## 5 BDS PPP with Different Clock Interval  
Due to the stochastic characteristic of the clock variations, the interpolation of the low-rate satellite clock products has a relatively large loss of precision. As a result, it is not sufficient for high-rate (up to 1 Hz) precise positioning and applications. When processing 1 Hz measurements at epochs that do not coincide with sampling epochs of the ephemeris products, the orbit and clock offset of the observed satellites have to be obtained through interpolation. In contrast to orbit data, high-order polynomial interpolation is not suitable for clock parameters due to the underlying random noise processes; therefore, linear interpolation is advisable [20].  
We utilized BDS WHU 1 s clock solutions to assess the errors associated with the interpolation of 5 s, 30 s, and 300 s clock data sets. Firstly, we resampled the BDS WHU 1 s clock products to 5 s, 30 s, and 300 s interval products. Secondly, the 5 s, 30 s, and 300 s data sets were interpolated to a 1 s interval, respectively. Finally, they were compared with the 1 Hz products using the double-difference approach described in Section 3.  
The 1 s WHU clocks were estimated based on the 13 GNSS stations with 1 s intervals, which are mainly deployed in the China-Australia area. When we calculated the interpolation errors, we took station LASA as a reference. In other words, we only compared the tracking arcs (epochs) that are visible in LASA station with elevation cutoff angle of 7\({}^{\circ}\).  
The clock interpolation errors are summarized in Figure 6 for the individual clock types. The best interpolation results are obtained from 5 s intervals. The largest errors are obtained from 300 s intervals. For 30 s intervals, the interpolation errors are better than 0.02 ns (i.e., 0.6 cm), while for 300 s intervals, the interpolation errors increase to 0.04 ns (1.2 cm) level.  
To further investigate the contribution of clock corrections with different sampling intervals, we conducted BDS PPP to process the same data as Section 4 by applying satellite clock products at 300 s, 30 s, 5 s, and 1 s intervals, respectively. To demonstrate the accuracy of BDS PPP solutions (prior to the earthquake), we randomly took five segments of BDS data, each with a length of 30 min, and computed the RMS of BDS PPP with clock intervals of 1 s, 5 s, 30 s, and 300 s for all four cases, which are listed in Table 8. Shown in Figure 7 is one segment of the error performances of BDS PPP in the east, north, and vertical components with clock intervals of 1 s, 5 s, 30 s, and 300 s respectively. From the  
Figure 6: STD of BDS clock interpolation error for 5 s, 30 s, and 300 s intervals.  
mean values of Table 8, it could be concluded that the PPP with 300 s clock intervals is the worst and that with 1 s clock interval is the best. Comparing the results with 1 s and 5 s clock intervals, they have almost the same precision, which means that the contribution of 5 s clock intervals are almost equal to 1 s clock interval.  
In addition, we retrieved the displacements waveforms with BDS PPP (during the earthquake) using different clock products at intervals of 1 s, 5 s, 30 s, and 300 s (Figure 8); results clearly show that 1 s and 5 s clock product demonstrate more stable and reliable waveforms. Considering the time consumption of clock estimates, we suggest that 5 s clock interval is competent for the requirement of high-rate BDS solutions. This phenomenon is consistent with that derived from GPS PPP results [18].