Three-cornered hat versus allan covariance

The Three-Cornered Hat is a widely used method to measure the oscillator stability (variance) by comparing three statistically independent units. The Grolambert (two-sample) Covariance (GCOV) is an alternate and equivalent approach, which has the advantage of rejecting the instrument PM noise. This method, left aside in the early time when the time-domain analysis was used only for slow phenomena, is now of renewed interest for recent oscillators (sapphire and photonic oscillators, and femtosecond combs) which exhibit the highest stability at short term. We revisit the Groslambert Covariance, we compare it to the Three-Cornered Hat, and we show analytically and experimentally its appealing properties.