## 3 Results and Analysis
### Comparison with a Precise Ephemeris  
The precise reduced dynamic orbit (with a sampling rate of 1 s) of Swarm satellites is provided by the ESA, which was solved by GHOST with an accuracy better than 2 cm [26]. The GFZ also provides a GRACE-FO precise orbit with a sampling rate of 1 s and accuracy better than 2 cm. In this section, the reduced dynamic orbits of Swarm satellites provided by the ESA and the precise orbits of GRACE-FO satellites provided by the GFZ are used as reference orbits, which are compared with our undifferenced kinematic orbits to assess the accuracy of the results. To visualize the jumping phenomenon in the kinematic orbit and to verify the effectiveness of the quality control measures for the kinematic orbit, the following two groups were set up in this section for the orbit comparison concerning whether or not quality control was applied:  
* Group 1: Applying quality control for the solved kinematic orbits before comparing with reference orbits. * Group 2: Comparing with reference orbits without applying quality control. Figures 6-10 show the comparison of the undifferenced kinematic orbits with the reference orbits for Swarm and GRACE-FO satellites. We set up colorful comparisons in these figures to highlight the RMS differences between the two groups and the orbit differences in each RTN direction. The RMS of the KPOD results for each satellite in different groups is also summarized and listed in Table 5. As we can see in Figures 6-10 and Table 5, in Group 2, the RMS of the undifferenced kinematic orbits for Swarm-A/B/C are between 3.0 and 5.0 cm in RTN directions, with total 3-D RMS between 2.5 and 5.0 cm for each day. The RMS of the undifferenced kinematic orbit of GRACE-C in RTN directions ranges from 1.5 to 3.0 cm, and the total 3-RMS are in the range of 2.0-2.8 cm for all days. Figure 5: SLR residuals for Swarm and GRACE-FO satellites’ kinematic and reduced dynamic orbits from DOY 152 to 165 in 2021 at each station. (**a**) SLR residuals for Swarm-A; (**b**) SLR residuals for Swarm-B; (**c**) SLR residuals for Swarm-C; (**d**) SLR residuals for GRACE-C; (**e**) SLR residuals for GRACE-D. Gray and black points in (**a–e**) are the residuals of the kinematic orbit and reduced dynamic orbit, respectively. The RMS of the undifferenced kinematic orbit of GRACE-D, as the leading satellite of the GRACE-FO binary system, is slightly worse with the RMS from 3.0 to 5.5 cm. Therefore, the accuracy of the kinematic orbit calculated in this paper is better than 5 cm for Swarm satellites and better than 5.5 cm for GRACE-FO satellites. Figure 6: Comparison between the kinematic orbits of Swarm-A and the precise orbits provided by the ESA. (**a**) 3D-RMS of the comparison results; (**b**) Difference in Radial direction; (**c**) Difference in Tangent direction; (**d**) Difference in Normal direction; (**e**) Average 3D-RMS statistics of the comparison results. The red line shows the results of Group 1, while the blue line shows the results of Group 2 in (**a–d**). The white blocks and black blocks in (**e**) represent the RMS of Group 1 and Group 2 on each day, respectively. Figure 7: Comparison between the kinematic orbits of Swarm-B and the precise orbits provided by the ESA. (**a**) 3D-RMS of the comparison results; (**b**) Difference in Radial direction; (**c**) Difference in Tangent direction; (**d**) Difference in Normal direction; (**e**) Average 3D-RMS statistics of the comparison results. Where the red line shows the results of Group 1 while the blue line shows the results of Group 2 in (**a–d**). The white blocks and black blocks in (**e**) represent the RMS of Group 1 and Group 2 on each day, respectively. Figure 8: Comparison between the kinematic orbits of Swarm-C and precise orbits provided by the ESA. (**a**) 3D-RMS of the comparison results; (**b**) Difference in Radial direction; (**c**) Difference in Tangent direction; (**d**) Difference in Normal direction; (**e**) Average 3D-RMS statistics of the comparison results.