Algorithms for the Atomic Clock Prediction within the Galileo System
Panfilo, G¹; Tavella, P^2
1BIPM; ²INRIM

In recent times, scientific interest in atomic clock and time scale prediction is becoming stronger due to some new applications of timekeeping. Network synchronization, high-speed communication as satellite navigation require higher and higher performances in timekeeping. The performances of the European Global Navigation Satellite System Galileo are in part related to the behaviour of the atomic clocks hosted on the satellites; prediction of the behaviour of such clocks helps to increase navigation performances of Galileo, optimising the uploading interval of the correction to the satellite clocks.

High precision timekeeping performances are also required to National Metrological Institutes and other entities that realize and disseminate standard time with real-time time scales referenced on the international time reference “Universal Coordinated Time” (UTC). As the UTC is not available real time but as a “paper” time scale, with a delay up to 45 days, the performance of a real-time time scale steered on the UTC relies on atomic clock prediction.

In this paper we present atomic clock prediction methods, focusing on the mathematical theory underneath. Different atomic clocks show very different behaviours, either with a random or a deterministic signature.

Standard approach on atomic clock prediction relies on the extrapolation past measurement data, using basically a linear or quadratic extrapolating function; extrapolated uncertainty is also estimated with the same polynomial models. Another approach consists in the modelisation of the atomic clock behaviour using stochastic processes. Actually atomic clocks can be described by different models; for some models is possible to infer analytically the clock prediction and also its uncertainty. For other models only approximate solutions are available. A mathematical model for the atomic clock behaviour can also be useful in time scale generation, as it helps to define the parameters of the algorithm (an average, or something more sophisticated), which define the composite clock. Prediction is also useful to avoid or minimize the frequency jumps of the composite clock when a clock is added or removed from the ensemble Several prediction methods has been tested on experimental data from the Italian time scale UTC(IT) and different atomic clocks, namely Cesium beams and Hydrogen masers using as reference the international time scale UTC; performances of the different approaches are investigated either in the short term prediction that may be of interest in satellite navigation system, or in the long term prediction which is essential for the national and international timekeeping functions.