A Historical Perspective on the Development of the Allan Variances and Their Strengths and Weaknesses

Over the past 50 years, variances have been developed for characterizing the instabilities of precision clocks and oscillators. These instabilities are often modeled as nonstationary processes, and the variances have been shown to be well-behaved and to be unbiased, efficient descriptors of these types of processes. This paper presents a historical overview of the development of these variances. The time-domain and frequency-domain formulations are presented and their development is described. The strengths and weaknesses of these characterization metrics are discussed. These variances are also shown to be useful in other applications, such as in telecommunication.