# High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Using Multi-Source Observations
## 4 Conclusions  
In order to improve the signal-in-space accuracy of the BDS-3 satellite, the paper introduces the two-way superimposition strategy and analyzes its problems in satellite clock offsets measured. The analysis shows that BDS-3 uses the two-way superimposition strategy that can effectively calculate the clock offsets, both including intraregional satellite and overseas, with respect to BDT in real-time. Nevertheless, suffering from antenna zero value error, the low elevation angle of antennas, and the large noise of C-band inter-station clock offsets, the clock offsets calculated by BDS-3 are not accurate enough. This problem is the main factor limiting the improvement of space-in-signal accuracy for BDS-3. Based on the above analysis, the paper optimizes and updates the BDS-3 strategy in BDS-3 satellite clock offsets estimation. Unlike the simple superposition of two-way observations, the new strategy from the perspective of least square estimation takes full advantage of the BDS-3 multi-source observation and the BDS-3 constellation characteristics to circumvent problems in the two-way superimposition strategy so as to improve the accuracy of the BDS-3 satellite clock offsets. The satellite clock offsets estimated by the new strategy have the following characteristic:  
* The two-way estimated clock offsets retain the advantages of two-way clock offsets, which are less affected by propagation and position errors than one-way downlink clock offsets. * All ISLs maintain the inter-satellite relative variation of two-way estimated clock offsets. The inter-satellite relative variation of two-way estimated clock offsets is independent of satellite-ground links. * All satellite clock offsets are traced to BDT by the same clock offsets, which are only affected by the observations of three large-diameter L-band antennas. By optimizing and updating, the BDS-3 is able to improve the accuracy of not only BDS-3 inter-satellite clock offsets but also the final BDS-3 satellite clock offsets with respect to BDT. Making the differences between the clock offsets estimated by the new strategy and the GBM products, the average STD of their clock offsets is 0.19 ns, wherein MEO is 0.14 ns. Furthermore, compared with the inter-satellite clock offsets of GBM products, the 24-h fitting residual of two-way estimated clock offsets is more stable. The above results indicate that: Only relying on ISLs and a few L-band large-diameter antennas, the BDS-3 can realize the global satellite clock offsets real-time estimation with the same accuracy level as the clock offsets estimated by more than one hundred global-distributed GNSS stations [33; 35]. After adopting the new strategy, the accuracy of the satellite clock offsets parameter can be improved from 1.05 ns (0.35 m) [8] to 0.29 ns (0.09 m), about 71%. This result indicates the ISL can not only solve the problems of insufficient observation in overseas satellite clock offsets estimation but also can enhance the accuracy of satellite clock offsets parameters of intraregional satellites. The signal-in-space errors of BDS-3 broadcast ephemeris are 0.09 m. Considering that the SISRE are less than the sum of the broadcast ephemeris errors and clock offsets parameter errors [8], after adopting the proposed strategy in the BDS-3 time synchronization system, the signal-in-space accuracy of the BDS-3 navigation message can be less than 0.2 m at least. This result is of great significance to the performance improvement of BDS. As shown in Table 2, after BDS-3 used the new strategy to estimate the clock offsets, a puzzling discovery is that despite the performance of all BDS-3 clock offsets are different, there is little difference between their prediction ability. The reason is plotted in Figure 13. Multi-day fitting residuals of all satellites with the highest-level-performance atomic clock present the almost common fluctuation, and the same fluctuation is found in the output signals of BDT.