# Precise Orbit Determination of BDS-2 and BDS-3 Using SLR  
[PERSON]  
1 Institute of Space Science, Shandong University, Weihai 264209, China; [EMAIL_ADDRESS] (H.Y. ); [EMAIL_ADDRESS] (W.N. );[EMAIL_ADDRESS] (F.G.); [EMAIL_ADDRESS] (M.G. )1  
[PERSON]  
Tianhe Xu  
satellites, as the 22 th and 23 th satellites of BDS-3, were successfully launched on 23 September 2019 ([[http://www.beidou.gov.cn/](http://www.beidou.gov.cn/)]([http://www.beidou.gov.cn/](http://www.beidou.gov.cn/))). In the three generations of BDS, BDS-1 has been completely retired. BDS-2 continues to operate and serve the world with a focus on the Asia-Pacific area at a constellation of 14 satellites, including five Geostationary Orbit (GEO) satellites, five Inclined Geosynchronous Orbit (IGSO) satellites, and four Medium Earth Orbit (MEO) satellites. So far, BDS-3 is gradually replenishing satellites to achieve full constellation operation with three GEO, three IGSO, and 24 MEO satellites in 2020 [1; 2]. All the BDS satellites are equipped with satellite Laser Retroreflect Arrays (LRAs) for Satellite Laser Ranging (SLR). The SLR, as a unique geodetic survey technique without ambiguity, can directly obtain an independent, sub-centimetre level of satellite-station distance measurement. Since the rise of Global Navigation Satellite System (GNSS) technology in the 1990s, two American Global Positioning System (GPS) satellites with LRAs--namely GPS35 and GPS36--had been tracked by SLR. Their basic characteristics and performance, such as the principles, the tracking properties, and their LRAs, were described in [PERSON] and [PERSON] [3]. The encouraging result was that for the two special sets of SLR-only determination orbits of GPS35 with 14-day arcs, the Root Mean Square (RMS) of the difference in the orbital overlaps was 3.2, 37.0, and 10.9 cm, while the mean residual offset is 5.1, 21.8, and \(-\)19.0 cm in terms of radial, cross-track, and along-track directions respectively. Compared with the orbits provided by the International GNSS Service (IGS), the orbit difference was about 10 cm in the radial direction, and 0.5-1.0 m in the cross-track and along-track directions [4]. In the technical report of [PERSON] [5], the RMS was about 24-31, 94-125, and 49-71 cm in Radial-Transverse-Normal (RTN) directions respectively, based on the comparison of GPS-35 L-band orbits with those of SLR, where the L-band orbits came from five different Analysis Centers (ACs). In addition, the optimal RMS can reach 8 cm after Helmert transformation in the middle 1-day of a 9-day arc, comparing the difference between the SLR-only and the IGS orbits of GPS35 [6]. With the International GLONASS (GLObal Navigation Satellite System) Experiment 98 (IGEX-98) campaign initialized, the GLONASS orbits were computed and compared using SLR and microwave-based data. The GLONASS satellites had a slightly more accurate SLR orbit than GPS35, with the RMS of 10, 40, and 45 cm in RTN directions respectively, even in the case of the mismodelled Solar Radiation Pressure (SRP) force assignment [7]. Comparing the differences between the SLR and microwave orbits for GPS and GLONASS orbits, the RMS was about 10 cm in the radial and about 50 cm both in the along-track and across-track directions, as reported in [PERSON] (2000), where the Helmert transformation and SLR system-dependent range bias were also discussed to explore the sources of systematic error. In terms of GLOVE-A, the first Galileo In-Orbit Validation Element (GLOVE) satellites, the RMS was 8, 45, and 37 cm in RTN directions for the orbit overlap misfit between a 10-day and a 30-day arc. The temporal evolution of mean metric elements of GLOVE-A, GPS-35, and GPS-36 satellites were studied to investigate the orbital dynamic characteristics [8]. A set of orbit difference between 3-day microwave-only and 7-day SLR-only solution was obtained by 9.3, 51.0, and 39.6 cm in RTN directions, as well as 65.2 cm for the corresponding 3D-RMS [9].