Recently, factor graph optimization (FGO)-based GNSS/INS integrated navigation has garnered widespread attention for its ability to provide more robust positioning performance in challenging environments like urban canyons, compared to traditional extended Kalman filter (EKF)-based methods. In existing GNSS/INS integrated navigation methods based on FGO, the primary approach involves combining single point positioning (SPP) or real-time kinematic (RTK) with INS by constructing factors between consecutive epochs to resist outliers and achieve robust positioning. However, the potential of a high-precision positioning system based on the FGO algorithm, combining INS and PPP-B2b and that does not rely on reference stations and network connections, has not been fully explored. In this study, we developed a loosely coupled PPP-B2b/INS model based on the EKF and FGO algorithms. Experiments in different urban road and overpass scenarios were conducted to investigate the positioning performance of the two different integration navigation algorithms using different degrades of inertial measurement units (IMUs). The results indicate that the FGO algorithm outperforms the EKF algorithm in terms of positioning with the combination of GNSS and different degrades of IMUs under various conditions. Compared to the EKF method, the application of the FGO algorithm leads to improvements in the positioning accuracy of approximately 15.8%~45.9% and 19%~41.3% in horizontal and vertical directions, respectively, for different experimental conditions. In scenarios with long and frequent signal obstructions, the advantages of the FGO algorithm become more evident, especially in the horizontal direction. An obvious improvement in positioning results is observed when the tactical-grade IMU is used instead of the microelectron-mechanical system (MEMS) IMU in the GNSS/INS combination, which is more evident for the FGO algorithm than for the EKF algorithm.

In this study, we investigate the performances of a commercial Global Navigation Satellite System (GNSS) Radio Occultation (RO) mission and a new-generation RO constellation, i.e., Spire and Constellation Observing System for Meteorology, Ionosphere, and Climate 2 (COSMIC-2), respectively. In the statistical comparison between Spire and COSMIC-2, the results indicate that although the average signal-to-noise ratio (SNR) of Spire is far weaker than that of COSMIC-2, the penetration of Spire is comparable to, and occasionally even better than, that of COSMIC-2. In our analysis, we find that the penetration depth is contingent upon various factors including SNR, GNSS, RO modes, topography, and latitude. With the reanalysis of the European Centre for Medium-Range Weather Forecasts and Radiosonde as the reference data, the identical error characteristics of Spire and COSMIC-2 reveal that overall, the accuracy of Spire’s neutral-atmosphere data products was found to be comparable to that of COSMIC-2.

The precise point positioning service on B2b signal (PPP-B2b) is a real-time decimeter-level positioning service provided by the BeiDou-3 Global Navigation Satellite System (BDS-3). The service provides users with high-precision orbit and clock corrections through geostationary orbit (GEO) satellites, which means that the PPP-B2b service would be unusable if GEO satellites were blocked. In this study, the performance of PPP-B2b corrections and real-time positioning results during outages of the PPP-B2b service are comprehensively investigated. The results showed that PPP can achieve satisfactory accuracy during outages of the PPP-B2b service by extending the nominal validity of the received PPP-B2b corrections. After extending the PPP-B2b corrections for 10 min, for BDS-3 medium earth orbit (MEO) satellites, the mean root-mean-square error (RMSE) values of the extended orbit were 0.16 m, 0.26 m, and 0.23 m in the radial, along-, and cross-track directions, respectively. The accuracy of the BDS-3 inclined geostationary orbit (IGSO) satellites was slightly worse than that of the BDS-3 MEO satellites; for Global Positioning System (GPS) satellites, the mean RMSE values of the extended orbit were 0.11 m, 0.45 m, and 0.33 m in the radial, along-, and cross-track directions, respectively. In terms of the extended clock, the mean standard deviation (STD) reached 0.17 ns, 0.20 ns, and 0.22 ns after 10 min for the BDS-3 MEO, BDS-3 IGSO, and GPS satellites, respectively. The positioning performance maintained with the extended corrections during the PPP-B2b service outage was evaluated based on five stations in and around China. Our experiments showed that, as long as the interruption time does not exceed 10 min, the real-time positioning with extended PPP-B2b corrections can achieve a comparable accuracy with that obtained following PPP-B2b correction.

The precise point positioning (PPP) service via the B2b signal (PPP-B2b) on the BeiDou Navigation Satellite System (BDS) provides high-accuracy orbit and clock data for global navigation satellite systems (GNSSs), enabling real-time atmospheric data acquisition without internet access. In this study, we assessed the quality of orbit, clock, and differential code bias (DCB) products from the PPP-B2b service, comparing them to post-processed products from various analysis centres. The zenith tropospheric delay (ZTD) and precipitable water vapour (PWV) were computed at 32 stations using the PPP technique with PPP-B2b corrections. These results were compared with post-processed ZTD with final orbit/clock products and ZTD/PWV values derived from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) and radiosonde data. For stations between 30° N and 48° N, the mean root mean square error (RMSE) of ZTD for the PPP-B2b solution was approximately 15 mm compared to ZTD from the International GNSS Service (IGS). However, accuracy declined at stations between 30° N and 38° S, with a mean RMSE of about 25 mm, performing worse than ZTD estimates using Centre National d’Études Spatiales (CNES) products. The mean RMSEs of PWV derived from PPP-B2b were 3.7 mm and 4.4 mm when compared to PWV from 11 co-located radiosonde stations and ERA5 reanalysis, respectively, and underperformed relative to CNES solutions. Seasonal variability in GNSS-derived PWV was also noted. This reduction in accuracy limits the global applicability of PPP-B2b. Despite these shortcomings, satellite-based PPP services like PPP-B2b remain viable alternatives for real-time positioning and atmospheric applications without requiring internet connectivity.