Precision point positioning (PPP) utilizing the Global Navigation Satellite System (GNSS) is a traditional and widely employed technology. Its performance is susceptible to observation discontinuities and unfavorable geometric configurations. Consequently, the integration of the Inertial Navigation System (INS) and GNSS makes full use of their respective advantages and effectively mitigates the limitations of GNSS positioning. However, the GNSS/INS integration faces significant challenges in complex and harsh urban environments. In recent years, the geometry between the user and the satellite has been effectively improved with the advent of lower-orbits and faster-speed Low Earth Orbit (LEO) satellites. This enhancement provides more observation data, opening up new possibilities and opportunities for high-precision positioning. Meanwhile, in contrast to the traditional extended Kalman filter (EKF) approach, the performance of the LEO-enhanced GNSS/INS tightly coupled integration (TCI) can be significantly improved by employing the factor graph optimization (FGO) method with multiple iterations to achieve stable estimation. In this study, LEO data and the FGO method were employed to enhance the GNSS/INS TCI. To validate the effectiveness of the method, vehicle data and simulated LEO observations were subjected to thorough analysis. The results suggest that the integration of LEO data significantly enhances the positioning accuracy and convergence speed of the GNSS/INS TCI. In contrast to the FGO GNSS/INS TCI without LEO enhancement, the average enhancement effect of the LEO is 22.16%, 7.58%, and 10.13% in the north, east, and vertical directions, respectively. Furthermore, the average root mean square error (RMSE) of the LEO-enhanced FGO GNSS/INS TCI is 0.63 m, 1.21 m, and 0.85 m in the north, east, and vertical directions, respectively, representing an average improvement of 41.91%, 13.66%, and 2.52% over the traditional EKF method. Meanwhile, the simulation results demonstrate that LEO data and the FGO method effectively enhance the positioning and convergence performance of GNSS/INS TCI in GNSS-challenged environments (tall buildings, viaducts, underground tunnels, and wooded areas).

In this paper, we propose a new method to quantitatively evaluate the quality of the carrier phase observation signals of the BeiDou Navigation Satellite System (BDS) during weak and moderate geomagnetic storms. We take a moderate geomagnetic storm that occurred on 12 May 2021 during the 25th solar cycle as an example. The results show that the newly defined PAS (Percentage of Affected Satellites) index shows significant anomaly changes during the moderate geomagnetic storm. Its variation trend has good correlations with the geomagnetic storm Kp index and Dst index. The anomaly stations are mainly distributed in the equatorial region and auroral region in the northern and southern hemispheres. The proposed PAS index has a good indication for both BDS2 and BDS3 satellites. We further validated this index by calculating the Precise Point Position (PPP) positioning error. We found that the anomaly period of PAS has strong consistency with the abnormal period of PPP positioning accuracy. This study could provide methodological support for the evaluation of the signal quality and analysis of positioning accuracy for the BeiDou satellite navigation system under different space weather conditions.

Positioning by means of the Global Positioning System (GPS) is a traditional and widely used method. However, its performance is affected by the user environment, such as multi-path effects and poor anti-interference abilities. Therefore, an Inertial Navigation System (INS) has been integrated with GPS to overcome the disadvantages of GPS positioning. INSs do not rely on any external system information and has strong autonomy and independence from the external environment. However, the performance of GPS/INS is visibly degraded in low-observability GPS environments (tall buildings, viaducts, underground tunnels, woods, etc.). Fortunately, with the emergence of Low-Earth-Orbit (LEO) satellites in recent years, the constellation configuration can be extended with the advantages of lower orbits, greater speeds, and richer geometric structures. LEO improves the geometric structure between users and satellites and provides many more observations. Meanwhile, a robust theory approach is applied that can restrain or remove the impact of low-accuracy observations. In this study, we applied LEO data and a robust theory approach to enhance the GPS/INS tight integration. To verify the effectiveness of this method, a set of vehicles and simulated LEO data were analyzed. The results show that robust Kalman filtering (RKF) provides a visible enhancement in the positioning accuracy of GPS/INS integration. This effectively restrains the mutation error and has a smoothing effect on the positioning results. In addition, the addition of LEO data significantly improves the positioning accuracy of a sole GPS and GPS/INS integration. The GPS/LEO/INS integration has the highest positioning accuracy, with Root-Mean-Square Errors (RMSEs) of the north, east, and vertical positions of 2.38 m, 1.94 m, and 2.49 m, respectively, which corresponds to an improvement of 30.21%, 47.43%, and 34.13% compared to sole GPS-based positioning and 8.60%, 17.24%, and 12.14% when compared to the GPS/INS mode. Simultaneously, the simulation results show that LEO and INSs can improve the positioning performance of GPS under GPS-blocked conditions.

Precise point positioning (PPP) technology is one of the core technologies in the field of GNSS high-precision positioning. It is used widely because it can realize centimeter-level positioning in outdoor environments by using only a single receiver. However, its convergence is time-consuming, particularly in urban areas where satellite occlusion is more severe. A combined BeiDou Navigation Satellite System (BDS) and fifth generation mobile communication technology (5G) PPP observation model is proposed, in which the two kinds of observations are combined and solved at the original observation level. The impact of different numbers and geometries of 5G base stations on the convergence time of PPP is analyzed from both static and dynamic perspectives. The results confirm that PPP technology combining BDS and 5G can effectively accelerate convergence while improving the accuracy of positioning.

In PPP-RTK, obtaining accurate atmospheric delay information for the user through interpolation is one of the keys to achieving high-precision real-time positioning. The ionospheric delay that is extracted by a reference network based on uncalibrated phase delay (UPD) products is often difficult to separate from errors such as receiver code hardware delay and UPD reference error. Inter-satellite single-difference (SD) ionospheric delay information is typically provided to the user. This paper proposes an interpolation model that uses the atmospheric delay coefficient to represent the SD ionospheric delay, based on the mean position of the ionospheric pierce point (IPP) of each satellite pair and the center position of the network, which is called the differenced surface model (DSM). We chose four scenarios to compare the interpolation accuracy of the proposed model with the inverse distance-based linear interpolation method (DIM) and USM based on the difference between the longitude and latitude of the reference and ionospheric pierce point (IPP) of every satellite (here, we call it USM for short). The four scenarios involve a medium-scale reference network with an average distance to the reference station of 41 km, a large-scale reference network with an average distance to the reference station of 98 km, and out-of-network users, and a network with a common minimum of three reference stations. The results show that the root mean square (RMS) of the SD residuals of ionospheric delay for DSM were 1.4, 3.2, 2.2, and 1.4 cm, respectively, for the four scenarios that were considered, which are slightly better delay values than those that were achieved using DIM and USM. For the scenario with three reference stations, the interpolation accuracies of DIM and DSM were no different from those for four reference stations, indicating that the server can still try to provide ionospheric correction service under the condition of fewer reference stations. In contrast, USM could not provide service because it lacked the sufficient number of reference stations. DSM was used as the ionospheric delay interpolation model to analyze GPS and Galileo dual-system PPP-RTK positioning performance. In addition, the atmospheric parameter constraint method of users was used in PPP-RTK in reference networks of different scales. For the 41-km and 98-km reference networks, the time to first fix (TTFF) were 14.5 s and 33.1 s, respectively, and the mean RMS values for the east (E), north (N), and up (U) directions were 0.80, 0.93, and 2.72 cm, respectively, and 1.0, 1.1, and 4.0 cm, respectively, for a period of 5 min after convergence. The fixing rate and positioning accuracy of DSM during the 5-min period were better than those of DIM when the same empirical model was used to determine the mean square error of atmospheric delay.