# Clock Ensemble Algorithm Test in the Establishment of Space-Based Time Reference
## 5 Conclusions  
The LEO constellation provides several advantages in satellite navigation, such as strong signals on the ground and rapidly changing geometric positions. These benefits complement other GNSS constellations, such as MEO and HEO, and enhance the accuracy, integrity, continuity, and availability of GNSS. As a result, the LEO constellation has become a research focus in the satellite navigation field.  
This paper presents a novel concept of establishing a network of space-based synchronized references for time synchronization. We discuss the infrastructure and system architecture needed to establish the time reference, taking advantage of the development of optical frequency reference and inter-satellite laser link technology. The study evaluates  
Figure 9: RMS of prediction residuals for each satellite clock at three timescales.  
the performance of three Kalman clock ensemble algorithms, the natural Kalman clock ensemble algorithm, the reduced Kalman clock ensemble algorithm, and the two-stage Kalman clock ensemble algorithm, using the GFZ GNSS clock corrections. The results show that the accuracy of NKT and RKT are close when the satellite clock type is the same, although TKT has higher short and medium-term stability. Given the need for higher stability on timescales, hydrogen clocks outperform rubidium and cesium clocks for onboard satellites. Furthermore, a polynomial model is applied to predict the timescale generated by each algorithm. For prediction durations of less than one day, the TKT algorithm exhibits prediction residuals that are 1-2 orders of magnitude lower than those of NKT and RKT algorithms. Finally, the prediction accuracy of Galileo is found to be superior to that of BDS, while BDS is superior to GPS.  
Subsequently, our goal is to acquire clock data from LEO satellites and integrate them with data from medium and high-orbit satellite clocks to produce space-based time references. This approach will result in a more stable timescale that can be employed in a wider array of circumstances.  
Conceptualization, N.X., C.T. and Z.C.; Methodology, G.C., N.X., C.T. and Z.C.; Software, G.C.; Validation, G.C.; Investigation, G.C.; Writing--original draft, G.C. and N.X.; Writing--review and editing, N.X., C.T. and Z.C.; Funding acquisition, Z.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Research on key technology for combined solution of BDS ephemeris and satellite clock error based on monitoring receivers and inter satellite link observations, grant number 42004028.  
The data used in this study were sourced from the Das Helmholtz-Zentrum Potsdam -Deutsches GeoForschungsZentrum(GFZ). Readers may download the data from the following address: [[ftp://ftp.gfz-potsdam.de/GNSS/products/mgex/](ftp://ftp.gfz-potsdam.de/GNSS/products/mgex/)]([ftp://ftp.gfz-potsdam.de/GNSS/products/mgex/](ftp://ftp.gfz-potsdam.de/GNSS/products/mgex/)) (accessed on 10 June 2021).  
This work was supported by the Research on key technology for the combined solution of BDS ephemeris and satellite clock error based on monitoring receivers and inter-satellite link observations.  
The authors declare no conflict of interest.