Composite Clock Algorithms for System Time in Global Navigation Satellite Systems

Clock ensembling is a well-established concept for creating robust and stable time frames, e.g. it is used to define the Universal Time Coordinated as well as the GPS system time. In order to reference Global Navigation Satellite Systems (GNSSs) to a terrestrial time scale, the provision of a robust, reliable and stable system time is a mandatory key aspect. Here, we propose a mixed clock ensemble for system time generation in future GNSSs that exploit inter-satellite optical links to synchronize all elements of the constellation. We consider a Kalman filter-based algorithm which combines several different clock types. The algorithm computes predictions based on advanced clock models and updates the predicted state vector by processing differential measurements between the clocks in the ensemble. The state vector, which includes all parameters describing the clock behavior (i.e. phase, frequency and potentially Gauss-Markov states) is then used to produce a weighted average, named Implicit Ensemble Mean (IEM). The so-formed Composite Clock (CC) typically performs at the level of the best frequency reference of the ensemble for all time intervals in terms of stability. However, the so computed IEM is only a software solution with no physical/electrical output signal. In some cases a real signal output of this IEM is desirable or even mandatory, i.e. if it is used for synchronization of signals broadcasted by navigation satellites. The proposed mixed clock ensemble consists of both optical frequency references and classical microwave clocks. With this ensemble it is possible to realize a CC with fractional frequency stability below 10^-15 [s/s] for time intervals between 10^0 and 10^5 s, serving as system time as well as an essential component of the synchronization scheme