Explicit Ensemble Mean Clock Synchronization for Optimal Atomic Time Scale Generation
This work provides a foundational theory for explainable timing systems, addressing the need for unified and optimal synchronization in atomic clock networks.
This paper introduces a unified theoretical framework, explicit ensemble mean (EEM) synchronization, for atomic time scale generation, clock synchronization, and oscillator frequency regulation. It proves that standard Kalman filtering is a special case of this framework and achieves optimal long-term frequency stability in terms of Allan variance.
This paper presents a novel theoretical framework, called explicit ensemble mean (EEM) synchronization. This framework unifies time scale generation, clock synchronization, and oscillator frequency regulation within the systems and control theory paradigm. By exploiting the observable canonical decomposition of a standard atomic ensemble clock model, the system is decomposed into two complementary components: the observable part, which represents the synchronization error, and the unobservable part, which captures the synchronization destination. Within this structure, we mathematically prove that standard Kalman filtering, which is widely used in current time scale generation, not only performs observable state estimation, but also significant unobservable state estimation, and it can be interpreted as a special case of the proposed framework that optimizes long-term frequency stability in terms of the Allan variance. Furthermore, applying state feedback control based on Kalman filtering to each component achieves optimal time scale generation, clock synchronization, and oscillator frequency regulation in a unified manner. The proposed framework provides a foundation for developing explainable timing systems.