A method for enhanced real-time tropospheric delay modeling for global positioning system

Abstract

This invention belongs to the interdisciplinary field of space geodesy, satellite navigation and positioning technology and atmospheric science, and discloses a real-time tropospheric delay modeling method to enhance the global forecast system. The specific steps are as follows: First, the zenith hydrostatic delay and zenith wet delay of the surface GFS forecast are obtained, and the regional grid difference time series is constructed with the fusion result of ERA5 data and GNSS tropospheric delay products as the reference benchmark; Second, the above differences are fitted to form the GFS enhancement core model; At the same time, a tropospheric delay correction model from grid height to target station height is constructed based on ERA5 layered atmospheric data, and the model coefficients are modeled in time series, so as to finally realize the refined tropospheric delay output at different heights. The advantages of this invention are: (1) high accuracy of real-time tropospheric model; (2) robust performance of real-time application without relying on GNSS network; (3) easy to expand and deploy; (4) strong real-time performance, which can be seamlessly integrated into precision positioning application.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of space geodesy, satellite navigation and positioning technology and atmospheric science, and specifically relates to a real-time tropospheric delay modeling method to enhance global forecasting systems. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) are the cornerstone of modern high-precision positioning services, supporting a wide range of applications from surveying and mapping to transportation and scientific research. However, to achieve real-time precision positioning at the decimeter or even centimeter level (such as RTK and PPP), a key obstacle must be overcome: the tropospheric delay caused by satellite signals passing through the Earth's neutral atmosphere.

[0003] The total tropospheric delay can reach 2 to 2.5 meters, and even exceed 20 meters at low satellite elevation angles, its impact being significant. This delay mainly consists of two parts: zenith static delay (ZHD) and zenith wet delay (ZWD). The former, caused by dry, stable gases, accounts for about 90% of the total delay and has relatively stable characteristics, which can be effectively corrected by accurate surface pressure models. The latter, caused by highly unevenly distributed water vapor, although accounting for only 10% (approximately 0–40 cm), varies drastically and is difficult to predict, representing the main source of error and the core challenge in tropospheric modeling. Even more challenging is that the troposphere exhibits non-dispersive characteristics towards GNSS signals, making it impossible to directly eliminate through multi-frequency observations as with ionospheric delay. Therefore, developing a tropospheric model capable of providing high-precision, high-resolution correction information in real time has become a technical bottleneck for wide-area precise positioning services.

[0004] Existing tropospheric correction models are mainly divided into three categories, each with its own shortcomings. The first category consists of empirical models built based on historical climate data (such as UNB3m, EGNOS, GPT / GPT2 / GPT2w / GPT3, and GZTD). Their advantage is simple calculation and no need for external data, but they only reflect the average climate state and are difficult to capture real-time weather changes. The ZTD (Zenith Tropospheric Delay) accuracy is typically around 4–5 centimeters, which is insufficient for high-precision applications. The second category comprises models utilizing measured parameters from ground meteorological stations (such as Saastamoinen and Hopfield). Although local meteorological information is incorporated, the correlation between surface parameters and the total atmospheric water vapor content is weak, and the deployment and maintenance costs of high-quality sensors are high, resulting in limited accuracy improvement and difficulties in widespread adoption. Thirdly, it is a regional model based on GNSS networks, which provides ZTD correction through inversion and interpolation using a dense network of reference stations. In densely populated areas (where the distance between stations is less than 60 kilometers), it can achieve high accuracy of 1–3 centimeters. However, in oceans, deserts, mountains, and areas with weak infrastructure, the sparse network of stations leads to a weakening of spatial correlation and a sharp drop in interpolation accuracy, which seriously restricts the wide-area coverage of high-precision services.

[0005] To overcome these limitations, the research community has turned to numerical weather models (NWM), such as ECMWF's ERA5 and NCEP's GFS. NWM provides global coverage, spatiotemporal continuity, and multi-layered meteorological parameters from the ground to the upper atmosphere. Based on this, the ZTD at any location can be obtained by integrating the refractive index, without being limited by ground observation conditions, which has significant advantages.

[0006] However, directly applying NWM still faces two key challenges: First, there is a conflict between timeliness and accuracy. High-precision reanalysis products (such as ERA5) have a release delay of 2–5 days, making them unsuitable for real-time applications; real-time forecast products (such as GFS) compromise on accuracy, and errors accumulate as forecast lead time increases. Second, there is insufficient spatial resolution. Grids typically spanning tens of kilometers are insufficient to depict the fine tropospheric structure caused by complex terrain and small- to medium-scale weather systems.

[0007] A currently effective approach is to integrate GNSS and NWM: using high-precision GNSS ZTD to correct or assimilate NWM biases, thereby simultaneously improving accuracy and timeliness. This integrated method has shown significant potential in improving PPP convergence and positioning accuracy, especially in areas with complex terrain. Nevertheless, generating accurate and real-time tropospheric products over vast areas with sparse GNSS observations remains a core technical challenge that urgently needs to be overcome, directly impacting whether high-precision positioning services can achieve seamless global coverage. Summary of the Invention

[0008] The purpose of this invention is to overcome the aforementioned problems in existing technologies, namely, the insufficient accuracy and poor timeliness of existing real-time tropospheric models in sparse GNSS regions, making it difficult to support wide-area high-precision real-time positioning services. To this end, this invention proposes a real-time tropospheric delay modeling method for the Enhanced Global Forecast System (GFS), constructing a GFS-based augmented tropospheric delay model (Augmented GFS, AGFS). The core idea of ​​this method is to employ an innovative two-step strategy: First, deeply fuse high-precision but non-real-time GNSS tropospheric products and ERA5 reanalysis data to form a high-precision background field; second, based on the high-precision background field, construct an improved GFS tropospheric delay model for real-time but slightly less accurate GFS forecast products. This results in a novel tropospheric delay model that achieves accuracy levels close to ERA5 while retaining the real-time capabilities of GFS.

[0009] To achieve the above-mentioned objectives, the technical solution adopted by this invention is summarized as follows:

[0010] A method for real-time tropospheric delay modeling to enhance global forecasting systems includes:

[0011] Constructing a high-precision background field (GERA5). This step aims to refine and enhance the globally leading-edge ERA5 reanalysis data using dense, high-precision GNSS ZTD post-processing data, generating a spatiotemporally homogeneous, highly accurate tropospheric delay "reference" background field, named GNSS-enhanced ERA5 (GERA5). Specifically, firstly, gridded ZHD and ZWD are inverted from multi-layer isobaric surface data of ERA5 and GFS; then, ZTD (or ZHD / ZWD) products from GNSS stations are normalized to the ERA5 grid surface through elevation correction; finally, a data fusion algorithm (such as the Kriegman weighting method) is used to weightedly fuse GNSS observation information within a certain radius of influence around each ERA5 grid point with the initial ERA5 values, thereby effectively correcting the systematic bias of ERA5. Through this step, a reference dataset that is continuous in time and space and whose accuracy is "anchored" by a large number of high-precision GNSS observations is obtained.

[0012] Among them, ZHD (Zenith Hydrostatic Delay) is the zenith hydrostatic delay, caused by dry, stable gases, accounting for about 90% of the total delay. Its characteristics are relatively stable and can be effectively corrected by an accurate surface pressure model. ZWD (Zenith Wet Delay) is the zenith wet delay, caused by water vapor with extremely uneven spatial and temporal distribution. Although it only accounts for 10% (about 0–40 cm), it varies drastically and is difficult to predict. It is the main source of error and the core difficulty in tropospheric modeling. ZTD (Zenith Total Delay) is the total zenith tropospheric delay that takes into account both ZHD and ZWD.

[0013] Construct a real-time augmentation model. This step aims to uncover and model the systematic differences between real-time GFS forecast data and the high-precision GERA5 background field, and to utilize this difference model to augment GFS forecast results in real time. Specifically,

[0014] First, the ZHD and ZWD difference sequences of long-term (e.g., several years) GFS forecast data and synchronized GERA5 data are calculated at each grid point.

[0015] Next, an in-depth spectral analysis (such as Fourier transform) is performed on the differential time series to identify the stable periodic signals contained therein, such as annual, semi-annual, and daily periodic variations.

[0016] Then, a mathematical model (such as a trigonometric function combination model) that can capture these periodic features is used to fit the difference sequence, thereby establishing a parameterized difference correction model for each grid point.

[0017] In the real-time application phase, it is only necessary to obtain the latest GFS forecast data and calculate the current correction amount using the established difference correction model. This correction amount is then superimposed onto the ZHD and ZWD forecasts of GFS to obtain the final, high-precision real-time tropospheric delay – AGFS.

[0018] Furthermore, to enable the model to serve users at any elevation, this invention also includes a step of vertical stratified modeling of tropospheric delay. This step utilizes ERA5 multilayer data analysis to study the variation of ZHD and ZWD with elevation, establishing an exponential decay model and its decay coefficient model that takes into account geographical location and seasonal variations. In real-time applications, this vertical correction model can be used to accurately interpolate the delay values ​​of the AGFS grid surface to the user's elevation.

[0019] The technical solution of this invention, through the above-mentioned interconnected steps, cleverly incorporates the high-precision characteristics of ERA5 and GNSS into real-time GFS forecasts, ultimately generating a novel tropospheric delay model that approximates post-processed products in terms of accuracy and fully meets the real-time application requirements in terms of timeliness, effectively solving the problem of high-precision tropospheric correction in sparse GNSS regions.

[0020] Furthermore, the detailed steps of the technical solution of the present invention are broken down as follows:

[0021] Step S1: Acquisition and preprocessing of multi-source data;

[0022] Step S11: Acquisition of multi-source heterogeneous data. Collect all the data required to build the model, mainly including:

[0023] ERA5 reanalysis data: acquired from ECMWF, covering several years (e.g., 2020-2023), with a spatial resolution of 0.25° × 0.25° and a temporal resolution of 1 hour. The data consists of multi-level isobaric products, including geopotential, temperature, specific humidity, and air pressure on each isobar.

[0024] GFS forecast data: acquired from NCEP, with a time range synchronized with ERA5. A 6-hour forecast product (f006) suitable for near real-time applications was selected, with a spatial resolution of 0.25° × 0.25° and a temporal resolution of 6 hours. The data consists of multi-level barometric products, including geopotential, temperature, relative humidity, and air pressure.

[0025] GNSS tropospheric products: acquired from high-precision GNSS data processing centers (such as the GAGE / PBO network), with a time range synchronized with NWM data and a time resolution of 5 minutes or higher. The data content is a station ZTD (or separate ZHD / ZWD) time series obtained through precise post-processing.

[0026] Topographic elevation data: Acquire a Digital Elevation Model (DEM) and resample it for matching with an NWM grid. For example, VMF grid elevation data provided by the Vienna University of Technology (TU Vienna) is used for unified elevation datum transformation and vertical correction. (The resampling and NWM grid matching method is existing technology.)

[0027] Step S12: Tropospheric Delay Inversion. Physical inversion is performed on the original ERA5 and GFS multi-level pressure data to calculate the gridded ZHD and ZWD. This process includes:

[0028] The vertical air column above each grid point is numerically integrated using the atmospheric refractive index integral formula (such as formulas (1)-(4)).

[0029]

[0030] in, and These are the hydrostatic refractive index and the wetted refractive index, respectively, and the calculation formulas are as follows:

[0031]

[0032] constant =77.689K / hpa, =71.2952K / hpa, =375463K 2 / hpa, dry air constant =287.053 J / (kg K), moist air constant =461.495 J / (kg K).

[0033] T is temperature (K), e is vapor pressure (hPa), and P is atmospheric pressure (hPa). It refers to altitude (m). Both ERA5 and GFS data include temperature, air pressure, and altitude data, but they differ in the parameters reflecting humidity; ERA5 uses specific humidity (m). GFS data uses relative humidity ( ), correspondingly, water vapor pressure ( For the calculation of ERA5, formula (5) is used, while formulas (6) and (7) are used for GFS. See below:

[0034]

[0035] RH represents relative humidity (%). q is the saturated vapor pressure (hpa) and q is the specific humidity (kg / kg). Formula (5) calculates the vapor pressure from the specific humidity, Formula (6) calculates the vapor pressure using relative humidity and saturated vapor pressure, and Formula (7) calculates the saturated vapor pressure using the Goff-Gratch formula.

[0036] The zenith static delay above the integration limit (top of the numerical weather model NWM, approximately 1 hPa) is calculated (as shown in formulas (8)-(9)).

[0037]

[0038] The zenith static delay (m) refers to the zenith static delay above the top layer of the NWM. It is the height of the top layer of the NWM. It is the air pressure value (hpa) at the top layer. It is latitude (rad).

[0039] The geopotential height provided by NWM is converted into geodetic height (ellipsoidal height) using gravity formulas, thus achieving unification with the GNSS elevation system (e.g., formulas (10)-(13)).

[0040]

[0041] Normal gravity value =9.80665 m / s 2 C is the potential (m) 2 / s 2 ), It is a high potential (m). It is the positive height (m), gravity By substituting equation (12) into formula (11), since both sides of the equation have ,therefore The final orthogonal height needs to be calculated through iterative calculations. Plus geoid difference Obtain the height of the ellipsoid (m). Geoid difference Obtained using Earth Gravity Model 2008 (EGM2008).

[0042] The ZHD and ZWD obtained from the NWM products (ERA5 and GFS) are then interpolated onto the terrain elevation grid height using cubic splines.

[0043] Step S2: High-precision background field construction;

[0044] Step S21: Spatiotemporal matching and fusion of ERA5 data and GNSS data to improve the accuracy of ERA5 tropospheric delay at the height of the terrain elevation grid. The ERA5 ZHD / ZWD grid data obtained in step S12 is spatiotemporally matched with the tropospheric products of the GNSS station. The Cressman weighting method (as shown in formulas (14)-(18)) is used as the data fusion algorithm.

[0045] Given the ERA5 tropospheric delay grid and the GNSS tropospheric delay at the GNSS station, for each ERA5 grid point (hereinafter referred to as the grid point, the grid point height in this step is consistent with the terrain elevation grid height), search for its surrounding preset influence radius. All GNSS stations within a 60km radius are weighted based on the horizontal distance between the GNSS stations and the grid points. The weighted average of the differences between the GNSS tropospheric delay and the ERA5 tropospheric delay is used as the total correction for that grid point. Specifically:

[0046] First, calculate the distance from GNSS stations within the influence radius to the grid points. ), and calculate the Cressman weights. .in, These are the planar coordinates of the GNSS station. These are the planar coordinates of the grid points.

[0047]

[0048] Next, the correction for tropospheric delay at the grid points is calculated as shown in Equation (16).

[0049]

[0050] in, It is the correction amount (m) for the tropospheric delay of the GNSS station at the grid point. It is the GNSS tropospheric delay (m) at the grid point height. It is the tropospheric delay (m) of ERA5 interpolated to the GNSS station's plane position and grid point height.

[0051] in, The calculation method is as follows: The ERA5 tropospheric delay at the GNSS station and the ERA5 tropospheric delay at the GNSS station's horizontal position and grid height are obtained through ERA5 tropospheric delay interpolation of multiple isobaric surfaces. The ratio of the former to the latter forms a conversion factor. Then, the tropospheric delay at the GNSS station is converted to the tropospheric delay at the GNSS station's horizontal position and grid height using the conversion factor. .

[0052] Then, the corrections for tropospheric delay at grid points by GNSS stations within the influence radius are summed to obtain the total correction, where... It is the total correction amount (m). It is the number of GNSS stations within the influence radius. It is the ratio of the tropospheric delay variance of GNSS to that of ERA5.

[0053]

[0054] Finally, the ERA5 tropospheric delay at the grid is corrected to obtain the corrected tropospheric delay, where... This refers to the tropospheric delay (m) corrected for the corresponding grid points. The tropospheric delay (m) is the ERA5 surface grid.

[0055]

[0056] The final high-precision background field is an ERA5 tropospheric delay corrected at the height of the terrain elevation grid, with a planar resolution. .

[0057] Step S22: Background Field Accuracy Assessment. The accuracy of the generated GERA5 background field data is assessed using an independent GNSS verification station that did not participate in the fusion process. Statistical indicators such as RMSE and Bias are calculated to quantitatively analyze the improvement in ZHD and ZWD accuracy of GERA5 compared to the original ERA5.

[0058] Step S3: Construction and enhancement of real-time tropospheric delay model;

[0059] Step S31: Differential sequence modeling. At each grid point, calculate the difference between GFS ZHD / ZWD and GERA5 ZHD / ZWD over a long training period (e.g., 2020-2022) to form a differential time series.

[0060] Step S32: Periodic Feature Extraction and Model Construction. Fourier spectrum analysis was performed on the difference time series of each grid point to identify significant daily, semi-annual, and annual periodic signals. Based on this, a trigonometric function model composed of a constant term, an annual periodic term (cos / sin), and a semi-annual periodic term (cos / sin) was constructed (as shown in formulas (19) and (20)), and the model coefficients were obtained by fitting using the least squares method. These coefficients were stored and constituted the core correction parameter library of AGFS.

[0061]

[0062] in, The difference between GFS and GERA5 is (m). What hour of the day is it? For years, , These are model coefficients.

[0063] In practical application, first substitute formula (20) into formula (19), and use the least squares method to solve the model coefficients.

[0064] Step S33: Real-time augmentation model construction. In the real-time application stage, the latest GFS forecast grid data is obtained. Using the difference correction model coefficients calibrated for each grid point in step S32 and the current time (year-day, day-hour), the real-time ZHD and ZWD correction amounts are calculated and added to the original GFS value. According to formula (19), AGFS is obtained (as in formulas (21) and (22)).

[0065]

[0066] here and These are the ZHD and ZWD of the AGFS model. and It's GFS's ZHD and ZWD. and It is the correction amount for GFS ZHD and ZWD, and the correction amount is calculated according to formula (19) and formula (20).

[0067] Step S34: Tropospheric delay vertical stratification modeling. The exponential decay law of ZHD and ZWD with elevation variation is analyzed using ERA5 multilayer data (e.g., formulas (23), (24)). Furthermore, the exponential decay coefficient is... The time-varying characteristics of the product itself (especially the annual and semi-annual cycles) are used for spectral analysis and modeling (as shown in formula (25)) to obtain a refined vertical correction model that varies with geographical location and time.

[0068]

[0069] here and It is any height The hydrostatic delay and wet delay (m) are (m), while and It is the height of the map grid. Hydrostatic delay (m) and wet delay (m). and It is the height attenuation coefficient (m) of ZHD and ZWD -1 ). Among them, in formula (25) These are the model coefficients, estimated using the least squares method.

[0070] Step S4: Model Validation and Application.

[0071] Step S41: Model Performance Comparison and Validation. Using independent validation period data (e.g., 2023) and validation stations, conduct a comprehensive and systematic evaluation of the accuracy of the final product of the AGFS model. Using the tropospheric delay from GNSS post-processing as the "true value," compare the AGFS forecast results with those of other real-time models (e.g., AGFS, GFS, VMF3-FC).

[0072] Step S42: Model Application and Promotion. Package the fully validated AGFS model and height correction algorithm into standardized products or services, and broadcast them to a wide range of GNSS users through standard interfaces (such as the NTRIP protocol). This will provide reliable and accurate tropospheric error correction services for high-precision applications such as real-time precise point positioning (PPP / PPP-RTK) and network RTK, demonstrating its unique application value, especially in areas with insufficient GNSS reference station coverage.

[0073] Beneficial effects

[0074] Compared with existing technologies, the real-time tropospheric delay modeling method for enhancing the Global Forecasting System (GFS) proposed in this invention has the following significant advantages and beneficial effects:

[0075] 1. Significantly Improved Forecast Accuracy and Obvious Technological Advantages. This invention, through an innovative two-step fusion strategy, successfully incorporates the accuracy advantages of high-precision post-processing data (such as GNSS observations and ERA5 reanalysis data) into real-time forecast models (such as GFS). This method results in significantly improved forecast accuracy for the final tropospheric delay product, whether in the relatively stable static delay (ZHD) or the rapidly changing and model-challenged wet delay (ZWD). This invention provides more reliable external tropospheric correction constraints for high-precision real-time positioning applications.

[0076] 2. Strong spatiotemporal adaptability and excellent model robustness. This invention, through long-term, refined modeling of the differences between the real-time forecast model and the high-precision background field, can effectively identify and compensate for the systematic biases in the former that vary with seasons and geographical locations. Therefore, the model of this invention maintains highly stable forecast performance throughout the year, with error fluctuations far less than existing technologies. Especially in seasons with the most intense water vapor activity and the greatest tropospheric delay changes (such as summer), the accuracy advantage of this model is particularly prominent, demonstrating its powerful ability to capture and correct complex spatiotemporal variations in water vapor. Spatially, whether in flat areas or high-altitude, complex mountainous regions, this model provides consistent high-precision corrections, with a more uniform geographical distribution of errors, less affected by local effects, and significantly enhanced robustness.

[0077] 3. This invention perfectly balances high precision and high real-time performance, solving a core pain point in the industry. Existing technologies have long faced the dilemma of high-precision products (such as ERA5) not being real-time enough, and real-time products (such as GFS) lacking sufficient precision. This invention cleverly circumvents this problem through an "offline modeling, online calibration" framework. Most of the computationally intensive work of the model (such as ERA5 construction and differential model parameter fitting) is completed offline. The real-time application stage only requires simple model calls and calculations, with minimal computational load, fully meeting the application requirements of real-time and near-real-time (within minutes of latency). This allows the invention to elevate the precision of tropospheric products to a new level without sacrificing real-time performance.

[0078] 4. The model design is comprehensive and widely applicable. This invention not only provides a high-precision tropospheric delay product for two-dimensional grid surfaces, but also establishes a refined vertical stratification correction model that takes into account seasonal variations. This model can accurately reduce the grid delay value to the user's actual altitude based on the user-provided three-dimensional coordinates, effectively solving the impact of altitude differences on tropospheric delay. This design enables the AGFS model to serve various users from the ground to high altitudes, including ground vehicles, handheld devices, drones, and aircraft, all of which can obtain accurate tropospheric corrections, greatly expanding the model's application scenarios and value.

[0079] 5. Effectively solves the positioning problem in sparse GNSS areas, with significant socio-economic benefits. The core advantage of this invention lies in its non-reliance on the density of real-time GNSS station networks. Once the difference correction model is established, high-precision forecasts can be performed over a vast area (theoretically globally) solely using real-time GFS data. This provides a revolutionary technical approach for providing high-precision real-time positioning services in areas with insufficient GNSS reference station coverage, such as oceans, deserts, and mountains. It will greatly promote the development of key industries such as autonomous driving, precision agriculture, geological disaster monitoring, and weather forecasting in these areas, yielding immeasurable social and economic benefits.

[0080] In summary, this invention, through its unique two-step fusion modeling concept and refined model building process, has achieved breakthrough progress in multiple dimensions such as accuracy, stability, real-time performance, and applicability of tropospheric delay real-time modeling. It effectively overcomes the inherent defects of traditional technologies and removes a key technical obstacle for the realization and popularization of wide-area high-precision real-time GNSS positioning services. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the overall technical process for constructing the two-step AGFS model proposed in this invention;

[0082] Figure 2 The above is a density scatter plot comparing the AGFS model, GFS model, VMF3-FC model and the measured tropospheric delay by GNSS in the embodiments of the present invention ((a) AGFS (b) VMF3-FC (c) GFS). Detailed Implementation

[0083] This invention provides a real-time tropospheric delay modeling method for enhancing the Global Forecasting System (GFS). Its core lies in a two-step process that fuses multi-source data to generate a tropospheric delay model with both high accuracy and real-time performance. The implementation process of this invention is described in detail below using a specific preferred embodiment.

[0084] Example

[0085] A method for real-time tropospheric delay modeling to enhance global forecasting systems, such as Figure 1 The specific steps are as follows:

[0086] Step S1: Multi-source data acquisition and preprocessing

[0087] S11: Acquisition of Multi-Source Heterogeneous Data

[0088] This embodiment selects a portion of the North American continent (latitude 30°N to 50°N, longitude 125°W to 75°W) as the study area. This region has diverse topography and climate, making it an ideal area for testing model performance.

[0089] ERA5 Data: Obtain 37 standard isobaric surface products with an ERA5 hourly resolution and 0.25° resolution from January 1, 2020 to December 31, 2023, published by ECMWF.

[0090] GFS data: Obtain GFS products released by NCEP at the same time, 0.25° resolution, and 6-hour forecast lead time (f006), 4 times a day (00, 06, 12, 18 UTC).

[0091] GNSS data: We acquired ZTD post-processed products from 1,539 continuously operating reference stations (CORS) of the US GAGE / PBO network at a 5-minute sampling rate during the same period. Data from 1,385 stations (2020-2022) was used for model training, and data from the remaining 154 stations (2023) was used for independent validation.

[0092] Terrain data: Obtain a 0.25° resolution digital elevation model that matches the NWM grid.

[0093] Comparison data: The VMF3-FC forecast product with a resolution of 1° for 2023, released by TU Vienna, was obtained and compared with the advanced models in the industry.

[0094] S12: Tropospheric Delayed Inversion:

[0095] For the acquired ERA5 and GFS multilayer data, numerical integration is performed along the zenith direction at each grid point to calculate ZHD and ZWD.

[0096] Integrating is performed using the Saastamoinen model principle and the atmospheric refractive index formulas (formulas (1)-(4)).

[0097] For the specific humidity of ERA5, the water vapor pressure is calculated using formula (5). For the relative humidity of GFS, the saturated water vapor pressure is calculated using the Goff-Gratch formula (formula (7)), and then the water vapor pressure is obtained using formula (6).

[0098] The residual ZHD of the atmosphere above 1 hPa was calculated using formula (8).

[0099] The geopotential height of NWM is converted to the ellipsoidal height consistent with that of GNSS using formulas (10)-(12).

[0100] Step S2: Construction of High-Precision Background Field (GERA5)

[0101] This step uses data from 2020 to 2022.

[0102] S21: Spatiotemporal matching and fusion of ERA5 and GNSS data:

[0103] For each 0.25°×0.25° ERA5 grid point in the study area, at each time step, search for all GNSS training stations within a 60km radius around it.

[0104] The ZHD / ZWD of the GNSS station are reduced to the elevation of the ERA5 grid points using a vertical correction model.

[0105] The Kriegman weighting method (formulas (14)-(18)) was adopted, with the influence radius set to 60km and the error variance ratio set to 0.3. The weighted average of the difference between the GNSS observation and the initial value of ERA5 was used to obtain the correction amount of the grid point.

[0106] Add the correction amount to the original ERA5 value to obtain the GERA5 product.

[0107] S22: Background Field Accuracy Assessment

[0108] Both the original ERA5 and GFS had RMSE values ​​ranging from several millimeters to tens of millimeters for ZHD / ZWD, with the error increasing significantly in summer. After this processing step, the ZHD RMSE of GERA5 decreased from 5.22 mm to 3.05 mm, and the ZWD RMSE decreased from 11.63 mm to 9.93 mm, showing a significant improvement in accuracy and proving the effectiveness of GERA5 as a high-precision background field.

[0109] Step S3: Construction and Enhancement of Real-Time Tropospheric Delay Model

[0110] This step also uses data from 2020 to 2022 for model training.

[0111] S31: Differential Sequence Modeling

[0112] At each grid point, the difference between GFS ZHD / ZWD and GERA5 ZHD / ZWD is calculated to form a three-year difference time series.

[0113] S32: Periodic Feature Extraction and Model Building

[0114] Fourier transform of the difference sequences revealed that the differences between ZHD and ZWD both exhibited obvious annual and semi-annual periodic signals.

[0115] Based on this, the trigonometric function combination model of formulas (19) and (20) is used to perform least squares fitting on the difference sequence. Formula (20) describes the change of the model principal coefficient with the annual and semi-annual cycles of the annual day, while formula (19) further introduces the daily cycle. Through fitting, 15 parameters of the ZHD and ZWD difference models at each grid point are obtained.

[0116] S33: Real-time Augmentation Model Building

[0117] In the real-time application stage, the latest GFS forecast grid data is obtained. Using the difference correction model coefficients calibrated for each grid point in step S32 and the current time (year-day, day-hour), the real-time ZHD and ZWD correction amounts are calculated and added to the original GFS value (formulas (21) and (22)) to obtain AGFS.

[0118] S34: Tropospheric Delayed Vertical Layering Modeling:

[0119] Using ERA5 multi-layer data, the ZHD and ZWD of different height layers were calculated, and their exponential decay law with elevation was analyzed (formulas (23) and (24)). The decay coefficient was obtained. .

[0120] right Spectral analysis of the time series revealed ZWD The coefficients exhibit distinct annual and semi-annual cycles, ZHD's The coefficient has an annual cycle.

[0121] Using the trigonometric function model of formula (25) to Modeling coefficients.

[0122] Step S4: Model Validation and Application

[0123] This step was performed using data from 2023 and 154 independent verification sites.

[0124] S41: Model Performance Comparison and Validation

[0125] To analyze model performance, tropospheric delays from 154 GNSS stations uniformly distributed within the experimental area were used as ground truth values ​​to evaluate the accuracy of three models: AGFS, GFS, and VMF3-FC. Figure 2The density scatter plots are shown, including (a) AGFS, (b) VMF3-FC, and (c) GFS. It can be seen that the AGFS model has the highest agreement between its ZHD and ZWD predictions and the true GNSS values, with data points most concentrated near the 1:1 line, and a smaller root mean square error (RMSE). Specifically, the AGFS model has a ZHD RMSE of 3.12 mm and a ZWD RMSE of 12.03 mm, significantly outperforming GFS (5.33 mm, 13.56 mm) and VMF3-FC (4.82 mm, 14.61 mm).

[0126] In summary, this embodiment successfully constructed a tropospheric delay enhancement model AGFS based on GFS. During the experimental phase, independent verification using GNSS ZTD throughout the year fully demonstrated that this invention has certain advantages over existing mainstream real-time models in terms of accuracy, spatiotemporal stability, and robustness, and can provide strong technical support for wide-area, all-weather high-precision GNSS real-time positioning applications.

[0127] The above description is merely a description of preferred embodiments of this application and is not intended to limit the scope of this application in any way. Any changes or modifications made by those skilled in the art based on the above-disclosed technical content should be considered as equivalent and valid embodiments and fall within the scope of protection of the technical solution of this application.

Claims

1. A method of enhanced real-time tropospheric delay modeling for global positioning system, characterized in that, include: Constructing a high-precision background field: First, gridded ZHD and ZWD are inverted from multi-layer isobaric surface data of numerical weather models ERA5 and GFS; then, ZTD or ZHD / ZWD products from GNSS stations are normalized to the ERA5 grid surface through elevation correction; finally, a data fusion algorithm is used to weightedly fuse GNSS observation information within the influence radius around each ERA5 grid point with the initial ERA5 values, thereby effectively correcting the systematic bias of ERA5. Constructing a real-time augmentation model: First, calculate the ZHD and ZWD difference time series at each grid point between the long-term GFS forecast data and the synchronized GNSS-enhanced ERA5 (GERA5) data. Next, an in-depth spectral analysis was conducted on the differential time series to identify the stable periodic signals contained therein, including annual, semi-annual, and daily periodic variations. Then, a mathematical model capable of capturing these periodic features is used to fit the difference sequence, thereby establishing a parameterized difference correction model for each grid point; In the real-time application phase, the latest GFS forecast data is acquired, and the current correction amount is calculated using the established difference correction model. This correction amount is then superimposed onto the ZHD and ZWD forecasts of the GFS to obtain the final, high-precision real-time tropospheric delay. Tropospheric delay vertical stratification modeling: Using ERA5 multi-layer data analysis, the variation of ZHD and ZWD with elevation is analyzed, and an exponential decay model and its decay coefficient model that take into account geographical location and seasonal variation are established; in real-time applications, this model is used to accurately interpolate the delay value of the AGFS grid surface to the user's height.

2. The method of claim 1, wherein the method is used to enhance real-time tropospheric delay modeling for global prediction systems. The processing steps are as follows: Step S1: Acquisition and preprocessing of multi-source data; Step S2: High-precision background field construction; Step S3: Construction and enhancement of real-time tropospheric delay model; Step S4: Model Validation and Application.

3. The method of claim 2, wherein the method further comprises: Step S1 is as follows: Step S11: Acquisition of multi-source heterogeneous data; Collect all the data needed to build the model, including: ERA5 reanalysis data: acquired from ECMWF, covering several years, with a spatial resolution of 0.25°×0.25° and a temporal resolution of 1 hour; the data consists of multi-layer isobaric products, including geopotential, temperature, specific humidity and air pressure on each isobaric surface; GFS forecast data: acquired from NCEP, with a time range synchronized with ERA5; the 6-hour forecast product f006, suitable for near real-time applications, is selected, with a spatial resolution of 0.25°×0.25° and a time resolution of 6 hours; the data content is a multi-level barometric product, including geopotential, temperature, relative humidity, and air pressure; GNSS tropospheric products: acquired from a high-precision GNSS data processing center, with a time range synchronized with NWM data and a time resolution of 5 minutes or higher; the data content is a station ZTD or a separated ZHD / ZWD time series obtained through precise post-processing. Topographic elevation data: Acquire digital elevation models and resample them for matching with NWM grids; Step S12: Tropospheric delayed inversion; Physical inversion was performed on the original ERA5 and GFS multi-level pressure data to calculate the gridded ZHD and ZWD; this process includes: Using the atmospheric refractive index integral formula, such as formulas (1)-(4), the vertical air column above each grid point is numerically integrated. wherein and are the fluid-static and wet refractive indices, respectively, and are calculated as follows: constant =77.689K / hpa, =71.2952K / hpa, =375463K 2 / hpa, dry air constant =287.053J / (kg K), moist air constant =461.495J / (kg K); T is temperature (K), e is vapor pressure (hPa), and P is atmospheric pressure (hPa). This refers to altitude (m); both ERA5 and GFS data include temperature, air pressure, and altitude data, but they differ in the parameters reflecting humidity. ERA5 uses specific humidity. GFS data uses relative humidity ( ), correspondingly, water vapor pressure ( For the calculation of ERA5, formula (5) is used, while formulas (6) and (7) are used for GFS; as follows: where RH is the relative humidity (%), is the saturation vapor pressure (hpa), q is the specific humidity (kg / kg); The zenith static delay above the NWM top layer is calculated as shown in formulas (8)-(9); The zenith static delay (m) refers to the zenith static delay above the top layer of the NWM. It is the height of the top layer of NWM. It is the air pressure value (hpa) at the top layer. It is latitude (rad); The geopotential height provided by NWM is converted into geodetic height using gravity formulas to achieve unification with the GNSS elevation system, as shown in formulas (10)-(13). Normal gravity value =9.80665m / s 2 C represents potential. It is a high position, It is positive altitude, gravity Substitute equation (12) into equation (11). Through iterative calculations, the final orthogonal height is... Plus geoid difference Obtain the height of the ellipsoid Geoid Disparity Obtained using the Earth Gravity Model 2008; The ZHD and ZWD obtained from the NWM product are then interpolated onto the terrain elevation grid height using cubic splines.

4. The method of claim 2, wherein the method further comprises: Step S2 is as follows: Step S21: Spatiotemporal matching and fusion of ERA5 data and GNSS data to improve the accuracy of ERA5 tropospheric delay at the height of the terrain elevation grid; spatiotemporal matching of ERA5 ZHD / ZWD grid data with tropospheric products from GNSS stations; using the Kriegman weighting method, as shown in formulas (14)-(18), as the data fusion algorithm: The ERA5 tropospheric delay grid and GNSS tropospheric delays at GNSS sites are known, for each ERA5 grid point, hereinafter grid point, all GNSS sites within its pre-set influence radius are searched The weight is calculated according to the horizontal distance between the GNSS site and the grid point The difference between the GNSS tropospheric delay and the ERA5 tropospheric delay is weighted averaged as the total correction for the grid point; Specifically as follows: First, the distances from the GNSS stations within the influence radius range to the grid points are calculated and the Cressman weights are calculated ; wherein is the planar coordinate of the GNSS station, is the planar coordinate of the grid point; Next, the correction amount for the tropospheric delay at the grid point is calculated as shown in formula (16); wherein, is the correction of the tropospheric delay at the grid point by the GNSS station, is the GNSS tropospheric delay at the grid point height, is the ERA5 tropospheric delay interpolated by planar interpolation to the tropospheric delay at the grid point height at the planar position of the GNSS station; wherein, The calculation method is as follows: the ERA5 tropospheric delay at the GNSS site and the ERA5 tropospheric delay at the grid height of the GNSS site plane position are obtained by interpolating the ERA5 tropospheric delay of multiple isobaric surfaces, and the conversion coefficient is formed by the ratio of the former and the latter. Then the GNSS site tropospheric delay is converted to the GNSS site plane position, grid height tropospheric delay through the conversion coefficient, that is, ; The correction amount of the GNSS station in the influence radius to the tropospheric delay at the grid point is summed up again to obtain the total correction amount, wherein is the total correction amount, is the number of GNSS stations in the influence radius, is the ratio of the GNSS and ERA5 tropospheric delay variance; Finally, the grid-point ERA5 tropospheric delay is corrected to obtain the corrected tropospheric delay, where, denotes the corrected tropospheric delay at the grid point, is the tropospheric delay at the ERA5 ground grid point; The final obtained high-precision background field is the corrected ERA5 tropospheric delay on the terrain elevation grid height, with a horizontal resolution of 0.25° x 0.25° ; Step S22: Background field accuracy assessment; The accuracy of the generated GERA5 background field data was evaluated using an independent GNSS verification station that did not participate in the fusion process. By calculating RMSE and Bias statistics, the improvement of GERA5 in ZHD and ZWD accuracy compared to the original ERA5 was quantitatively analyzed.

5. The method of claim 2, wherein the method further comprises: Step S3 is as follows: Step S31: Differential sequence modeling; At each grid point, the difference between GFS ZHD / ZWD and GERA5 ZHD / ZWD during the long training period is calculated to form a difference time series. Step S32: Periodic feature extraction and model construction; Fourier spectrum analysis was performed on the difference time series of each grid point to identify significant daily, semi-annual and annual periodic signals. Based on this, a trigonometric function model composed of constant term, annual periodic term and semi-annual periodic term was constructed, as shown in formulas (19) and (20), and the model coefficients were obtained by fitting using the least squares method. These coefficients were stored to form the core correction parameter library of AGFS. wherein, is the difference of GFS and GERA5, is the hour of the day, is the cumulative day of the year, , is the model coefficient; Step S33: Real-time augmentation model construction; In the real-time application stage, the latest GFS forecast grid data is obtained, and the real-time ZHD and ZWD correction values ​​are calculated using the difference correction model coefficients calibrated for each grid point in step S32 and the current time. These values ​​are then added to the original GFS value. According to formula (19), AGFS is obtained, as shown in formulas (21) and (22). Here and are the ZHD and ZWD of the AGFS model, and are the ZHD and ZWD of the GFS, and are the corrections for the GFS ZHD and ZWD, which are calculated according to equation (19), equation (20); Step S34: Tropospheric delay vertical stratification modeling; The exponential decay law of ZHD and ZWD with height is analyzed using ERA5 multi-layer data, such as formulas (23) and (24); the exponential decay coefficients The time-varying characteristics of the model itself are analyzed and modeled by spectrum, such as formula (25), so as to obtain a refined vertical correction model that changes with geographic location and time; Here and are the hydrostatic delay and wet delay of arbitrary height , while and are the hydrostatic delay and wet delay of the height of the surface grid , and are the height attenuation coefficients of ZHD and ZWD; wherein in formula (25) is a model coefficient, which is estimated by least squares method.

6. The method of claim 2, wherein the real-time tropospheric delay modeling of global prediction system is enhanced, and Step S4 is as follows: Step S41: Model performance comparison and verification; Using independent validation period data and validation stations, a comprehensive and systematic evaluation of the accuracy of the final product of the AGFS model was conducted; using the tropospheric delay of GNSS post-processing as the "true value", the forecast results of AGFS were compared with those of AGFS, GFS, and VMF3-FC. Step S42: Model application and promotion; The fully validated AGFS model and altitude correction algorithm are packaged into standardized products or services and broadcast to GNSS users through standard interfaces, providing reliable and accurate tropospheric error correction services for real-time precise point positioning and network RTK high-precision applications.

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