Allan variance
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan and expressed mathematically as .The Allan deviation (ADEV), also known as sigma-tau, is the square root of the Allan variance, . The M-sample variance is a measure of frequency stability using M samples, time T between measurements and observation time . M-sample variance is expressed as The Allan variance is intended to estimate stability due to noise processes and not that of systematic errors or imperfections such as frequency drift or temperature effects. The Allan variance and Allan deviation describe frequency stability. See also the section below. There are also different adaptations or alterations of Allan variance, notably the modified Allan variance MAVAR or MVAR, the , and the . There also exist time-stability variants such as time deviation (TDEV) or time variance (TVAR). Allan variance and its variants have proven useful outside the scope of timekeeping and are a set of improved statistical tools to use whenever the noise processes are not unconditionally stable, thus a derivative exists. The general M-sample variance remains important, since it allows dead time in measurements, and bias functions allow conversion into Allan variance values. Nevertheless, for most applications the special case of 2-sample, or "Allan variance" with is of greatest interest. (Wikipedia).
