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 wellestablished approach for the generation of 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 has a better stability than every single clock in the ensemble for all sample intervals. However, this quantity is not directly available, since it requires knowing the exact (and unobservable) states of each clock at each time step. A solution to achieve a physical output consists in realizing the IEM by steering a clock signal towards the IEM. To do so, a second Kalman filter is employed. The measurement of an additional clock, which does not contribute to the IEM, is combined with the estimated states produced by the first Kalman filter. This signal is used to estimate the states of the steered clock, which in turn allow the computation of the steering action by a regulator. The output of the steered clock provides in this way a physical realization of the IEM. The system for the IEM realization is quite complex and the resulting performances depend on a variety of factors, such as type and number of clocks in the ensemble, type of steered clock, the parameters of the regulator and the clock models. Given this complexity, it is not possible to exactly predict the stability of the generated IEM, once a set of settings is applied. 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 the entire system realizing the IEM can be simulated, in particular the clock ensemble, the first Kalman filter for IEM generation, the second Kalman filter for its realization and the control feedback loop. The simulation provides a flexible environment to prove a given setup of clocks and settings: the user can set the number and types of clocks generating the ensemble, as well as the clock being steered. Different steering techniques can then be used in order to steer the signal towards the IEM, for instance pole placement or the linear quadratic Gaussian regulator. The stability of the generated IEM is evaluated in terms of Overlapping Allan Deviation (OADEV). The simulation algorithm is tested with scenarios of increasing complexity: firstly, for validation purposes, the simulation results are compared with real measurements. In this case, a homogeneous ensemble and the correspondent IEM realization are measured and the simulated behavior shows good agreement with the measured one. Secondly, mixed ensembles are simulated: different scenarios are tested, where clocks of different types are composed together to achieve the desired performances. These results cannot be currently compared with real measurements since a hardware realization is still being implemented. Then, the parameters of the ensembling algorithm are changed and experimented. In particular, testing different regulators leads to achieving better steering performances in the various cases. Finally, the clock models used in the measurement generation and the state estimation are modified, in order to assess the effects of mismodelling on the resulting IEM. 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 in the composition algorithm must be researched with particular care. This work is supported by the Helmholtz-Gemeinschaft Deutscher Forschungszentren e.V. under grant numberZT-0007 (ADVANTAGE, Advanced Technologies for Navigation and Geodesy)