Evaluation of Stability of Higher-Order Atomic Clocks by Higher-Order Allan Variance

Abstract

In this paper, we analyze a generalized version of the Allan variance, referred to as a higher-order Allan variance, that can evaluate the frequency stability of multi-dimensional atomic clocks as a function of the measurement interval. It is known that the standard Allan variance, a measure to evaluate the frequency stability of atomic clocks, has a concern that its value for third-order atomic clocks, such as hydrogen maser, is dependent not only on the sampling interval of measurement data, but also on the time of measurement. To resolve this issue, this paper introduces the higher-order Allan variance defined for the higher-order difference of clock reading deviations. The main contribution of this paper is to mathematically prove that the higher-order Allan variance depends only on the sampling interval of clock reading deviations, for which a sufficiently high order of difference is considered. Furthermore, we present numerical simulation studying the numerical stability of the higher-order Allan variance computation for time series data of clock reading deviations.