# High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Using Multi-Source Observations
## 3 Results
Wherein the red curves are the clock offsets directly calculated by L-band two-way clock offsets or superimposed by L-band two-way clock offsets and C-band inter-satellite clock offsets. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Satellite PRN**} & \multirow{2}{*}{ \begin{tabular}{c} **The STD of the Differences between Two** \\ **Kinds of Clock Offsets (ns)** \\ \end{tabular}  } & \multicolumn{2}{c}{**24 h Fitting Residual (ns)**} \\ \cline{3-4}  & & **ODTS Clock** & **Two-Way** \\ \hline C38 & 0.25 & 0.26 & 0.12 \\ C39 & 0.36 & 0.37 & 0.09 \\ C40 & 0.39 & 0.39 & 0.08 \\ C25 & 0.16 & 0.18 & 0.11 \\ C26 & 0.16 & 0.14 & 0.09  
By comparing the two curves, it can be found that although the red curves are in good agreement with the blue curves in most cases, the red curves become more divergent than the blue curves at the beginning and end of each segment, which indicate the two-way estimated clock offsets have more advantages than two-way clock offsets. The above phenomenon is because the new strategy effectively solves problems in the two-way superimposition strategy:  
* Because the new strategy uses the least square estimation method to estimate clock offsets and will not consider C-band two-way inter-station clock offsets with large noise, the clock offsets can always keep higher precision. * The final two-way clock offsets between the satellite atomic clock onboard and BDT are only realized through the two-way observation between the MCS larger diameter  
Figure 11: Satellite clock offset differences between the Ka-band inter-satellite estimated clock offsets and GBM products for 9 days. All of them are deducted the same trends per day (since 19 May 2022). Wherein, (**a**) are their detrended clock offsets, (**b**) are their differences. Figure 12: Satellite clock offset differences between the two-way estimated clock offsets and the two-way intraregional satellite clock offsets measured by superimposition strategy (since 19 May 2022). antennas and GEOs, and the elevation of antennas tracking to GEOs is unchanged all the time. The problem of antennas with low elevation no longer exists. * The new strategy only introduces three larger-diameter L-band antennas, each of which tracks to the specific GEO anytime. On this basis, the new strategy introduces the bias parameters to absorb the inconsistencies of observations of larger-diameter L-band antennas. All of the above considerations are able to suppress the \"step errors.\"
* In the new strategy, the concept of intraregional satellite and overseas satellite no longer exist. All satellites play the same role in the inter-satellite clock offsets estimation. Furthermore, their clock offsets with respect to BDT are not dependent on ISL plans and antenna status but can be calculated through the same clock offsets (reference GEO). Therefore, even if IGSOs and MEOs are not able to be observed by ground antenna, the accuracy of their clock offsets will not be lost. After obtaining the satellite clock offsets with higher accuracy, the BDS-3 is able to generate the satellite clock offsets parameters with higher accuracy. In most cases, BDS-3 satellite clock offsets parameters are generated by the satellite clock offsets of 2 h in history. Moreover, their prediction duration is less than 2 h. The Table 2. shows the statistical results of 2-h prediction errors of two-way estimated clock offsets for 9-day. From Table 2, the averaged RMS of all satellites is 0.29 ns, which is 29% of those calculated by the BDS-3 two-way superimposition strategy. Considering the clock offsets parameters errors of Galileo is 0.14 m (0.42 ns), the above results indicate that after using the new clock offsets estimation strategy, the accuracy of BDS-3 clock offsets parameters could reach or exceed those of Galileo.