Tropospheric delay is one of the main errors affecting high-precision positioning and navigation and is a key parameter of water vapor detection in the Global Navigation Satellite System (GNSS). The second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) is the latest generation of reanalysis data collected by the National Aeronautics and Space Administration (NASA), which can be used to calculate tropospheric delay products with high spatial and temporal resolution. However, there is no report analyzing the accuracy of the zenith tropospheric delay (ZTD) and zenith wet delay (ZWD) calculated from MERRA-2 data. This paper evaluates the performance of the ZTD and ZWD values derived from global MERRA-2 data using global radiosonde data and International GNSS Service (IGS) precise ZTD products. The results are as follows: (1) Taking the precision ZTD products of 316 IGS stations from around the world from 2015 to 2017 as the reference, the average root mean square (RMS) of the ZTD values calculated from the MERRA-2 data is better than 1.35 cm, and the accuracy difference between different years is small. The bias and RMS of the ZTD values show certain seasonal variations, with a higher accuracy in winter and a lower accuracy in summer, and the RMS decreases from the equator to the poles. However, those of the ZTD values do not show obvious variations according to elevation. (2) Relative to the radiosonde data, the RMS of the ZWD and ZTD values calculated from the MERRA-2 data are better than 1.37 cm and 1.45 cm, respectively. Furthermore, the bias and RMS of the ZWD and ZTD values also show some temporal and spatial characteristics, which are similar to the test results of the IGS stations. It is suggested that MERRA-2 data can be used for global tropospheric vertical profile model construction because of their high accuracy and good stability in the global calculation of the ZWD and ZTD.

Accurate and robust positioning is a critical enabler for Unmanned Aerial Vehicle (UAV) applications, ranging from mapping and inspection to emerging Urban Air Mobility (UAM). While Global Navigation Satellite Systems (GNSS) remain the backbone of absolute positioning, their performance is severely constrained by UAV platform characteristics and complex low-altitude environments. This paper presents a system-level review of GNSS-based UAV positioning. Instead of treating GNSS in isolation, we first link mission requirements and platform constraints, such as aggressive dynamics and Size, Weight, and Power (SWaP) limitations, to specific positioning challenges. We then critically evaluate the spectrum of GNSS techniques, from standalone and Satellite-Based Augmentation System (SBAS) modes to high-precision carrier-phase methods including Real-Time Kinematic (RTK), Post-Processed Kinematic (PPK), Precise Point Positioning (PPP), and PPP-RTK. Furthermore, we discuss multi-sensor fusion with inertial, visual, and Light Detection and Ranging (LiDAR) sensors to mitigate vulnerabilities in urban canyons and GNSS-denied conditions. Finally, we outline key challenges and future directions, highlighting integrity-aware architectures, Artificial Intelligence (AI)-enhanced signal processing, and multi-layer Positioning, Navigation, and Timing (PNT) concepts. The review provides a structured framework and system-level insights to guide resilient navigation for UAV operations in low-altitude airspace.

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

Tropospheric delay products play a critical role in achieving high-precision positioning in Precise Point Positioning Real-Time Kinematic (PPP-RTK) applications. The short-term prediction of these products remains a significant challenge that warrants further exploration. This study proposes a novel short-term prediction method for tropospheric delay products in PPP-RTK applications, leveraging a multi-scale sliding window and Long Short-Term Memory (LSTM) network. The multi-scale sliding window approach effectively captures data features across different temporal scales, while LSTM, a well-established and robust time series forecasting technique, ensures the accurate modeling of temporal dependencies. The integration of these two methods significantly enhances the precision of short-term tropospheric delay predictions. Experimental analysis utilizing one week of data from the Hong Kong Continuously Operating Reference Stations (CORS) network demonstrates that the proposed method achieves a maximum prediction error of less than 1.5 cm. Furthermore, compared to the standard LSTM approach, the Root Mean Square Error (RMSE) values are improved by 18.9% and 36.6% for different reference values, respectively. PPP-RTK positioning experiments reveal that the predicted products generated by this method exhibit notable improvements in Root Mean Square (RMS) values for the east, north, and up directions, with enhancements of 10.7%, 19.1%, and 4.1%, respectively, over those obtained using the conventional LSTM method. These results comprehensively validate the effectiveness and superiority of the proposed approach.

Vertical deformations caused by non-tidal mass variations still remain in global navigation satellite system (GNSS) height time series, and can be computed from both Gravity Recovery and Climate Experiment (GRACE) and geophysical models. In this study, we provide a thorough evaluation of the relationships between these different techniques in the global scale by comparing non-tidal vertical deformations from IGS second reprocessing campaign (IG2), GRACE and Global Geophysical Fluid Center (GGFC) solutions, and investigate the noise properties of the GNSS corrected by GRACE solutions and GNSS corrected by GGFC solutions for global stations using optimal noise models. Our results demonstrate that the consistency between seasonal vertical deformations derived from GNSS, GRACE and GGFC is high. When correcting GNSS deformations with GRACE and GGFC solutions, 81% and 73% of the 186 stations have the weight root mean square ($WRMS$) reduction, respectively. The $WRMS$ variations averaged over all stations are −12.3% and −5.6%, respectively for GNSS corrected by GRACE and GNSS corrected by GGFC solutions. The obvious difference occurs in the GNSS corrected by GGFC solutions $WRMS$ increase, with the mean increase value up to 29%, mainly happening to stations located on islands or small peninsulas. In addition, noise properties of the GNSS corrected by GRACE solutions and GNSS corrected by GGFC solutions for global stations are investigated using optimal noise models. After correcting non-tidal loading effects, the solutions of GNSS corrected by GRACE solutions have the lowest noise level, and can occupy 5% of the noise behavior presenting in global stations, while the solutions of GNSS corrected by GGFC solutions can bring more than 5% of the noise into global stations, implying that GRACE correction solutions can present more favorable results when interpreting GNSS non-tidal loading deformations.