# Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning
## 5 BDS-2 and BDS-3 ISB Analysis and PPP Solutions
### PPP Solutions  
As discussed in Section 4.1, BDS-3 atomic clock stability has been improved significantly, the accuracy of broadcast ephemeris clock model may profit thereby. Accordingly, PPP solutions were processed with broadcast ephemeris to evaluate its positioning performance. In this paper, solutions calculated with broadcast ephemeris were different to the traditional single point positioning. Both code and phase observations were adopted when using broadcast ephemeris. As comparisons, precise products of GFZ and WHU were also utilized to process PPP solutions. The two-month (MJD 59154-59214) data were selected to process kinematic PPP solutions. To avoid the effects of broadcast ephemeris update, solution processes are restarted for every hour. Taking the fixed coordinates as references, positioning errors are calculated for each epoch. For more details of PPP strategy, we refer to Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Rec Type** & **GFZ** & **WHU** & **BRDC** & **GFZ-WHU** \\ \hline BjF1 & CETC & \(-0.21\) & \(-3.24\) & \(5.51\) & \(3.03\) \\ GUA1 & BD070 & \(2.69\) & \(-0.58\) & \(6.66\) & \(3.27\) \\ GUAM & JAVAD & \(-2.25\) & \(-6.03\) & \(2.98\) & \(3.78\) \\ KUN1 & UR4B0 & \(0.68\) & \(-2.42\) & \(4.86\) & \(3.1\) \\ LHA1 & CETC & \(0.11\) & \(-3.12\) & \(5.37\) & \(3.23\) \\ SGOC & JAVAD & \(-3.06\) & \(-6.90\) & \(0.54\) & \(3.84\) \\ SHA1 & UR4B0 & \(0.48\) & \(-2.35\) & \(5.63\) & \(2.83\) \\ WUH1 & CETC & \(0.58\) & \(-2.72\) & \(5.91\) & \(3.3\) \\ WUH2 & JAVAD & \(-2.83\) & \(-6.45\) & \(1.30\) & \(3.62\) \\ XIA1 & BD070 & \(3.73\) & \(0.10\) & \(7.07\) & \(3.63\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average values (ns) of the daily average differences. Figure 6: Time series of the receiver clock offset difference over a 3-day period. The results of 10 tracking stations are shown with an interval of 30 s in red (GFZ), blue (WHU) and green (BRDC). Figure 7 presents the time series of 68% level PPP error for vertical (up) and horizontal (N-E) components. The RMS values were calculated with the results after convergence (latter 40 min) and provided in Table 5. Five strategies with broadcast ephemeris, including GPS-only (GPS), BDS-3-only (BDS-3), BDS-2+BDS-3 as one system (BDS), BDS-2+BDS-3 with ISB parameter estimation (BDS-23) and with constant ISB in Table 3 (Constant ISB), were applied for comparison. According to the character of ISB in Section 5.1, it is estimated as a constant. The 68% level visible satellite number is 9, 10 and 21 for GPS, BDS-3 and BDS-2+BDS-3, respectively. The BDS-3 positioning performs significantly better compared with GPS under the same satellite number nearly, especially in vertical. This is probably because the vertical component is relatively sensitive to the ranging error that is affected by satellite clock offset, but the horizontal component is limited by the satellite network, thus it is less affected. It is interesting to find that the PPP performance of BDS-3 is pretty close to BDS in both vertical and horizontal, despite the fact that the visible satellite number is less than half of that of BDS, which indicates that the BDS-3 positioning service improved more than BDS-2. Moreover, a better convergence speed and accuracy for BDS-23 and Constant ISB compared with BDS reflect that the precise data processing is affected by the ISB between BDS-2 and BDS-3. Similar positioning performance for BDS-23 and Constant ISB further indicate the long-term stable characteristic of ISB. The 68% PPP accuracies at 10 min for BDS-3, BDS-23 and Constant ISB are better than 0.65 and 0.60 m, respectively. Due to the similar results between estimated ISB and constant ISB with precise products from GFZ and WHU, we only present the constant ISB results that have slightly faster convergence speed compared with the strategy of estimated ISB.