## 4 Results and Discussion
### GEO Residual Analysis  
Since the GEO satellites (C01-C05) are basically stationary relative to a point on the Earth's surface, the change rate of elevation angle is nearly zero, which means that the multipath from the ground should be close to a constant bias in the carrier-phase observation, theoretically. This is shown by [PERSON] et al. (2012), where the phase residuals of C01 satellite for about three hours at station CHPS are almost a constant with only a few fluctuations. To further investigate the characteristics of GEO residuals, the residuals at 27 globally distributed stations were calculated for 81 days. The station distribution map is depicted in Figure S1 (Supplementary Materials), and the information of five stations presented in this paper is listed in Table 2. Figure 5 typically delineates the residuals of C01 and C02 for about seven days. In contrast, excluding the daily peaks which are caused by the discontinuity  
Figure 4: The mean percentage errors of differences between the observed and projected phase residuals for L1/L2, R1/R2, and B1/B2.  
of orbit and clock products at adjacent days, pronounced periodic errors of up to \(\pm\) 3 cm can be found at some stations with the period of about a sidereal day. The residuals differ among stations for the same satellite. For example, the residuals of C01 and C02 for station GMSD contain subtle or even no periodic signal, which is consistent with the results provided by [PERSON] et al. (2020), whereas those for station CIBG reveal a conspicuous period. The residuals also differ among satellites for the same station. For example, for station JFNG, the residuals of C02 are totally different from those of C01 both in the amplitude and phase. This interesting periodic bias can be eliminated if differencing the observations between two nearby stations. That could be the reason why there are no relevant reports in the previous studies ([PERSON] et al., 2019; [PERSON] et al., 2020).  
Figure 6 presents the residual series of C01 and C03 from DOY 223 to 303, 2018 at stations DAE2, DAEJ, and GMSD, respectively. It is noteworthy that the amplitudes of residuals change rapidly on DOY 265 for C01 and on DOY 264 for C03, as the green dashed line shows. The residuals for C01 from DOY 223 to 264 and for C03 from DOY 263 to 303 are several times smaller than those on other days. Similar observations can also be made for C02, C04, and C05, as shown in Figure S2. Since these stations are hundreds of kilometers away from each other, it should not be associated with the environment. A preliminary conclusion is that this periodic bias originates from the satellite. The identification of the kind of bias is out of the scope of this paper, and will be investigated in the future.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Station** & **Location (Lat/Long.)** & **Receiver Type** & **Antenna Type** \\ \hline GMSD & \(30.56^{\circ}/131.02^{\circ}\) & TRIMBLE NETR9 & TRM59800.00 SCIS \\ \hline CIBG & –\(6.49^{\circ}/106.85^{\circ}\) & LEICA GR10 & LEIAR25.R3 NONE \\ \hline JFNG & \(30.52^{\circ}/114.49^{\circ}\) & TRIMBLE NETR9 & TRM59800.00 NONE \\ \hline DAE2 & \(36.40^{\circ}/127.37^{\circ}\) & TRIMBLE NETR9 & TRM59800.00 SCIS \\ \hline DAEJ & \(37.00^{\circ}/127.37^{\circ}\) & TRIMBLE NETR9 & TRM59800.00 SCIS \\ \hline \end{tabular}
\end{table}
Table 2: Information about five stations presented in this paper.  
Figure 5: Carrier-phase residuals of C01 and C02 on two frequencies at station GMSD, CIBG, and JFNG from DOY 202 to 208, 2018. The opposite values of residuals on the second frequency are used.