## 4 Discussion
### Cycle Slip  
In our triple-differencing approach, the availability of GNSS observations, and therefore the number of constructed PCC measurements, are susceptible to cycle slips since the carrier-phase ambiguities are to be eliminated by the time-differencing operation. Figure 13 shows the numbers of detected cycle-slips. It is obvious that at the eighth day, there were a remarkably large number of cycle-slips. This explains why only a small number of PCC measurements were obtained on the eighth day, while the number of common-view satellites was normal. Both Figures 5 and 7g have already illustrated this. In addition to the eighth day, the other days also suffered from a considerable number of cycle slips. Specifically, the average numbers of cycle slips in one minute were 24.53 and 61.49 for GPS and BDS, respectively. The quantity as well as the frequency of cycle slip can severely reduce the number of available GNSS observations. For example, if the time-differencing interval is set to one hour, and a satellite suffers from a cycle-slip every 50 min, then all the observations of this satellite cannot be used to construct the triple-differenced PCC measurements.  
Figure 12: BDS antenna calibration deviations (**a**–**h**) different examples.  
Figure 13: Number of detected cycle-slips at each day.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Statistics** & **a** & **b** & **c** & **d** & **e** & **f** & **g** & **h** \\ \hline RMSE (mm) & 3.547 & 3.149 & 3.566 & 3.174 & 3.084 & 3.149 & 3.587 & 3.767 \\ Max. (mm) & 14.884 & 9.434 & 13.328 & 10.997 & 9.351 & 9.422 & 17.973 & 12.432 \\ Min. (mm) & \(-14.934\) & \(-7.666\) & \(-7.445\) & \(-9.066\) & \(-9.438\) & \(-7.678\) & \(-9.651\) & \(-8.764\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistics of BDS antenna calibration deviations.  
Furthermore, when the low-cost GNSS antennas are adopted, the cycle slips can be even more severe. In our tests, we used a combination of real GNSS observations and simulated PCCs to construct the test data, where the original GNSS observations were collected by high-grade antennas. Compared with the high-grade antennas, the low-cost antennas have difficulty suppressing multipath interference, and the output signal strength is relatively weak, all of which can cause cycle slips.  
Consequently, some compensation methods are needed to cease cycle slips during the data collection process: (1) collect data using high-quality GNSS receivers with stabilized clocks, and choose the cables with good low-loss characteristics; (2) carefully select the data collection site, and keep the surrounding area clear of objects that may block satellite signals, therefore reducing the case of signal interruption; and (3) adopt appropriate methods, such as installing a choke ring, to suppress signals of the negative elevation angle. Considering that the antennas are static during the data collection process, the above method should be able to relieve frequent cycle slips. Moreover, under harsher cases, it is possible to increase the number of constructed PCC measurements by extending the data collection duration by a few days, or decreasing the time-differencing interval as long as it can be guaranteed that there is a significant change of satellite distribution over the interval.