High Precision Distributed Time Synchronization with Mobile Atomic Clock Network

The National Institute of Information and Communications Technology (NICT) generates and supplies Japan Standard Time (JST), which is essential to our modern lives, to all regions of Japan. JST is generated by integrating about 20 high-precision atomic clocks, including hydrogen maser clocks, cesium beam atomic clocks, and optical lattice clocks. Current atomic clocks are too large to be portable, but it is envisioned that in the near future, after 2030, smartphones and other mobile devices will be equipped with inexpensive, compact atomic clock chips.

As a joint research project with NICT, Gunma University, Tokyo University of Marine Science and Technology, Seiko Solutions Corporation, and Raidrix Inc, we are conducting research and development of distributed time synchronization technology in anticipation of the widespread use of atomic clock chips. In this research project, by making full use of advanced systems control theory, we will develop a distributed algorithm to achieve ultra-precise time synchronization for a group of atomic clocks whose network structure changes from moment to moment. Specifically

Development of a maximum likelihood time estimation algorithm that takes into account the delay of time comparison information

Development of a distributed cooperative control algorithm for aggregating a large number of atomic clocks

Development of anomaly detection algorithms to detect degradation of atomic clocks

Development of an algorithm to optimize the frequency of time comparison

and so forth. Integration of technologies and knowledge in the field of systems control, such as distributed cooperative control, stochastic systems, Kalman filter, maximum likelihood estimation, machine learning, and event-triggered control, is essential for these research and development efforts.

The distributed time synchronization algorithm developed by our research group will be validated through emulation using NICT's comprehensive testbed environment (StarBED4), and then implemented in an actual device with an atomic clock chip developed by Seiko Solutions and others. Ultra-precise time synchronization using a mobile atomic clock network is also positioned as the basis for the realization of Beyond 5G. Deployment areas range from smart grids, financial transactions, broadcasting, and automated driving. Through this research and development, we aim at contributing to the future advanced information and communication society through systems control theory.

Ministry of Internal Affairs and Communications (MIC): R&D for Expansion of Radio Resources

Subject: R&D of Radio Time and Frequency Synchronization Technology with Compact Atomic Clocks: Development of Distributed Time Synchronization Algorithm (2022.08.01-2026.03.31)

NICT, Tokyo Institute of Technology, Gunma University, Tokyo University of Marine Science and Technology, Seiko Solutions Corporation, Raidrix Inc.

Please contact us if you are interested in working as a post-doctoral researcher.

## Research Achievements

### Development of Mathematical Foundation for Evaluating Various Time Fluctuations in Atomic Clocks: Contribution to High-Precision Time Synchronization Indispensable for Beyond 5G/6G

Tokyo Tech News (2023.12.20) Explaining the article "T. Ishizaki, T. Ichimura, T. Kawaguchi, Y. Yano, Y. Hanado: Higher-Order Allan Variance for Atomic Clocks of Arbitrary Order: Mathematical Foundation. Metrologia, 60(1), 2024" [⎋]

### International Conference Proceedings

Yuyue Yan, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Spectral Decomposition in Kalman Filter Algorithm for Homogeneous Atomic Clock Ensembles. Proc. of The 62nd IEEE Conference on Decision and Control (CDC 2023), to appear.

Yuyue Yan, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Equivalence of JST Algorithm and Kalman Filtering Algorithm for Time Scale Generation. Proc. of The 2023 IEEE International Symposium on Precision Clock Synchronization for Measurement, Control, and Communication (ISPCS 2023), to appear.

Takayuki Ishizaki, Taichi Ichimura, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado: Analytical Expression of Higher-Order Allan Variance for Atomic Clock Models. The 2023 Joint Conference of the IEEE International Frequency Control Symposium & European Frequency & Time Forum (IFCS-EFTF 2023), to appear.

Takahiro Kawaguchi, Yuto Kakinuma, Takayuki Ishizaki, Yuichiro Yano, Yuko Hanado: State Estimation of Atomic Clocks by Kalman Filter Using Time-Delayed Observation. The 2023 Joint Conference of the IEEE International Frequency Control Symposium & European Frequency & Time Forum (IFCS-EFTF 2023), to appear.

Taichi Ichimura, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Evaluation of Stability of Higher-Order Atomic Clocks by Higher-Order Allan Variance. Proc. of The 22nd IFAC World Congress (IFAC WC 2023), to appear.

Yuyue Yan, Nicholas John Jensen, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Possibility of Prediction Improvements for Atomic Clock Ensembles: Basis Selection in Undetectable Systems. Proc. of The 22nd IFAC World Congress (IFAC WC 2023), to appear.

### Journal Papers

Yuyue Yan, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Structured Kalman Filter for Time Scale Generation in Atomic Clock Ensembles. IEEE Control Systems Letters. in press. [arXiv]

Takayuki Ishizaki, Taichi Ichimura, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado: Higher-Order Allan Variance for Atomic Clocks of Arbitrary Order: Mathematical Foundation. Metrologia, in press, 2023. (DOI: 10.1088/1681-7575/ad02fe) [arXiv] Tokyo Tech News

Murugesan Sathishkumar, Takayuki Ishizaki, Yen-Chen Liu: Resilient Annular Finite-Time Synchronization for Master-Slave Systems Under Scaling Attacks. IET Control Theory & Applications. in Press.

Taichi Ichimura, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Higher-Order Allan Variance for Frequency Stability Evaluation of Multi-Dimensional Atomic Clocks, IEEJ Transactions on Electronics, Information and Systems, in press (in Japanese).

### Working Papers

Yuyue Yan, Takahiro Kawaguchi, Yuichiro Yano, Yuko Hanado, Takayuki Ishizaki: Relations Between Generalized JST Algorithm and Kalman Filtering Algorithm for Time Scale Generation. [arXiv]