# BeiDou Geostationary Satellite Code Bias Modeling Using Fengyun-3C Onboard Measurements
## 1 Introduction  
After the US GPS and the Russian GLONASS, the Chinese BeiDou navigation satellite system (BDS) officially began to provide position, navigation, and timing services in most of the Asia-Pacific area on 27 December 2012 and will offer global services by 2020 [1; 2]. Unlike the GPS and GLONASS, which use only medium earth orbit (MEO) satellites, BDS also uses satellites in geostationary earth orbit (GEO) and inclined geostationary orbit (IGSO). Currently, its constellation comprises 14 BDS-2 satellites and 5 new-generation satellites. Equipment supporting BDS has been widely used [2]. In particular, the onboard BDS sensors are also applied to low-earth orbiter (LEO) platforms as a key tracking system for precise orbit determination and occultation missions. For instance, the GNSS Occultation Sounder (GNOS) instrument on the Fengyun-3C satellite is the first BDS/GPS compatible radio occultation sounder in the world, developed by the Center for Space Science and Applied Research, Chinese Academy of Sciences [3; 4]. The precise orbits of Fengyun-3C were determined by [PERSON] et al. [5] using onboard GPS- and BDS-only measurement data. The results show that the 3D root mean square (RMS) of overlapping orbit differences can reach the 2- to 3-cm level for the GPS-only solution, and the 3D RMS of orbit differences between GPS- and BDS-only solutions is approximately 15 cm, which is easily affected by the available tracking BDS data.  
However, much of the literature argues that BDS code measurements are affected by severe multipath (MP) effects, which inevitably exist in precise applications. The well-known BDS systematic long-term variation was first investigated by [PERSON] et al. [6] in the B1 and B2 signals of theBDS M-1 satellite. [PERSON] et al. [7] analyzed BDS code MP variations for all 3 frequency signals using the Multi-GNSS experiment (MGEX) data, which vary by 0.4 to 0.6 m with changes of satellite elevation angle. To tackle this problem, [PERSON] and [PERSON] [8] proposed an elevation- and frequency-dependent linear piece-wise correction model for BDS IGSO and MEO satellites. They found a remarkable improvement in their single-frequency point positioning tests after applying the corrections. The BDS GEO satellites remain stationary at an altitude of approximately 36,000 km directly above the equator between 58\({}^{\circ}\) E and 140\({}^{\circ}\) E. They show very small elevation variations of several degrees in the view field of ground-fixed stations, so the model proposed by [PERSON] and [PERSON] [8] are not applicable to GEO satellites using ground data. Therefore, [PERSON] et al. [9] modeled the biases for GEO satellites based on single-differenced fractional cycle biases, but that requires widespread ground stations and still fits only a limited range of elevation variations. One method to overcome the restriction is to put the receiver on space vehicles; for example, on board LEO satellites. Due to the rapid movement of LEO relative to that of GEO satellites, the geometry variations between them can greatly increase, thus onboard observables can be obtained in wide elevation-angle ranges. Even for IGSO and MEO, better sky-view coverage can be obtained with the available tracking data. Fortunately, the onboard BDS measurements collected by the Fengyun-3C satellite can be used for such investigations.  
The aim of this study is to offer further insight into the described systematic biases existing in BDS code measurements using the Fengyun-3C onboard data and to model these biases, particularly for GEO satellites. In this paper, the quality of the onboard data and the code multipath is analyzed and these biases are investigated. Then a set of model corrections is given and applied to orbit determination for Fengyun-3C based on single-frequency BDS data. Finally, we present a discussion of the results from different orbit determination solutions, focusing on the orbit precision improvement after applying the model corrections, to verify their success.