# Research on Distributed Autonomous Timekeeping Algorithm for Low-Earth-Orbit Constellation
## 1 Introduction  
Satellite navigation systems provide accurate positioning, navigation, and timing services around the clock, playing a crucial role in transportation, communications, national defense, energy management, and other fields. Time synchronization is fundamental to the ability of satellite navigation systems to deliver these services. To ensure high-precision time synchronization and satisfy the internal user requirements of each system, every navigation system establishes and maintains its time reference, known as the GNSS time [1]. For multi-system compatibility and interoperability, navigation satellites broadcast signals that include conversion parameters, allowing for the translation between different systems' time references. Additionally, the time references of the four major navigation systems are regularly traced back to Universal Time Coordinated (UTC), thereby better serving human production and daily life. However, the time reference for current satellite navigation systems is predominantly generated by the ground-based main control station, which compromises the system's ability to provide continuous time services to the equipment and users when the ground station fails. This reliance reveals significant weaknesses in the reliability and robustness of existing systems, particularly in harsh environments orwhen ground facilities are damaged. For instance, the Galileo global satellite navigation system experienced a 139 h service interruption from 12 to 17 July 2019, severely impacting users. Therefore, next-generation satellite navigation systems must have autonomous onboard timekeeping capabilities to continue providing services even when the ground control center is unavailable [2]. The LEO constellation has the characteristics of high signal power, rapid change of geometric configuration, and low transmission delay, which can be used to accelerate the convergence speed of high-precision point positioning and broadcast navigation enhancement information. Currently, countries across the world are accelerating the deployment of low-Earth-orbit constellations to achieve higher-quality navigation services. The LEO constellation consists of a large number of satellites, and relying on ground infrastructure to establish time references can place a significant load on the satellite-ground links and lead to reliability issues. Establishing and maintaining a space-based time reference, known as LEO time, by utilizing inter-satellite links and clock resources from low-Earth-orbit constellations is therefore important. This system fulfills the time synchronization requirements of LEO constellations and simultaneously serves as a backup for GNSS time, thereby enhancing the overall system reliability [3; 4; 5]. The German Aerospace Center has conducted preliminary theoretical research on the space-based time reference system by deploying iodine molecular clocks on 4-6 Kepler satellites and establishing laser bidirectional links with MEO satellites to achieve time synchronization, which can contribute to the establishment of more stable time references [6; 7]. Currently, numerous scholars have extensively researched autonomous timekeeping technologies based on inter-satellite links, yielding significant theoretical advancements. Studies have proposed the use of rubidium and hydrogen clocks to establish two independent time references, where the hydrogen clocks control the rubidium clocks, thereby fully utilizing the characteristics of the clocks [8; 9]. A two-level time reference generation framework has been introduced, employing the simulation of mercury ion optical clocks and passive hydrogen clocks to enhance the time reference stability [10]. It has been highlighted that centralized processing methods are constrained by the onboard computational capacity, prompting the design of a distributed autonomous timekeeping algorithm based on Kalman filtering [11].