## 1 Introduction  
The BeiDou system (BDS) is a navigation and positioning system developed in China that provides two service modes, the radio navigation satellite service (RNSS) and the radio determination satellite service (RDSS) [1, 2, 3]. The benefits of RDSS as a featured part of BDS are to provide regional short message communication, global short message communication, fast location reporting, and international search and rescue (SAR) services. RDSS users can not only know where they are but also tell others where they are. They can also transmit information to other RDSS users and send distress signals to rescue coordination centres (RCC) in distress. Therefore, the RDSS is an important component and a distinctive feature of the BDS. With more than ten years of development, the application scope of the BeiDou RDSS has been continuously expanded, including aviation, maritime, land transportation, and emergency rescue, et al. Therefore, the RDSS is an important component and a distinctive feature of the BDS, as GPS, GLONASS, and Galileo do not feature this component [4; 5; 6; 7]. Scholars at home and abroad have conducted extensive research on BeiDou short-message communication ranging data, including the RDSS positioning algorithm, signal design, generalised RDSS design and extension, and combined navigation of the RDSS and strap-down inertial navigation system (SINS). A series of research results have been achieved, and the connotation of the satellite navigation system has been enriched [8]. However, the deep integrated application of BeiDou short-message communication and BeiDou navigation services has not been realised yet. The short-message communication ranging data have not been applied to the field of BeiDou satellite orbit determination, and the orbit accuracy for BeiDou satellites based on RDSS data has not been systematically analysed by the measured short-message communication ranging data. GEO satellites, as an indispensable part of the BDS constellation composition, bear not only the responsibility of communication transmission but also the task of enhancing the geometric dilution of precision (GDOP) [9; 10]. At present, BeiDou GEO satellite orbit determination mainly adopts L-band multi-frequency pseudorange, phase data, and kaband inter-satellite link data of the RNSS system. The Overlap Orbit Differences (OOD) method is used to evaluate the accuracy of the 3D position of its post-precision products, which is a 2 m level for the BDS-2 GEO satellite based on the L-band multi-frequency pseudorange and phase data [11; 12], and about 24 cm for the BDS-3 GEO satellite in the orbital arc based on the L-band data and Ka-band inter-satellite link data [2; 13; 14]. The laser ranging (SLR) data internationally jointly measured were used to evaluate the orbit accuracy in radial direction, which was 40 cm for the BDS GEO satellites [15; 16; 17]. In the case of abnormal RNSS and inter-satellite link data due to uncontrollable factors such as satellite navigation unit failure and inter-satellite link equipment failure, GEO satellite orbit determination accuracy can considerably decrease or orbit determination may fail, which undermines the positioning and timing service performance and availability of the BDS [18]. In case such anomalies occur during the orbit manoeuvre or recovery of GEO satellites, the kinematic orbit determination method is adopted for GEOs. L-band data are the only data resource, if the L-band data are abnormal in this period, the orbit error increases sharply and seriously affects RDSS service performance. Currently, when the aforementioned problems occur, the out-station beam of this GEO satellite will be closed forcibly, and then the RDSS service of this GEO satellite will be stopped. However, only three GEO satellites of the BDS-3 provide the RDSS services, and the beam coverage areas of the three satellites are different.