Estimating the stability of N clocks with correlations

Estimation of an atomic clock´s frequency stability, separate from its reference, is often done using Gray and Allan´s three-cornered hat procedure (1974). A major requirement for the success of this method is that clocks be uncorrelated. If this requirement is not satisfied, the three-cornered hat procedure can lead to misleading or even negative variance estimates. Tavella and Premoli have considered this problem (1982) and developed an analysis which allows for the possibility of cross-correlation between clocks. We have extended and applied their ideas to obtain mathematically consistent frequency stability estimates on atomic clock data from the US Naval Observatory