Editing Allan variance (section)

===Overlapped variable ''τ'' estimators===
A technique presented by J. J. Snyder<ref name=Snyder1981>Snyder, J. J.: ''An ultra-high resolution frequency meter'', pages 464–469, Frequency Control Symposium #35, 1981.</ref> provided an improved tool, as measurements were overlapped in ''n'' overlapped series out of the original series. The overlapping Allan variance estimator was introduced by Howe, Allan and Barnes.<ref name=Howe1981/> This can be shown to be equivalent to averaging the time or normalized frequency samples in blocks of ''n'' samples prior to processing. The resulting predictor becomes

:<math>
\begin{align}
\sigma_y^2(n\tau_0, M) & = \operatorname{AVAR}(n\tau_0, M) = \frac{1}{2n^2(M - 2n + 1)} \sum_{j=0}^{M-2n} \left( \sum_{i=j}^{j+n-1} y_{i+n} - y_i \right)^2 \\[5pt]
& = \frac{1}{2(M - 2n + 1)} \sum_{j=0}^{M-2n} \left(\bar{y}_{j+n} - \bar{y}_j \right)^2,
\end{align}
</math>

or for the time series:

:<math>\sigma_y^2(n\tau_0, N) = \operatorname{AVAR}(n\tau_0, N) = \frac{1}{2n^2\tau_0^2(N - 2n)} \sum_{i=0}^{N-2n-1} (x_{i+2n} - 2x_{i+n} + x_i)^2.</math>

The overlapping estimators have far superior performance over the non-overlapping estimators, as ''n'' rises and the time-series is of moderate length. The overlapped estimators have been accepted as the preferred Allan variance estimators in IEEE,<ref name=IEEE1139/> ITU-T<ref name=itutg810>ITU-T Rec. G.810: [http://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.810-199608-I!!PDF-E&type=items ''Definitions and terminology for synchronization and networks''], ITU-T Rec. G.810 (08/96).</ref> and ETSI<ref name=ETSIEN3004610101>ETSI EN 300 462-1-1: [http://www.etsi.org/deliver/etsi_en/300400_300499/3004620701/01.01.01_20/en_3004620701v010101c.pdf ''Definitions and terminology for synchronisation networks''], ETSI EN 300 462-1-1 V1.1.1 (1998–05).</ref> standards for comparable measurements such as needed for telecommunication qualification.