Low Earth orbit (LEO) satellites located at altitudes of 500 km~1500 km can carry much stronger signals and move faster than medium Earth orbit (MEO) satellites at about a 20,000 km altitude. Taking advantage of these features, LEO satellites promise to make contributions to navigation and positioning where global navigation satellite system (GNSS) signals are blocked as well as the rapid convergence of precise point positioning (PPP). In this paper, LEO-based optimal global navigation and augmentation constellations are designed by a non-dominated sorting genetic algorithm III (NSGA-III) and genetic algorithm (GA), respectively. Additionally, a LEO augmentation constellation with GNSS satellites included is designed using the NSGA-III. For global navigation constellations, the results demonstrate that the optimal constellations with a near-polar Walker configuration need 264, 240, 210, 210, 200, 190 and 180 satellites with altitudes of 900, 1000, 1100, 1200, 1300, 1400 and 1500 km, respectively. For global augmentation constellations at an altitude of 900 km, for instance, 72, 91, and 108 satellites are required in order to achieve a global average of four, five and six visible satellites for an elevation angle above 7 degrees with one Walker constellation. To achieve a more even coverage, a hybrid constellation with two Walker constellations is also presented. On this basis, the GDOPs (geometric dilution of precision) of the GNSS with and without an LEO constellation are compared. In addition, we prove that the computation efficiency of the constellation design can be considerably improved by using master–slave parallel computing.

GNSS signals are blocked in forests, urban canyons, and indoors. Precise positioning can hardly be guaranteed in these challenging environments. A low earth orbit (LEO) constellation serving as a navigation system can provide stronger signal power to ground receivers due to its shorter transmission path than GNSS. The fast motion of LEO satellites contributes to the fast change of spatial geometry, allowing for rapid convergence of precise point positioning (PPP), and is effective in detecting carrier phase cycle slips. This study comprehensively analyzed the LEO-constellation-augmented multi-GNSS for real-time PPP in various challenging environments, including the blocking of satellite signals, cycle slips, the two issues occurring simultaneously, and significant multipath effects. An improved cycle slip detection and fixing algorithm taking advantage of LEO satellites is proposed. The GPS, BDS, and a 96-satellite polar-orbiting LEO constellation are designed, and observations at a mid-latitude station are simulated. The results show that the inclusion of LEO satellites shortens the convergence time and significantly improves the cycle slip fixing performance of multi-GNSS PPP. Three to four visible LEO satellites can shorten the GPS/BDS/LEO (GCL, C is the designation used in RINEX for BDS) PPP convergence time to 4 min compared to 20 min for the GPS/BDS (GC) solutions. Additionally, the correct cycle slip fixing time shortens from 3.3 min for the GC solution to 0.8 min for the GCL solution. When LEO satellites are free of cycle slips, the GNSS integer cycle ambiguities can be instantaneously fixed, and PPP instantaneous re-convergence is obtained. When significant multipath effects are considered, the time for GNSS/LEO first correct fixing is 3 min longer. The PPP solutions are noisier because the relatively shorter continuous observation time of LEO satellites is not beneficial for the smooth of multipath errors. In the case of GNSS and LEO satellites under both signal shielding and cycle slips, the GNSS/LEO PPP re-convergence and cycle slip fixing both degrade when the cut-off elevation increases from 20° to 40°, since LEO satellites are almost out of sight at a cut-off elevation of 40°. It is concluded that the inclusion of LEO satellites considerably improves the GNSS PPP in terms of the (re-)convergence and cycle slip fixing performance.

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The BeiDou Navigation Satellite System (BDS) of China is currently in the hybrid-use period of BDS-2 and BDS-3 satellites. All of them are equipped with Laser Retroreflect Arrays (LRAs) for Satellite Laser Ranging (SLR), which can directly obtain an independent, sub-centimetre level of distance measurement. The main purpose of this contribution is to use the solely SLR Normal Points (NPs) data to determinate the precise orbit of BDS-2 and BDS-3 satellites, including one Geostationary Earth Orbit (GEO), three Inclined Geo-Synchronous Orbits (ISGO), and one Medium Earth Orbit (MEO) of BDS-2 satellites, as well as four MEO of BDS-3 satellites, from 1 January to 30 June 2019. The microwave-based orbit from Wuhan University (WUM) are firstly validated to mark and eliminate the bad SLR observations in our preprocessing stage. Then, the 3-, 5-, 7-, and 9-day arc solutions are performed to investigate the impact of the different orbital arc lengths on the quality of SLR-derived orbits and test the optimal solution of the multi-day arc. Moreover, the dependency of SLR-only orbit determination accuracy on the number of SLR observations and the number of SLR sites are discussed to explore the orbit determination quality of the 3-,5-, 7-, and 9-day arc solutions. The results indicate that (1) during the half-year time span of 2019, the overall Root Mean Square (RMS) of SLR validation residuals derived from WUM is 19.0 cm for BDS-2 GEO C01, 5.2-7.3 cm for three BDS-2 IGSO, 3.4 cm for BDS-2 MEO C11, and 4.4-5.7 cm for four BDS-3 MEO satellites respectively. (2) The 9-day arc solutions present the best orbit accuracy in our multi-day SLR-only orbit determination for BDS IGSO and MEO satellites. 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. Owing to its extremely rare SLR observations, the SLR-only orbit determination accuracy of BDS-2 GEO satellite can only reach a level of 10 metres or worse. (3) To obtain a stable and reliable SLR-only precise orbit, the 7-day to 9-day arc solutions are necessary to provide a sufficient SLR observation quantity and geometry, with more than 50-80 available SLR observations at 5-6 SLR sites that are evenly distributed, both in the Northern and Southern Hemispheres.

Positioning of spacecraft (e.g., geostationary orbit (GEO), high elliptical orbit (HEO), and lunar trajectory) is crucial for mission completion. Instead of using ground control systems, global navigation satellite system (GNSS) can be an effective approach to provide positioning, navigation and timing service for spacecraft. In 2020, China finished the construction of the third generation of BeiDou navigation satellite system (BDS-3); this global coverage system will contribute better sidelobe signal visibility for spacecraft. Meanwhile, with more than 100 GNSS satellites, multi-GNSS navigation performance on the spacecraft is worth studying. In this paper, instead of using signal-in-space ranging errors, we simulate pseudorange observations with measurement noises varying with received signal powers. Navigation performances of BDS-3 and its combinations with other systems were conducted. Results showed that, owing to GEO and inclined geosynchronous orbit (IGSO) satellites, all three types (GEO, HEO, and lunar trajectory) of spacecraft received more signals from BDS-3 than from other navigation systems. Single point positioning (SPP) accuracy of the GEO and HEO spacecraft was 17.7 and 23.1 m, respectively, with BDS-3 data alone. Including the other three systems, i.e., GPS, Galileo, and GLONASS, improved the SPP accuracy by 36.2% and 19.9% for GEO and HEO, respectively. Navigation performance of the lunar probe was significantly improved when receiver sensitivity increased from 20 dB-Hz to 15 dB-Hz. Only dual- (BDS-3/GPS) or multi-GNSS (BDS-3, GPS, Galileo, GLONASS) could provide continuous navigation solutions with a receiver threshold of 15 dB-Hz.