# Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses
## 3 Swarm Orbit Strategy
Thus, in order to evaluate orbit quality, Swarm orbit solutions are compared with Swarm PSOs released by ESA. In addition, Swarm GPS phase residuals permit the quality of the force models and observation models. Root Mean Square (RMS) of Swarm GPS phase residuals are at the level of data precision if the force models and observations are modeled perfectly [10]. Pseudo-stochastic pulse parameter is determined using a priori standard deviation (STD) and time interval. So, pseudo-stochastic pulse parameter optimization can effectively absorb force model and modeled mechanical error, thus improving orbit determination accuracy. Therefore, we obtain a set of optimized pseudo-stochastic pulses by analyzing Swarm GPS phase residuals and orbit differences. The relevant experiments are shown below. For time interval, relevant experts conducted corresponding research. [PERSON] et al. [22] discussed that a time interval of 6 min was proper, two main reasons support this view. One is that filtering effect of LEO orbits is well by a time interval of 6 min. Another is that an interval of 6 min is short enough to reduce the orbit differences of LEO short-periodic variation. The time interval of 6 min is chosen in the article to maintain continuity. For a priori STD, when a priori STD is too large for pseudo-stochastic pulse, the filter cannot fully use the observed information. When a priori STD is too small, owing to the recursive nature of the filter, model error significantly increases. More serious change possibly leads to filter divergence. Therefore, a priori STD is set as follows from Experiments (1) to (6). 1. A priori STD is \(10^{1}\) mm/s
2. A priori STD is \(10^{0}\) mm/s
3. A priori STD is \(10^{-1}\) mm/s
4. A priori STD is \(10^{-2}\) mm/s
5. A priori STD is \(10^{-3}\) mm/s
6. A priori STD is \(10^{-4}\) mm/s  
The orbit arc length is usually 24 h, which is equivalent to one full day. Therefore, we randomly selected data on 1 November 2014, to participate in the Swarm ZD reduced-dynamic POD and better understand the effect of pseudo-stochastic pulses on the Swarm ZD reduced-dynamic POD. The conclusion is applicable to orbit arc length of 24 h.  
Figure 1 indicates the RMS values of GPS phase residuals for all three Swarm satellites from the above six experiments. The RMS values of GPS phase residuals from Experiments (1) to (4) are basically the same; however, the RMS values of GPS phase observation residuals from Experiments (5) to (6) are rapidly increasing. Figure 2 shows the RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA on 1 November 2014: \(3\mathrm{D}=\sqrt{\mathrm{R}^{2}+\mathrm{T}^{2}+\mathrm{N}^{2}}\). The RMS values of orbit differences for Swarm in 3D direction from Experiments (1) to (4) are well and stable. The result  
is consistent with GPS phase residuals, and the only difference is that the RMS of orbit differences for Swarm in 3D direction from Experiment (4) is the best. According to Figures 1 and 2, we can conclude that the Swarm orbit solutions are basically the same when a priori STD is better than \(10^{-2}\) mm/s, and the Swarm orbit solutions are worse when a priori STD is less than \(10^{-2}\) mm/s. Moreover, F10.7 of the chosen day is 118.1 sfu, which indicates that ionospheric activity is high on the chosen day. If pseudo-stochastic pulses are not optimized (e.g., a priori STD is less than \(10^{-2}\) mm/s), Swarm ZD reduced-dynamic POD cannot obtain high-quality precision orbit determination. The above experiments show that when a priori STD of the pseudo-stochastic pulses is set to \(10^{-2}\) mm/s in R, T and N directions, the Swarm orbit solution is the best. In order to keep the consistency of the experiments, this paper studies the Swarm orbit accuracy when a priori STD of pseudo-stochastic pulses is different settings in different directions on the basis of the above experiments.