Estimating the Instabilities ofNClocks by Measuring Differences of their Readings

The estimation of individual instabilities of N clocks, when only differences of clock readings are available, is examined without any a priori assumption about the lack of correlation between clocks. The instability of the N clocks is described by the N × N covariance matrix R but only the ( N - 1) × ( N - 1) covariance matrix S of the differences referred to the N -th clock may be estimated directly from measurements. The estimation of R from S is not unique but the solution domain is limited by the positive definiteness of R . The features of this domain are analysed and the conditions for the validity of the uncorrelation hypothesis are established. The modifications of the solution domain, when the number N of compared clocks increases, is examined showing that each added clock can reduce the domain and therefore the arbitrariness in estimating R . Examples with some experimental data illustrate the capabilities of this approach.