Search Results (126)

To accurately estimate Zenith Tropospheric Delay (ZTD) for high-precision positioning of the Global Navigation Satellite System (GNSS), this study proposes a modeling method of ZTD based on the UNB3m model and Kriging spatial interpolation, in which the optimal spatial interpolation parameters are determined based on the errors corresponding to different combinations of the interpolation parameters, and the spatial distribution of the GNSS modeling stations is determined by the interpolation errors of the randomly selected GNSS stations for several times. To verify the accuracy and reliability of the proposed model, the ZTD estimates of 132,685 epochs with 1 h or 2 h temporal resolution for 28 years from 1997 to 2025 of the global network of continuously operating GNSS tracking stations are used as inputs; the ZTD results at any position and the corresponding observation moment can be obtained with the proposed model. The experimental results show that the model error is less than 30 mm in more than 85% of the observation epochs, the ZTD estimation results are less affected by the horizontal position and height of the GNSS stations than traditional models, and the ZTD interpolation error is improved by 10–40 mm compared to the GPT3 and UNB3m models at the four GNSS checking stations. Therefore, this technology can provide ZTD estimation results for single- and dual-frequency hybrid deformation monitoring, as well as dense ZTD data for Precipitable Water Vapor (PWV) inversion. Since the proposed method has the advantages of simple implementation, high accuracy, high reliability, and ease of promotion, it is expected to be fully applied in other high-precision positioning applications. Full article

BeiDou navigation satellite system (BDS) precise point positioning (PPP)-B2b has significant potential for application in meteorological fields, such as standalone water vapor monitoring in depopulated area without Internet. In this study, the practical ability of water vapor monitoring using the BDS PPP-B2b service is illustrated through a continuously operated water vapor monitoring system in Wuhan, China, with a 25-day experiment in 2025. Original observations from the Global Positioning System (GPS) and BDS are collected and processed in the near real-time (NRT) mode using ephemeris from the PPP-B2b service. Precipitable water vapor PWV monitored with B2b ephemeris are evaluated with radiosonde and ERA5 reanalysis, respectively. Taking PWV from radiosonde observations as the reference, RMS of PWV based on B2b ephemeris varies from 3.71 to 4.66 mm for different satellite combinations. While those values are with a range from 3.95 to 4.55 mm when compared with ERA5 reanalysis. These values are similar to those processed with the real-time ephemeris from the China Academy of Science (CAS). In general, this study demonstrates that the practical accuracy of water vapor monitored based on the BDS PPP-B2b service can meet the basic demand for operational meteorology for the first time. This will provide a scientific reference for its wide promotion to meteorological applications in the near future. Full article

Water vapor plays a crucial role in maintaining global energy balance and water cycle, and it is closely linked to various meteorological disasters. Precipitable water vapor (PWV), as an indicator of variations in atmospheric water vapor content, has become a key parameter for meteorological and climate monitoring. However, due to limitations in observation costs and technology, traditional atmospheric monitoring techniques often struggle to accurately capture the distribution and variations in space–time water vapor. With the continuous advancement of Global Navigation Satellite System (GNSS) technology, ground-based GNSS monitoring technology has shown rapid development momentum in the field of meteorology and is considered an emerging monitoring tool with great potential. Hence, based on the GNSS observation data from July 2023, this study retrieves PWV using the Global Pressure and Temperature 3 (GPT3) model and evaluates its application performance in the “7·31” extremely torrential rain event in Beijing in 2023. Research has found the following: (1) Tropospheric parameters, including the PWV, zenith tropospheric delay (ZTD), and zenith wet delay (ZWD), exhibit high consistency and are significantly affected by weather conditions, particularly exhibiting an increasing-then-decreasing trend during rainfall events. (2) Through comparisons with the PWV values through the integration based on fifth-generation European Centre for Medium-Range Weather Forecasts (ERA-5) reanalysis data, it was found that results obtained using the GPT3 model exhibit high accuracy, with GNSS PWV achieving a standard deviation (STD) of 0.795 mm and a root mean square error (RMSE) of 3.886 mm. (3) During the rainfall period, GNSS PWV remains at a high level (>50 mm), and a strong correlation exists between GNSS PWV and peak hourly precipitation. Furthermore, PWV demonstrates the highest relative contribution in predicting extreme precipitation, highlighting its potential value for monitoring and predicting rainfall events. Full article

The performance of Precise Point Positioning (PPP) using different Global Navigation Satellite System (GNSS) product sets, including broadcast ephemerides, International GNSS Service Real-Time Service (IGS-RTS) corrections, Galileo High Accuracy Service (HAS) corrections, and precise products from the Center for Orbit Determination in Europe (CODE) Multi-GNSS Experiment (MGEX), has been evaluated. The availability of solutions, convergence time, position accuracy and Zenith Tropospheric Delay (ZTD) estimation across these products were analyzed using simulated real-time and postprocessing static modes, using data from globally distributed stations with a 1 s observation interval. The results indicate that precise products from the MGEX provide the highest accuracy, achieving centimeter-level precision in post-processed mode. Real-time simulated solutions, such as HAS and IGS-RTS, deliver promising results, with Galileo HAS meeting its target accuracy of 20 cm horizontally and 40 cm vertically and a convergence time under 5 min. However, Global Positioning System (GPS) performance within HAS is limited by a significantly lower correction availability—around 67% on average compared to over 95% for Galileo—which negatively impacts PPP performance. ZTD estimation results show that real-time services (HAS, IGS-RTS) achieved errors within 1–3 cm, sufficient for meteorological applications. This study highlights the growing importance of HAS in real-time positioning applications and suggests further improvements in GPS for enhanced performance. Full article

Tropospheric delay is the main error source that affects the further improvement of the accuracy of space geodesy. High-precision zenith tropospheric delay (ZTD) can be used as a prior value for precise point positioning (PPP) in global navigation satellite systems (GNSSs) to enhance the speed and accuracy of real-time PPP solutions. Using the Saastamoinen ZTD model, we computed ZTDs using different meteorological elements. One ZTD was termed MZTD and was obtained from 80 reference sites in the China Mainland Crustal Movement Observation Network (CMONOC), the other was termed HZTD and was obtained from elements acquired from the improved version of the hourly global pressure and temperature atmospheric model (HGPT2). The results indicate that the accuracy of the MZTD was 12.94% higher than that of the HZTD, with the ZTDs estimated by post-processing GNSS values as the reference values. Additionally, the MZTD and HZTD were both applied as constraints to the PPP solution. The application of the MZTD constraints to the PPP floating-point solution resulted in a 28.9% improvement in accuracy and a 36.4% decrease in convergence time in the U-direction as a maximum, compared with the application of the HZTD constraints. Full article

Zenith Tropospheric Delay (ZTD) is a significant source of atmospheric error in the Global Navigation Satellite System (GNSS). Developing a high-accuracy ZTD prediction model is essential for both GNSS positioning and GNSS meteorology. To address the challenges of incomplete information extraction and gradient explosion present in current single and combined neural network models that utilize serial ensemble learning, this study proposes a VMD-Informer-BiLSTM-EAA hybrid model based on a parallel ensemble learning strategy. Additionally, it takes into account the non-stationarity of the ZTD sequence. The model employs the Variational Mode Decomposition (VMD) method to address the non-stationarity of ZTD. It utilizes both the informer and Bidirectional Long Short-Term Memory (BiLSTM) architectures to learn ZTD data in parallel, effectively capturing both long-term trends and short-term dynamic changes. The features are then fused using the Efficient Additive Attention (EAA) mechanism, which assigns weights to create a more comprehensive representation of the ZTD data. This enhanced representation ultimately leads to improved predictions of ZTD values. We fill in the missing parts of the GNSS-derived ZTD using the ZTD data from ERA5, sourced from the IGS stations in the Australian region, specifically at 12 IGS stations. These interpolated data are then used to develop a VMD-Informer-BiLSTM-EAA hybrid model for ZTD predictions with a one-year forecast horizon. We applied this model to predict the ZTD for each IGS station in our study area for the year 2021. The numerical results indicate that our model outperforms several comparative models, such as VMD–Informer, Transformer, BiLSTM and GPT3, based on the following key metrics: a Root Mean Square Error (RMSE) of 1.43 cm, a Mean Absolute Error (MAE) of 1.15 cm, a Standard Deviation (STD) of 1.33 cm and a correlation coefficient (R) of 0.96. Furthermore, our model reduces the training time by 8.2% compared to the Transformer model, demonstrating superior prediction performance and robustness in long-term ZTD forecasting. This study introduces a novel approach for high-accuracy ZTD modeling, which is significantly beneficial for precise GNSS positioning and the detection of water vapor content. Full article

Zenith tropospheric delay (ZTD) is a significant atmospheric error that impacts the Global Navigation Satellite System (GNSS). Developing a high-precision, long-term forecasting model for ZTD can provide valuable insights into the overall trends of predicted ZTD, which is essential for improving GNSS positioning and analyzing changes in regional climate and water vapor. To address the challenges of incomplete information extraction and gradient explosion in a single neural network when forecasting ZTD long-term, this study introduces an Informer–LSTM Hybrid Prediction Model. This model employs a parallel ensemble learning strategy that combines the strengths of both the Informer and LSTM networks to extract features from ZTD data. The Informer model is effective at capturing the periodicity and long-term trends within the ZTD data, while the LSTM model excels at understanding short-term dependencies and dynamic changes. By merging the features extracted by both models, the prediction capabilities of each can complement one another, allowing for a more comprehensive analysis of the characteristics present in ZTD data. In our research, we utilized ERA5-derived ZTD data from 11 International GNSS Service (IGS) stations in Europe to interpolate the missing portions of GNSS-derived ZTD. We then employed this interpolated data from 2016 to 2020, along with an Informer–LSTM Hybrid Prediction Model, to develop a long-term prediction model for ZTD with a prediction duration of one year. Our numerical results demonstrate that the proposed model outperforms several comparative models, including the LSTM–Informer based on a serial ensemble learning model, as well as the Informer, Transformer, LSTM, and GPT3 empirical ZTD models. The performance metrics indicate a root mean square error (RMSE) of 1.91 cm, a mean absolute error (MAE) of 1.45 cm, a mean absolute percentage error (MAPE) of 0.60, and a correlation coefficient (R) of 0.916. Spatial distribution analysis of the accuracy metrics showed that predictive accuracy was higher in high-latitude regions compared to low-latitude areas, with inland regions demonstrating better performance than those near the ocean. This study introduced a novel methodology for high-precision ZTD modeling, which is significant for improving accurate GNSS positioning and detecting water vapor content. Full article

Utilizing real-time precise point positioning (PPP) technology is an effective approach for obtaining high-precision zenith tropospheric delay (ZTD). Without relying on the terrestrial internet, Galileo high accuracy service (HAS) can provide precise orbit and precise clock products for the world. A thorough assessment of the ZTD accuracy of real-time PPP calculations based on Galileo HAS products in global regions is necessary to promote its application in the field of global navigation satellite system (GNSS) meteorology. The observation data of HAS from 1 to 7 September 2023 were selected for the experiment. Firstly, the accuracy of satellite orbit and clock products of the HAS GPS and HAS Galileo system are evaluated. Then, real-time PPP positioning accuracy within and outside the HAS service area is analyzed. Finally, 104 IGS stations in the world are selected to analyze the ZTD accuracy of real-time PPP calculations based on Galileo HAS products. The experimental results show that during the test period, the RMSE values of the satellite orbit products of the HAS GPS in the radial, along, and cross directions were 4.57 cm, 10.62 cm, and 7.56 cm, respectively. The HAS Galileo RMSE values were 2.81 cm, 8.02 cm, and 7.47 cm, respectively. The RMSE values of the clock products were 0.38 ns and 0.15 ns, respectively. At the selected stations, the real-time PPP positioning accuracies outside the HAS service area and within the service area were similar, and the correlation coefficient between HAS ZTD and IGS ZTD was above 0.90. In the global region, the average bias and RMSE values of the real-time PPP ZTD of the HAS GPS were −0.31 mm and 16.78 mm. Those of the HAS Galileo were 2.30 mm and 15.89 mm, and those of the HAS GPS/Galileo were −0.25 mm and 16.11 mm, respectively. Moreover, each system showed that the accuracy of the HAS ZTD inside the service area was better than that outside the service area. Compared with the single system, the real-time PPP ZTD continuity and stability of the dual system were better. Full article

Empirical tropospheric models can improve the performance of GNSS precise point positioning (PPP) by providing a priori zenith tropospheric delay (ZTD) information. However, existing models experience insufficient ZTD profile refinement, inadequate correction for systematic bias between the ZTD used in empirical modelling and the GNSS ZTD, and low time efficiency in model updating as more data become available. Therefore, a refined spatiotemporal empirical ZTD model was developed in this study on the basis of the fifth generation of European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) data and GNSS data. First, an ENM-R profile model was established by refining the modelling height of the negative exponential function model (ENM). Second, a regression kriging interpolation method was designed to model the systematic bias correction between the ERA5 ZTD and the GNSS ZTD. Last, the final refined ZTD model, ENM-RS, was established by introducing systematic bias correction into ENM-R. Experiments suggest that, compared with the ENM-R and GPT3 models, ENM-RS can effectively suppress systematic bias and improve ZTD modelling accuracy by 10~17%. To improve model update efficiency, the idea of updating an empirical model with sequential least square (SLSQ) adjustment is proposed for the first time. When ENM-RS is modelled via 12 years of ERA data, our method can reduce the time consumption to one-fifth of that of the traditional method. The benefits of our ENM-RS model are evaluated with PPP. The results show that relative to PPP solutions with ENM-R- and GPT3-derived ZTD constraints as well as no constraint, the ENM-RS ZTD constraint can decrease PPP convergence time by approximately 10~30%. Full article

This study addresses the challenges associated with single-system long-baseline real-time kinematic (RTK) navigation, including limited positioning accuracy, inconsistent signal reception, and significant residual atmospheric errors following double-difference corrections. This study explores the effectiveness of long-baseline RTK navigation using an integrated system of the BeiDou Navigation Satellite System (BDS), Global Positioning System (GPS), and Galileo Satellite Navigation System (Galileo). A long-baseline RTK approach that incorporates Kalman filtering and partial ambiguity resolution is applied. Initially, error models are used to correct ionospheric and tropospheric delays. The zenith tropospheric and inclined ionospheric delays and additional atmospheric error components are then regarded as unknown parameters. These parameters are estimated together with the position and ambiguity parameters via Kalman filtering. A two-step method based on a success rate threshold is employed to resolve partial ambiguity. Data from five long-baseline IGS monitoring stations and real-time measurements from a ship were employed for the dual-frequency RTK positioning experiments. The findings indicate that integrating additional GNSSs beyond the BDS considerably enhances both the navigation precision and the rate of ambiguity resolution. At the IGS stations, the integration of the BDS, GPS, and Galileo achieved navigation precisions of 2.0 cm in the North, 5.1 cm in the East, and 5.3 cm in the Up direction while maintaining a fixed resolution exceeding 94.34%. With a fixed resolution of Up to 99.93%, the integration of BDS and GPS provides horizontal and vertical precision within centimeters in maritime contexts. Therefore, the proposed approach achieves precise positioning capabilities for the rover while significantly increasing the rate of successful ambiguity resolution in long-range scenarios, thereby enhancing its practical use and exhibiting substantial application potential. Full article

Zenith Tropospheric Delay (ZTD) is a significant error source affecting the accuracy of certain space geodetic measurements. This study evaluates the performance of Artificial Intelligence (AI) based meteorological models, such as Fengwu and Pangu, in estimating real-time ZTD. The results from these AI models were compared with those obtained from the Global Navigation Satellite System (GNSS), the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Reanalysis (ERA5), and the third generation of the Global Pressure–Temperature data model (GPT3) to assess their accuracy across different time intervals, seasons, and geographic locations. The findings reveal that AI-driven models, particularly Fengwu, offer higher long-term forecasting accuracy. An analysis of data from 81 stations throughout 2023 indicates that Fengwu’s 7-day ZTD forecast achieved an RMSE of 2.85 cm when compared to GNSS-derived ZTD. However, in oceanic regions and areas with complex climatic dynamics, the Fengwu model exhibited a larger error compared to in other land regions. Additionally, seasonal variations and station altitude were found to influence the accuracy of ZTD predictions, emphasizing the need for detailed modeling in complex climatic zones. Full article

This paper investigates the applicability of the Numerical Weather Prediction (NWP) data for characterizing the gradient of zenith wet delay in horizontal direction observed on short baselines over larger territories. A three-year period of data for an area covering Scandinavia and Finland is analyzed, and maximum gradients during the considered period are identified. To assess the quality of the NWP-based estimates, results for a smaller region are compared with the estimates obtained using Global Navigation Satellite System (GNSS) measurements processed by the GipsyX/RTGx software package (version 2.1) from a cluster of GNSS reference stations. Additionally, the NWP data from 7 to 9 August 2023 covering a period that includes a storm with high rain intensities over Southern Norway leading to sustained flooding are processed and analyzed to assess if the gradient of zenith wet delay in the horizontal direction increases significantly during such events. The results show that maximum gradients in the range of 40–50 mm/km are detected. When comparing NWP-based estimates to GNSS-based estimates, the tropospheric delays show a very strong correlation. The tropospheric gradients, however, show a weak correlation, probably due to the uncertainty in the NWP data exceeding the gradient values. The data captured during the storm show that while the tropospheric delay increases significantly it is difficult to see increases in the gradient of zenith wet delay in the horizontal direction using this data source and resolution. Full article

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. Full article

GNSS precise point positioning (PPP) plays an important role in retrieving atmospheric water vapor values and performing numerical weather prediction. However, traditional PPP relies on real-time orbits and clocks, which require continuous internet or satellite communication. Improved broadcast ephemerides of GNSSs offer new opportunities for PPP with broadcast ephemerides (BE-PPP) instead of using precise ephemeride products. Therefore, we investigated the feasibility of utilizing BE-PPP for retrieving zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) data. We processed the GPS/Galileo observations from 80 IGS stations during a 30-day experiment to retrieve ZTD values using both real-time PPP (RT-PPP) and BE-PPP solutions. Then, we processed observations from 20 EUREF Permanent GNSS Network (EPN) stations to retrieve PWV data. The IGS final tropospheric products were used to validate the ZTD, and radiosonde (RDS) and ERA5 data were used to validate the PWV. The results show that the real-time ZTD from BE-PPP agrees well with that from RT-PPP: the standard deviation (STD) of the ZTD is 1.07 cm when using BE-PPP and 0.6 cm when using RT-PPP. Furthermore, the STD of the PWV is 1.69 mm when using BE-PPP, and 0.96 mm when using RT-PPP, compared to the ERA5-PWV. Compared to the RDS-PWV, the STD is 3.09 mm when using BE-PPP and 1.39 mm when using RT-PPP. In conclusion, the real-time ZTD/PWV products obtained using the BE-PPP solution are consistent with those of RT-PPP and meet the requirements of NWP, so this method can be used as an effective complement to RT-PPP to expand its application potential. Full article

Accurate tropospheric delays are of great importance for both Global Navigation Satellite System (GNSS)-based positioning and precipitable water vapor monitoring. The gridded tropospheric delay products, including zenith hydrostatic delays (ZHD) and zenith wet delays (ZWD), are the most ideal method for accessing accurate tropospheric delays. The vertical adjustment method is critical for implementing the gridded tropospheric products. In this work, we consider the different models used for grid products and assess their performance over Yunnan mountains with complex topography. We summarize the main results as follows: (1) The products can provide accurate ZHD with mean biases of −2.6 mm and mean Standard Deviation (STD) of 1.5 mm while the ZWD results from grid products show a performance with biases of −0.4 mm and STD of 1.3 cm over the Yunnan area. (2) The $T_v$-based model shows a better performance than the $T_0$-based model and IGPZWD in rugged areas with large height differences. The grid products can provide hourly ZHD with biases of 3 mm and wet delay with mean biases of within 2 cm and mean STD of below 3 cm in the Yunnan mountains, which exhibit a large height difference of around 1.5 km. (3) The radiosondes results confirm that the $T_v$-based model has an obvious advantage in calculating ZHD height corrections for differences within 2 km while the $T_0$-model suffers from a loss in accuracy in the case of large height differences. If the site is located more than 1 km below the reference height, the IGPZWD model can provide a better ZWD with a mean bias of 1.5 cm and a mean STD of 1.7 cm. With vertical reduction models, the grid products can provide accurate ZHD and ZWD in real time, even if in complex area. Full article