Search Results (8)

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

Uranium–niobium (U-Nb) alloys, used in a variety of industrial and energy applications that require high density, ductility, and good corrosion resistance, comprise a highly complex, multiphasic system with a phase diagram well established through decades of extensive experimental and theoretical research. They are also one of the best candidates for a metallic fuel alloy with high-temperature strength sufficient to support the core, acceptable nuclear properties, good fabricability, and compatibility with usable coolant media. The key factor determining the performance and safety of a metallic fuel such as U-Nb is its operational limits in the application environment, which are closely related to material’s structure and thermodynamic stability. They are in turn closely related to the ambient (zero-pressure) melting point $\left(T_m\right);$ thus, $T_m$ is an important engineering parameter. However, the current knowledge of $T_m$ of the U-Nb system is limited, as the only experimental study of its Nb-rich portion dates back to 1958. In addition, it has not yet been adequately modeled based on general thermodynamics principles or using an equation-of-state approach. In this study, we present a theoretical model for the melting curve (liquidus) of a mixture, and apply it to U-Nb, which is considered as a mixture of pure U and pure Nb. The model uses the known melting curves of pure constituents as an input and predicts the melting curve of their mixture. It has only one free parameter, which must be determined independently. The ambient liquidus of U-Nb predicted by the model appears to be in good agreement with the available experimental data. We calculate the melting curve (the pressure dependence of $T_m$) of pure U using ab initio quantum molecular dynamics (QMD), the knowledge of which is required for obtaining the model parameters for U. We also generalize the new model to nonzero pressure and consider the melting curve of U-6 wt.% Nb (U-6Nb) alloy as an example. The melting curve of U-6Nb alloy predicted by the model appears to be in good agreement with the ab initio melting curve obtained from our QMD simulations. We suggest that the U-18Nb alloy can be considered as a proxy for protactinium (Pa) and demonstrate that the melting curves of U-18Nb and Pa are in good agreement with each other. Full article

To obtain a higher accuracy for the real-time Zenith Tropospheric Delay (ZTD), a refined tropospheric delay correction model was constructed by combining the tropospheric delay correction model based on meteorological parameters and the GPT3 model. The meteorological parameters provided by the Global Geodetic Observing System (GGOS) Atmosphere and the zenith tropospheric delay data provided by Centre for Orbit Determination in Europe (CODE) were used as references, and the accuracy and spatial–temporal characteristics of the proposed model were compared and studied. The results show the following: (1) Compared with the UNB3m, GPT and GPT2w models, the accuracy and stability of the GPT3 model were significantly improved, especially the estimation accuracy of temperature, the deviation (Bias) of the estimated temperature was reduced by 90.60%, 32.44% and 0.30%, and the root mean square error (RMS) was reduced by 42.40%, 11.02% and 0.11%, respectively. (2) At different latitudes, the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models had great differences in accuracy and applicability. In the middle and high latitudes, the Biases of the GPT3 + Saastamoinen model and the GPT3 + Hopfield model were within 0.60 cm, and the RMS values were within 4 cm; the Bias of the UNB3m model was within 2 cm, and the RMS was within 5 cm; in low latitudes, the accuracy and stability of the GPT3 + Saastamoinen model were better than those of the GPT3 + Hopfield and UNB3m models; compared with the GPT3 + Hopfield model, the Bias was reduced by 22.56%, and the RMS was reduced by 5.67%. At different heights, the RMS values of the GPT3 + Saastamoinen model and GPT3 + Hopfield model were better than that of the UNB3m model. When the height was less than 500 m, the Biases of the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models were 3.46 cm, 3.59 cm and 4.54 cm, respectively. At more than 500 m, the Biases of the three models were within 4 cm. In different seasons, the Bias of the ZTD estimated by the UNB3m model had obvious global seasonal variation. The GPT3 + Saastamoinen model and the GPT3 + Hopfield model were more stable, and the values were within 5 cm. The research results can provide a useful reference for the ZTD correction accuracy and applicability of GNSS navigation and positioning at different latitudes, at different heights and in different seasons. Full article

The tropospheric delay is one of the main error sources that degrades the accuracy of Global Navigation Satellite Systems (GNSS) Single Point Positioning (SPP). Although an empirical model is usually applied for correction and thereby to improve the positioning accuracy, the residual tropospheric delay is still drowned in measurement noise, and cannot be further compensated by parameter estimation. How much this type of residual error would sway the SPP positioning solutions on a global scale are still unclear. In this paper, the biases on SPP solutions introduced by the residual tropospheric delay when using nine conventionally Zenith Tropospheric Delay (ZTD) models are analyzed and discussed, including Saastamoinen+norm/Global Pressure and Temperature (GPT)/GPT2/GPT2w/GPT3, University of New Brunswick (UNB)3/UNB3m, European Geostationary Navigation Overlay System (EGNOS) and Vienna Mapping Functions (VMF)3 models. The accuracies of the nine ZTD models, as well as the SPP biases caused by the residual ZTD (dZTD) after model correction are evaluated using International GNSS Service (IGS)-ZTD products from around 400 globally distributed monitoring stations. The seasonal, latitudinal, and altitudinal discrepancies are analyzed respectively. The results show that the SPP solution biases caused by the dZTD mainly occur on the vertical direction, nearly to decimeter level, and significant discrepancies are observed among different models at different geographical locations. This study provides references for the refinement and applications of the nine ZTD models for SPP users. Full article

As one of the atmosphere propagation delays, the tropospheric delay is a significant error source that should be properly handled in high-precision global navigation satellite system (GNSS) applications. We propose an improved zenith tropospheric delay (ZTD) modeling method whereby the piecewise model of the atmospheric refractivity is introduced. Compared with using the exponential model to fit ZTD in vertical direction, the ZTD piecewise model has a better performance. Based on ERA5 2.5° × 2.5° reanalysis data produced by the European Centre for Medium-Range Weather Forecasting (ECMWF) from 2013 to 2017, we establish the regional gridded ZTD model (RGZTD) using a trigonometric function for China and the surrounding areas, which ranges from 70° E to 135° E in longitude and from 15° N to 55° N in latitude. To verify the performance of RGZTD model, the ERA5 ZTD data in 2017–2018, the radiosonde ZTD data from 86 radiosonde stations over China in 2017–2018, and the tropospheric delay products on 251 GNSS stations from Crustal Movement Observation Network of China (CMONOC) in 2016–2017 are used as external compliance check data. The results show that the overall accuracy of RGZTD model is better than that of exponential model, UNB3m model, and GPT3 model. Moreover, the accuracy can be improved by about 13.4%, 7.1%, and 6.2% when ERA5 reanalysis data, radiosonde data, and CMONOC data are used as reference values, respectively. High-accuracy ZTD data can be provided because the RGZTD model takes into account the vertical variation of ZTD through the new piecewise model. Full article

A regional zenith tropospheric delay (ZTD) empirical model, referred to as SHAtropE (SHanghai Astronomical observatory tropospheric delay model—Extended), is developed and provides tropospheric propagation delay corrections for users in China and the surrounding areas with improved accuracy. The SHAtropE model was developed based on the ZTD time series of the continuous GNSS sites from the Crustal Movement Observation Network of China (CMONOC) and GNSS sites of surrounding areas. It combines the exponential and periodical functions and is provided as regional grids with a resolution of 2.5° × 2.0° in longitude and latitude. At each grid point, the exponential function converts the ZTD from the site height to the ellipsoid, and the periodical terms, including both annual and semi-annual periods, describe ZTD’s temporal variation. Moreover, SHAtropE also provides the predicted ZTD uncertainty, which is valuable in Precise Point Positioning (PPP) with ZTD being constrained for faster convergence. The data of 310 GNSS sites over 7 years were used to validate the new model. Results show that the SHAtropE ZTD has an accuracy of 3.5 cm in root mean square (RMS) quantity, which has a mean improvement of 35.2% and 5.4% over the UNB3m (5.4 cm) and GPT3 (3.7 cm) models, respectively. The predicted uncertainty of SHAtropE ZTD shows seasonal variations, where the values are larger in summer than in winter. By applying the SHAtropE model in the static PPP, the convergence time of GPS-only and BDS-only solutions are reduced by 8.1% and 14.5% respectively compared to the UNB3m model, and the reductions are 6.9% and 11.2% respectively for the GPT3 model. As no meteorological data are required for the implementation of the model, the SHAtropE could thus be a refined tropospheric model for GNSS users in mainland China and the surrounding areas. The method of modeling the ZTD uncertainty can also be used in further global tropospheric delay modeling. Full article

This paper proposes a new Asian single site tropospheric correction model called the Single Site Improved European Geostationary Navigation Overlay Service model (SSIEGNOS) by refining the European Geostationary Navigation Overlay Service (EGNOS) model at a single site. The performance of the SSIEGNOS model is analyzed. The results show that (1) the bias and root mean square (RMS) error of zenith tropospheric delay (ZTD) calculated from the EGNOS model are 0.12 cm and 5.87 cm, respectively; whereas those of the SSIEGNOS model are 0 cm and 2.52 cm, respectively. (2) The bias and RMS error show seasonal variation in the EGNOS model; however, little seasonal variation is observed in the SSIEGNOS model. (3) The RMS error decreases with increasing altitude or latitude in the two models; however, no such relationships were found in the bias. In addition, the annual predicted bias and RMS error in Asia are −0.08 cm and 3.14 cm for the SSIEGNOS model, respectively; however, the EGNOS and UNB3m (University of New Brunswick) models show comparable predicted results. Relative to the EGNOS model, the annual predicted bias and RMS error decreased by 55% and 48%, respectively, for the SSIEGNOS model. Full article

Tropospheric delays are one of the main sources of errors in the Global Navigation Satellite System (GNSS). They are usually corrected by using tropospheric delay models, which makes the accuracy of the models rather critical for accurate positioning. To provide references for suitable models to be chosen for GNSS users in China, we conduct herein a comprehensive study of the performances of the IGGtrop, EGNOS and UNB3m models in China. Firstly, we assess the models using 5 years’ Global Positioning System (GPS) derived Zenith Tropospheric Delay (ZTD) series from 25 stations of the Crustal Movement Observation Network of China (CMONOC). Then we study the effects of the models on satellite positioning by using various Precise Point Positioning (PPP) cases with different tropospheric delay resolutions, the observation data processed in PPP is from 21 base stations of CMONOC for a whole year of 2012. The results show that: (1) the Root Mean Square (RMS) of the IGGtrop model is about 4.4 cm, which improves the accuracy of ZTD estimations by about 24% for EGNOS and 19% for UNB3m; (2) The positioning error in the vertical component of the PPP solution obtained by using the IGGtrop model is about 15.0 cm, which is about 30% and 21% smaller than those of the EGNOS and UNB3m models, respectively. In summary, the IGGtrop model achieves the best performance among the three models in the Chinese region. Full article