Characterization of Frequency Stability: Uncertainty Due to the Autocorrelation of the Frequency Fluctuations

We considered the general sampling form for the estimate of the Allan variance which is the proposed measure of frequency stability in the time domain, and we defined a variable proportional to the difference between the average fractional frequency fluctuations over the time interval ¿ to derive the autocorrelation coefficient of the process to which the variable belongs. Calculations of the variance of the estimated Allan variance proved that it may be convergent to its true value with infinite sample number for considered spectral densities of frequency noise. We also applied the results to estimations of frequency measurements to know the influence of the autocorrelation of the process considered. In order to obtain some direct estimates of the confidence of the estimate, distributions of the estimate were plotted by means of computer simulations, and were compared with the chi-square distribution. Those results suggested that for white-and flicker-phase noises (and white-frequency noise) we have to take into account the autocorrelation of the process, while for flicker-or random-walk-frequency noise we may regard the process as a nearly independent (and Gaussian) one.