## 5 Conclusions  
For this study, the performance of multi-GNSS PPP, especially BDS PPP, in monitoring subtle deformation was investigated. The sidereal filtering approach was employed to mitigate the multipath in phase observations to improve the precision of PPP. The equations describing the relationship between phase residuals on different frequencies were rigorously derived, which could significantly reduce the complexity of multipath processing. A satellite-dependent periodic error term with an amplitude of up to \(\pm\) 3 cm was found in the BDS GEO phase residuals, one of the main sources that limits the precision of BDS PPP. The results indicated that the systematic errors originated mainly from GEO, had periods longer than 2000 s, and could not be alleviated by the fusion of multi-GNSS, whereas the multipath errors from IGSO and MEO had periods from 50 to 5000 s. Traditionally, GEO observations are weighted lower to account for the imprecise orbit and clock products, but this also reduces the GEO's contribution to the solution. The SF approach can effectively mitigate the periodic errors, thus improving the precision of the GEO phase to around 10 mm. Compared with the BDS-only PPP solutions without sidereal filtering, the one using the SF approach can effectively improve the  
Figure 13: Displacements at station GSZQ during the Jüuzhaigou earthquake. The lines are shifted vertically to avoid overlap. The yellow dashed horizontal lines denote the mean of displacements. The black, blue, and purple lines refer to the sidereally filtered G, C, and GRC solutions, respectively, while the green lines refer to the GRC solution without sidereal filtering.  
positioning accuracy, with respect to the weekly averaged positioning solutions, by 75.2%, 42.8%, and 56.7% to 2.00, 2.23, and 5.58 cm in the east, north, and up components, respectively. It is comparable to that of GPS in the east component, and slightly worse in the north and up components. After applying sidereal filtering, the accuracy of the combined GPS, GLONASS, and BDS solution can also be improved by 71.2%, 27.7%, and 37.9% to 1.25, 0.81, and 3.79 cm in the three directions, respectively, compared to the unfiltered results.  
The following are available online at [[http://www.mdpi.com/2072-4292/11/19/2232/s1](http://www.mdpi.com/2072-4292/11/19/2232/s1)]([http://www.mdpi.com/2072-4292/11/19/2232/s1](http://www.mdpi.com/2072-4292/11/19/2232/s1)), Figure S1: Distribution of 27 stations used for BDS GEO residual analysis. The blue triangles denote the stations, while the red cycles denote the GEO satellite positions, Figure S2: Carrier-phase residuals of C02, C04, and C05 at two frequencies at station NTUS, GAMG, PTGG, GMSD, DJIG, KITG, and KRGG from DOY 22 to 303, 2018.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the research; [PERSON] and [PERSON] wrote the paper; [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] provided advice and reviewed the paper.  
This work was funded by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 41721003).  
We gratefully acknowledge financial support from the China Scholarship Council (CSC, file 201706270123).  
The authors declare no conflict of interest.