Autonomous time synchronization scheme design for cislunar space navigation system

A cislunar space navigation system (CSNS), constructed based on halo orbits and special long-period orbits (SLPO) near the Earth-Moon L₁ libration point, promises significant augmentations in the positioning, navigation, and timing (PNT) services. The cornerstone of CSNS lies in the autonomous time synchronization and clock frequency stability of SLPO satellites. In this study, an autonomous time synchronization scheme is proposed utilizing libration point navigation satellites as “space-based tracking stations” to establish inter-satellite links (ISLs) with SLPO satellites and integrate X-ray pulsar timing data, thus achieving satellite time synchronization and frequency stability. By simulating high-fidelity X-ray photon timestamps and precise inter-satellite ranging data as raw measurement data, we implemented orbit determination and time synchronization for SLPO satellites using an extended Kalman filter (EKF). Additionally, we propose the onboard Vondrak-Cepek joint timing algorithm, which fully exploits the long-term stability of pulsars and the short-term stability of atomic clocks. Experimental results demonstrate that SLPO satellites equipped with high-stability and low-stability atomic clocks achieve timing precisions of 20 ns and 100 ns, respectively. Although the integration of X-ray pulsar data increases system complexity, it enhances the stability of the timing reference. The onboard joint ensemble timescale generated by the timing algorithm exhibits an order of magnitude improvement over the pulsar timescale in the short term, and maintains enhancements of 1 and 3 orders of magnitude in the long term compared to the two atomic time scales, the high-stability and the low- stability, respectively. This autonomous time synchronization scheme fully leverages the stability of pulsars and atomic clocks and can be applied to space time transfer services in similar contexts.