Characterizing a newly developed heterogeneous and continuously observing low-cost GNSS station network

Variability and accuracy of Zenith Total Delay over the East African tropical region

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.

The meteorological reanalysis data has been widely applied to derive zenith tropospheric delay (ZTD) with a high spatial and temporal resolution. With the rapid development of artificial intelligence, machine learning also begins as a high-efficiency tool to be employed in modeling and predicting ZTD. In this paper, we develop three new regional ZTD models based on the least squares support vector machine (LSSVM), using both the International GNSS Service (IGS)-ZTD products and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over Europe throughout 2018. Among them, the ERA5 data is extended to ERA5S-ZTD and ERA5P-ZTD as the background data by the model method and integral method, respectively. Depending on different background data, three schemes are designed to construct ZTD models based on the LSSVM algorithm, including the without background data, with the ERA5S-ZTD, and with the ERA5P-ZTD. To investigate the advantage and feasibility of the proposed ZTD models, we evaluate the accuracy of two background data and three schemes by segmental comparison with the IGS-ZTD of 85 IGS stations in Europe. The results show that the overall average Root Mean Square Errors (RMSE) value of all sites is 30.1 mm for the ERA5S-ZTD, and 10.7 mm for the ERA5P-ZTD. The overall average RMSE is 25.8 mm, 22.9 mm, and 9 mm for the three schemes, respectively. Moreover, the overall improvement rate is 19.1% and 1.6% for the ZTD model with ERA5S-ZTD and ERA5P-ZTD, respectively. In order to explore the reason of the lower improvement for the ZTD model with ERA5P-ZTD, the loop verification is performed by estimating the ZTD values of each available IGS station. In actuality, the monthly improvement rate of estimated ZTD is positive for most stations, and the biggest improvement rate can even reach about 40%. The negative rate mainly comes from specific stations, these stations are located on the edge of the region, near the coast, as well as the lower similarity between the individual verified station and training stations.

The tropospheric delay is one of the main errors for earth observation and a variety of radio navigation technologies, and the UNB3m model can be used to calculate the zenith tropospheric delay (ZTD) without any real measured meteorological data, which taking the major changes in water vapor profiles with latitude into account, and it widely applied in Wide Area Augmentation System in America. However, there are few researches carried out on the assessment of ZTD from UNB3m model over Asia area. In this study, three years of the ZTD data observed from 56 IGS (International GNSS service) sites distributed in Asia area is used to assess the effectiveness and accuracy of ZTD calculated from UNB3m model. The results are: (1) relative to IGS observed ZTD, the bias and root mean square (RMS) for ZTD calculated from UNB3m model are -0.1 cm and 6.0 cm, respectively. Besides, the bias shows significant periodic characteristics in Asia area. (2) The bias and RMS present seasonal variations, which generally show larger values in summer months. (3) The precision of ZTD calculated from UNB3m model increases with increasing altitude or latitude, and also the bias and RMS show inconsistently in different Asia areas. At last, the best results can be achieved in inland area where presents the mean yearly RMS of 2.4 cm. These results provide a reference for the study of the tropospheric delay correction model and the applications of real-time GNSS navigation and positioning.

Tropospheric delay acts as a systematic error source in the Global Navigation Satellite Systems (GNSS) positioning. Empirical models UNB3, UNB3m, UNB4 and EGNOS have been developed for use in Satellite-Based Augmentation Systems (SBAS). Model performance, however, is limited due to the low spatial resolution of the look-up tables for meteorological parameters. A new design has been established in this study for improving performance of the tropospheric delay model by more effectively eliminating the error produced by tropospheric delay. The spatiotemporal characteristics of the Zenith Tropospheric Delay (ZTD) were analyzed with findings that ZTD exhibits different annual variations at different locations and decreases exponentially with height increasing. Spherical harmonics are utilized based on the findings to fit the annual mean and amplitude of the ZTD on a global scale and the exponential function is utilized for height corrections, yielding the ZTrop model. On a global scale, the ZTrop features an average deviation of -1.0 cm and Root Mean Square (RMS) of 4.7 cm compared with the International GNSS Service (IGS) ZTD products, an average deviation of 0.0 cm and RMS of 4.5 cm compared with the Global Geodetic Observing System (GGOS) ZTD data, and an average deviation of -1.3 cm and RMS of 5.2 cm compared with the ZTD data from the Constellation Observing System of Meteorology, Ionosphere, and Climate (COSMIC). The RMS of the ZTrop model is 14.5% smaller than that of UNB3, 6.0% smaller than that of UNB3m, 16% smaller than that of UNB4, 14.5% smaller than that of EGNOS and equivalent to the sophisticated GPT2+Saas model in comparison with the IGS ZTD products. The ZTrop, UNB3m and GPT2+Saas models are finally evaluated in GPS-based Precise Point Positioning (PPP), as the models act to aid in obtaining PPP position error less than 1.5 cm in north and east components and relative large error (>5 cm) in up component with respect to the random walk approach.

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.

In order to study the characteristics of zenith tropospheric delay (ZTD) at sea, the Precise Point Positioning (PPP) was used to process the data from 7 International GNSS Service (IGS) reference stations distributed in South China Sea. These stations can process GPS, BDS, and GLONASS data simultaneously. The offshore ZTD was estimated by random walk model. In order to evaluate the accuracy of the estimated ZTD, the ZTD data from three of the stations were used to compare with ZTD products of 300 s sampling from IGS. The results show that the ZTD estimation results from GPS/BDS/GLONSS-based PPP is consistent with the trend of the ZTD products provided by IGS, and the position error in the convergence state is less than 10 mm. By calculating the ZTD time series of day of year (DOY) 14–154, 2016, the mean diurnal ZTD values at each of local time (LT = 1, 2, …, 24) were obtained. The results shows that the mean diurnal ZTD time series have two peak values, which are around noon and midnight local time, moreover, the maximum peak is around midnight. The ZTD estimation results of offshore and inland are compared and analyzed. The results show that ZTD of offshore stations is about 6–19 cm larger than that of inland stations. The maximum ZTD value can be observed at equatorial locations. Moreover, the change of ZTD from offshore stations is more intense, its peak-to-peak value of mean diurnal ZTD time series is larger than the inland by approximately 6 mm.

Real-time retrieval of high-precision ZTD maps using GNSS observation

The growing demand for Global Navigation Satellite System (GNSS) technology has necessitated the establishment of a vast and ever-growing network of International GNSS Service (IGS) tracking stations worldwide. The IGS provides highly accurate and highly reliable daily time-series Zenith Tropospheric Delay (ZTD) products using data from the member sites towards the use of GNSS for precise geodetic, climatological, and meteorological applications. However, if for reasons like poor internet connectivity, equipment failure, and power outages, the IGS station is inaccessible or malfunctioning, and gaps are created in the data archive resulting in degrading the quality of the ZTD and precipitable water vapour (PWV) estimation. To address this challenge as a means of providing an alternative data source to improve the continuous availability of ZTD data and as a backup data in the event that the IGS site data are missing or unavailable in West Africa, this paper compares the sitewise operational Vienna Mapping Functions 3 (VMF3) ZTD product with the IGS final ZTD product over five IGS stations in West Africa. Eight different statistical evaluation metrics, such as the mean bias (MB), mean absolute error (MAE), root mean squared error (RMSE), Pearson correlation coefficient (r), coefficient of determination (r2), refined index of agreement (IAr), Nash–Sutcliffe coefficient of efficiency (NSE), and the fraction of prediction within a factor of two (FAC2), are employed to determine the degree of agreement between the VMF3 and IGS tropospheric products. The results show that the VMF3-ZTD product performed excellently and matches very well with the IGS final ZTD product with an average MB, MAE, RMSE, r, r2, NSE, IAr, and FAC2 of 0.38 cm, 0.87 cm, 1.11 cm, 0.988, 0.976, 0.967, 0.992, and 1.00 (100%), respectively. This result is an indication that the VMF3-ZTD product is accurate enough to be used as an alternative source of ZTD data to augment the IGS final ZTD product for positioning and meteorological applications in West Africa.

Tropospheric delay has a major effect on the accuracy of navigation and positioning when using the Global Navigation Satellite System (GNSS). Zenith tropospheric delay (ZTD) modelling has been used to weaken the influence of the atmosphere. The work reported here focused on ZTD modelling based on real-time surface meteorological parameters, traditionally represented by the Saastamoinen model. However, Saastamoinen accuracy only reaches scale of centimetres, even to scale of centimetres when the water vapour is active, whereas the scale of ground-based GNSS-ZTD data (i.e. ZTD derived from ground GNSS data) is on the millimetre scale and is considered to be the ‘true’ value. An important direction in GNSS studies is how to make good use of ground-based GNSS-ZTD data to improve the accuracy of the Saastamoinen model. Authors studied the residuals in the Saastamoinen model using high-precision GNSS-ZTD data provided by the International GNSS Service (IGS) product and then carried out modelling based on a back propagation neural network. A new ZTD model (ISAAS) based on real-time surface meteorological parameters is proposed based on this method. The ISAAS model has good accuracy: its BIAS and root mean square error (RMSE) at the test area in Russia were -4.4 and 20.4 mm, respectively, which are lower than the results obtained using the Saastamoinen model (-10.4 and 23.3 mm, respectively). The ISAAS model can improve the ZTD prediction accuracy by more than 12.4% and therefore has important implications for precision engineering measurements in Russia.

When processing the carrier phase, the global navigation satellite system (GNSS) grants the highest precision for geodetic measurements. The analysis centers (ACs) from the International GNSS Service (IGS) provide different data such as precise clock data, precise orbits, reference frame, ionosphere and troposphere data, as well as other geodetic products. Each individual AC has its own strategy for delivering the abovementioned products, with one of the key elements being the cutoff elevation angle. Typically, this angle is arbitrarily chosen using generic values without studying the impact of this choice on the obtained results, in particular when very precise positions are considered. This article addresses this issue. To this end, the article has two key sections, and the first is to evaluate the impact of using the two different cutoff elevation angles that are most widely used: (a) 3 degrees cutoff and (b) 10 degrees cutoff elevation angle. This analysis is completed in two major parts: (i) the analysis of the root mean square (RMS) for the carrier phase and (ii) the analysis of the station position in terms of repeatability. The second key section of the paper is a comprehensive carrier phase analysis conducted by adopting a new approach using a mean of the 25-point average RMS (A-RMS) and the single-point RMS and using an ionosphere-free linear combination. By using the ratio between the 25-point average RMS and the single-point RMS we can define the type of scatter that dominates the phase solution. The analyzed data span a one-year period. The tested GNSS stations belong to the EUREF Permanent Network (EPN) and the International GNSS Service (IGS). These comprise 55 GNSS stations, of which only 23 GNSS stations had more than 95% data availability for the entire year. The RMS and A-RMS are analyzed in conjunction with the precipitable water vapor (PWV), which shows clear signs of temporal correlation. Of the 23 GNSS stations, three stations show an increase of around 50% of the phase RMS when using a 3° cutoff elevation angle, and only four stations have a difference of 5% between the phase RMS when using both cutoff elevation angles. When using the A-RMS, there is an average improvement of 37% of the phase scatter for the 10° cutoff elevation angle, whereas for the 3° cutoff elevation angle, the improvement is around 33%. Based on studying this ratio, four stations indicate that the scatter is dominated by the stronger-than-usual dominance of long-period variations, whereas the others show short-term noise. In terms of station position repeatability, the weighted root mean square (WRMS) is used as an indicator, and the results between the differences of using a 3° and 10° cutoff elevation angle strategy show a difference of −0.16 mm for the North component, −0.21 mm for the East component and a value of −0.75 mm for the Up component, indicating the importance of using optimal cutoff angles.

Accurate estimation of tropospheric delay is significant for global navigation satellite system’s (GNSS) high-precision navigation and positioning. However, due to the random and contingent changes in weather conditions and water vapor factors, the classical tropospheric delay model cannot accurately reflect changes in tropospheric delay. In recent years, with the development of meteorological observation/detection and numerical weather prediction (NWP) technology, the accuracy and resolution of meteorological reanalysis data have been effectively improved, providing a new solution for the inversion and modeling of regional or global tropospheric delays. Here, we evaluate the consistency and accuracy of three different types of reanalysis data (i.e., ERA5, MERRA2, and CRA40) used to invert the zenith tropospheric delay (ZTD) from 436 international GNSS service (IGS) stations in 2020, based on the integral method. The results show that the ZTD inversion of the three types of reanalysis data was consistent with the IGS ZTD, even in heavy rain conditions. Furthermore, the average precision of the ZTD inversion of the ERA5 reanalysis data was higher, where the mean deviation (bias), mean absolute error (MAE), and root mean square (RMS) were –3.39, 9.69, and 12.55 mm, respectively. The ZTD average precisions of the MERRA2 and CRA40 inversions were comparable, showing slightly worse performance than the ERA5. In addition, we further analyzed the global distribution characteristics of the ZTD errors inverted from the reanalysis data. The results show that ZTD errors inverted from the reanalysis data were highly correlated with station latitude and climate type, and they were mainly concentrated in the tropical climate zone at low latitudes. Compared to dividing error areas by latitude, dividing error areas by climatic category could better reflect the global distribution of errors and would also provide a data reference for the establishment of tropospheric delay models considering climate type.

The latest reanalysis of the European Center for Medium-Range Weather Forecasts (ECMWF), ERA5, can provide atmospheric data for calculating Zenith Tropospheric Delay (ZTD) with hourly temporal resolution, which is a key factor in Global Navigation Satellite System (GNSS) high-precision application. This paper is aimed at evaluating the performance of ZTD derived from ERA5 reanalysis data over China using 219 GNSS stations of the Crustal Movement Observation Network of China (CMONOC) covering the period from 2015 to 2016. The site-specific hourly ZTD at these stations is obtained by integration method and Saastamoinen model method on ERA5 pressure-level and surface-level reanalysis data with the temporal resolution of 1 h and the spatial resolution of 0.25° × 0.25°. Firstly, the atmospheric temperature and pressure that derived from ERA5 are compared with temperature and pressure obtained from meteorological sensors available at 193 GNSS stations. The biases are 2.31 °C and 1.26 mbar implying the accuracy and feasibility of ERA5 pressure and temperature for calculating ZTD over China. Secondly, the performance of ERA5 ZTD is systematically evaluated using ZTD from 219 GNSS sites. The average bias and Root Mean Square (RMS) of ERA5 pressure-level ZTD at all test stations in integration method are approximately 2.97 mm and 11.49 mm respectively, and those of ERA5 surface-level ZTD in model method are 7.97 mm, 39.25 mm, which indicates that ERA5 pressure-level ZTD has a higher accuracy over China. Further analysis indicates that the accuracies of ZTD derived from ERA5 pressure-level and surface-level data are approximately 13.8% and 10.9% higher than those from of ERA-Interim pressure-level and surface-level data. Moreover, ERA5 is able to accurately capture the short-term (hourly) variation of ZTD, which further indicates the better performance of ERA5. Thirdly, the temporal and spatial variation characteristics of ERA5 ZTD accuracy are further analyzed over China. The results show that the ZTD in the southern region has the lower accuracy compared with that in the northern region over China due to the influence of latitude and altitude. Furthermore, it is found that the ERA5 ZTD over China has obvious seasonality, with higher accuracy in winter and lower accuracy in summer.

The ability to precisely and accurately model and predict tropospheric delay is essential for precise global navigation satellite system (GNSS) and meteorological applications. The International GNSS Service (IGS) provides highly accurate and highly reliable daily time series zenith tropospheric delay (ZTD) products for all its member sites using data from each IGS site. Nevertheless, if for reasons such as poor internet connectivity, equipment failure, and power outages the IGS station is inaccessible, gaps are created in the data archive, resulting in degrading the quality of the ZTD estimation, as well as inhibits the quality of precipitable water vapour (PWV) estimation, needed for precise positioning applications, meteorological studies, and weather forecasting. To address this challenge, five regression models are proposed in this study to model and predict daily ZTDs using daily datasets from four IGS stations in West Africa over a period of 5 years (2015–2019). The site‐specific Vienna Mapping Functions 3 (VMF3) products (ZTD, pressure, temperature, water vapour partial pressure) and stations' coordinates (latitudes and longitudes) are used as the predictors, while the IGS final ZTD product as the response variable in fitting the models. Several performance measures are calculated to compare the predictive performance of the models. The results show that the five regression models performed outstandingly and agree very well with the IGS‐ZTD data, and hence provide a useful alternative for ZTD predictions and also in the event the West African IGS stations' ZTD data are unavailable. Nonetheless, the support vector regression model outperformed the remaining four models.

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.