## 3 Results and Analysis
### Carrier Phase Residual Analysis  
The residuals of the phase observations were calculated to evaluate the accuracy of the LEO satellite orbiting results. They were close to the observation noise level when the quality of the observations and the preprocessing results were satisfactory [33]. Figure 2 shows the residual RMS of the phase observations of Swarm and GRACE-FO satellites and the solar flux index F10.7 on that day. Meanwhile, all satellites' mean RMS of the residuals for all phase observations are summarized in Table 2.  
According to Figure 2 and Table 2, the solar flux index F10.7 fluctuated between 70 and 80 during DOY 152 to 165 in 2021, which means that no excessively intense solar activity occurred during this time. The RMS of residuals of the phase observation for Swarm satellites KPOD solution is distributed between 4 and 5 mm, while the RMS for the RDPOD solution is mostly distributed between 6.5 and 7.5 mm (except for Swarm-C with an RMS of 15.8 mm on DOY 162). The RMS of the phase observations of GRACE-FO satellites for the KPOD solution is in the range of 5.0-6.5 mm, and the RMS for the RDPOD solution is in the range of 7.5-8.5 mm.  
Figure 1: The 3-D RMS time series and jumping phenomenon in the kinematic orbit of Swarm-C occurred between 14:00 and 16:00 on DOY 162, 2021.  
Figure 2: RMS of the phase observation residuals: (**a**) Swarm-A; (**b**) Swarm-B; (**c**) Swarm-C; (**d**) GRACE-C; and (**e**) GRACE-D, where white blocks and black blocks in (**a–e**) mean the RMS of the kinematic orbit and reduced dynamic orbit on each day, respectively. The diamond-shaped lines show the solar flux index F10.7 for each day (unit: \(10^{-22}\) W/m\({}^{2}\)/Hz).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Satellite** & **Orbit** & **Average Residual RMS (mm)** \\ \hline \multirow{2}{*}{Swarm-A} & Kinematic & 4.74 \\  & Reduced dynamic & 7.01 \\ \hline \multirow{2}{*}{Swarm-B} & Kinematic & 4.71 \\  & Reduced dynamic & 6.78 \\ \hline \multirow{2}{*}{Swarm-C} & Kinematic & 4.76 \\  & Reduced dynamic & 7.66 \\ \hline \multirow{2}{*}{GRACE-C} & Kinematic & 6.04 \\  & Reduced dynamic & 7.94 \\ \hline \multirow{2}{*}{GRACE-D} & Kinematic & 5.52 \\  & Reduced dynamic & 7.84 \\ \hline \hline \end{tabular}
\end{table}
Table 2: All satellites’ average RMS of the residuals for all phase observations.  
The phase observation residuals' RMS for the RDPOD solution of Swarm-C on DOY 162 reached 15.8 mm, which was higher than that in any other days. Analyzing the number of tracked GPS satellites after data preprocessing and the RTN accelerations estimated by RDPOD for Swarm-C on DOY 162 (shown in Figure 3), we found that lots of observations between 14:00 and 16:00 were deleted during data preprocessing, resulting in a fewer number of observations than six in many epochs. As we set the minimum number of observations when processing data, the estimation of Epoch Clock Offsets and RTN accelerations in RDPOD are affected when the number of observations is less than six, which reduces the accuracy of RDPOD. The accuracy of KPOD is also reduced for the same reason.  
Therefore, the models, data sets, and solving strategies adopted in this paper are reasonable, and the results are stable. Furthermore, the number of tracked GPS satellites in many epochs between 14:00 and 16:00 is less than five, which reduces the accuracy of RDPOD. The residual RMS of the phase observation of Swarm-C for the RDPOD solution is 15.8 mm on DOY 162, 2021.