A novel approach to deriving closed form expressions for frequency stability variance measures

An approach is developed for obtaining closed-form expressions for variance estimators of frequency stability as functions of several parameters. It is based on a direct integration method and therefore expressions for autocorrelation functions of phase and frequency instabilities are not needed. The method is particularly useful when the transfer function approach of J. Rutman (1974) and E. Boileau (1978) is used, according to which the integral expressions of the variance estimate are chosen a priori. Using this method, the integrals can be evaluated without the need of calculating the corresponding sample of the variance. The relationship between this approach and the structure function characterization of frequency stability developed by W.C. Lindsey and C.M. Chie (1976) is also presented