## 4 Results and Discussion
### Assessment of Multi-GNSS PPP with Multipath Correction  
As revealed by [PERSON] et al. (2016), the integration of GPS and GLONASS data led to a substantial reduction of the high-rate displacement noise by up to 40% compared to a GPS-only solution within European regions. In this section, the two major purposes investigated are presented. One shows the benefits from multi-GNSS in improving the precision of displacements; the other one concerns the question of whether the multi-GNSS data can suppress the effect of GEO periodic error. Four experiments numbered from (1) to (4) were designed, and the corresponding results of station GSWX in the east, north, and up direction are displayed in Figure 9a-d, Figure 10a-d, and Figure 11a-d, respectively. Table 3 lists the data filtering strategy for the four experiments. Experiment (1) gives the results without sidereal filtering, whereas Experiments (2) to (4) present the sidereally filtered results. Note that the GEO observations are not filtered in Experiment (2), and they are excluded in Experiment (4). From Figure 9a, it is observed that although the combined GPS/GLONASS/BDS (GRC) solution shows about 12.7% improvement compared to the GC combination, both of them are evidently inferior to the GPS-only solution. The fusion of GRC can effectively reduce most noise in contrast to the BDS solution without sidereal filtering, leading to a decline in the RMS values from 7.51, 3.50, and 11.38 cm to 4.34, 1.12, and 6.10 cm in the three components, respectively (see Figure 10; Figure 11), but there are still many fluctuations over the period of 5000 s remaining. After the sidereal filtering, a considerable reduction of 21.9% and 23.5% in terms of RMS can be found in the east and up components (see Figure 11), respectively, for GPS, whereas the SF approach may occasionally introduce undesirable ramps as shown in the north component around 6 to 7 h (see Figure 10). From a comparison between Figure 9a and 9b, the application of SF on BDS IGSO and MEO observations can slightly reduce them by about 3.2 dB noise over periods from 50 s to 5000 s, but it fails in alleviating noise over longer  
Figure 8: Averaged power spectral density (PSD) (in dB) on a frequency band from 2 to 100,000 s over all five stations for the east, north, and up components on DOY 219, 2018. The sidereally filtered BDS solutions are exhibited by purple lines, while the solutions, for which all BDS satellites except for the GEO satellites are filtered, are exhibited by dark green lines. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **GRC with SF** & **GEO with SF** & **GEO Excluded** \\ \hline (1) & No & No & / \\ \hline (2) & Yes & No & / \\ \hline (3) & Yes & Yes & / \\ \hline (4) & Yes & / & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data strategy of the designed four experiments. periods. The RMS values for sidereally filtered GC and GRC solutions are comparable to those without sidereal filtering, which are 4.91 and 4.13 cm, respectively. Once the GEO observations are sidereally filtered (Experiment (3)), as delineated in Figure 9c, Figure 10c, and Figure 11c, the RMS values of the GRC solutions are reduced to 1.25, 0.81, and 3.79 cm from 4.34, 1.12, and 6.10 cm of Experiment (1), for the east, north, and up components, respectively, which are dramatic improvements of about 71.2%, 27.7%, and 37.9%, respectively. The PSDs across almost the entire frequency band decline substantially, especially for the longer periods where the PSDs decline on average by about 10.2 dB. Excluding the GEO satellites can improve the precision of GC and GRC solutions to some extent; however, it also increases the RMS values by 14.8% and 13.6% to 1.63 and 1.42 cm, respectively, compared with the sidereally filtered counterparts. Moreover, it seriously deteriorates the precision of the BDS-only PPP because of the poor geometry of the satellite constellation.