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This work gives an algorithm for computing the degrees of freedom of estimators of Allan and Hadamard variances, including their modified versions. A consistent approach is used throughout.
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.
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.
Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to half the test duration.
This study gives strategies for estimating the modified Allan variance (mvar) and formulas for computing the equivalent degrees of freedom (edf) of the estimators. A third-difference formulation of mvar leads to a tractable formula for edf in the presence of power-law phase noise. The effect of estimation stride on edf is tabulated. First-degree rational-function approximations for edf are derived.
Tektites vs. terrestrial rocks - comparison of variance in compositions
Errors in a priori statistics in minimum variance estimation of regression parameters and effects on a posteriori estimates
Sequential trajectory estimation improved by implementing simple running estimates of observation error variances
Sequential trajectory estimation improved by implementing simple running estimates of observation error variances
Conditions for asymptotic stability of discrete minimum variance estimation formulas
Minimum variance estimation for gyroscopic drift parameters, discussing optimal estimation procedure and noise model
Phase variance and autocorrelation measurement during radio star visibility fades
Minimum variance technique for analysis of ionospheric data acquired by satellite retarding potential analyzer
Temporal stability and individual differences in human EEG from variance analysis of normalized power spectra data under rest and perceptual stress conditions
Least squares, minimum variance, and Kalman estimation applied to mathematical model of free flight trajectories
Variance in selected attributes in granite
Recursive equation for estimating variance of sequential random numbers
Asymptotic stability of discrete homogeneous linear minimum-variance estimation formulas