AI-weather driven GNSS real-time wide-area troposphere modeling method

Abstract

This invention discloses an AI-weather-driven GNSS real-time wide-area tropospheric modeling method, comprising the following steps: (1) Initializing the AI-weather model with ERA5 reanalysis data as the background field to predict a high-resolution three-dimensional meteorological parameter field, which is obtained by numerical integration of the meteorological parameters; (2) Using non-difference non-combined PPP-AR to estimate the reference station in real time; (3) Selecting three representative machine learning algorithms to perform spatial nonlinear training and verification on the residual sample set between GNSS-ZWD, in order to select the optimal fusion algorithm; (4) Generating a residual correction field on a regular grid and superimposing it to form a spatially continuous enhanced ZWD grid service; (5) Further combining the ZWD elevation transformation model and spatial interpolation algorithm to obtain the ZWD at any user location and use it for real-time PPP positioning constraints. This invention fully integrates the wide-area continuity of AI-weather with the high-precision advantages of GNSS observation, significantly improving the accuracy of tropospheric wet delay modeling and the PPP vertical convergence speed, and is suitable for wide-area real-time high-precision positioning services.

Description

Technical Field

[0001] This invention relates to the fields of satellite navigation and positioning and atmospheric remote sensing technology, specifically to a method and system for modeling, enhancing and broadcasting tropospheric wet delay (ZWD) for real-time wide-area high-precision positioning services. Background Technology

[0002] Tropospheric delay is a systematic error caused by the elongation of the propagation path of electromagnetic waves as they pass through the troposphere due to atmospheric refraction. It is one of the main error sources of Global Navigation Satellite Systems (GNSS) and directly affects the accuracy of satellite positioning and atmospheric parameter inversion. Typically, the slant path delay of a signal can be decomposed into zenith static delay (ZHD) and zenith wet delay (ZWD) using projection functions and tropospheric horizontal gradient models. ZHD can be accurately obtained using the Sasstamoinen model combined with measured instantaneous air pressure, while ZWD is influenced by the vertical structure of water vapor, surface meteorological conditions, and regional climate characteristics, exhibiting significant spatiotemporal nonlinear variations and being a key factor affecting high-precision GNSS positioning.

[0003] In precise point positioning, accurate ZWD prior information helps weaken the coupling between tropospheric delay and other parameters, improves ambiguity fixation rate, and accelerates convergence to achieve centimeter-level positioning accuracy. This is especially important in dynamic scenarios such as drones, autonomous driving, precision agriculture, deformation monitoring, and emergency rescue, where GNSS signals are easily blocked and interrupted. Insufficient accuracy of the tropospheric delay model will significantly reduce the reliability and availability of real-time positioning. Furthermore, ZWD contains rich atmospheric water vapor information, which can be used to obtain high-precision precipitable water products through inversion from multi-source atmospheric observation data. Therefore, constructing a high-precision, spatiotemporally continuous, and robust real-time wide-area ZWD model framework is of great significance for improving satellite-based GNSS positioning service capabilities and supporting severe convective weather warnings and mesoscale meteorological event monitoring.

[0004] In existing technologies, the acquisition of tropospheric wet delay mainly relies on the following three types of methods: The first type is empirical models, which use harmonic functions to describe the periodic variation characteristics of ZWD and combine high-resolution grids and exponential functions to characterize the spatial distribution of ZWD. This type of method has high computational efficiency, but it is difficult to accurately characterize the strong randomness and regional differences dominated by water vapor. The model accuracy and adaptability are limited under complex terrain, land-sea transition zones, and severe convective weather conditions. The second type is real-time wide-area tropospheric methods based on the inversion of continuously operating GNSS reference station networks and the construction of multinomial or grid interpolation. This type of method has high accuracy, but it is subject to the limitations of GNSS station network density and spatial distribution. The uniformity of the stations is highly dependent, and its stability and generalization ability are significantly insufficient in sparse station areas or cross-regional applications. The fourth category is the tropospheric wet delay modeling method based on machine learning and artificial intelligence. Its automatic feature learning ability can deeply explore the implicit correlation between multi-source atmospheric parameters and performs well in dealing with high-dimensional and strongly nonlinear problems. However, such models usually rely on a huge coefficient matrix. Especially when fusing multi-source meteorological fields and GNSS observations, the model dimension expands sharply, resulting in a large communication burden for broadcasting model parameters and a high amount of inference calculations. It is difficult to run efficiently on real-time application platforms with limited computing power, such as vehicle terminals, drones, and mobile devices.

[0005] In recent years, new-generation AI meteorological models, such as Huawei's Pangu-Weather and FengWu from the Shanghai Artificial Intelligence Laboratory, have directly learned the evolution of massive reanalysis data and atmospheric states through end-to-end frameworks. While maintaining physical consistency, they can complete global high-resolution meteorological field predictions in seconds under GPU acceleration. Their inference speed is more than 10,000 times faster than the operating Integrated Forecasting System (IFS), significantly reducing computational overhead and providing new technical support for real-time wide-area tropospheric modeling. The 2024 paper "Forecasting of Tropospheric Delay using AI Foundation Models in support of Microwave Remote Sensing" by Junsheng Ding et al. proposed using AI foundation models (FM) to generate global medium-range weather forecasts and further derived tropospheric delay-related products (including ZHD, ZWD, mapping functions, gradients, etc.) through physical integration / ray tracing, and conducted system verification using ERA5, GNSS, and radiosonde as references. This work indicates that the FM scheme can rapidly generate tropospheric products for up to 15 days locally, and its overall accuracy remains superior to the empirical model GPT3 for approximately 10 days. However, as the forecast duration increases, the model error gradually increases and approaches that of GPT3, with differences in performance among different FM schemes (FengWu / GraphCast generally outperforms Pangu, while Pangu is limited by fewer pressure layers). The 2024 paper "Methods and Evaluation of AI-Based Meteorological Models for Zenith Tropospheric Delay Prediction" by Si Xiong et al. systematically evaluated the performance of AI meteorological models (represented by Fengwu and Pangu) in ZTD prediction and compared them with traditional models. Their research, starting from a global station scale, analyzed the impact of different regions, seasons, land-sea distribution, and station elevations on the error, indicating that AI models can significantly reduce RMSE in short- and medium-term forecasts, but the error is greater in ocean regions or regions with complex climate dynamics; furthermore, the error exhibits a cumulative effect with increasing recursive step size.

[0006] While the two studies mentioned above demonstrated the potential of AI meteorological models in refined tropospheric modeling from the perspectives of "model feasibility verification" and "accuracy system evaluation," existing work mainly focuses on "deriving tropospheric products from AI forecast fields" or "evaluating the performance of AI predictions," without exploring the actual gains of AI meteorological models in real-time wide-area tropospheric modeling and PPP services. Furthermore, under the current constraints of high dependence on CORS station network density and spatial continuity in wide-area tropospheric modeling, the accuracy, regional adaptability, and generalization ability of traditional physical models are clearly insufficient. Therefore, constructing an effective data fusion framework that organically integrates the spatial continuity and high-resolution advantages of AI meteorological model forecast ZWD fields with the high accuracy and stability of GNSS station-based ZWD is a new approach to achieving real-time wide-area tropospheric modeling. However, how to balance accuracy, timeliness, and computational efficiency during the fusion process, and fully leverage the complementary advantages of the two types of data, remains a key issue that urgently needs to be addressed in building high-precision tropospheric grid enhancement services with good applicability and generalization capabilities for various GNSS users. Summary of the Invention

[0007] The purpose of this invention is to overcome the problems of strong station network dependence, insufficient spatial continuity, and difficulty in simultaneously satisfying accuracy, timeliness and computational efficiency in existing tropospheric wet delay modeling methods for real-time wide-area high-precision GNSS positioning applications. This invention proposes an AI-weather driven GNSS real-time wide-area tropospheric modeling method to provide continuous, stable and broadcastable real-time wide-area tropospheric services.

[0008] The core idea of ​​this invention is as follows: (i) Using the spatiotemporally continuous ZWD generated by AI-weather as the background field, the ZWD of the GNSS reference station estimated in real time by PPP-AR is introduced as a high-precision constraint. A nonlinear mapping model of the residuals of the two in space is constructed through machine learning algorithms to realize the residual correction of the AI-weather background field; (ii) By introducing a grid enhancement scheme, the corrected ZWD is extended to a regular grid and a broadcastable gridded service is provided. Subsequently, a ZWD transformation model and an inverse distance weighting scheme are further introduced to make the grid ZWD comparable and consistent in different altitude regions, thereby providing a broadcastable, continuous and stable ZWD prior constraint for the high-precision real-time positioning of user stations.

[0009] The technical solution of the present invention is as follows: An AI-weather-driven method for real-time wide-area tropospheric modeling of GNSS includes the following steps: [1] The AI-weather model was initialized based on ERA5 reanalysis data as the background field to predict the high-resolution three-dimensional meteorological parameter field at the target time; [2] A regular grid is obtained by numerical integration inversion of the meteorological parameters in step [1]. ; [3] Real-time estimation of reference stations using non-difference, non-combined PPP-AR. ; [4] Extract the corresponding spatial location of the reference station mentioned in step [3]. Calculate its relationship with residual Using machine learning algorithms to Spatial nonlinear training and validation are performed on the residual sample set between GNSS-ZWD and the model to generate a fusion model; 【5】Input the spatial location parameters of the grid points provided by the ERA5 surface layer and the corresponding The residual correction amount of the grid points is predicted by the residual mapping model in step [4]. and with Superimposed, generating a spatially continuous enhanced ZWD grid framework; [6] For GNSS users, the enhanced ZWD grid frame in step [5] is vertically corrected based on the IGPZWD elevation transformation model, and then the ZWD at the user's location is obtained by inverse distance weighted interpolation and used for real-time PPP positioning constraints; Furthermore, the AI-weather model mentioned in step [1] includes the Pangu-Weather and FengWu models. Since there is a release delay of about 5 days in the ERA5 reanalysis field, the AI ​​meteorological model is initialized with a background field that backtracks 5.25 days from the target time. Furthermore, the formula for calculating the ZWD numerical integral in step [2] is as follows: ; ; ; In the formula, It is the height of the target point. It is the refractive index. and These are water vapor pressure and temperature, It refers to air pressure and the refractive index constant. , To ensure consistent elevation datum, the elevations of all basic data and models have been converted to ellipsoidal heights using the EGM2008 model. When calculating the ZWD of a target point, the four nearest grid profiles around it must first be retrieved, and the height of the grid points must be adjusted to match the target height. Then, the vapor pressure and wet refractive index profile are calculated. To obtain a more accurate ZWD, the target height is treated as a separate layer. The air pressure and vapor pressure are obtained by weighted interpolation of variables from adjacent isobaric layers, while the temperature is estimated by linear extrapolation. ; ; ; In the formula, , , and These represent altitude, air pressure, water vapor pressure, and temperature, respectively, with subscripts. and Used to represent observations of the upper and lower layers. Indicates the target height. As a weighting factor, if the target altitude is lower than the bottom layer, the meteorological elements of the bottom two layers are extrapolated downwards to obtain the water vapor pressure and wet refractive index at the target altitude, and then integrated to calculate the ZWD of four grid points. After obtaining the ZWD of the target location, inverse distance weighted interpolation is used to obtain the ZWD of the target location. Finally, the obtained 6-hour resolution ZWD is upsampled to a 5-minute time resolution through interpolation to meet the data matching requirements for GNSS fusion modeling and broadcasting grid ZWD products.

[0010] Furthermore, the GNSS non-differential, non-combined observation equation described in step [3] is expressed as: ; In the formula, It is the unit vector from the satellite to the receiver. It is the receiver coordinate correction vector. It's the speed of light. and These are the receiver and the satellite clock bias, and These represent the dry and wet quantities, respectively. and It is the corresponding mapping function. For the satellite elevation angle, The slant path ionospheric delay at the L1 frequency, Represents the ionospheric frequency coefficient. It is the carrier wavelength. It is phase ambiguity. and It is the pseudorange hardware delay between the receiver and the satellite. and These are uncalibrated phase delays (UPDs). and The noise consists of pseudorange and carrier phase observations. The horizontal gradient parameter is estimated using a random walk process to absorb variations in tropospheric delay caused by atmospheric asymmetry, and its expression is as follows: ; In the formula, and These represent the satellite's elevation angle and azimuth angle, respectively. and These represent the tropospheric horizontal gradients in the north-south and east-west directions, respectively. Given the strong correlation between carrier ambiguity and ionospheric parameters, to improve the stability of non-differential integer ambiguity estimation and ambiguity fixation, the uncalibrated phase delay product (UPD) is estimated using IGS multi-system station observation data within the PPP framework without ionospheric ambiguity (IF). In this process, the wide lane (WL) UPD is calculated using the MW (Melbourne-Wübbena) combination, and then the narrow lane (NL) UPD is estimated using fixed WL ambiguity integers and IF ambiguities. Considering the aforementioned error terms, the reference station's ZWD is estimated in real-time using forward Kalman filtering based on CNES orbit, clock bias products, and self-calculated UPD products. The user station's ZWD is then accurately estimated using batch least squares with the final CODE product and IF-UPD to verify the model algorithm's performance. The broadcast interval for reference station ZWD modeling and service products is set to 5 minutes to fully quantify its time-varying bias.

[0011] Furthermore, the machine learning algorithms described in step [4] include Extreme Gradient Boosting (XGBoost), Feedforward Neural Network (MLPNN), and K-Nearest Neighbor (KNN) algorithms, respectively using the latitude, longitude, elevation, and corresponding coordinates of the GNSS reference station. Information as input features, and The residuals between the two values ​​are used as regression labels to train and validate each model. The regression function mapping relationship is as follows: ; ; In the formula, A fusion regression model representing machine learning. The ZWD inversions of Pangu-Weather and FengWu are represented. During training, key hyperparameters are optimized using a grid search combined with cross-validation. In the ten-fold cross-validation, the reference station sample data is randomly divided into ten subsets (folds), with each fold serving as the validation set. The remaining 90% of the stations are used to train the model. The root mean square error (RMS) is used as the evaluation metric for cross-validation to select the optimal combination of hyperparameters. Furthermore, the grid described in step [5] is a 1°×1° resolution grid point defined by the ERA5 surface layer height. After step [4], KNN is finally selected as the fusion algorithm to combine the latitude, longitude, elevation, and corresponding coordinates of each grid point. The ZWD correction amount is predicted in the input fusion model. ), and then match it with the corresponding Background fields are superimposed to generate a spatially continuous gridded ZWD field. Based on the different AI meteorological background fields used, this invention constructs two enhancement model frameworks: The first uses the ZWD field predicted by FengWu as the background field, and performs residual modeling and correction based on machine learning algorithms combined with ZWD information obtained through real-time PPP-AR inversion from GNSS reference stations; the enhanced tropospheric grid model is denoted as Trop_GF. The second uses the ZWD field obtained through inversion from the Pangu-Weather meteorological model for residual correction; the enhanced tropospheric grid model is denoted as Trop_GP. ; Further, in step [6], for any GNSS user location, the four nearest neighboring grid points are first selected, and the elevation scaling factor provided by the IGPZWD model is used ( The ZWD at the grid points is vertically pushed outward to the user station height. This process is based on the user's geodetic surveying. The inputs are location, year-day (DOY), and hour (HOD), and the mathematical expression is as follows: ; ; In the formula, , and ZWD No. Annual average of the elevation scaling factor, annual amplitude, and semi-annual amplitude coefficient. and These represent the grid heights respectively. and user station height The ZWD at the user's location is then obtained by horizontal interpolation using the inverse distance weighted (IDW) method. ; In the formula, ZWD at the user site Indicates the first ZWD of each grid point at the user's height The normalized weights corresponding to the grid points, and These are the Earth's radius and distance weighting indices, respectively. The spherical angular distance between a user station and a grid point is defined as follows: ; in, and These represent the latitude and longitude of the user station and the grid point, respectively.

[0012] Compared with the prior art, the present invention has the following advantages: I. This invention introduces a high-resolution, spatially continuous atmospheric background field predicted by an AI-weather meteorological model, and obtains a regular grid through numerical integration. This invention combines high-precision ZWD information obtained from GNSS reference stations via PPP inversion and constructs a residual nonlinear mapping model between the two using machine learning algorithms, achieving fusion modeling of tropospheric wet delay. Compared to traditional tropospheric modeling methods that rely solely on GNSS station networks, this invention fully leverages the advantages of AI meteorological models in terms of spatial continuity and high resolution, and performs residual correction through GNSS observations, thereby significantly improving the accuracy of tropospheric wet delay estimation while ensuring spatial continuity. This method effectively reduces the dependence on reference station density and spatial uniformity, maintaining stable tropospheric wet delay modeling capabilities even in sparsely populated areas, cross-regional applications, and complex terrain conditions.

[0013] II. Because GNSS reference stations are typically discretely distributed, their spatial density varies significantly across different regions. If a wide-area tropospheric model is built solely using interpolation methods between stations, large spatial extrapolation errors can easily occur in areas with sparse station networks or complex terrain. To address the problem of discrete distribution and uneven spatial density of GNSS reference stations, this invention introduces a grid enhancement scheme to effectively extend the tropospheric wet delay from discrete reference stations to a continuous spatial field, significantly improving the spatial continuity, consistency, and stability of the tropospheric wet delay grid product. Compared to traditional wide-area tropospheric models built solely based on station interpolation, this method has better adaptability in areas with sparse stations and complex terrain, while reducing dependence on GNSS reference station network density, making it more suitable for real-time broadcasting and wide-area positioning service applications.

[0014] Third, in traditional PPP models, tropospheric wet delay parameters typically need to be estimated simultaneously with receiver altitude parameters and carrier phase ambiguity parameters during the positioning process. Because these parameters exhibit strong correlations in their effects on the observation equations, especially when observation times are short or satellite geometry changes are limited, tropospheric delay errors easily couple with altitude errors, leading to unstable parameter estimation and significantly prolonging PPP convergence time. This invention introduces enhanced Trop_GF ZWD as prior information into the PPP solution, providing reliable initial information for tropospheric parameters. This effectively weakens the correlation between tropospheric delay and altitude and ambiguity parameters. This method significantly shortens the vertical convergence time of PPP and reduces positioning errors in both static and dynamic positioning modes, thereby improving the reliability and stability of real-time high-precision positioning services. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method of the present invention.

[0016] Figure 2 The process of initializing the Pangu-Weather and FengWu models to predict meteorological parameters for ERA5 reanalysis data.

[0017] Figure 3 RMS statistics for the validation sets of three machine learning algorithms, XGBoost, MLPNN, and KNN, in three regions.

[0018] Figure 4 Statistics on convergence time and improvement rate of PPP-AR in the U direction for standard PPP-AR and Trop_GF enhanced PPP-AR. Detailed Implementation

[0019] The present invention will now be further described with reference to the accompanying drawings.

[0020] Reference Figure 1 The specific implementation steps of the present invention are as follows: Step 1: Initialize two AI meteorological models, Pangu-Weather and FengWu, using ERA5 reanalysis data to predict meteorological parameters. Since the ERA5 reanalysis field has a release delay of approximately 5 days, a background field 5.25 days back to the target time is used to initialize the AI ​​meteorological models. For Pangu-Weather, its forecast relies on only a single initial field; this invention uses a 6-hour step size for rolling extrapolation. The FengWu model requires two initial fields 6 hours apart; therefore, in addition to the 5.25-day backtracking, a second set of background fields 6 hours earlier is needed. Its extrapolation is rolled hourly to the target time using the method of "using the previous hourly forecast as the initial condition for the next hourly forecast." For example, when the initial background fields are 00:00 and 06:00, the model first generates a forecast for 12:00, then uses the fields of 06:00 and 12:00 as new initial conditions to obtain the result for 18:00, and so on until the meteorological field at the target time is obtained. Figure 2 This invention demonstrates the process of initializing the Pangu-Weather and FengWu models for forecasting meteorological parameters using ERA5.

[0021] Step 2: Numerically integrate the meteorological parameters predicted in Step 1 to obtain... The calculation formula is: ; ; ; In the formula, It is the height of the target point. It is the refractive index. and These are water vapor pressure and temperature, It refers to air pressure and the refractive index constant. , To ensure consistent elevation datum, the elevations of all basic data and models have been converted to ellipsoidal heights using the EGM2008 model. When calculating the ZWD of a target point, the four nearest grid profiles around it must first be retrieved, and the height of the grid points must be adjusted to match the target height. Then, the vapor pressure and wet refractive index profile are calculated. Here, the target height is treated as a separate layer, and the air pressure and vapor pressure are obtained by weighted interpolation of variables from adjacent isobaric layers. Temperature is estimated by linear extrapolation. ; ; ; In the formula, , , and These represent altitude, air pressure, water vapor pressure, and temperature, respectively, with subscripts. and Used to represent observations of the upper and lower layers. Indicates the target height. As a weighting factor, if the target altitude is lower than the bottom layer, the meteorological elements of the bottom two layers are extrapolated downwards to obtain the water vapor pressure and wet refractive index at the target altitude, and then integrated to calculate the ZWD of four grid points. After obtaining the ZWD of the target location, inverse distance weighted interpolation is used to obtain the ZWD of the target location. Finally, the obtained 6-hour resolution ZWD is upsampled to a 5-minute time resolution through interpolation to meet the data matching requirements for GNSS fusion modeling and broadcasting grid ZTD products.

[0022] Step 3: Estimate the ZWD of the GNSS reference station in real time from the GNSS multi-frequency real-time data stream by fixing the PPP ambiguity. The GNSS unequal and uncombined observation equation is expressed as: ; In the formula, It is the unit vector from the satellite to the receiver. It is the receiver coordinate correction vector. It's the speed of light. and These are the receiver and the satellite clock bias, and These represent the dry and wet quantities, respectively. and It is the corresponding mapping function. For the satellite elevation angle, The slant path ionospheric delay at the L1 frequency, Represents the ionospheric frequency coefficient. It is the carrier wavelength. It is phase ambiguity. and It is the pseudorange hardware delay between the receiver and the satellite. and These are uncalibrated phase delays (UPDs). and The noise consists of pseudorange and carrier phase observations. The horizontal gradient parameter is estimated using a random walk process to absorb variations in tropospheric delay caused by atmospheric asymmetry, and its expression is as follows: ; In the formula, and These represent the satellite's elevation angle and azimuth angle, respectively. and These represent the tropospheric horizontal gradients in the north-south and east-west directions, respectively.

[0023] Given the strong correlation between carrier ambiguity and ionospheric parameters, to improve the stability of non-differential integer ambiguity estimation and ambiguity fixation, the uncalibrated phase delay product (UPD) is estimated using IGS multi-system station observation data within the PPP framework without ionospheric ambiguity (IF). In this process, the wide lane (WL) UPD is calculated using the MW (Melbourne-Wübbena) combination, and then the narrow lane (NL) UPD is estimated using fixed WL ambiguity integers and IF ambiguities. Considering the aforementioned error terms, the reference station's ZWD is estimated in real-time using forward Kalman filtering based on CNES orbit, clock bias products, and self-calculated UPD products. The user station's ZWD is then accurately estimated using batch least squares with the final CODE product and IF-UPD to verify the model algorithm's performance. The broadcast interval for reference station ZWD modeling and service products is set to 5 minutes to fully quantify its time-varying bias. The detailed PPP strategy is as follows: Step 4: Calculation and The residuals between Using three representative models—Extreme Gradient Boosting (XGBoost), Mini-LPNN (MLPNN), and K-Nearest Neighbor (KNN) algorithms—with the latitude, longitude, and elevation of the GNSS reference station and their corresponding coordinates, this study employed three methods. Information as input features, and The residuals between the two models are used as regression labels to train and validate each model in order to select the optimal fusion model. The regression function mapping relationship is as follows: ; ; In the formula, A fusion regression model representing machine learning. The ZWD representing the inversion of Pangu-Weather and FengWu is used to optimize key hyperparameters during training through grid search combined with cross-validation. In the ten-fold cross-validation, the reference station sample data is randomly divided into ten subsets (folds), with each fold serving as the validation set. The remaining 90% of the stations are used to train the model. The root mean square error (RMS) is used as the evaluation metric for cross-validation to select the optimal combination of hyperparameters. The parameter settings for the three machine learning algorithms are shown in Table 2.

[0024] from Figure 3The RMS statistics of the validation sets for the three machine learning algorithms in the three regions show that KNN outperforms XGBoost and MLPNN in regression accuracy across all three regions. Specifically, FengWu and... The fusion accuracy of FengWu-ZWD is slightly higher than that of Pangu-Weather, with RMS values ​​of 13.24, 16.87, and 17.56 mm in the three regions, respectively. This is mainly due to the inherent accuracy advantage of FengWu-ZWD. Because this study has low feature dimensionality and a small sample size for epoch-wise modeling, XGBoost and MLPNN cannot fully realize their potential advantages. KNN, however, can utilize local sample similarity to characterize the spatial variation of ZWD residuals. Furthermore, KNN has short training and prediction times and high computational efficiency. Therefore, KNN was ultimately selected as the regression algorithm for subsequent real-time wide-area ZWD fusion modeling.

[0025] Step 5: Following Step 4, KNN is ultimately selected as the fusion algorithm. Since GNSS reference stations are typically discretely distributed, their spatial density varies significantly across different regions. If only interpolation methods between stations are used to establish a wide-area tropospheric model, large spatial extrapolation errors are likely to occur in sparsely populated areas or complex terrain conditions. Furthermore, traditional interpolation methods often fail to adequately reflect the complex spatial nonlinear variations of tropospheric wet delay. To address these issues, this invention utilizes a spatially continuous background field provided by an AI meteorological model as the basic framework, and combines it with ZWD information retrieved from GNSS reference stations. A residual correction model is established using machine learning methods to achieve adaptive correction of the AI ​​background field. Based on this, this study introduces a grid enhancement scheme (including Steps 5 and 6) to extend tropospheric information from discrete stations to a continuous spatial field. Step 5 generates a spatially continuous enhanced ZWD grid framework; Step 6 maps the grid ZWD to any GNSS user location through vertical extrapolation and horizontal interpolation. These two steps form a complete real-time wide-area tropospheric grid service system.

[0026] Specifically, this invention selects a 1°×1° spatial resolution grid defined by the ERA5 surface layer height as the modeling framework, and sets the latitude, longitude, elevation, and corresponding coordinates of each grid point. In the fusion model constructed in step 4 of the input fusion process, the ZWD correction amount of the predicted grid points is ( ), and then match it with the corresponding Background fields are superimposed to generate a spatially continuous gridded ZWD field. Based on the different AI meteorological background fields used, this invention constructs two enhancement model frameworks: The first uses the ZWD field predicted by FengWu as the background field, and performs residual modeling and correction based on machine learning algorithms combined with ZWD information obtained through real-time PPP-AR inversion from GNSS reference stations; the enhanced tropospheric grid model is denoted as Trop_GF. The second uses the ZWD field obtained through inversion from the Pangu-Weather meteorological model for residual correction; the enhanced tropospheric grid model is denoted as Trop_GP. ; Step 6: Based on the enhanced ZWD grid framework constructed in Step 5, obtain the ZWD at the user's location. To make the grid ZWD generated in Step 5 applicable to GNSS users at different altitudes and spatial locations, this invention further maps the grid ZWD to the user station location using a ZWD transformation model and an inverse distance weighted interpolation method. Specifically, first, the four nearest neighboring grid points around the user station are selected, and the elevation scaling factor provided by the IGPZWD model is used (…). The ZWD (Zero-Wave Dimension) at the grid points is vertically extrapolated outward to the user station height. This process takes the user's geodetic location, day of year (DOY), and hour of day (HOD) as input, and its mathematical expression is as follows: ; ; In the formula, , and ZWD No. Annual average of the elevation scaling factor, annual amplitude, and semi-annual amplitude coefficient. and These represent the grid heights respectively. and user station height The ZWD at the user's location is then obtained by horizontal interpolation using the inverse distance weighted (IDW) method. ; In the formula, ZWD at the user site Indicates the first ZWD of each grid point at the user's height The normalized weights corresponding to the grid points, and These are the Earth's radius and distance weighting indices, respectively. The spherical angular distance between a user station and a grid point is defined as follows: ; in, and These represent the latitude and longitude of the user station and the grid point, respectively.

[0027] Furthermore, to verify the accuracy advantages and feasibility of the model framework, this study compared and analyzed two enhanced model frameworks (Trop_GF / Trop_GP) with a ZWD model built using only single Pangu-Weather, FengWu, and GNSS data. Pangu-Weather and FengWu models obtained the ZWD at grid points by numerically integrating the meteorological parameters predicted by their respective AI meteorological models. Since GNSS reference stations only provide ZWD information for discrete stations and cannot directly obtain tropospheric information at the grid scale, it is necessary to first obtain the elevation scaling factor corresponding to each reference station through spatial interpolation based on the IGPZWD model. Subsequently, the station ZWD, combined with its elevation scaling factor, was extrapolated to the ERA5 grid point height, and inverse distance weighting was used to fuse the ZWD of reference stations within a 500 km radius around each grid point, ultimately generating a grid-scale ZWD field. The grid ZWD model built solely based on GNSS observations is denoted as Trop_G. After obtaining the grid ZWD, the subsequent process for obtaining the user station ZWD for the three models is consistent with the processing method of the enhancement models Trop_GP and Trop_GF in step 6. After obtaining the user station ZWD, the enhancement effect of Trop_GF on real-time PPP is evaluated in both static and pseudo-dynamic modes.

[0028] The effects of this invention can be illustrated by the following experiments: 1. Experimental Environment The research area for the verification experiments of this invention is North America, Europe, and Australia. This experiment predicted tropospheric wet delay information for February 1-15, 2024 (winter) and July 1-15, 2024 (summer). To evaluate the performance of Trop_GP / Trop_GF for real-time wide-area tropospheric delay services, external compliance verification was conducted based on post-processed ZWD from GNSS stations independent of the modeling set, comparing and analyzing its accuracy differences with Pangu-Weather, FengWu, and Trop_G. Secondly, the effect of Trop_GF ZWD on enhancing PPP-AR positioning performance was tested.

[0029] 2. Experimental Results Post-processed ZWD products from 32 GNSS user stations in North America, 25 in Europe, and 19 in Australia were used as reference values. Bias and root mean square error (RMS) were used as validation metrics to compare and analyze the model accuracy. Table 3 presents the Bias and RMS statistics for the five models in the three regions. Trop_GF and Trop_GP are two AI-weather-driven tropospheric grid enhancement models proposed in this invention, respectively using FengWu and Pangu-Weather... The background field was constructed using Trop_GF and Trop_GP. The RMS values ​​of both Trop_GF and Trop_GP were significantly lower than those of FengWu and Pangu-Weather across all regions, resulting in an overall accuracy improvement of 36%–45%. Trop_GF performed best, with average RMS values ​​of 11.80, 16.12, and 18.13 mm in North America, Europe, and Australia, respectively. Compared to Trop_G, Trop_GF improved the RMS by approximately 13%, 26%, and 14% in the three regions, respectively. This demonstrates that the scheme using only single GNSS data is limited by the density of site-specific ZWD and cannot fully quantify the complex spatial variations of ZWD. Furthermore, the global average RMS values ​​of Trop_GF and Trop_GP were 15.35 and 16.16 mm, respectively, representing improvements of 40.3% and 41.9% compared to FengWu and Pangu-Weather's 25.71 and 27.83 mm. Bias statistics show that although the mean bias of Trop_G is lower than that of the two AI meteorological models in the three regions, this advantage mainly comes from the statistical cancellation of positive and negative biases between stations, rather than the spatial consistency of the models. Due to the sparsity of the GNSS station network, regional errors are inevitably introduced during extrapolation and interpolation, resulting in larger fluctuations in the bias of individual stations. In contrast, by fusing the spatiotemporally continuous background field provided by the AI ​​meteorological model with GNSS observations, Trop_GF and Trop_GP can adaptively correct the offset in the background field, effectively eliminating systematic errors and thus maintaining a smaller and more uniform bias in each region. FengWu and Pangu-Weather show relatively significant positive and negative biases in the European and Australian regions, respectively. These results indicate that AI-weather ZWD, as a reliable initial value provided by the background field, and the effective correction of spatial nonlinear residuals by the KNN algorithm, reduce random errors in tropospheric wet delay estimation, resulting in Trop_GF / GPm having better overall accuracy and stability.

[0030] High-precision tropospheric delay information helps improve the vertical positioning accuracy and convergence speed of real-time PPP. To verify the application value of the Trop_GF model in actual location services, this invention evaluates the enhancement effect of Trop_GF on real-time PPP under both static and pseudo-dynamic (station coordinate estimation is white noise) modes. GPS and Galileo observation data from three regional user stations were selected for winter and summer periods, and the UDUC PPP-AR strategy in Table 1 was used for calculation. Among them, Trop_GF enhanced PPP-AR uses Trop_GF ZWD information as a priori constraint, and ZHD is corrected by Saastamoinen and GPT3 models. Convergence is defined as the positioning error being less than 0.1 m for 10 consecutive epochs.

[0031] Figure 4 The convergence time in the U-direction and the convergence improvement of the Trop_GF-enhanced PPP-AR scheme compared to the standard PPP-AR are shown. In static models, the convergence times of Trop_GF PPP-AR in North America during winter and summer are 9.5 min and 10.5 min, respectively, which are 36.7% and 32.3% shorter than the 15 min and 15.5 min of the standard PPP-AR, respectively. Among them, the European dual-system PPP-AR has the shortest convergence time, which is 15.4% and 30% shorter than the standard scheme in winter and summer, respectively, because the Galileo system has higher observation quality in this region. Australia shows the opposite seasonality to the Northern Hemisphere, with a relatively longer convergence time in summer, but the improvement rate still reaches 25%. In dynamic mode, the overall convergence time is prolonged, but Trop_GFPPP-AR still significantly shortens the convergence time. In winter, the convergence time in North America is reduced from 37 min for standard PPP-AR to 26.5 min for Trop_GFPPP-AR, in Europe from 25.5 min to 22.5 min, and in Australia from 12 min to 10 min, with an improvement rate between 11.8% and 28.4%. The improvement rate in summer is slightly lower than in winter, at 19.7%, 16.7%, and 8.6%, respectively. In summary, the Trop_GF-enhanced PPP-AR scheme can effectively accelerate convergence in different regions and seasons, significantly improving the efficiency of PPP initialization. This verifies the universality and transferability of the proposed real-time wide-area tropospheric modeling framework based on AI-weather ZWD and fused with GNSS, which can be quickly extended to multiple regions and is of great significance for improving satellite-based positioning services and navigation performance in complex geographical and climatic environments.

Claims

1. An AI-weather-driven GNSS real-time wide-area tropospheric modeling method, characterized in that, Includes the following steps: [1] The AI-weather model was initialized based on ERA5 reanalysis data as the background field to predict the high-resolution three-dimensional meteorological parameter field at the target time; [2] A regular grid is obtained by numerical integration inversion of the meteorological parameters in step [1]. ; [3] Real-time estimation of reference stations using non-difference, non-combined PPP-AR. ; [4] Extract the corresponding spatial location of the reference station mentioned in step [3]. Calculate its relationship with residual Using machine learning algorithms to and Spatial nonlinear training and validation are performed on the residual sample set between them to generate a fusion model; [5] Input the latitude, longitude, and elevation information of the grid points provided by ERA5 surface layer, as well as the corresponding... The residual correction amount of the grid points is predicted by the residual mapping model in step [4]. and with Superimposed, generating a spatially continuous enhanced ZWD grid framework; [6] For any GNSS user location, the enhanced ZWD grid frame in step [5] is vertically corrected based on the IGPZWD elevation transformation model, and then the ZWD at the user location is obtained by inverse distance weighted interpolation and used for real-time PPP positioning constraints.

2. The AI-weather-driven GNSS real-time wide-area tropospheric modeling method according to claim 1, characterized in that: The AI-weather model described in step [1] includes the Pangu-Weather and FengWu models, and the AI ​​meteorological model is initialized with a background field back 5.25 days from the target time.

3. The AI-weather-driven GNSS real-time wide-area tropospheric modeling method according to claim 1, characterized in that: The formula for calculating the ZWD numerical integral in step [2] is as follows: ； ； ； In the formula, It is the height of the target point. It is the refractive index. and These are water vapor pressure and temperature, It refers to air pressure and the refractive index constant. , All basic data and model elevations have been converted to ellipsoidal heights using the EGM2008 model; When calculating the ZWD of a target point, the four nearest grid profiles around it must first be retrieved, and the height of the grid points is adjusted to match the target height. Then, the vapor pressure and wet refractive index profile are calculated, and the target height is treated as a separate layer. The air pressure and vapor pressure are obtained by weighted interpolation of variables from adjacent isobaric layers, while the temperature is estimated by linear extrapolation. ； ； ； In the formula, , , and These represent altitude, air pressure, water vapor pressure, and temperature, respectively, with subscripts. and Used to represent observations of the upper and lower layers. Indicates the target height. These are weighting coefficients; If the target height is lower than the bottom layer, the meteorological elements of the bottom two layers are used to extrapolate downwards to obtain the water vapor pressure and wet refractive index at the target height and perform integral calculation. After obtaining the ZWD of four grid points, the ZWD of the target position is obtained by inverse distance weighted interpolation. Finally, the obtained 6-hour resolution ZWD is upsampled to 5-minute time resolution through interpolation to meet the data matching requirements of GNSS fusion modeling and broadcasting grid ZWD products.

4. The AI-weather-driven GNSS real-time wide-area tropospheric modeling method according to claim 1, characterized in that: The GNSS non-differential, non-combined observation equation described in step [3] is expressed as follows: ； In the formula, It is the unit vector from the satellite to the receiver. It is the receiver coordinate correction vector. It's the speed of light. and These are the receiver and the satellite clock bias, and These represent the dry and wet quantities, respectively. and It is the corresponding mapping function. For the satellite elevation angle, The slant path ionospheric delay at the L1 frequency, Represents the ionospheric frequency coefficient. It is the carrier wavelength. It is phase ambiguity. and It is the pseudorange hardware delay between the receiver and the satellite. and These are uncalibrated phase delays (UPDs). and It consists of pseudorange and carrier phase observation noise; The horizontal gradient parameter is estimated using a random walk process to absorb variations in tropospheric delay caused by atmospheric asymmetry, and its expression is as follows: ； In the formula, and These represent the satellite's elevation angle and azimuth angle, respectively. and These represent the tropospheric horizontal gradients in the north-south and east-west directions, respectively. Within the PPP framework without ionospheric ambiguity (IF), the uncalibrated phase delay product (UPD) is estimated using IGS multi-system station observation data. In this process, the MW combination is used to calculate the UPD of the wide lane (WL), and then the UPD of the narrow lane (NL) is estimated using fixed integer WL ambiguities and IF ambiguities. Considering the aforementioned error terms, the reference station's zone delay (ZWD) is estimated in real-time using forward Kalman filtering based on CNES orbital, clock error products, and self-calculated UPD products. Finally, using the CODE final product and IF-UPD, the user station's ZWD is accurately estimated using batch least squares to verify the model algorithm's performance. The broadcast interval for reference station ZWD modeling and service products is set to 5 minutes to fully quantify its time-varying bias.

5. The AI-weather-driven GNSS real-time wide-area tropospheric modeling method according to claim 1, characterized in that: The machine learning algorithms described in step [4] include Extreme Gradient Boosting (XGBoost), Feedforward Neural Network (MLPNN), and K-Nearest Neighbor (KNN) algorithms, respectively using the latitude, longitude, and elevation of the GNSS reference station and the corresponding... Information as input features, and The residuals between As regression labels, each model is trained and validated, and the regression function mapping relationship is as follows: ； ； In the formula, A fusion regression model representing machine learning. The ZWD represents the inversion of Pangu-Weather and FengWu. During training, key hyperparameters are optimized using a grid search combined with cross-validation. In the ten-fold cross-validation, the reference station sample data is randomly divided into ten subsets, with each fold serving as the validation set. The remaining 90% of the stations are used to train the model. The root mean square error (RMS) is used as the evaluation metric for cross-validation to select the optimal combination of hyperparameters.

6. The AI-weather-driven GNSS real-time wide-area tropospheric modeling method according to claim 1, characterized in that: The grid described in step [5] is a 1°×1° resolution grid of ERA5 surface height. After step [4], KNN is finally selected as the fusion algorithm to combine the latitude, longitude, elevation and corresponding coordinates of each grid point. The ZWD correction is predicted in the input fusion model. Then match it with the corresponding Background fields are superimposed to generate a spatially continuous gridded ZWD field. ; ； Depending on the different AI meteorological background fields used, this invention constructs two enhanced model frameworks: using the ZWD field predicted by FengWu as the background field, and performing residual modeling and correction based on the ZWD information obtained by real-time inversion through PPP-AR using machine learning algorithms and GNSS reference stations. The enhanced tropospheric grid model is denoted as Trop_GF. The residuals of the ZWD field obtained by inversion from the Pangu-Weather meteorological model were corrected, and the enhanced tropospheric grid model was denoted as Trop_GP.

7. The AI-weather-driven GNSS real-time wide-area tropospheric modeling method according to claim 1, characterized in that: Step [6] describes the process of selecting the four nearest neighboring grid points for any GNSS user location and then using the elevation scaling factor provided by the IGPZWD model. The ZWD at the grid points is vertically extrapolated outward to the user station height. This process takes the user's geodetic location, annual day of year (DOY), and hourly HOD as input, and its mathematical expression is as follows: ； ； In the formula, , and ZWD No. Annual average of the elevation scaling factor, annual amplitude, and semi-annual amplitude coefficient. and These represent the grid heights respectively. and user station height ZWD at the location; Subsequently, the inverse distance weighted IDW method is used for horizontal interpolation to obtain the ZWD at the user's location: ； In the formula, ZWD at the user site Indicates the first ZWD of each grid point at the user's height The normalized weights corresponding to the grid points, and These are the Earth's radius and distance weighting indices, respectively. The spherical angular distance between a user station and a grid point is defined as follows: ； in, and These represent the latitude and longitude of the user station and the grid point, respectively.

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