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Towards an optimal weighting scheme for TAI computation

International atomic time (TAI) is an ensemble timescale based on a weighted average of clocks. The basic properties of the algorithm have been fixed since its inception: that is, the weight of a clock is inversely proportional to a variance measuring the instability of the clock, and it cannot exceed a maximum value. On the other hand, the procedure used to set the maximum weight has been subject to several changes over the years. While the most stable timescale would ideally be computed without an upper limit of weights, such an upper limit is introduced to bring reliability. Up to now, however, there has been no adopted measure of the reliability. In this paper, a quantitative estimator of the reliability is proposed, which therefore helps in choosing a weighting scheme. Different procedures for setting the maximum weight are examined in light of the application of the reliability criterion defined here. Tests using simulated and real data are presented. A weighting scheme to be used for TAI computation is proposed in which the reliability estimator is optimized.