Degrees of Freedom for Allan Deviation Estimates of Multiple Clocks.

The three-cornered-hat (TCH) technique is used frequently in the timing community to estimate the stability of single frequency standards (clocks) when the only measurement data available are paired differences. In previous work, we presented an analytic method to estimate the reduced degrees of freedom produced when using the TCH estimation technique. In this paper, we extend that method to estimate the reduced degrees of freedom related to the more general case of the M-cornered-hat.

Estimating the stability of N clocks with correlations.

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.

Error bars for three-cornered hats.

Abstract-The three-cornered hat is a procedure for extracting the stabilities of three clocks when the only available data is the time or frequency differences between the clocks. To our knowledge, there has been no method of determining a confidence interval for such a stability estimate. In this paper, we present a method for determining the number of degrees of freedom of the estimate, which allows the assignment of a confidence interval to a three-cornered hat stability estimate.