TAI computation: study of an alternative choice for implementing an upper limit of clock weights

The international reference time scale TAI computed by the Bureau International des Poids et Mesures (BIPM) relies on a weighted average of data from a large number of atomic clocks. In it, the weight attributed to a given clock represents its long-term stability. In this paper the TAI algorithm is used as a basis for discussion about the problem of how to implement an upper limit of weight for clocks contributing to the ensemble time. This problem is approached both theoretically and experimentally through the comparison of two different techniques: (i) In one case, a maximum relative weight is fixed: no individual clock can contribute more than a given fraction to the resulting time scale. The weight of each clock is then adjusted according to the qualities of the whole set of contributing elements. (ii) In the other case, a minimum parameter characteristic of frequency stability is implemented: no individual clock can be more stable than the stated limit. This is equivalent to choosing an absolute limit of weight and attributing this to the most stable clocks independently of the other elements of the ensemble. The first technique is more robust than the second and it optimizes the stability of the time scale at the expense of a more complicated computation. The second technique has always been a feature of the TAI algorithm. Analysis of real clock data shows that the stability of the time scale can be improved by periodic revision of the fixed value chosen for the upper limit of absolute weight. Our results confirm the wisdom of the decision by the Comité Consultatif pour la Définition de la Seconde (CCDS) Working Group on TAI to increase the absolute upper limit by a factor of 2,5. They also show that setting an upper limit to the relative contribution of a single clock may improve the stability and may lead to better use of the ensemble of HP 5071A clocks contributing to TAI.