# Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses
## 4 Experiments
### SLR Validation  
Swarm-A/B/C satellites were not only equipped with a GPS receiver, but also with an array of SLR retro-reflectors. Thus, we can use high-precision SLR measurements to validate the Swarm reduced-dynamic orbits. Using the SLR measurements to validate the Swarm reduced-dynamic orbits, it is actually the difference between the SLR measurements and the distance between the SLR ground stations and the Swarm reduced-dynamic orbits. Moreover, the related corrections (e.g., tropospheric delay, tide correction, satellite center mass correction, and relativistic correction) to SLR measurements should be considered [35].  
The Swarm ZD reduced-dynamic orbits were independently validated with SLR measurements over the same 25 days (days 274-298, 2014). SLR measurements which have been compressed in normal point are obtained from the EUROLAS Data Center (EDC). During the processing, related corrections are applied in SLR measurements. In addition, an elevation cut-off angle of 10\({}^{\circ}\) has been applied to all SLR ground stations and tropospheric delay has been modeled according to the International Earth Rotation Service (IERS) 2010 [29]. The coordinates of the SLR stations are based on the Station Location Reference Frame (SLRF) 2008 ([[https://ilrs.cddis.eosdis.nasa.gov/science/awg/SLRF2008.html](https://ilrs.cddis.eosdis.nasa.gov/science/awg/SLRF2008.html)]([https://ilrs.cddis.eosdis.nasa.gov/science/awg/SLRF2008.html](https://ilrs.cddis.eosdis.nasa.gov/science/awg/SLRF2008.html))). It is  
Figure 9: Orbit differences for Swarm-A, Swarm-B and Swarm-C in the R, T and N directions on the DOY 296, 2014.  
very difficult to track for the SLR ground station, because Swarm-A/B/C satellites fly fast at the altitude of 480-530 km. During this period, 1023 SLR residuals were computed using measurements from 10 SLR stations for Swarm-A, 3438 SLR residuals were computed using measurements from 15 SLR stations for Swarm-B, and 1045 SLR residuals were computed using measurements from 12 SLR stations for Swarm-C, respectively. See Table 4 for details.  
SLR residuals of Swarm-A/B/C are summarized in Table 4 and Figure 10, respectively. From Table 4 and Figure 10, we can conclude that the RMS of SLR residuals for Swarm-A/B/C is 3.3 cm, 2.7 cm and 3.6 cm, respectively. In addition, the mean SLR residuals for Swarm-A/B/C is 0.05 cm, \(-\)0.01 cm and 0.14 cm, respectively. These results show that there is no significant bias in the Swarm reduced-dynamic POD, and the computed reduced-dynamic orbits for Swarm-A/B/C are of high quality under high ionospheric activity.  
1. The chosen force models and observation models used in the reduced-dynamic determination have good fit under high ionospheric activity. The orbital fits to GPS tracking data for Swarm-B are better than those of Swarm-A and Swarm-C.
2. Pseudo-stochastic pulses with a time interval of 6 min and a priori STD of 10\({}^{-2}\) mm/s in the R, T and N directions are optimized in the Swarm ZD reduced-dynamic POD.
3. The mean RMS values of orbit differences for all three Swarm satellites are within 2-4 cm in R, T and N directions and 3-6 cm in 3D direction. Independent SLR validation indicates that the accuracy of the Swarm reduced-dynamic orbits is in the range of 2-4 cm. Moreover, Swarm-B orbit accuracy is better than those of Swarm-A and Swarm-C. Therefore, no obvious systematic bias is found between PSOs produced by ESA and orbit solutions computed using the force models and orbit strategy.  
This work is supported by the National Natural Science Foundation of China (No. 41274032, No. 41210006, No. 41474018), Beijing Key Laboratory of Urban Spatial Information Engineering (No. 2016204).  
[PERSON] carried out all of the analyses and algorithms under the supervision of [PERSON]. [PERSON] and [PERSON] performed the experiments. [PERSON] and [PERSON] provided some of the plots shown in the manuscript.  
The authors declare no conflict of interest.