## 4 Results and Discussion
### Assessment of BDS-Only PPP with Multipath Correction  
The a priori precision of GEO phase observations is usually set lower than GPS and GLONASS to account for the lower precision of orbit and clock products. However, the constant bias at the satellite can be partially absorbed by the time-invariant parameters such as ambiguities, and the remaining periodic errors can be mitigated by the SF approach. Therefore, it is expected that the positioning precision improves by properly setting the weight of the GEO phase observation. For this paper, four weighting schemes with a priori precisions of 15 mm, 10 mm, 6 mm, and 3 mm, named as (1) to (4), respectively, were designed. The smaller the precision value, the higher the observation weight, which contributes more to the PPP solution. For each scheme, two types of BDS-only solutions were calculated. For one solution, all the BDS observations were sidereally filtered. whereas for the other one, only the observations from the MEO and IGSO BDS satellites were filtered. About eight BDS satellites were visible on average during the observation, of which five were GEO satellites. Figure 7a shows the results without sidereal filtering for the GEO satellites at station GSWX on DOY 219, 2018, along with the mean root-mean-square (RMS) statistics for all stations. The weekly averaged positioning solutions are used as references. As can be seen, large wiggles, varying from a few centimeters to tens of centimeters, occur in all three components, especially for the up component. The best accuracies of the estimated displacements are achieved by weighting scheme (1) with the RMS values of 7.51, 3.50, and 11.38 cm for the east, north, and up components, respectively, and then they decrease with the increase of the a priori phase precision. The statistics are consistent with that of [PERSON] et al. (2018). This occurs because improperly setting the a priori precision higher magnifies the negative effects of the periodic errors in the GEO phases on the PPP solution. After applying sidereal  
Figure 6: Carrier-phase residuals of C01 and C03 on two frequencies at stations DAE2, DAEJ, and GMSD from DOY 222 to 303, 2018. The opposite values of residuals on the second frequency are used. filtering on GEO carrier-phase observations, the displacement noises are effectively alleviated for all schemes, as shown in Figure 7b. As the optimal results among four schemes, scheme (2) has the smallest RMS values, which are dramatically reduced by 75.2%, 42.8%, and 56.7%, compared to the unfiltered ones, to 2.00, 2.23, and 5.58 cm for the three components, respectively. This indicates that the SF approach can significantly improve the precision of GEO phase observations to around 10 mm, thereby making a better contribution to the PPP solution. Consequently, the a priori phase precision of GEO satellites was set to 10 mm for the following experiments. The power spectral densities (PSDs) for scheme (2) were also calculated using [PERSON]'s method for each station, and then averaged for all the PSDs for the specific frequency from all stations, as shown in Figure 8. It is clear that the SF approach mainly reduces the PSDs on the longer periods over 2000 s. In other words, the periodic errors of the GEO phase observations primarily weigh on the lowest frequency band. The PSD reductions are 3 dB and 5 dB, for the north and up components. In contrast, for the east component, the reduction can reach up to 20 dB since the periodic errors are primarily projected to the east-west direction due to the special distribution of the GEO satellites. Figure 7: 12 h displacements (cm) with respect to weekly averaged positioning solutions for the east, north, and up components at station GSWX on DOY 219, 2018. The results with a priori phase precision of the GEO satellites of 15 mm, 10 mm, 6 mm, and 3 mm are depicted by black, blue, green, and purple lines, respectively, with the RMS statistics shown above the curves.