Historicity, strengths, and weaknesses of Allan variances and their general applications

Abstract

Over the past 50 years, Allan variance and its modifications have been developed for characterizing the instabilities in precision clocks and oscillators. These instabilities are often modeled by non-stationary processes, and these variances have been shown to be efficient descriptors of these processes. The timedomain and frequency-domain relationships are shown along with the strengths and weaknesses of the proposed variances. These variances are also shown to be useful elsewhere, as in navigation.