Global navigation satellite system (GNSS) signals are affected by refraction when traveling through the troposphere, which result in tropospheric delay. Generally, the tropospheric delay is estimated as an unknown parameter in GNSS data processing. With the increasing demand for GNSS real-time applications, high-precision tropospheric delay augmentation information is vital to speed up the convergence of PPP. In this research, we estimate the zenith tropospheric delay (ZTD) from 2018 to 2019 by static precise point positioning (PPP) using the fixed position mode; GNSS observations were obtained from the National Geomatics Center of China (NGCC). Firstly, ZTD outliers were detected, and data gaps were interpolated using the K-nearest neighbor algorithm (KNN). Secondly, The ZTD differences between the KNN and periodic model were employed as input datasets to train the long short-term memory (LSTM) neural network. Finally, LSTM forecasted ZTD differences and the ZTD periodic signals were combined to recover the final forecasted ZTD results. In addition, the forecasted ZTD results were applied in static PPP as a prior constraint to reduce PPP convergence time. Numerical results show that the average root-mean-square error (RMSE) of predicting ZTD is about 1 cm. The convergence time of the PPP which was corrected by the LSTM-ZTD predictions is reduced by 13.9, 22.6, and 30.7% in the summer, autumn, and winter, respectively, over GPT2-ZTD corrected PPP and unconstrained conventional PPP for different seasons.

Accurate and high-spatiotemporal-resolution predictions of precipitable water vapor (PWV) play a crucial role in numerous atmospheric processes, including global navigation satellite system (GNSS) meteorological evaluation, weather forecasting, water cycle analysis, climate trend detection, and related fields. The calculation of PWV typically relies on meteorological parameters and conversion coefficients, leading to low accuracy and dependence on the availability of meteorological data. This research has formulated a high-accuracy, spatiotemporal-resolution PWV retrieval model that leverages non-meteorological parameters through the implementation of a multi-layer perceptron (MLP) neural network. The new retrieval model utilizes spatiotemporal information and the zenith tropospheric delay (ZTD) datasets from each GNSS station as training input parameters, with numerical weather model PWV serving as the training output parameters. The MLP neural network was trained using datasets from 229 stations of the Crustal Movement Observation Network of China (CMONOC) and numerical weather model PWV data collected from 2005 to 2015. The experimental results indicate that the root mean square (RMS) fitting accuracy between MLP PWV and ERA PWV is 1.36 mm. The MLP PWV model demonstrates an accuracy of approximately 1.6 mm on both temporal and spatial scales, with a spatiotemporal RMS accuracy indicator of 1.92 mm. The testing accuracy of the MLP PWV, approximately 2 mm when compared with the numerical meteorological parameters model PWV, underscores the reliability of this work. The MLP PWV retrieval model, relying on non-meteorological parameters, has demonstrated exceptional accuracy. By incorporating high spatiotemporal zenith tropospheric delay (ZTD), station spatial data, and temporal information, this model achieves superior spatiotemporal PWV accuracy, showcasing the effectiveness of the methodology presented in this study.

Global Navigation Satellite Systems (GNSS) have undergone more than half a century of development and construction, with more than a hundred navigation satellites currently providing precise and reliable positioning, navigation, and timing (PNT) services for various users. Meanwhile, efficient utilization of these satellites has become a topic of interest. Selecting an appropriate satellite set in a proper manner can reduce computational burden while ensuring positioning accuracy. Geometric Dilution of Precision (GDOP) is commonly used in satellite selection as it quantifies the impact of satellite geometry on positioning accuracy. Due to its computational simplicity, GDOP has been widely applied in satellite selection, but it only considers the satellite geometric configuration while ignoring the quality of satellite observations. As a result, the selected satellite set may lead to poor positioning accuracy. To address this issue, we use a satellite selection criterion based on the combination of near-real-time accuracy of satellite observations and geometric configuration. This criterion utilizes the combination of Geometry-Free Ionosphere-Free (GFIF) and Melbourne–Wübbena (MW) linear combinations of observations. Through a sliding window, we estimate the near-real-time accuracy of observations and use it to calculate the Weighted Geometric Dilution of Precision (WGDOP) for satellite selection. In a global International GNSS Service (IGS) station validation experiment, the satellite set selected based on WGDOP using near-real-time accuracy of GFIF and MW observations improved overall positioning accuracy by 11.6% and 12% when compared with the GDOP-based selection, and by 6% and 6.4% when compared with the Signal-to-Noise Ratio (SNR) weighting method. In a low-cost device validation experiment, the satellite selection method based on near-real-time accuracy of GFIF and MW improved positioning accuracy by 22.5% and 19.7% when compared with the GDOP-based method, and by 23.3% and 20.5% when compared with the SNR-based method. A set of dynamic observation experiments further demonstrates that the satellite selection method based on the near-real-time accuracy of GFIF and MW combinations outperforms the other two selection criteria in dynamic scenarios.