Ahao Wang

Signal-in-Space Monitoring Accuracy (SISMA) is regarded as a key indicator for the integrity monitoring of the BeiDou Navigation Satellite System (BDS-3). It is used to evaluate the quality of broadcast ephemeris in real time. However, the conventional SISMA estimation method in the BDS-3 ground operation and control system is severely constrained by the deployment of ground monitoring stations, which are mainly located within China. As a result, the monitoring arcs for BDS-3 in regions outside China are incomplete and exhibit considerable latency. To overcome these limitations, this paper proposes an integrated space–ground SISMA monitoring method. Observations from Low Earth Orbit (LEO) spaceborne receivers are combined with those from ground monitoring stations. A globally distributed space-based monitoring network is constructed using 26 LEO satellites (18 near-polar, 8 inclined-orbit). These satellites act as dynamic extension nodes, while the ground network provides the backbone reference. This integrated network fuses the two types of observations through a weighted strategy, where the weights are determined by a priori observation precision of each data source. The proposed method is validated using measured data from 6 November 2025. Experimental results show that, compared with the conventional BDS-3 SISMA monitoring approach, the proposed method reduces the overall unmonitored proportion from 71.62% to below 3%. The monitoring arc coverage for Medium Earth Orbit (MEO) satellites increases from 21.12% to 97.43%, and that for IGSO satellites rises from 64.39% to 100.00%. These results confirm that the integrated space–ground approach effectively enables global SISMA monitoring for BDS-3. The integrated space–ground approach effectively fills monitoring gaps in oceanic, polar, and other areas outside China, achieving continuous and stable global SISMA monitoring for BDS-3. This advancement can strongly support high-integrity services such as civil aviation and autonomous driving.

Although the traditional Carrier-to-Code Leveling (CCL) method can provide ideal slant total electron content (STEC) observables for establishing ionospheric models, it must rely on dual-frequency (DF) receivers, which results in high hardware costs. In this study, an ionosphere-weight (IW) single-frequency (SF) precise point positioning (PPP) method for extracting STEC observables is proposed, and multi-global navigation satellite system (GNSS)-integrated processing is adopted to improve the spatial resolution of the ionospheric model. To investigate the advantages of this novel method, 41 European stations are used to establish the regional ionospheric model, and both low- and high-solar-activity conditions are considered. The results show that the IW SFPPP-derived regional ionospheric model has a significantly better quality of vertical total electron content (VTEC) than the CCL method when using the final global ionospheric map (GIM) as a reference, especially in areas with sparse monitoring stations. Compared with the CCL method, the RMS VTEC accuracy of the IW SFPPP method can be improved by 17.4% and 12.7% to 1.09 and 2.83 total electron content unit (TECU) in low- and high-solar-activity periods, respectively. Regarding GNSS carrier-phase-derived STEC variation (dSTEC) as the reference, the dSTEC accuracy of the IW SFPPP method is comparable to that of the CCL method, and its RMS values are about 1.5 and 2.8 TECU in low- and high-solar-activity conditions, respectively. This indicates that the proposed method using SF-only observations can achieve the same external accord accuracy as the CCL method in regional ionospheric modeling.

Japan’s Quasi-Zenith Satellite System (QZSS) as an important supplement to the Global Navigation Satellite System (GNSS) can provide great positioning, navigation and timing (PNT) services in the Asia-Pacific region. Many researches related to QZSS have focused on dual-/multi-frequency precise point positioning (PPP) or real-time kinematic (RTK) technology with high user costs. In this study, the contribution of QZSS to BDS-3/2 single-frequency (SF) PPP is investigated for the first time. Experimental results show that the three-dimensional (3D) positioning accuracy of the BDS-3-only and BDS-3 + 2 ionosphere-corrected (IC) SF-PPP through QZSS enhancement can be improved by 9.3% and 1.7% to 0.883 and 0.852 m, respectively. In the ionosphere-free (IF) SF-PPP, with the introduction of QZSS, the convergence time of the BDS-3-only or BDS-3 + 2 solutions can be improved by at least 21% and 8.2% in the horizontal and vertical directions, respectively. After convergence, the positioning accuracy of the BDS-3-only and BDS-3 + 2 IF SF-PPP can be improved by about 10% to 0.15 m in horizontal and 0.25 m in vertical. Compared to the IF SF-PPP, the convergence time of the ionosphere-weighted (IW) SF-PPP in the BDS-3-only and BDS-3 + 2 solutions can be improved by at least 57.6% to 13.5 min in horizontal and no more than 23% to 35.0 min in vertical. In this case of rapid convergence, it is hard to further optimize the convergence time of the BDS-3/2 IW SF-PPP by integrating the QZSS. Similar phenomena also appeared in the positioning accuracy of the IW SF-PPP. Nowadays, the 3D positioning accuracy of both IF and IW SF-PPP using BDS-3/2 + QZSS observations can reach 0.3 m in the Asia-Pacific region. Graphical abstract

The multi-global navigation satellite system (GNSS) undifferenced and uncombined precise point positioning (UU-PPP), as a high-precision ionospheric observables extraction technology superior to the traditional carrier-to-code leveling (CCL) method, has received increasing attention. In previous research, only dual-frequency (DF) or multi-frequency (MF) observations are used to extract slant ionospheric delay with the UU-PPP. To reduce the cost of ionospheric modeling, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency (SF) UU-PPP was investigated in this study. Meanwhile, the between-satellite single-differenced (SD) method was applied to remove the effects of the receiver differential code bias (DCB) with short-term time-varying characteristics in regional ionospheric modeling. In the assessment of the regional real-time (RT) between-satellite SD ionospheric model, the internal accord accuracy of the SD ionospheric delay can be better than 0.5 TECU, and its external accord accuracy within 1.0 TECU is significantly superior to three global RT ionospheric models. With the introduction of the proposed SD ionospheric model into the multi-GNSS kinematic RT SF-PPP, the initialization speed of vertical positioning errors can be improved by 21.3% in comparison with the GRAPHIC (GRoup And PHase Ionospheric Correction) SF-PPP model. After reinitialization, both horizontal and vertical positioning errors of the SD ionospheric constrained (IC) SF-PPP can be maintained within 0.2 m. This proves that the proposed SDIC SF-PPP model can enhance the continuity and stability of kinematic positioning in the case of some GNSS signals missing or blocked. Compared with the GRAPHIC SF-PPP, the horizontal positioning accuracy of the SDIC SF-PPP in kinematic mode can be improved by 37.9%, but its vertical positioning accuracy may be decreased. Overall, the 3D positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be better than 0.3 m.

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively.

Extensive observation collection, unified and rigorous data processing, and accurate construction of the station motion model are the three essential elements for the accuracy and reliability of the Global Navigation Satellite System (GNSS) velocity field. GNSS data reprocessing not only can weaken the influence of untrue nonlinear site signals caused by imperfect models but also can eliminate the displacement offset caused by frame transformation, solution strategy, and model change. Based on the new repro3 criteria of the International GNSS Service (IGS), we process rigorously GNSS observations of continental China from the period 2000 to 2020 to refine GNSS station secular velocities and analyze the present-day crustal deformation in continental China. The main contributions of this work included the followings. Firstly, the repro3 algorithm and model are used to uniformly and rigorously process the two-decade GNSS historical observations to obtain more reliable GNSS coordinate time series with mm-level precision. Combined with the historical records of major earthquakes in continental China, we build a GNSS time series model considering nonlinear factors (velocity, offset, period, co-seismic/post-seismic deformation) to extract GNSS horizontal velocity field whose root mean square (RMS) mean is 0.1 mm/a. Secondly, the GNSS horizontal grid velocity field in continental China is interpolated using the gpsgridder method (the minimum radius is set to 16, and the Poisson’s ratio is set to 0.5). Estimation and analysis of the crustal strain rate solution lead to the conclusion that the strain degree in West China (the high strain region is mainly located in the Qinghai Tibet Plateau and Tianshan Mountains) is much more intense than that in the east (the main strain rate is less than 5 nstrain/year). In addition, most strong earthquakes in the Chinese mainland occurred on active blocks and their boundary faults with large changes in the GNSS velocity field and strain field. Then, an improved K-means++ clustering analysis method is proposed to divide active blocks using GNSS horizontal velocity field. Furthermore, different relative motion models of different blocks are constructed using the block division results. Among them, the Eurasian block has the lowest accuracy (the RMS of residual velocity in the east and north directions are 5.60 and 9.65 mm/a, respectively), and the China block 7 has the highest accuracy (the RMS mean of relative velocity in the east and north directions are 2.60 and 2.65 mm/a, respectively). More observations (2260+ sites), longer time (20 years), and updated criteria (Repro3) are to finely obtain the GNSS velocity field in continental China, and depict crustal deformation and active block with the gpsgridder and improved K-means++ methods.