statistics that distinguish between different noise types [1,2,3]
Summary
Time series measurements of clocks and oscillators must be spaced to characterize noise models using ADEV. Random gaps (“dead times”) cause ADEV and related statistics to mischaracterize noise or to fail outright for gaps greater than 10% of the data set. Trying to characterize noise with gaps introduces biases and significant ADEV uncertainty.
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