Takahiro Kawaguchi

Takayuki Ishizaki, Takahiro Kawaguchi, Yuichiro Yano et al.

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.

Jiayu Chen, Takahiro Kawaguchi, Yuichiro Yano et al.

In this paper, we propose a hierarchical distributed timing architecture based on an ensemble of miniature atomic clocks. The goal is to ensure synchronized and accurate timing in a normal operating mode where Global Navigation Satellite System (GNSS) signals are available, as well as in an emergency operating mode during GNSS failures. At the lower level, the miniature atomic clocks employ a distributed control strategy that uses only local information to ensure synchronization in both modes. The resulting synchronized time or generated time scale has the best frequency stability, as measured by the Allan variance, over the short control period. In the upper layer, a supervisor controls the long-term behavior of the generated time scale. In the normal operating mode, the supervisor periodically anchors the generated time scale to the standard time based on GNSS signals, while in the emergency operating mode, it applies optimal floating control to reduce the divergence rate of the generated time scale, which is not observable from the measurable time difference between the miniature atomic clocks. This floating control aims to explicitly control the generated time scale to have the least Allan variance over the long control period. Finally, numerical examples are provided to show that the proposed architecture achieves an Allan variance on the order of $10^{-23}$ over averaging times ranging from one second to several days. This demonstrates its effectiveness and feasibility for high-precision, GNSS-resilient atomic timing.