arXiv subjects

Takahiro Kawaguchi

Publications and source records attributed to Takahiro Kawaguchi.

8 recordsLinked to original sources

arXiv2026

Hierarchical Distributed Architecture for the Least Allan Variance Atomic Timing

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.

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arXiv2026

Explicit Ensemble Mean Synchronization for Time Scale Generation with Mixed Atomic Clock Ensembles

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.

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arXiv2026

Explicit Ensemble Mean Clock Synchronization for Optimal Atomic Time Scale Generation

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.

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arXiv2023

Structured Kalman Filter for Time Scale Generation in Atomic Clock Ensembles

In this article, we present a structured Kalman filter associated with the transformation matrix for observable Kalman canonical decomposition from conventional Kalman filter (CKF) in order to generate a more accurate time scale. The conventional Kalman filter is a special case of the proposed structured Kalman filter which yields the same predicted unobservable or observable states when some conditions are satisfied. We consider an optimization problem respective to the transformation matrix where the objective function is associated with not only the expected value of prediction error but also its variance. We reveal that such an objective function is a convex function and show some conditions under which CKF is nothing but the optimal algorithm if ideal computation is possible without computation error. A numerical example is presented to show the robustness of the proposed method in terms of the initial error covariance

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arXiv2023

Higher-Order Allan Variance for Atomic Clocks of Arbitrary Order: Mathematical Foundation

In this paper, we perform a time-domain analysis of the higher-order Allan variance for atomic clock models of arbitrary order. Adopting a standard atomic clock model where the time series of the clock reading deviation is expressed as a Wiener or integrated Wiener process, we define the higher-order Allan variance as the mean squared higher-order difference of the clock reading deviation. The main results of this paper are threefold. First, we prove that the higher-order difference operation of the clock reading deviation, which can be interpreted as a linear aggregation with binomial coefficients, is not only sufficient but also necessary for a resulting aggregated time series to be an independent and identically distributed Gaussian process. Second, we derive a complete analytical expression of the higher-order Allan variance, which consists of both time-dependent and time-independent terms. Third, we prove that the higher-order Allan variance is time-independent if and only if the order of difference operation is greater than or equal to the order of the atomic clock model.

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arXiv2023

Relations Between Generalized JST Algorithm and Kalman Filtering Algorithm for Time Scale Generation

In this paper, we present a generalized Japan Standard Time algorithm (JST-algo) for higher-order atomic clock ensembles and mathematically clarify the relations of the (generalized) JST-algo and the conventional Kalman filtering algorithm (CKF-algo) in the averaged atomic time and the clock residuals for time scale generation. In particular, we reveal the fact that the averaged atomic time of the generalized JST-algo does not depend on the observation noise even though the measurement signal is not filtered in the algorithm. Furthermore, the prediction error of CKF- algo is rigorously shown by using the prediction error regarding an observable state space. It is mathematically shown that when the covariance matrices of system noises are identical for all atomic clocks, considering equal averaging weights for the clocks is a necessary and sufficient condition to ensure equivalence between the generalized JST-algo and CKF-algo in averaged atomic time. In such homogeneous systems, a necessary and sufficient condition for observation noises is presented to determine which algorithm can generate the clock residuals with smaller variances. A couple of numerical examples comparing the generalized JST-algo and CKF-algo are provided to illustrate the efficacy of the results.

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arXiv2020

Modularity-in-Design of Dynamical Network Systems: Retrofit Control Approach

In this paper, we develop a modular design method of decentralized controllers for linear dynamical network systems, where multiple subcontroller designers aim at individually regulating their local control performance with accessibility only to their respective subsystem models. First, we derive a constrained version of the Youla parameterization that characterizes all retrofit controllers for a single subcontroller, defined as an add-on type subcontroller that manages a subsystem. The resultant feedback system is kept robustly stable for any variation in the neighboring subsystems, other than the subsystem of interest, provided that the original system is stable prior to implementing the retrofit control. Subsequently, we find out a unique internal structure of the retrofit controllers, assuming that the interaction input signal from the neighboring subsystems is measurable. Furthermore, we show that the simultaneous implementation of multiple retrofit controllers, designed by individual subcontroller designers, can improve the upper bound of the overall control performance. Finally, the practical significance of the method is demonstrated via an illustrative example of frequency regulation using the IEEE 68-bus power system model.

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arXiv2018

Retrofit Control with Approximate Environment Modeling

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.

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