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 information 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. We also investigate using the total variance and biases in the three-cornered-hat estimate.