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- W4387606497 abstract "Abstract In this paper, we perform a time-domain analysis of the higher-order Allan variance for atomic clock models of arbitrary order. Adopting a standard atomic clock model where the time series of the clock reading deviation is expressed as a Wiener or integrated Wiener process, we define the higher-order Allan variance as the mean squared higher-order difference of the clock reading deviation. The main results of this paper are threefold. First, we prove that the higher-order difference operation of the clock reading deviation, which can be interpreted as a linear aggregation with binomial coefficients, is not only sufficient but also necessary for a resulting aggregated time series to be an independent and identically distributed Gaussian process. Second, we derive a complete analytical expression of the higher-order Allan variance, which consists of both time-dependent and time-independent terms. Third, we prove that the higher-order Allan variance is time-independent if and only if the order of difference operation is greater than or equal to the order of the atomic clock model." @default.
- W4387606497 created "2023-10-14" @default.
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- W4387606497 date "2023-10-13" @default.
- W4387606497 modified "2023-10-14" @default.
- W4387606497 title "Higher-Order Allan Variance for Atomic Clocks of Arbitrary Order: Mathematical Foundation" @default.
- W4387606497 doi "https://doi.org/10.1088/1681-7575/ad02fe" @default.
- W4387606497 hasPublicationYear "2023" @default.
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