1. Introduction
Currently, the BeiDou Navigation Satellite System (BDS) of China is in the period when BDS-2 and BDS-3 satellites are used together, and both generations of BDS continue to reinforce and complete their constellation. According to official reports, China has successfully launched its 45th BDS satellite, which is the fourth backup satellite of BDS-2, on 17 May 2019. Also, the 47th and 48th BDS satellites, as the 22th and 23th satellites of BDS-3, were successfully launched on 23 September 2019 (
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 Degnan and Pavlis [
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 Schutz [
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 Appleby & Otsubo (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]. Meanwhile, the SLR-only orbit overlap of 9-day arcs for the SLR-only GLOVE-A satellite were about 10 cm, 0.5 m, and 1 m [
10]; the same results were obtained in Flohrer [
11].
For BDS, the 3D-RMS of BeiDou-G1, -I3, -I5, and -M3 were on the level of one metre to a few metres, while the radial accuracy was on the level of decimetres [
12]. In Zhao et al. [
13], the 7-day arcs of SLR-only orbits for GPS, GLONASS, Galileo, and BDS were implemented, and the orbit accuracy were evaluated and compared, based on the different satellite types, as well as on different satellite constellations. For MEO, the radial accuracy was around 4–10 cm while the 3D-RMS are tens of cm, either for orbit overlaps or for comparisons with microwave-based orbits.
Overall, most previous studies show that for a selected arc, the SLR-derived orbit for the GNSS satellites is not universal. It is not quite clear what accuracy can be achieved under different conditions. The multi-GNSS orbit of long-term time series—using solely SLR observations—was determined by Bury et al. [
14] and Bury et al. [
15]. The contribution demonstrated that 60 SLR observations—as many SLR sites as possible—and optimal 5-day to 7-day arc length were necessary in order to provide a better geometry of observations and preclude deterioration of the along-track component caused by excessive arc length. However, the SLR-only orbit for BDS is not analysed in detail, especially for the BDS GEO satellites. Moreover, the SLR-only orbit determination for BDS-3 satellites, as a fresh constellation, has hardly been explored. Based on these, the SLR-only orbit for BDS-2 and BDS-3 satellites are determined from 1 January 2019 to 30 June 2019 in this contribution. The 3-, 5-, 7-, and 9-day arc solutions are calculated to test and determine the magnitude of accuracy of the SLR-only orbit of BDS-2 and BDS-3 satellites, including a total of nine BDS satellites, which cover all the three types of satellites: GEO, IGSO, and MEO. Among them, five satellites belong to BDS-2—namely C01, C08, C10, C11, and C13. The remaining four satellites belong to BDS-3, which are C20, C21, C29, and C30. The accuracy of SLR-only orbit determination is evaluated by the orbit overlaps and by the comparison with the microwave-based precise orbit of WUM. Besides, the dependency of SLR-only orbit determination accuracy on the number of SLR observations and on the number of SLR sites is explored in detail.
The paper is organized as follows. In
Section 2, the methodology of SLR-only orbit determination and the corresponding accuracy assessment strategy are described. Then,
Section 3 presents the time series of processed SLR data and the SLR validation residuals derived from WUM while the results of SLR-only orbit determination are shown in
Section 4.
Section 5 discusses the accuracy dependency of the SLR-only orbit determination on the number of SLR observations and on the number of SLR sites. Finally, we summarize and comment on the conclusions in the last section.
6. Conclusions
SLR is capable of making significant contributions to the orbit determination of GNSS satellites when a sufficient number of available SLR observations is provided [
11], and not just for SLR validation in GNSS satellite applications. Influenced by the number of the SLR observations and the SLR sites, the SLR-only orbit determination of GNSS satellites has received less attention than that of GNSS microwave-based orbit determination. In fact, the multi-day arc solution of SLR-only orbit determination can reach a satisfactory accuracy that is comparable with that of GNSS microwave-based orbit determination. In this contribution, we determinate the SLR-only orbit of BDS-2 and BDS-3 satellites for a half-year time span since the beginning of 2019, and discuss the dependency of median RMS on the number of SLR observations and on the number of SLR sites to explore their orbit determination quality of the 3-,5-, 7-, and 9-day arc solutions.
Before SLR orbit determination, the SLR validation is performed to screen the available SLR observations. The accuracy of the microwave-based orbit of WUM is much better than that before March 2018 for BDS-2 GEO C01 [
20], whose RMS of SLR residuals is 19.0 cm, with a mean offset of −7.5 cm now. The BDS-2 IGSO satellites have the credible RMS of 5.2–7.3 cm, with the mean offset of −4.2– −1.8 cm. Remarkably, the overall mean offset and RMS of BDS-3 MEO satellites is −1.4–0.3 cm and 4.4–5.7 cm, while the RMS of the only BDS-2 MEO C11 is 3.4 cm, with a mean offset of 0.9 cm. As the number and geometric distribution of GNSS stations that are tracking BDS-3 signal is worse than that of BDS-2, the accuracy of BDS-3 is slightly worse than that of BDS-2.
With only a slight difference in SLR observations data preprocessing strategies, BDS GEO C01 is processed synchronously with BDS IGSO and MEO satellites for SLR-only orbit determination. Unfortunately, the SLR-only orbit determination accuracy of C01 is not very promising on account of the extremely rare SLR observations. Overall, the SLR-only orbit determination accuracy of BDS-2 GEO satellite only can reach a level of 10 metres or worse while the 9-day arc solutions present the best orbit accuracy in our multi-day SLR-only orbit determination for BDS IGSO and MEO satellites. Although the SLR-only orbit determination accuracy of BDS-3 MEO satellites are slightly worse than BDS-2 MEO C11 under the same number of SLR sites and SLR observations, the SLR-only orbit determination accuracies of all BDS MEO are on the same level. The 9-day overlaps median RMS of BDS MEO in RTN directions are evaluated at 3.6–5.7, 12.4–21.6, and 15.6–23.9 cm respectively, as well as 5.7–9.6, 15.0–36.8, and 16.5–35.2 cm for the comparison with WUM precise orbits, while these values of BDS IGSO are larger by a factor of about 3–10 than BDS MEO orbits in their corresponding RTN directions. Furthermore, the optimal average 3D-RMS of 9-day overlaps is 0.49 and 1.89 m for BDS MEO and IGSO respectively, as well as 0.55 and 1.85 m in comparison with WUM orbits. Besides, the SLR-only orbit determination accuracy of IGSO C13 is better than that of IGSO C08 and C10, since it has more available SLR observations. However, limited by the geographical distribution and number of the available SLR sites, the SLR-only orbit determination accuracy of IGSO is worse than that of MEO, even with the same SLR observations.
In summary, SLR is the space geodetic technique with the highest single independent ranging and absolute positioning accuracy relative to the centre of the Earth. As things stand, the SLR-only orbit determination accuracy of BDS GEO is more than tens of metres while that of BDS IGSO and MEO is at the level of submetre and decimetre. Though the SLR-only orbit determination of GNSS satellites suffers from some limitations, it will play an important and positive role in scientific research that does not require so high an orbital accuracy, such as the orbit determination and prediction of space debris. Also, the combined orbit determination using the space geodesy technologies of GNSS, SLR, as well as VLBI and DORIS, are bound to be the development trends of space technology in the future.