Simulating the Realization of a Mixed Clock Ensemble

Global navigation satellite systems need a stable and robust system time in order to provide services with high accuracy. A well established approach for the generation of such a time scale is the composite clock method. Differently from single clock approaches, a set of clocks is used to define a system time scale by generating a weighted average of their single contributions. The clocks are measured with respect to each other and the measured signals are fed into a Kalman filter, which implicitly provides the system time of the ensemble, in terms of the implicit ensemble mean(IEM), a so called paper clock. The IEM generally exhibits a better stability than every single clock in the ensemble for all sample intervals. However, this quantity is not directly available in hardware, but can be realized by steering a clock with a dedicated control loop containing a second Kalman filter and a regulator. The output of the steered clock provides in this way a physical realization of the IEM. The system realizing the IEM is quite complex and the resulting performances depend on a variety of factors. Furthermore, the resulting behavior can only be evaluated after a sufficient amount of data is collected, which can take a long time. For these reasons, it is desirable to have a tool for simulating this system and thus analyzing the resulting IEM before launching extensive measurements. This paper describes how such a system can be simulated, by providing a flexible environment to prove a given setup of clocks and settings. The simulation algorithm is tested with scenarios of increasing complexity: firstly, for validation purposes, the simulation results are compared with real measurements. Secondly, different compositions of mixed ensembles are simulated. Then, the simulation is run by using different regulators and different parameters. Finally, the effects of mismodelling on the resulting IEM and its realization are assessed. In light of the long term goal of setting up a mixed clock ensemble in hardware, these analyses can reduce the invested time, as well as pointing out which aspects of the composition algorithm must be researched with particular care.