Tracking nonstationarities in clock noises using the dynamic Allan variance

In a previous paper [4] we have introduced the concept of dynamic Allan variance, an extension of the classical Allan variance that is commonly used to evaluate the stability of atomic clocks. The Allan variance assumes the stationarity of the (increment of the) clock error signal, a condition that is valid for ideal clocks only. For real clocks one has to pay attention in the evaluation of the clock stability, because even for short time intervals the clock can exhibit a nonstationary behavior. Possible reasons for the lack of stationarity are sudden breakdowns, or, in the long term, clock ageing. Even cyclostationary behaviors can be observed due to daily or seasonal variation of temperature, humidity and other physical quantities that have a direct influence on the clock behavior. The main purpose of the Dynamic Allan variance is to describe the variation in time of the clock stability. In this paper we give a mathematical definition of this quantity. We apply our method to simulated data and to real data coming from a Rubidium clock. The results are very interesting, and they show that the proposed method can track and reveal in a clear and intuitive manner the changes in the behavior of atomic clock data.