Search Results (99)

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

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

The detection of potential rural mountain landslide displacements using time-series interferometric Synthetic Aperture Radar has been challenged by both atmospheric phase screens and decoherence noise. In this study, we propose the use of a combined distributed scatterer (DS) and the Prophet_ZTD-NEF model to rapidly map the landslide surface displacements in Diqing Tibetan Autonomous Prefecture, China. We conducted tests on 28 full-resolution SENTINEL-1A images to validate the effectiveness of our methods. The conclusions are as follows: (1) Under the same sample conditions, confidence interval estimation demonstrated higher performance in identifying SHPs compared to generalized likelihood ratio test. The density of DS points was approximately eight times and five times higher than persistent scatterer interferometry and small baseline subset methods, respectively. (2) The proposed Prophet_ZTD-NEF model considers the spatial and temporal variability properties of tropospheric delays, and the root mean square error of measured values was approximately 1.19 cm instead of 1.58 cm (PZTD-NEF). (3) The proposed Prophet_ZTD-NEF method reduced the mean standard deviation of the corrected interferograms from 1.88 to 1.62 cm and improved the accuracy of the deformation velocity solution by approximately 8.27% compared to Global Position System (GPS) measurements. Finally, we summarized the driving factors contributing to landslide instability. Full article

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. 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

Prior tropospheric information, especially zenith tropospheric delay (ZTD), is particularly important in GNSS data processing. The two types of ZTD models, those that require and do not require meteorological parameters, are the most commonly used models, whether the non-difference or double-difference mode is applied. To improve the accuracy of prior tropospheric information, the Vienna Mapping Functions (VMFs) data server provides a gridded set of global tropospheric products based on the ray-tracing technique using Numerical Weather Models (NWMs). Note that two types of gridded tropospheric products are provided: the VMF3_OP for the post-processing applications and the VMF3_FC for real-time applications. To explore the accuracy and adaptability of these two grid products, a comprehensive analysis and discussion were conducted in this study using the ZTD data from 255 stations of the Crustal Movement Observation Network of China (CMONOC) as references. The numerical results indicate that both VMF3_FC and VMF3_OP exhibit high accuracy, with RMSE/Bias values of 17.53/2.25 mm and 14.62/2.67 mm, respectively. Both products displayed a temporal trend, with larger RMSE values occurring in summer and smaller values in winter, along with a spatial trend of higher values in the southeast of China and lower values in the northwest of China. Additionally, VMF3_OP demonstrated superior performance to VMF3_FC, with smaller RMSE values for each month and each hour. For the RMSE difference between these two products, 108 stations had a difference of more than 3 mm, and the number of stations with a difference exceeding 1 mm reached 217. Moreover, the difference was more significant in the southeast than in the northwest. This study contributes to the understanding of the differences between the two precision products, aiding in the selection of suitable ZTD products based on specific requirements. Full article

Global Navigation Satellite System (GNSS) signals experience delays when passing through the atmosphere due to the presence of free electrons in the ionosphere and air density in the non-ionized part of the atmosphere, known as the troposphere. The Precise Point Positioning (PPP) technique demonstrates highly accurate positioning along with Zenith Tropospheric Delay (ZTD) estimation. ZTD estimation is valuable for various applications including climate modelling and determining atmospheric water vapor. Current GNSS network resolutions are not completely sufficient for the scale of a few kilometres that regional climate and weather models are increasingly adopting. The Centipede-RTK network is a low-cost option for increasing the spatial resolution of tropospheric monitoring. This study is motivated by the question of whether low-cost GNSS networks can provide a viable alternative without compromising data quality or precision. This study compares the performance of the low-cost Centipede-RTK network in calculating the Zenith Tropospheric Delay (ZTD) to that of the existing EUREF Permanent Network (EPN), using two alternative software packages, RTKLIB demo5 version and CSRS-PPP version 3, to ensure robustness and software independence in the findings. This investigation indicated that the ZTD estimations from both networks are almost identical when processed by the CSRS-PPP software, with the highest mean difference being less than 3.5 cm, confirming that networks such as Centipede-RTK could be a reliable option for dense precise atmospheric monitoring. Furthermore, this study revealed that the Centipede-RTK network, when processed using CSRS-PPP, provides ZTD estimations that are very similar and consistent with the EUREF ZTD product values. These findings suggest that low-cost GNSS networks like Centipede-RTK are viable for enhancing network density, thus improving the spatial resolution of tropospheric monitoring and potentially enriching climate modelling and weather prediction capabilities, paving the way for broader application and research in GNSS meteorology. Full article

Improving the accuracy of zenith tropospheric delay (ZTD) models is an important task. However, the existing ZTD models still have limitations, such as a lack of appropriate vertical adjustment function and being unsuitable for China, which has a complex climate and great undulating terrain. A new approach that considers the time-varying vertical adjustment and delicate diurnal variations of ZTD was introduced to develop a new grid ZTD model (NGZTD). The NGZTD model employed the Gaussian function and considered the seasonal variations of Gaussian coefficients to express the vertical variations of ZTD. The effectiveness of vertical interpolation for the vertical adjustment model (NGZTD-H) was validated. The root mean squared errors (RMSE) of the NGZTD-H model improved by 58% and 22% compared to the global pressure and temperature 3 (GPT3) model using ERA5 and radiosonde data, respectively. The NGZTD model’s effectiveness for directly estimating the ZTD was validated. The NGZTD model improved by 22% and 31% compared to the GPT3 model using GNSS-derived ZTD and layered ZTD at radiosonde stations, respectively. Seasonal variations in Gaussian coefficients need to be considered. Using constant Gaussian coefficients will generate large errors. The NGZTD model exhibited outstanding advantages in capturing diurnal variations and adapting to undulating terrain. We analyzed and discussed the main error sources of the NGZTD model using validation of spatial interpolation accuracy. This new ZTD model has potential applications in enhancing the reliability of navigation, positioning, and interferometric synthetic aperture radar (InSAR) measurements and is recommended to promote the development of space geodesy techniques. Full article

Atmospheric delay correction remains a major challenge for interferometric synthetic aperture radar (InSAR) technology. In this paper, we first reviewed several commonly used methods for tropospheric delay correction in InSAR. Subsequently, considering the large volume and high temporal resolution of global navigation satellite system (GNSS) station measurement data, we proposed a method for spatial prediction of the InSAR tropospheric delay phase based on the backpropagation (BP) neural network and GNSS zenith total delay (ZTD). Using 42 Sentinel-1 interferograms over the Los Angeles area in 2021 as an example, we validated the accuracy of the BP + GNSS method in spatially predicting ZTD and compared the correction effects of BP + GNSS and five other methods on interferograms using the standard deviation (StaD) and structural similarity (SSIM). The results demonstrated that the BP + GNSS method reduced the root-mean-square error (RMSE) in spatial prediction by approximately 95.50% compared to the conventional interpolation method. After correction using the BP + GNSS method, StaD decreased in 92.86% of interferograms, with an average decrease of 52.03%, indicating significantly better correction effects than other methods. The SSIM of the BP + GNSS method was lower in mountainous and high-altitude areas with obvious terrain changes in the east and north, exhibiting excellent and stable correction performance in different seasons, particularly outperforming the GACOS method in autumn and winter. The BP + GNSS method can be employed to generate InSAR tropospheric delay maps with high temporal and spatial resolution, effectively addressing the challenge of removing InSAR tropospheric delay signals in areas with significant terrain variations. Full article

An accurate model of the Zenith Tropospheric Delay (ZTD) plays a crucial role in Global Navigation Satellite System (GNSS) precise positioning, water vapor retrieval, and meteorological research. Current empirical models (such as the GPT3 model) can only reflect the approximate change trend of ZTD but cannot accurately reflect nonlinear changes such as rapid fluctuations in ZTD. In recent years, the application of machine learning methods in the modeling and prediction of ZTD has gained prominence, yielding commendable results. Utilizing the ZTD products from 53 International GNSS Service (IGS) stations in Europe during the year 2021 as a foundational dataset, a Generalized Regression Neural Network (GRNN) is employed to model IGS ZTD while considering spatiotemporal factors and its association with GPT3 ZTD. This endeavor culminates in the development of a refined GRNN model. To verify the performance of the model, the prediction results are compared with two other ZTD values. One is obtained based on the European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data, and the other is obtained by the GPT3 model. The results show that the bias of the GRNN refined model is almost 0 mm, and the average Root-Mean-Square Error (RMSE) and Mean Absolute Error (MAE) are 18.33 mm and 14.08 mm, respectively. Compared with ERA5 ZTD and GPT3 ZTD, the RMSE of GRNN ZTD has decreased by 19.5% and 63.4%, respectively, and the MAE of GRNN ZTD has decreased by 24.8% and 67.1%. Compared with the other two models, the GRNN refined model has better performance in reflecting the rapid fluctuations of ZTD. In addition, also discussed is the impact of spatial factors and time factors on modeling. The findings indicate that modeling accuracy within the central region of the modeling area surpasses that at the periphery by approximately 17.8%. The period from June to October is associated with the lowest accuracy, whereas the optimal accuracy is typically observed from January to April. The most substantial differences in accuracy were observed at station OP71 (Paris, France), with the highest accuracy recorded (9.51 mm) in April and the lowest (24.00 mm) in September. Full article

Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution. Full article