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.

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 availability of Global Navigation Satellite System (GNSS) raw observations in smartphones has driven research into low-cost GNSS solutions, especially in challenging urban environments, which have garnered significant attention from scholars in recent years. This study proposes an improved smartphone-based velocity-aided positioning method and conducts vehicle-mounted experiments in urban roads representing typical scenarios. The results show that when transitioning from low- to high-multipath environments, the number of visible satellites and carrier phase observations are highly sensitive to environmental factors, with frequent multipath effects. The introduction of robust pre-fit and post-fit residual algorithms has proven to be an effective quality control method. Additionally, using more refined observation models and appropriate parameter estimation algorithms led to a slight 6% improvement in velocity performance. The improved Kalman filter position estimation model (KFSPP-P) strategy, by incorporating velocity uncertainty into the state estimation process, overcomes the limitations of conventional velocity-aided smartphone positioning methods (KFSPP-V) in complex urban environments. In low-multipath environments, the accuracy of the KFSPP-P strategy is comparable to that of KFSPP-V, with an approximate 8% improvement in horizontal accuracy. However, in more challenging environments, such as tree-lined roads and urban environments, the KFSPP-P strategy shows significant improvements, particularly enhancing horizontal positioning accuracy by approximately 50%. These advancements demonstrate the potential of using smartphones to provide reliable positioning services in complex urban environments.