Estimation of an atomic clock's frequency stability, separate from its reference, is often done using a three-cornered hat procedure. 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. Others have considered this problem and developed an analysis that allows for the possibility of cross correlation between clocks. We have extended and applied these ideas to obtain mathematically consistent frequency stability estimates on atomic clock data from the U.S. Naval Observatory. In addition, we derived an expression for the clock weights that produce a minimum variance combination of clocks in the presence of correlations.
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