# Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference
## 2 Clock Ensemble Algorithm  
### Infrastructure and System Architecture of Space-Based Time Reference  
A space-based timescale hinges upon the manufacture and measurement of high-precision space atomic frequency standards (SAFS). As to the former aspect, besides three classical options: the thermal Cs beam, the hydrogen maser (H-maser) (passive or active), and the Rb atomic frequency standard (RAFS), there come several successors such as mercury trapped-ion [18; 19], and some other Cs beam or Rb vapor cell clocks with new optical technologies [20; 21; 22; 23; 24]. The frequency stability of new generation clocks in both the short and long term is higher than that of classic satellite clocks in half or even one order of magnitude [1], and our approach to optical lattice clock, whose uncertainty is currently known as the least on the ground [25].  
As to the latter aspect, the measurement and synchronization of the space-borne atomic clocks are carried out by orbit determination and time synchronization (ODTS) technologies. Though GPS, Galileo, and BDS use different ODTS strategies, the basic means are satellite-ground unidirectional and bidirectional time comparison techniques [26]. They can lead to orbit precision of 5-30 cm for MEO in most GNSSs [27]. According to the Multi-GNSS Experiment (MGEX) final products, the accuracy of satellite clock bias is about 0.3 ns for GPS and 0.6-1.2 ns for MEO in BDS [28; 29]. Only using a satellite-ground link makes the estimated parameters, such as the radial direction of the orbit, the clock bias, and the antenna phase center offset, have strong degeneracy. Inter-satellite Link(ISL) can bring great profit to break this degeneracy and improve the precision of orbit and clock bias [30]. BDS began to test ISL in Ka-band in 2016 and applied ISL to BDS-3 to promote global service capability [31; 32]. Thanks to ISL, the clock predicting error can be improved from 2-4 ns to less than 1 ns [33]. Compared to the precision of time comparison of the clock ensemble on the ground, there remains a certain disparity. To compare time over a long distance, two-way satellite time and frequency transfer (TWSTFT) and precise point positioning (PPP) are advised by BIPM [34; 35; 36]. The stability of time comparison using PPP and TWSTFT are 0.3 and 0.2 ns, respectively, and the accuracy with TWSTFT is 0.5-0.75 ns [35]. Optical fiber brings the highest accuracy of time and frequency transferring, which is better than 0.1 ns [37; 38]. Since laser inter-satellite link leads to higher time comparison accuracy, it may push space-based timescale to catch up with ground-based timescale.  
At present, the majority of LEO constellations are in the testing or basic setup stages. Some of them aim to provide stable and reliable broadband Internet communication services worldwide, and some of them aim to augment current GNSS. With high precision SAFS, it also has the potential to expand into a navigation constellation, and its capability to provide positioning, navigation, and timing services has been confirmed [39]. Especially high-quality GNSS products can obtain from IGS or its analysis centers, and high-accuracy services are provided by BDS and Galileo with B2b and E6-B signals, respectively [40; 41; 42]. LEO can achieve centimeter orbit precision by PPP technique with high accuracy carrier phase bias correction [40].  
Based on all the technical progress mentioned above, the idea of establishing a space-based time system has been widely discussed. For instance, the Kepler system provides one possible architecture, that is, six LEOs adding to the Galileo-like system, where the LEOs serve as reference stations. With the continuous development of LEO satellite technology and the GNSS system, it is expected that more space-based time systems will be proposed in the future.