Due to the cuboid satellite body of BeiDou-3 satellites, the accuracy of their orbit showed a trend of systematic variation with the sun-satellite-earth angle (ε) using the Extend CODE Orbit Model (ECOM1). Therefore, an a priori cuboid box-wing model (named the cuboid model) is necessary to compensate ECOM1. Considering that the body-dimensions and optical properties of the BeiDou-3 satellites used to construct the box-wing model have not yet been fully released, the adjustable box-wing model (ABW) was used for precise orbit determination (POD). The a priori cuboid box-wing model was directly estimated by the precision radiation accelerations, obtained from ABW POD. When using ECOM1 model, for 14 < β < 40°, a linear systematic variation of D0 related to the elevation of the sun above the orbital plane (β-angle) with a slope of 0.048 nm/s²/°, was found for C30. After adding the cuboid model to assist ECOM1 (named Cuboid + ECOM1), the slope was reduced to 0.005 nm/s²/°, and for C20 satellite, the standard deviation (STD) of D0 was improved, from 1.28 to 0.85 nm/s² (34%). For satellite laser ranging (SLR) validation, when using the ECOM1 model, the systematic variation with the ε angle was about 14 cm for C20 and C30. After using the Cuboid + ECOM1 model, the variation was significantly reduced to about 5 cm. For C20 and C21, compared with the ECOM1 model, the root mean square (RMS) of the ECOM2 and Cuboid + ECOM1 model was improved by about 0.54 (10.3%) and 0.43 cm (8.7%). For C29 and C30, the RMS of ECOM2 and Cuboid + ECOM1 model was improved for about 0.7 (10.9%) and 1.6 cm (25.6%). Finally, the RMS of the SLR residuals of 4.37 to 4.88 cm was achieved for BeiDou-3 POD.

The frequent maneuvering of BeiDou Geostationary Orbit (GEO) and Inclined Geosynchronous Orbit (IGSO) satellites affects the availability of real-time orbit, and decreases the accuracy and performance of positioning, navigation and time (PNT) services. BeiDou satellite maneuver information cannot be obtained by common users. BeiDou broadcast ephemeris is the only indicator of the health status of satellites, which are broadcast on an hourly basis, easily leading to ineffective observations. Sometimes, identification errors of satellite abnormity also appear in the broadcast ephemeris. This study presents a real-time robust detection method for a satellite orbital maneuver with high frequency and high reliability. By using the broadcast ephemeris and pseudo-range observations, the time discrimination factor and the satellite identification factor were defined and used for the real-time detection of start time and the pseudo-random noise code (PRN) of satellites was used for orbital maneuvers. Data from a Multi-GNSS Experiment (MGEX) was collected and analyzed. The results show that the start time and the PRN of the satellite orbital maneuver could be detected accurately in real time. In addition, abnormal start times and satellite abnormities caused by non-maneuver factors also could be detected using the proposed method. The new method not only improves the utilization of observations for users with the data effective for about 92 min, but also promotes the reliability of real-time PNT services.

Satellite antenna phase center offsets (PCOs) and phase variations (PVs) for BeiDou-3 satellites are estimated based on the tracking data of the Multi-GNSS Experiment (MGEX) and the international GNSS Monitoring and Assessment System (iGMAS) network. However, when estimating the (PCOs) of BeiDou-3 medium Earth orbit (MEO) satellites by pure Extending the CODE Orbit Model (ECOM1), the x-offset estimations of the PCOs have a systematic variation of about 0.4 m with the elevation of the Sun above the orbital plane (β-angle). Thus, a priori box-wing solar radiation pressure (SRP) model of BeiDou-3 MEO was assisted with ECOM1. Then, the satellite type-specific PCOs and common PVs were obtained. The estimations of PCOs and PVs were compared with the MGEX PCOs from the precise orbit and clock offset. When the MGEX PCOs were used, the root mean square (RMS) of 24 h overlap was 6.76, 4.36, 1.46 cm, in along-track, cross-track, and radial directions, respectively; the RMS and standard deviations (STD) of the 24 h clock offset overlap were 0.28 and 0.15 ns; the fitting RMS of the 72 h clock offset of the quadratic polynomial was 0.243 ns. After comparing this with the estimated PCOs and PVs, the RMS of the 24 h orbit overlap was decreased by 6.5 mm (10.54%), 1.8 mm (4.4%), and 1.1 mm (8.03%) in the along-track, cross-track, and radial directions, respectively; the RMS and STD of the 24 h clock offset overlap were decreased by 0.024 ns (8.6%) and 0.020 ns (13.1%), respectively; the fitting RMS of the 72 h clock offset of the quadratic polynomial was reduced by about 0.016 ns (6.5%).

Efficient monitoring and early warning are the preconditions of realizing expansive soil landslide hazard prevention and control. Previous early warning of expansive soil landslides was evaluated through soil sampling experiments to analyze the stability coefficient. However, the existing methods lack timeliness and ignore the inconsistent deformation characteristics of different parts of the landslide mass. There are still difficulties in the dynamic numerical early warning of landslides at multiple points. Considering that the degradation of expansive soil landslides’ strength is directly reflected by surface displacement, for the Ningming expansive soil demonstration area and based on the GNSS shallow real-time displacement monitoring sequence, a landslide early-warning method based on the GNSS displacement rate combined with the GNSS displacement tangent angle model was proposed, and we thus designed early-warning thresholds for different warning levels. Combined with multi-source data such as soil moisture, soil pressure, and rainfall, the feasibility of accurate early warning of expansive soil landslides based on GNSS real-time surface displacement was verified. The proposed method does not require numerical calculation of internal stress and achieved two successful early warnings of landslides in the test area, which has a certain promotional value.

Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products in some older smart devices are applied in current studies. The performances of precise point positioning (PPP) with the smartphone using real-time products and newly smartphones are still unrevealed, which is more valuable for real-time applications. This study investigates the observation data quality and multi-GNSS real-time PPP performance using recent smartphones. Firstly, the observed carrier-to-noise density ratio (C/N0), number of satellites and position dilution of precision (PDOP) of GNSS observations are evaluated. The results demonstrate that the C/N0 received by Huawei Mate40 is better than that of the Huawei P40 for GPS, BDS, QZSS and Galileo systems, while the GLONASS is poorer, and the PDOP of the Huawei P40 is slightly better than that of Mate40. Additionally, a comprehensive analysis of real-time precise orbit and clock offset products performance is conducted. The experiment result expresses that the orbit and clock offset performance of GPS and Galileo is better than that of BDS-3 and GLONASS, and BDS-2 is the worst. Finally, single- and dual-frequency multi-GNSS combined PPP experiments using observations received from smartphones and real-time products are conducted; the results indicate that the real-time static PPP using a smartphone can achieve decimeter-level positioning accuracy, and kinematic PPP can achieve meter-level positioning accuracy after convergence.

Since BeiDou Navigation Satellite System (BDS) and Japan’s Quasi-Zenith Satellite System (QZSS) have more visible satellites in the Asia-Pacific region, and navigation satellites of Global Positioning System (GPS), Galileo satellite navigation system (Galileo), and GLONASS satellite navigation system (GLONASS) are uniformly distributed globally, the service level of multi-mode Global Navigation Satellite System (GNSS) in the Asia-Pacific region should represent the best service capability. Based on the observation data of 10 Multi-GNSS Experiment (MGEX) stations, broadcast ephemeris and precision ephemeris from 13 to 19 October 2021, this paper comprehensively evaluated the service capability of multi-GNSS in the Asia-Pacific region from three aspects of observation data quality, broadcast ephemeris performance, and precision positioning level. The results show that: (1) the carrier-to-noise-density ratio (C/N0) quality of the GPS and Galileo is the best, followed by BDS and GLONASS, and QZSS is the worst. GPS, BDS-2, GLONASS, and QZSS pseudorange multipath values range from 0 to 0.6 m, while Galileo system and BDS-3 pseudorange multipath values range from 0 to 0.8 m. (2) In terms of broadcast ephemeris accuracy, BDS-3 broadcast ephemeris has the best orbit, and the three-dimensional (3D) Root Mean Square (RMS) is 0.21 m; BDS-2 was the worst, with a 3D RMS of 1.99 m. The broadcast ephemeris orbits of GPS, Galileo, QZSS, and GLONASS have 3D RMS of 0.60 m, 0.62 m, 0.83 m, and 1.27 m, respectively. For broadcast ephemeris clock offset: Galileo has the best performance, 0.61 ns, GLONASS is the worst, standard deviation (STD) is 3.10 ns, GPS, QZSS, BDS-3 and BDS-2 are 0.65 ns, 0.75 ns, and 1.72 ns, respectively. For signal-in-space ranging errors (SISRE), the SISRE results of GPS and Galileo systems are the best, fluctuating in the range of 0 m–2 m, followed by QZSS, BDS-3, Galileo, and BDS-2. (3) GPS, BDS, GLONASS, Galileo, GPS/QZSS, and BDS/QZSS were used for positioning experiments. In static PPP, the convergence time and positioning accuracy of GPS show the best performance. The positioning accuracy of GPS/QZSS and BDS/QZSS is improved compared with that of GPS and BDS. In terms of kinematic PPP, the convergence time and positioning accuracy of GPS/QZSS and BDS/QZSS are improved compared with that of GPS and BDS. In addition to GLONASS and Galileo systems, the other combinations outperformed 3 cm, 3 cm, and 5 cm in the east, north, and up directions.