A re-revisited three cornered hat method for estimating clock instabilities

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. The method will be detailed and different examples of clocks, more or less correlated, will be given. The limitation of this method in terms of correlations will also be studied.