# Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses
## 3 Swarm Orbit Strategy
(7) A priori STD is \(10^{1}\) mm/s in R direction,  
(8) A priori STD is \(10^{0}\) mm/s in R direction,  
Figure 1: Root Mean Square (RMS) values of GPS phase residuals for all three Swarm satellites on 1 November 2014. Figure 2: RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and Precise Science Orbits (PSOs) released by the European Space Agency (ESA), 1 November 2014. (9) A priori STD is \(10^{-1}\) mm/s in R direction,  
(10) A priori STD is \(10^{-2}\) mm/s in R direction,  
(11) A priori STD is \(10^{-3}\) mm/s in R direction,  
(12) A priori STD is \(10^{-4}\) mm/s in R direction. Figure 3 shows RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA from Experiments (7) to (12). The RMS values of orbit differences for Swarm in 3D direction from Experiments (7) to (9) are worse than Experiments (10) to (12). Moreover, Experiments (10) to (12) have the same results. According to Case 1, in R direction, when a priori STD was reduced to \(10^{-2}\) mm/s, orbit accuracy was increased, but when we continued to reduce a priori STD, orbit accuracy was no longer improved. (13) A priori STD is \(10^{1}\) mm/s in T direction,  
(14) A priori STD is \(10^{0}\) mm/s in T direction,  
(15) A priori STD is \(10^{-1}\) mm/s in T direction,  
(16) A priori STD is \(10^{-2}\) mm/s in T direction,  
(17) A priori STD is \(10^{-3}\) mm/s in T direction,  
(18) A priori STD is \(10^{-4}\) mm/s in T direction. Figure 4 shows RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA from Experiments (13) to (18). The RMS values of orbit differences for Swarm in 3D direction from Experiments (17) to (18) are worse than Experiments (13) to (16). Moreover, Experiments (13) to (16) have the same results. According to Case 2, in T direction, when a priori STD was increased to \(10^{-2}\) mm/s, orbit accuracy was improved rapidly, but when we continued to increase a prior STD, orbit accuracy was no longer improved. (19) A priori STD is \(10^{1}\) mm/s in N direction,  
(20) A priori STD is \(10^{0}\) mm/s in N direction,  
Figure 3: RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA from Experiments (7) to (12), 1 November 2014. * A priori STD is \(10^{-1}\) mm/s in N direction,
* A priori STD is \(10^{-2}\) mm/s in N direction,
* A priori STD is \(10^{-3}\) mm/s in N direction,
* A priori STD is \(10^{-4}\) mm/s in N direction. Figure 5 shows RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA from Experiments (19) to (24). Experiment (22) has the best result. According to Case 3, in N direction, when a priori STD was reduced to \(10^{-2}\) mm/s, orbit accuracy was improved, but when we continued to reduce a priori STD, orbit accuracy was reduced. In summary, based on a set of experiments and characteristics of pseudo-stochastic pulse parameters, the present study provides an optimal a priori STD and time interval for pseudo-stochastic pulses. When we choose 24 h arc length to participate in the calculation of Swarm ZD reduced-dynamic POD, pseudo-stochastic pulses in R, T and N directions with a time interval of 6 min and a priori STD of \(10^{-2}\) mm/s are optimized. Therefore, we introduce optimized pseudo-stochastic pulses to compute Swarm ZD reduced-dynamic POD under high ionospheric activity and evaluate the Swarm POD in this study. Figure 4: RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA from Experiments (13) to (18), 1 November 2014. Figure 5: RMS values of orbit differences for all Swarm satellites in 3D direction between Swarm POD and PSOs released by ESA from Experiments (19) to (24), 1 November 2014