The three cornered hat method: an attempt to identify some clock correlations

The three cornered hat is a well known method for estimating the instabilities of each clock in a set of three clocks. The first assumption lies in the hypothesis of total uncorrelation between the clocks. A revisited method has been proposed which no longer assumes the uncorrelation hypothesis, but yields a more realistic approach estimating the covariance matrix by ensuring suitable properties such as positive variances. Finally we propose a new method which goes further by assuming a power law model for the spectral density of frequency deviation of each clock, and hence of the clock differences. In this case negative noise levels may be directly interpreted as the effects of some correlations between certain clocks. The originality of this method lies in the estimation of the noise levels by using the multivariance method which provides an assessment of the uncertainties on these levels. Depending on their confidence interval, negative noise levels may be discarded as measurement artefacts or taken into account as correlation effects.