Takahiro Kawaguchi

Priyanka Dey, Takahiro Kawaguchi, Yuichiro Yano et al.

In this paper, we consider a mixed ensemble containing a mixture of cesium-type and hydrogen maser-type atomic clocks. For the mixed ensemble, the conventional Kalman filtering algorithm has certain limitations due to divergence of the error covariance matrix. To overcome these limitations, we obtain a Kalman filtering algorithm based on observable canonical decomposition that does not have any diverging terms. We use the estimates from the transformed Kalman filter to propose a time scale generation algorithm called explicit ensemble mean synchronization algorithm for the mixed ensemble. In this algorithm, we synchronize the time deviation of each clock from the ideal clock behavior to the unobservable ensemble mean of the phases where the weighting can be decided by the user. By regulating the free-running dynamics associated with the unobservable state, through choosing an appropriate weight vector, the frequency stability of the generated time scale or the synchronized time shared by the clocks is optimized over shorter (resp. longer) intervals, as measured by Hadamard variance. An illustrative example is given to demonstrate the efficiency of our algorithm.

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.

Takayuki Ishizaki, Takahiro Kawaguchi, Hampei Sasahara et al.

In this paper, we develop a retrofit control method with approximate environment modeling. Retrofit control is a modular control approach for a general stable network system whose subsystems are supposed to be managed by their corresponding subsystem operators. From the standpoint of a single subsystem operator who performs the design of a retrofit controller, the subsystems managed by all other operators can be regarded as an environment, the complete system model of which is assumed not to be available. The proposed retrofit control with approximate environment modeling has an advantage that the stability of the resultant control system is robustly assured regardless of not only the stability of approximate environment models, but also the magnitude of modeling errors, provided that the network system before implementing retrofit control is originally stable. This robustness property is practically significant to incorporate existing identification methods of unknown environments, because the accuracy of identified models may neither be reliable nor assurable in reality. Furthermore, we conduct a control performance analysis to show that the resultant performance can be regulated by adjusting the accuracy of approximate environment modeling. The efficiency of the proposed retrofit control is shown by numerical experiments on a network of second-order oscillators.