Estimating the stability of N clocks with correlations

摘要

Estimation of an atomic clock's frequency stability, separate fromnits reference, is often done using a three-cornered hat procedure. Anmajor requirement for the success of this method is that clocks benuncorrelated. If this requirement is not satisfied, the three-cornerednhat procedure can lead to misleading or even negative variancenestimates. Others have considered this problem and developed an analysisnthat allows for the possibility of cross correlation between clocks. Wenhave extended and applied these ideas to obtain mathematicallynconsistent frequency stability estimates on atomic clock data from thenU.S. Naval Observatory. In addition, we derived an expression for thenclock weights that produce a minimum variance combination of clocks innthe presence of correlations