NASA NTRS · 20060035171
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Greenhall, C. A.. 1997-05-28. Does Allan Varianced Determine the Specrum. https://ntrs.nasa.gov/citations/20060035171
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A drift-rate estimator constructed from four values of the cumulative sum of clock residuals is shownn to have good error performance in the presence of the five standard power-law noises.
The third-difference approach to modified Allan variance (MVAR) leads to a tractable formula for a measure of MVAR estimator confidence, the equivalent degrees of freedom (edf), in the presence of power-law phase noise. The effect of estimation stride on edf is tabulated. A simple approximation for edf is given, and its errors are tabulated. A theorem allowing conservative estimates of edf in the presence of compound noise processes is given.
A paper at the 1992 FCS showed how to express the modified Allan variance (mvar) in terms of the third difference of the cumulative sum of time residuals. Although this reformulated definition was presented merely as a computational trick for simplifying the calculation of mvar estimates, it has since turned out to be a powerful theoretical tool for deriving the statistical quality of those estimates in terms of their equivalent degrees of freedom (edf), defined for an estimator V by edf V = 2(EV)2/(var V). Confidence intervals for mvar can then be constructed from levels of the appropriate 2 distribution.