# Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses
## 1 Introduction  
Swarm is a European Space Agency (ESA) project that was launched on 22 November 2013, which consists of three Swarm satellites. Swarm-A and Swarm-C are flying at orbital altitude of 480 km, Swarm-B is flying at orbital altitude of 530 km. All three Swarm satellites carry advanced scientific equipment to achieve the project's primary objective [1; 2; 3], which is to investigate the mechanism of the geomagnetic field [3]. The secondary objective is to monitor the change of Earth's gravity field via the on-board GPS tracking of Swarm [2]. Vector and scalar magnetometers were used on the Swarm satellites to monitor the change of the geomagnetic field; a thermal ion imager and a Langmuir probe were applied to monitor the geoelectric field information; space-borne GPS receivers were used to research the precise orbit determination (POD) and laser retro-reflectors were applied to validate Swarm POD [2; 3]. Given the successful use of space-borne GPS POD, more satellites are expected to carry space-borne GPS receivers to fulfill their orbit accuracy requirements, which may range from one centimeter to hundreds of meters [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. Geodetic and oceanographic satellites (e.g., HY2A,Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), Gravity field and steady-state Ocean Circulation Explorer (GOCE), Constellation Observation System for Meteorology, Ionosphere and Climate (COSMIC) and Swarm) have more stringent orbit accuracy requirements. Swarm space-borne GPS receivers are produced by Rustungs Unternehmen Aktiengesellschaft Space, which are used to make tracks for GPS satellite signal [15]. All three Swarm satellites are equipped with space-borne dual-frequency GPS receivers. Swarm precise orbits can be applied to the geomagnetic field, geoelectric field and the recovery of the Earth's static and time-variable gravity field. Thus, after the launch of Swarm satellites, some scholars have studied Swarm POD using on-board GPS data. For example, [PERSON] et al. [3] used GPS High precision Orbit determination Software Tools (GHOST) to calculate Swarm zero-differenced reduced-dynamic POD and kinematic POD, the consistency between the two orbits is at 4-5 cm. Furthermore, [PERSON] et al. [2] computed the reduced-dynamic orbits and kinematic orbits by Bernese Global Navigation Satellite System (GNSS) Software and then used 18 months of Swarm kinematic orbits to calculate the Earth gravity field model. The above studies introduce empirical accelerations to absorb force modeling errors and deficiencies based on the zero-differenced (ZD) reduced-dynamic technique. However, few studies are conducted on pseudo-stochastic pulses used in Swarm ZD reduced-dynamic orbit solutions. In addition, ESA released a four-day delay in Swarm on-board GPS observations, whereas Swarm Precise Science Orbits (PSOs) had a delay of three weeks. To obtain Swarm precise orbits in time, autonomous orbit determination is important to carry out follow-up research work (e.g., Earth gravity field and geomagnetic field research). Thus, it is necessary to study Swarm precise orbit solutions. We study the orbit quality that Swarm orbits can achieve under high ionospheric activity by using optimized pseudo-stochastic pulses based on the ZD reduced-dynamic technique. During the process, space-borne dual-frequency GPS observations and suitable force models are used, especially with the aid of a highly advanced gravity field model, EIGEN-6S4 [16]. This article presents a new POD strategy for all three Swarm satellites using the space-borne dual-frequency GPS data together with reduced dynamic models. The study computes Swarm precise orbits via a ZD reduced-dynamic approach based on Bernese software. The approach combines space-borne GPS observation from Swarm level 1B products released by ESA [17] and suitable force models. The optimized pseudo-stochastic pulses are introduced into the Swarm satellite's deterministic motion equation.