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).

Since 2020, the BDS-3 has been providing real-time corrections via the B2b signal, enabling users in China and its neighboring regions to achieve kinematic positioning accuracy at the decimeter level. The rapid geometric changes of Low-Earth-Orbit (LEO) satellites facilitate the rapid resolution of phase ambiguities and accelerate the convergence of Precise Point Positioning (PPP). Therefore, this study proposes an LEO-enhanced BDS-3 PPP-B2b positioning model. Firstly, a novel BDS-3 PPP model accounting for satellite clock bias characteristics is proposed, and experimental validation confirms its efficacy. Subsequently, an LEO-enhanced BDS-3 PPP model is developed. Finally, the positioning performance is rigorously evaluated using combined LEO simulation observations and BDS-3 observations. The results indicate that, compared with the traditional PPP model, the new model yields an average convergence time of 25.1 min for experiments where the convergence criterion is jointly satisfied, representing a 35.6% improvement in convergence speed, while maintaining the same positioning accuracy after convergence. When augmented with LEO satellites, the convergence time of the BDS-3 PPP-B2b solution is reduced to less than 2 min. Furthermore, when more than three LEO satellites are available, the mean convergence time is shortened to within 1 min.

Global Navigation Satellite System (GNSS) buoys are widely used to retrieve wave parameters such as significant wave heights (SWHs) and dominant wave periods. In addition to the statistical methods employed to estimate wave parameters, spectral-analysis-based approaches are also frequently utilized to analyze them. This study presents statistical and spectral methods for retrieving wave parameters at GNSS buoy positioning resolution in the Huanghai Sea area. To verify the method’s effectiveness, the zero-crossing method and three spectral analysis techniques (periodogram, autocorrelation function, and autoregressive model methods) were used to estimate wave height and period for comparison. The vertical positioning resolution was decomposed into low-frequency ocean-tide level information and high-frequency wave height and period information with the Complete Ensemble Empirical Mode Decomposition (CEEMD) method and moving average filtering. The horizontal positioning results and velocity parameters were used to determine the wave direction using directional spectrum analysis. The results show that the three spectral methods yield consistent effective wave heights, with a maximum difference of 0.02 s in the wave period. Compared with the zero-crossing method results, the wave height and period obtained through spectral analysis differ by 0.05 m and 0.79 s, respectively, while the average wave height and period differ by 0.09 m and 0.08 s, respectively. The GNSS-derived wave heights also closely match tidal gauge observations, confirming the method’s validity. Directional spectrum analysis indicates that wave energy is concentrated in the 0.2–0.25 Hz frequency band and within a directional range of 0° ± 30°, with a dominant northward propagation trend. These findings demonstrate that the proposed approach can provide high accuracy and physical consistency for GNSS-based wave monitoring under complex sea conditions.

Determining the sea surface height using Global Navigation Satellite System (GNSS) buoys is an important method for satellite altimetry calibration. The buoys observe the absolute height of the sea surface using GNSS positioning technology, which is then used to correct the systematic deviation of the altimeter of the orbiting satellite. Due to the challenging observational conditions, such as significant multipath errors in GNSS code observation and complex variations in buoy position and attitude, gross errors in GNSS buoy positioning reduce the accuracy and stability of the calculated sea surface heights. To accurately detect and remove these gross errors from GNSS coordinate time series, the complementary ensemble empirical mode decomposition (CEEMD) method and the interquartile range (IQR) method were adopted to enhance the accuracy and stability of GNSS sea surface altimetry. Firstly, the raw GNSS sequential coordinate series are decomposed into main terms, such as trend contents and periodic contents, and high-frequency noise terms using the CEEMD method. Subsequently, the high-frequency noise terms of the GNSS coordinate series are regarded as the residual sequences, which are used to detect gross errors using the IQR method. This approach, which integrates the CEEMD and IQR methods, was named CEEMD-IQR and enhances the ability of the traditional IQR method to detect subtle gross errors in GNSS coordinate time series. The results indicated that the CEEMD-IQR method effectively detected gross errors in offshore GNSS coordinate time series using GNSS buoys, presenting a significant enhancement in the gross error detection rate of at least 35.3% and providing a “clean” time series for sea level measurements. The resulting GNSS sea surface altimetry accuracy was found to be better than 1.51 cm.

The economic and strategic value of high-latitude maritime regions is increasingly significant, yet traditional Global Navigation Satellite Systems remain constrained by unfavorable geometric configurations and slow convergence speeds at high latitudes, failing to meet the growing demand for real-time centimeter-level high-precision positioning in these areas. Benefiting from their rapid motion and superior coverage over high-latitude zones, Low Earth Orbit (LEO) satellites offer an effective means to enhance positioning performance in such regions. This paper uses the real BDS data collected by an unmanned surface vessel in the high-latitude waters of the Southern Hemisphere, jointly simulates polar and medium-inclination LEO constellations, and systematically assess the enhancement effects of LEO augmentation on Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) techniques. The results demonstrate that the polar-orbiting constellation markedly improves the observation environment, increasing the number of visible satellites by 70.2% and reducing the Position Dilution of Precision from 2.4 to 1.7, whereas the medium-inclination orbit constellation offered negligible improvement due to insufficient visibility. The rapid geometric change brought by LEO constellations is the core key to achieving fast convergence. Incorporating LEO observations drastically shortened the BDS PPP convergence time from 45.3 min to under 1 min, achieving a reduction of over 97%. Simultaneously, it improved the three-dimensional Root Mean Square accuracy by 54.7%, from 0.086 m to 0.039 m. Convergence within one minute was consistently achieved when at least 5.4 LEO satellites were included in the solution. Moreover, the addition of LEO signals increased the fixed solution rate of short-baseline RTK from 96.5% to 100%, while improving horizontal and vertical accuracy by 31.5% and 12.3%, respectively. This study confirms that LEO constellations, especially those in polar orbits, can substantially enhance BDS precise positioning performance in high-latitude maritime environments, thereby providing critical technical support for related navigation applications.

Reliable positioning and mapping in roadway tunnels are crucial for vehicle-based monitoring and inspection, especially considering the challenging environmental conditions such as rapidly changing illumination, low-texture environments, and repetitive structural elements. While general LiDAR-inertial odometry (LIO) frameworks and loop-closure detection methods are effective in general scenarios, they often suffer from severe drift or incorrect loop constraints under these specific conditions. These challenges are further exacerbated by the inherent uncertainties associated with low-cost sensors. This paper introduces a narrow field-of-view LiDAR-centric RTK-visual-inertial SLAM system enhanced by three key modules: semantic-assisted loop detection and matching, two-stage RTK quality control, and adaptive factor graph optimization (FGO). In the first module, the proposed semantic loop descriptor (SLD) matching is used to determine the potential loop closure locations and then integrates the corresponding constraint as graph nodes. The quality control module addresses RTK outlier rejection during tunnel entry and exit, employing an event-driven stochastic model to characterize the uncertainty between RTK and the other sensors, effectively suppressing RTK-induced errors. FGO module performs optimization by incorporating LIO, RTK, and loop closure factors, employing a keyframe-based strategy to produce globally optimized poses while continuously updating the map. The proposed Tunnel-SLAM was evaluated against state-of-the-art SLAM algorithms in four extended roadway tunnels, ranging in traveling distance approximately from 5 to 10 km. Experimental results demonstrate that the proposed SLAM achieved a final drift of less than 2 m with loop closure, demonstrating significantly reducing the drift, while other existing SLAM frameworks fail catastrophically or have large drift.