# Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning
## 6 Conclusions  
The atomic clock stability of most BDS satellites is assessed systematically with overlapping Allan deviation. For comparison, three sets of results were calculated using clock products from GFZ, WHU and broadcast ephemeris, respectively, in which the results with GFZ products show a slightly better performance than that of WHU products. However, the products from GFZ and WHU have an excellent agreement in Allan deviation. The comparison of Allan deviation results for BDS-2 and BDS-3 has shown that BDS-3 Rb and PHM clocks exhibit significant improvement in stability, and BDS-3 PHM clocks are much more stable than Rb clocks for long-term intervals. Meanwhile, all GPS Block IIF and Galileo FOC satellites were selected to compare the clock stability behavior with BDS satellites. The results indicate that BDS-3 Rb and PHM clocks are comparable to GPS Block IIF Rb and Galileo FOC-PHM clocks. Two methods, clock datum comparison and PPP, were applied to analyze the inter-system bias between BDS-2 and BDS-3. Through the comparison of clock products, the existence of clock datum discrepancy between BDS-2 and BDS-3 is confirmed indirectly. The time series of results for a total of 400 days indicates that the datum discrepancy performs quite stable. Thereafter, 10 static stations' data were collected to investigate the receiver clock offset for BDS-2 and BDS-3 by ionosphere-free PPP solutions. As expected, there is an obvious inter-system bias between BDS-2 and BDS-3, which is not only affected by the clock datum discrepancy but also by the difference of hardware delay. Similarly, the inter-system bias seems to be a constant after convergence and is excellently stable as well, across different days. Therefore, the inter-system bias must be considered in joint BDS-2 and BDS-3 applications. Furthermore, PPP solutions of five strategies are processed with broadcast ephemeris. The comparison results indicate that BDS-3 PPP performance based  
Figure 7: Time series of 68% level PPP error in vertical (top) and horizontal (bottom). The color of scattered plots indicates different strategies (black—GPS-only; red—BDS-3-only; blue—BDS-2+BDS-3 as one system; green—BDS-2+BDS-3 with ISB parameter estimation; yellow—BDS-2+BDS-3 with constant ISB; broadcast ephemeris are used for the above strategies; purple—BDS-2+BDS-3 with constant ISB used GFZ precise products; cyan—BDS-2+BDS-3 with constant ISB used WHU precise products). on broadcast ephemeris is enormously better than GPS. Owing to the improved satellite clock stability, the 68% level positioning accuracy for BDS-3 can be better than 0.65 m at 10 min, which is ameliorated greatly compared with BDS-2. The positioning performance for BDS-2+BDS-3 has great progress when estimating the ISB parameter or taking the ISB as a constant, which demonstrates that the BDS precise data processing is affected greatly by the ISB. Conceptualization, S.G. and X.G. ; methodology, F.M. ; software, S.G.; validation, F.M. and X.G. ; formal analysis, X.G. ; investigation, F.M. ; resources, Y.L. ; data curation, Y.Z. ; writing--original draft preparation, F.M. ; writing--review and editing, S.G. and X.G. ; visualization, X.X. ; supervision, Y.L. ; project administration, Y.L. ; funding acquisition, S.G. and X.G. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 41904016 and 42174029; and the China Postdoctoral Science Foundation, grant number 2019M662714. The precise clock products in this work were provided by the GeosForschungsZentrum and Wuhan University ([[ftp://igs.gnsswhu.cn/pub/gps/products/mgex](ftp://igs.gnsswhu.cn/pub/gps/products/mgex)]([ftp://igs.gnsswhu.cn/pub/gps/products/mgex](ftp://igs.gnsswhu.cn/pub/gps/products/mgex)), accessed on 10 December 2021). The authors express great gratitude to IGS and iGMAS for providing the GNSS data. The authors declare no conflict of interest.