Jinglei Zhang

The performance of integrated navigation using global navigation satellite systems (GNSS) and inertial navigation systems (INS) in challenging urban environments is highly dependent on the quality of GNSS observations, particularly under multipath and non-line-of-sight conditions. Conventional weighting strategies based on predefined empirical relationships with satellite elevation angle or signal quality are limited in characterizing the nonlinear and time-varying characteristics of GNSS measurement errors. To address this issue, this study proposes a deep learning-based adaptive weighting method for tightly coupled GNSS/INS integration. Satellite elevation angle, signal-to-noise ratio (SNR), observation residuals, and normalized observation residuals are jointly utilized to characterize observation quality, and a neural network is employed to estimate satellite-specific measurement noise parameters for constructing the measurement noise covariance matrix. Since ground-truth measurement noise is difficult to obtain directly, the network is optimized using position, velocity, and attitude errors as the training objective. Vehicle-based experiments were conducted in representative environments, including open-sky areas, tree-lined roads, urban street canyons, and overpass sections. The proposed method achieves east, north, and up position root mean square errors (RMSEs) of 0.38, 0.75, and 1.14 m along route A, corresponding to reductions of 15.6%, 17.6%, and 17.4% compared with the combined elevation angle and SNR weighting strategy. Along route B, the corresponding RMSEs are 0.56, 0.71, and 1.18 m, representing reductions of 25.3%, 43.2%, and 34.1%, respectively. Consistent improvements are also achieved in velocity and attitude estimation. These results demonstrate that the proposed adaptive weighting strategy effectively improves the accuracy and stability of tightly coupled GNSS/INS integration under challenging observation conditions.

Accurate and continuous onboard real-time orbit determination (RTOD) is essential for Low Earth Orbit (LEO) satellites, but temporary interruptions of onboard Global Navigation Satellite Systems (GNSS) observations can degrade orbit continuity and delay filter re-convergence. Although predicted-orbit constraints can accelerate RTOD re-convergence after GNSS outages, their effectiveness largely depends on a realistic stochastic representation of the accumulated prediction uncertainty. Here, we develop a prior-state covariance model to characterize the time-dependent prediction uncertainty and provide uncertainty-consistent predicted-orbit constraints after observation recovery. Using onboard GNSS data from LuTan-1A as the primary dataset, orbit prediction residuals were analyzed through marginal-distribution analysis, envelope statistics, and a Mahalanobis-distance-based goodness-of-fit test. Results indicate that prediction errors are consistent with an approximate Gaussian model over the investigated prediction interval, supporting construction of a time-continuous prior-state covariance matrix. The proposed model was subsequently evaluated using a temporally independent LT-1A dataset. For GNSS interruptions of 15–90 min, the proposed model achieved average re-convergence times of 0.59–1.53 min, compared with 1.41–3.90 min for the state transition matrix (STM)-propagated covariance strategy and 9.18–19.12 min for the loose-prior strategy, while maintaining post-convergence 3D position RMS errors of 12.26–13.83 cm. Relative to STM propagation, average re-convergence time decreased from 1.41 to 0.59 min for the 15 min interruption and from 3.12 to 1.46 min for the 60 min interruption. Additional validation using GRACE-FO C, Sentinel-3A, and Sentinel-6A demonstrated applicability across different orbital and GNSS observation conditions. Overall, these results demonstrate that realistic characterization of prediction uncertainty can substantially improve RTOD re-convergence while preserving post-convergence orbit accuracy.

The quality of Global Navigation Satellite System (GNSS) observations on smartphones is highly susceptible to multipath and non-line-of-sight (NLOS) effects in urban environments, resulting in complex and highly variable observation errors. These challenges highlight the necessity of a reliable stochastic model to ensure robust and unbiased parameter estimation. However, conventional empirical stochastic models, such as elevation-dependent or signal-to-noise ratio (SNR)-based weighting schemes, are often insufficient to capture the rapidly changing stochastic behavior of observations in dense urban environments. To overcome this limitation, an adaptive GNSS stochastic model based on a deep neural network (DNN) is developed by integrating SNR, satellite elevation angle, and post-fit pseudorange residuals, which provide a strong indicator of observation quality and environmental context. Specifically, a fully connected DNN is designed to use SNR, satellite elevation angle, and post-fit pseudorange residual as input features, representing signal strength, satellite geometry, and residual information, respectively, and to learn their nonlinear relationship with measurement uncertainty. The network output is then used to adaptively update the diagonal elements of the measurement noise covariance matrix, thereby realizing epoch-wise adaptive weighting within the Kalman filtering process. The proposed DNN-based stochastic model, together with several conventional models, was evaluated using GNSS observations collected by a low-cost u-blox ZED-F9P receiver (u-blox AG, Thalwil, Switzerland) and a Samsung Galaxy S21+ smartphone (Samsung Electronics Co., Ltd., Suwon, Republic of Korea) during vehicle experiments in dense urban canyons. The code-based single point positioning (SPP) results demonstrate that the DNN-based model consistently outperforms traditional stochastic models under both open-sky and urban conditions. The improvement is particularly pronounced for smartphone observations in severely obstructed environments. The proposed DNN-based model reduces the 3D RMSE from 14.25 m, 13.68 m, and 13.05 m, obtained with the elevation-, SNR-, and integrated elevation–SNR-based models, respectively, to 8.94 m, representing an improvement of approximately 35%. A similar improvement is observed for the u-blox ZED-F9P receiver, where the 3D RMSE decreases from 5.71 m, 4.69 m, and 5.15 m to 3.10 m. These results suggest the effectiveness of the proposed DNN-based stochastic model in mitigating complex observation errors and improving positioning accuracy, providing a promising solution for reliable positioning of low-cost GNSS receivers in challenging urban environments.

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.

Currently, ground-based global navigation satellite system (GNSS) techniques have become widely recognized as a reliable and effective tool for atmospheric monitoring, enabling the retrieval of zenith total delay (ZTD) and precipitable water vapor (PWV) for meteorological and climate research. The International GNSS Service analysis centers (ACs) have initiated their third reprocessing campaign, known as IGS Repro3. In this campaign, six ACs conducted a homogeneous reprocessing of the ZTD time series spanning the period from 1994 to 2022. This paper primarily focuses on ZTD products. First, the data processing strategies and station conditions of six ACs were compared and analyzed. Then, formal errors within the data were examined, followed by the implementation of quality control processes. Second, a combination method is proposed and applied to generate the final ZTD products. The resulting combined series was compared with the time series submitted by the six ACs, revealing a mean bias of 0.03 mm and a mean root mean square value of 3.02 mm. Finally, the time series submitted by the six ACs and the combined series were compared with VLBI data, radiosonde data, and ERA5 data. In comparison, the combined solution performs better than most individual analysis centers, demonstrating higher quality. Therefore, the advanced method proposed in this study and the generated high-quality dataset have considerable implications for further advancing GNSS atmospheric sensing and offer valuable insights for climate modeling and prediction.

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.

The accurate determination of Atmospheric Boundary Layer Height (ABLH) is crucial in various atmospheric studies and practical applications. In this study, we present a comprehensive comparative analysis of five distinct methods for estimating ABLH using Global Navigation Satellite System (GNSS) Radio Occultation (RO) data. These methods encompass the use of bending angle and refractivity profiles, namely Minimum Gradient methods of the Bending Angle (MGBA) and Refractivity (MGR) profiles, breaking point, Wavelet Covariance Transform (WCT), and Double-Parameter Model Function (DPMF). GNSS-RO data from COSMIC-2 and Spire are used. To establish robust validation, radiosonde data are employed as a reference, ensuring the reliability of our findings. The results reveal notable variations in the performances of these ABLH estimation methods. Specifically, the MGBA, MGR, breaking point, and DPMF methods exhibit strong correlations with the reference data. Conversely, the WCT method displays weaker correlations, higher biases, and elevated root-mean-square-errors, suggesting limitations in capturing the true ABLH. Furthermore, we remove outlier screening to facilitate a comparison of the differences among the five methods. The WCT and DPMF methods can detect strong variations in the profiles near the Earth’s surface and consider them as ABLH. However, these variations are caused by errors. The MGBA method emerges as a reliable and stable option, while the WCT and DPMF methods should be used with caution due to the lower quality of the GNSS-RO profiles near the Earth’s surface.

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.