# Centimeter-Level Precise Orbit Determination for the Luojia-1A Satellite Using BeiDou Observations
## 1 Introduction  
Low-Earth-Obiter (LEO) satellites have been used widely for space applications such as gravity field measurement, high-resolution images, synthetic-aperture laser radar, and Global Navigation Satellite System (GNSS) radio occultation [1; 2; 3]. Apart from these traditional scientific missions, LEO satellites have also risen in the communication as well as navigation mission in recent years [4]. Recently, the LEO navigation augmentation (LEO-NA) technology has been considered as a promising technique to reduce the slow convergence issue in GNSS precise positioning [5; 6]. The LEO satellite navigation augmentation technology includes the signal-based augmentation and information based augmentation [7]. The LEO satellite navigation signal augmentation method is achieved by generating and broadcasting the ranging signals to users, whereas the information augmentation method is achieved by transmitting the GNSS corrections information using the LEOsatellite communication channels. Some research has demonstrated that the LEO satellite signal augmentation method can dramatically reduce the convergence time of Precise Point Positioning (PPP) [8] as well as long-baseline real-time kinematic (RTK) positioning by taking the advantages of the rapid geometric change of LEO satellites [9; 10]. Moreover, it also can improve the usability and reliability of the present Global Navigation Satellite System (GNSS) and supporting the Positioning Navigation Timing (PNT) systems as well as the space-based real-time Positioning, Navigation, Timing, Remote-sensing, and Communication (PNTRC) information service systems [11; 12]. Luojia-1A satellite is operated by Wuhan University, which was launched in June 2018 to carry out the LEO-based navigation signal augmentation experiment. The experiment was successful, and its initial performance has been assessed from a different perspective [5; 13]. As for the LEO navigation signal augmentation system, it is critical to maintaining the precise orbit and time systems as well as operating the precise and stable ranging signals to users. Therefore, LEO precise orbit determination (POD) is of great importance to the LEO navigation signal augmentation system. Presently, the reduced-dynamic POD method using GPS observations has been extensively studied and widely used in many LEO satellites. Since demonstrated centimeter-level orbit precision of the TOPEX/POSEIDON satellite with onboard GPS observations [14], various LEO missions have achieved high precision with the GPS-based POD, such as CHAMP, GRACE, GOCE, and SWARM [15; 16; 17; 18]. The BeiDou system consists of geostationary earth orbit (GEO) satellites, inclined geostationary (IGSO) satellites, and medium earth orbit (MEO) satellites, which is going to provide the global navigation services in 2020 [19; 20]. With the emerging BeiDou system, there is only a few LEO satellites carried BeiDou receiver for orbit determination. The LINGQIAO satellite, a mobile communication experimental satellite in China, equipped with a Beidou system (BDS) receiver, demonstrated the initial performance of BDS based orbit determination [21]. The major challenge for BeiDou-based LEO POD is the poor precision of the GEO satellite precise orbit. The Chinese meteorological satellite FengYun-3C achieved centimeters-level POD with the BeiDou system by excluding the GEOs observations [22]. [PERSON], et al. [23] improved the BDS based precise orbit result of FengYun-3C with the calibration of orbit biases in BeiDou GEO satellites. However, the strategies of BDS-based LEO POD are still far from fully understood. In this study, we make use of BDS dual-frequency observations from the Luojia-1A satellite to investigate the BDS based LEO POD methods. Firstly, the Luojia-1A satellite is briefly introduced, including the satellite-body-fixed (SBF) system. Secondly, the visibility and continuity of onboard BDS measurements are analyzed. The BDS elevation-dependent code biases are modeled with the Luojia-1A observations.