Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference

A new concept of a space-based synchronized reference network is proposed with the development of an optical frequency reference and laser inter-satellite link. To build such time reference, three clock ensemble algorithms, namely the natural Kalman timescale (NKT) algorithm, the reduced Kalman timescale (RKT) algorithm, and the two-stage Kalman timescale (TKT) algorithm are considered. This study analyzes and compares the performance of these algorithms using BDS, GPS, and Galileo satellite clock data from the GFZ GNSS clock corrections, which will be used in constructing future space-based time references. The study shows that the NKT algorithm improves frequency stability by 0.1-0.2 orders of magnitude in the short and medium term. When the satellite clock is mostly a hydrogen clock, the RKT and NKT are close, and the short and medium-term frequency stability slightly increases. In contrast, the TKT algorithm produces a timescale that improves frequency stability by 1-3 orders of magnitude. A quadratic polynomial model predicts the three timescales, with the results indicating that the short-term prediction accuracy of the satellite clock is within 1ns, and the TKT algorithm's prediction accuracy is 1-2 orders of magnitude higher than that of the NKT and RKT algorithms. With the deployment of next-generation Low Earth Orbit (LEO) satellites equipped with higher-precision clocks, the space-based time reference system will achieve improved accuracy and greater potential for practical applications.