Post-processing ROA data clocks for optimal stability in the ensemble timescale

Abstract

In recent years, a certain correlation detected between clocks at time and frequency laboratories has been the main reason behind the development of a revised version of the classical `Three-Cornered Hat' method as a mathematical tool to estimate the frequency instability of a set of clocks. The method has been formulated keeping in mind the possibility of dependence among clocks and has been generalized to an ensemble of N clocks [1–5]. It basically consists of the minimization of an objective function, the quadratic sum of cross-correlation coefficients, with the constraint condition established by the positive definiteness of the (estimated) absolute covariance matrix related to the clocks.Later on, a matrix formulation to calculate the optimal weights in the case of correlated clocks was presented in [6]. The impact of this weighting procedure on the instability of the ensemble time was evaluated, on the basis of simulated clocks, when correlation was appropriately taken into account and in the case when it was neglected. That paper established, as a main conclusion, the mathematical treatment to be used in the usual case of weak dependence.In this paper, we present a summary of the theory involved, and then apply the procedures to optimal weighting of clocks using real data clocks at Real Observatorio de la Armada (San Fernando, Spain). Finally, we discuss the results obtained.