Method for constructing space-based occultation atmospheric retrieval system fusing ground-based GNSS horizontal gradient

Abstract

The application provides a method for constructing an air-based occultation atmospheric inversion system fusing a ground-based GNSS horizontal gradient, which can construct a high-precision atmospheric horizontal gradient inversion model, establish an air-based occultation atmospheric inversion system fusing the horizontal gradient model, and eliminate the spherical symmetry assumption in air-based occultation low-layer atmospheric inversion. The method for constructing a high-precision low-layer atmospheric profile inversion system based on the fusion of the two is first proposed, so as to maximize the complementarity between them. Meanwhile, the measured air-based experimental data are used to complete the occultation atmospheric inversion based on the newly proposed method, and the results of the sounding balloon during the experiment are compared to complete the analysis and demonstration of the effectiveness of the inversion system and improvement, and finally a set of air-based occultation detection system fusing the ground-based GNSS atmospheric inversion result is constructed.

Description

Technical Field

[0001] This invention relates to the field of atmospheric inversion technology, specifically to a method for constructing an airborne occultation atmospheric inversion system that integrates ground-based GNSS horizontal gradients. Background Technology

[0002] With the development of ground-based GNSS technology and the continuous development and improvement of new-generation GNSS systems, including my country's BeiDou, the spatial distribution of multi-system ground-based GNSS observations has become more uniform, providing abundant observational information for studying atmospheric anisotropy. As my country's independently developed satellite navigation system, the BeiDou Navigation Satellite System has extremely broad application prospects in atmospheric sounding. In particular, the geosynchronous Earth Orbit (GEO) satellites of the BeiDou system, because their signal paths through the atmosphere remain unchanged, allow for direct estimation of the slant path delay as a parameter, without the need for zenith delay and mapping functions. Theoretically, the slant path delay directly solved using GEO has higher accuracy than the slant path atmospheric delay obtained by the mapping method, and can be used to analyze and verify the accuracy of gradient parameters solved by other GNSS satellites (non-GEO). Simultaneously, the development of multi-system GNSS has also led to a significant increase in the number of occultation events while maintaining the same number of occultation receivers, greatly improving the accuracy and spatiotemporal resolution of atmospheric refractive index retrieval from occultation.

[0003] However, current research on ground-based GNSS atmospheric inversion focuses on obtaining high-precision precipitable water vapor (PWV), while in-depth research on horizontal gradient models under different terrain and weather conditions is lacking. Furthermore, there is a lack of systematic theoretical research and experimental verification on how to integrate external atmospheric gradient information to improve the inversion accuracy of space-based occultation in the lower atmosphere below 10 km, which has abundant water vapor content. Summary of the Invention

[0004] In view of this, the present invention provides a method for constructing an airborne occultation atmospheric inversion system that integrates ground-based GNSS horizontal gradients. This method can construct a high-precision atmospheric horizontal gradient inversion model and establish an airborne occultation atmospheric inversion system that can integrate the horizontal gradient model, thereby eliminating the spherical symmetry assumption in the inversion of the lower atmosphere of airborne occultations.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for constructing a spaceborne occultation atmospheric inversion system that integrates ground-based GNSS horizontal gradients includes the following steps:

[0007] The horizontal gradient characteristics of atmospheric horizontal gradient are modeled and analyzed based on ERA5 atmospheric reanalysis data to obtain the spatiotemporal variation characteristics of atmospheric horizontal gradient; the atmospheric horizontal gradient parameters of ground-based GNSS are estimated; and atmospheric horizontal gradient grid modeling is performed based on the Kriging interpolation method.

[0008] The total atmospheric curvature angle, collision parameters, and occultation tangency point are obtained using traditional occultation inversion methods, while the atmospheric refractive index is determined using the same methods. For ERA5, the atmospheric curvature angle and refractive index are solved using ray tracing. The atmospheric curvature angle and refractive index determined using the spherical symmetry assumption are compared and analyzed to investigate the influence of the spherical symmetry assumption on the occultation inversion error. The optimal spherical occultation inversion method is determined. After calculating the total curvature angle, the atmospheric refractive index is solved using the Abel transform. The accuracy of the Abel inverse transform atmospheric inversion method, which incorporates prior gradient information, is verified using simulated new space-based occultation events. If the accuracy verification fails, the space-based occultation experiment is resimulated, incorporating new prior gradient information to seek the optimal spherical occultation inversion method that incorporates prior information. This process continues until the accuracy verification is successful, ultimately determining the optimal spherical occultation inversion method that incorporates prior information.

[0009] In the process of calculating the signal bending angle using GNSS phase and amplitude observations, the atmospheric refraction center is first corrected using an atmospheric gradient model so that the local atmosphere roughly conforms to the balloon symmetry assumption on both sides of the line connecting the corrected atmospheric refraction center and the occultation tangent point. Thus, the total atmospheric bending angle, collision parameters, and occultation tangent point are obtained using the traditional occultation inversion method.

[0010] Specifically, by adding atmospheric horizontal gradient information to the atmospheric curvature angle integral formula, the inverse Abel transform formula containing this prior information is derived, resulting in the atmospheric refractive index calculation formula that incorporates prior gradient information.

[0011] The specific analysis method for modeling and analyzing the horizontal gradient characteristics based on ERA5 atmospheric reanalysis data is as follows: The ray-tracing method is used to solve for the oblique path atmospheric delay and the total zenith delay at different observation elevations and azimuths above the station using ERA5 data. The first-order gradient parameters are solved using least squares for the equations containing the gradient model, oblique path delay, and zenith delay. The accuracy of the first-order gradient model, which ignores higher-order gradient parameters, is analyzed. Based on this first-order gradient, a higher-order gradient parameter model is introduced, and the accuracy of the first-order gradient model and the higher-order model are compared, along with their applicability under different weather and terrain conditions. The determined optimal atmospheric horizontal gradient model is used to analyze the spatiotemporal variation characteristics of the atmospheric horizontal gradient under different terrain and weather conditions.

[0012] The specific process for estimating the atmospheric horizontal gradient parameters of ground-based GNSS is as follows: Modify the atmospheric gradient model in the existing GNSS data processing software; based on the regional CORS network, estimate the atmospheric gradient parameters over the stations in the region using the selected optimal time resolution; study the method for directly calculating the atmospheric slant path delay of BeiDou GEO satellites, compare the results with those calculated by ERA5, and analyze the advantages of GEO satellite observation characteristics in inverting slant path delay; use atmospheric reanalysis data to obtain regional atmospheric gradient parameters as reference values, comprehensively analyze the accuracy differences of atmospheric gradient parameters calculated by different data processing strategies, and determine the optimal method for inverting the atmospheric horizontal gradient based on ground-based GNSS.

[0013] The process involves establishing a grid model of gradient parameters using atmospheric gradient parameter values ​​retrieved from GNSS inversion. The accuracy of the grid model is verified using atmospheric gradient values ​​retrieved from GNSS stations not involved in the modeling. If the accuracy verification fails, a suitable data processing strategy is selected, and the ground-based GNSS atmospheric horizontal gradient parameters are repeatedly estimated to determine the optimal method for ground-based GNSS inversion of the atmospheric horizontal gradient. This process continues until the accuracy verification is successful, ultimately determining the optimal method for GNSS horizontal gradient inversion and modeling.

[0014] Beneficial effects:

[0015] 1. This invention proposes a method for constructing an airborne GNSS occultation atmospheric inversion system by studying high-precision atmospheric horizontal gradient value inversion and modeling, and integrating a ground-based GNSS horizontal gradient model. It fully considers the advantages and limitations of both ground-based and airborne GNSS atmospheric inversion in certain aspects. Utilizing the observational characteristics of ground-based and airborne GNSS technologies, it proposes for the first time a method for constructing a high-precision lower atmospheric profile inversion system based on the fusion of these two technologies, maximizing their complementarity. Furthermore, it proposes using measured airborne experimental data to complete the occultation atmospheric inversion based on the newly proposed method, comparing it with the results from radiosonde balloons during the experiment, and conducting analysis, demonstration, and improvement of the effectiveness of the inversion system. Finally, it constructs an airborne occultation detection system that integrates ground-based GNSS atmospheric inversion results. The atmospheric data obtained by fusing airborne and ground-based GNSS occultation data has significant scientific research and application value in local atmospheric sounding, meteorological services, and the study of ocean / atmosphere coupling processes.

[0016] 2. This invention utilizes ground-based GNSS observations at different azimuth and elevation angles to solve for the total atmospheric delay along the oblique path, which contains information on the three-dimensional anisotropic distribution of the atmosphere. This includes the Zenith Tropospheric Delay (ZTD), the mapping function, and a function model expressing the atmospheric horizontal gradient parameters. A high-precision atmospheric horizontal gradient inversion model is constructed, and a space-based occultation atmospheric inversion system that can integrate this horizontal gradient model is established. This eliminates the spherical symmetry assumption in the lower atmosphere inversion of space-based occultations. At the same time, the effectiveness of the new method can be comprehensively analyzed and verified using experimental data from space-based GNSS occultation observations.

[0017] 3. In order to construct an airborne GNSS atmospheric inversion method that integrates atmospheric horizontal gradient information, this invention first analyzes the spatiotemporal variation characteristics of atmospheric horizontal gradient, providing basic data and theoretical reference for the study of atmospheric gradient models based on ground-based GNSS; at the same time, it analyzes the influence of the balloon symmetry assumption on the bending angle and atmospheric refractive index error of airborne GNSS inversion, laying the foundation for the theoretical system of constructing an airborne GNSS occultation atmospheric inversion system that integrates ground-based GNSS horizontal gradient.

[0018] 4. The atmospheric gradient parameters retrieved from GNSS are only the gradient parameters above the station. To facilitate the subsequent occultation atmospheric inversion by fusing gradient models, it is necessary to establish a grid model of gradient parameters using the parameter values ​​of these stations. This invention uses atmospheric gradient values ​​retrieved from GNSS stations that are not involved in the modeling to verify the accuracy of the grid model. If the accuracy verification fails, a suitable data processing strategy is selected again to meet the accuracy requirements. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] Occultation technology based on low-Earth orbit (LEO) satellite navigation and positioning systems (GNSS) offers advantages such as high vertical resolution, high precision, global coverage, and all-weather observation. The atmospheric parameters obtained from GNSS occultation play a crucial role in weather forecasting and climate change research, holding significant value for scientific research and the national economy. However, due to the characteristics of LEO occultation observations and limitations in the number of constellations, satellite-based GNSS occultation cannot achieve effective continuous monitoring of specific regions. Furthermore, the signal gain of satellite-based GNSS occultation antennas is limited by satellite payload weight constraints, making them prone to signal loss in the lower troposphere, where water vapor content is abundant. In contrast, airborne GNSS occultation atmospheric sounding technology, using airships, high-altitude balloons, or aircraft as carriers, can effectively overcome the difficulties of controlling the ground position and the relatively poor quality of lower atmospheric observations inherent in traditional satellite-based occultation, thus enabling continuous monitoring of atmospheric profiles in specific regions. Compared to satellite platforms, airborne observation platforms have relatively relaxed weight restrictions on payloads, allowing for the design and customization of high-gain occultation antennas to achieve continuous and stable observations of the lower troposphere. Therefore, atmospheric data acquired by space-based GNSS occultation has significant scientific and applied value in local atmospheric sounding, meteorological services, and the study of ocean / atmosphere coupling processes.

[0022] Traditional space-based occultation atmospheric inversion algorithms are based on the assumption that Earth's atmospheric distribution satisfies local spherical symmetry. This means that under Earth's gravitational field and rotation, assuming hydrostatics hold, the atmospheric refractive index gradient only varies radially and remains unchanged horizontally. While the spherical symmetry assumption is reasonable over long periods and large-scale statistical results, in regions with complex topography, such as land-sea boundaries, mountainous terrain, or areas with cloud cover and fronts or inversions, the horizontal non-uniformity of atmospheric refractive index is still significant. Ignoring this non-uniformity will introduce substantial errors into the obtained curvature angle and atmospheric refractive index. Without considering the presence of water vapor, the balloon symmetry assumption introduces approximately 2% error into space-based occultation inversion results. In the lower atmosphere with abundant water vapor, the error introduced by the spherical symmetry assumption increases significantly and varies considerably, with the maximum error near the ground potentially reaching around 10%. Ignoring the horizontal atmospheric gradient not only affects the calculated curvature angle but also leads to significant calculation deviations in the occultation tangent point and collision parameters of space-based GNSS occultation events. In space-based GNSS occultation detection, the spherical symmetry assumption has a greater impact on the inversion results, mainly because: (1) In a typical space-based GNSS occultation event, the occultation tangent point only takes about 30 seconds to cross the 0-10km altitude range, during which the horizontal drift of the occultation tangent point is only about 0-60km; however, for space-based atmospheric occultation detection, the occultation tangent point takes about several minutes to tens of minutes to cross the 0-10km altitude range in a single occultation event, and the horizontal drift of the occultation tangent point can reach 200-500km throughout the process. Therefore, space-based occultation event inversion needs to assume spherical symmetry in a larger spatial range, thus making the existence of the horizontal gradient more significant and difficult to ignore in terms of inversion accuracy. (2) The space-based occultation inversion algorithm is developed on the basis of space-based occultation, and introduces some bending angle concepts compared to space-based occultation. The partial curvature angle refers to the signal curvature caused by atmospheric refraction below the altitude of the airborne occultation receiver. It is determined by simultaneously observing rays at negative and positive elevation angles and based on the difference in curvature angles between the two rays. This process still relies on the assumption of no horizontal atmospheric gradient. These two factors make airborne occultation inversion more dependent on the balloon symmetry assumption and more sensitive to the influence of atmospheric horizontal gradients. Regardless of whether geometrical optics inversion, canonical transformation, or backpropagation methods are used, it is impossible to avoid errors caused by the discrepancy between the spherical symmetry assumption and actual atmospheric conditions.

[0023] This disclosure proposes a theoretical method for constructing an airborne occultation atmospheric inversion system that incorporates ground-based GNSS horizontal gradients, such as... Figure 1As shown, this paper first analyzes the impact of atmospheric horizontal gradient on the error of inversion of the lower atmosphere below 10km based on simulation experimental data. Simultaneously, it establishes an optimal atmospheric horizontal gradient model and data calculation strategy based on multi-system GNSS. A gridded modeling method for atmospheric gradient inversion based on multiple ground stations is determined. A priori gradient model is used to improve the calculation accuracy of bending angle, collision parameters, and occultation tangency points. A universal Abel transform algorithm that fuses priori atmospheric gradient models is proposed. Experimental data is used to verify and optimize the method. Details are as follows:

[0024] (1) Based on the horizontal gradient characteristics of ERA5 atmospheric reanalysis data, modeling and analysis were performed to obtain the spatiotemporal variation characteristics of the atmospheric horizontal gradient. Specifically:

[0025] Assuming spherical symmetry and neglecting the influence of atmospheric horizontal gradients, the neutral atmospheric delay of the oblique path of signal propagation can be expressed as the product of the total tropospheric delay in the zenith direction and the mapping function. The influence of the atmospheric horizontal gradient can be described by adding a first-order gradient model to this. This model, based on the total zenith tropospheric delay, mapping function, and first-order gradient parameters, is widely used in ground-based GNSS data processing. This study investigates the spatiotemporal variation characteristics and modeling methods of atmospheric horizontal gradients using ERA5 atmospheric reanalysis data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). The specific analysis methods are as follows: (a) The ray-tracing method is used to solve for the oblique path atmospheric delay and the total zenith delay of the station at different observation elevation angles and azimuth angles over ERA5. The first-order gradient parameters are solved using least squares for the equations containing the gradient model, oblique path delay, and zenith delay; (b) The accuracy of the first-order gradient model that ignores higher-order gradient parameters is analyzed. Based on the first-order gradient, a higher-order gradient parameter model that can more accurately describe the non-uniform distribution of the atmosphere is considered. The accuracy of commonly used first-order gradient models and higher-order models and their applicability under different weather and terrain conditions are compared; (c) The determined optimal atmospheric horizontal gradient model is used to analyze the spatiotemporal variation characteristics of the atmospheric horizontal gradient under different terrain and weather conditions, providing a theoretical reference for subsequent GNSS gradient parameter inversion and modeling.

[0026] (2) Estimate the ground-based GNSS atmospheric horizontal gradient parameters. Details are as follows:

[0027] Based on the conclusions above, the atmospheric gradient model in existing GNSS data processing software is modified. Using a regional CORS network and the selected optimal time resolution, atmospheric gradient parameters over stations in the region are estimated. A method for directly calculating the atmospheric slant path delay of BeiDou GEO satellites is studied, and the results are compared with those calculated by ERA5 to analyze the advantages of GEO satellite observation characteristics in inverting slant path delay. Regional atmospheric gradient parameters obtained from atmospheric reanalysis data are used as reference values. A comprehensive analysis is conducted on the accuracy differences of atmospheric gradient parameters calculated by different data processing strategies (differential network solution and precise point positioning) to determine the optimal method for inverting atmospheric horizontal gradients based on ground-based GNSS.

[0028] (3) Atmospheric horizontal gradient grid modeling based on the Kriging interpolation method. Details are as follows:

[0029] The atmospheric gradient parameters retrieved from GNSS are only the gradient parameters above the station. To facilitate the subsequent occultation atmospheric inversion of the gradient model, it is necessary to use the parameter values ​​of these stations to establish a grid model of the gradient parameters. The accuracy of the grid model is verified by using the atmospheric gradient values ​​retrieved from GNSS stations that are not involved in the modeling. If the accuracy verification fails, a suitable data processing strategy is selected again, and the method of determining the optimal ground-based GNSS inversion atmospheric horizontal gradient in step (2) is repeated until the accuracy verification is qualified. Finally, the optimal method for GNSS horizontal gradient inversion and modeling is determined.

[0030] (4) Simulation analysis of atmospheric inversion for space-based occultation fusion with prior atmospheric gradient models. This is conducted using ERA5 to simulate space-based occultation events, following these steps:

[0031] (a) In the process of calculating the signal curvature angle using GNSS phase and amplitude observations, the atmospheric refraction center is first corrected using an atmospheric gradient model. This ensures that the local atmosphere roughly conforms to the balloon symmetry assumption on both sides of the line connecting the corrected atmospheric refraction center and the occultation tangent point. The total atmospheric curvature angle, collision parameters, and occultation tangent point are then obtained using traditional occultation inversion methods. Simultaneously, the atmospheric refractive index is determined using traditional methods. (b) The atmospheric curvature angle and refractive index are solved using ray tracing for ERA5. A comparative analysis is conducted on the atmospheric curvature angle and refractive index determined using the spherical symmetry assumption. The influence of the spherical symmetry assumption on the occultation inversion error is studied, providing a theoretical basis for determining the optimal occultation atmospheric inversion method. (c) After a thorough study of the influence of the spherical symmetry assumption on the occultation inversion error, the optimal spherical occultation inversion method needs to be determined. After calculating the total curvature angle, the atmospheric refractive index needs to be solved using the Abel transform. The traditional Abel transform assumes no gradient in the horizontal direction of the refractive index, thus simplifying the integral formula for the curvature angle to include only the gradient information of the atmospheric refractive index in the radial direction. By adding atmospheric horizontal gradient information to the atmospheric curvature angle integral formula, the Abel inverse transform formula incorporating this prior information is derived, thus obtaining the atmospheric refractive index calculation formula that incorporates prior gradient information. (d) The accuracy of the Abel inverse transform atmospheric inversion method incorporating prior gradient information is verified using simulated new space-based occultation events. If the accuracy verification fails, the space-based occultation experiment is resimulated, and the new prior gradient information is incorporated to seek the optimal spherical occultation inversion method that incorporates prior information until the accuracy verification is successful. Finally, the optimal spherical occultation inversion method incorporating prior information is determined.

[0032] Experimental verification and algorithm optimization were also conducted for the method of this invention. Details are as follows:

[0033] Using measured airborne experimental data, occultation atmospheric inversion based on the newly proposed method was completed. The results were compared with those from weather balloons during the experiment to analyze and verify the effectiveness and accuracy of the method. If the accuracy verification failed, the above steps were repeated until the accuracy verification was successful, ultimately constructing an optimal airborne and spaceborne GNSS occultation detection method that integrates ground-based GNSS atmospheric inversion results.

[0034] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a spaceborne occultation atmospheric inversion system that integrates ground-based GNSS horizontal gradients, characterized in that, Includes the following steps: The horizontal gradient characteristics of atmospheric horizontal gradient are modeled and analyzed based on ERA5 atmospheric reanalysis data to obtain the spatiotemporal variation characteristics of atmospheric horizontal gradient; the atmospheric horizontal gradient parameters of ground-based GNSS are estimated; and atmospheric horizontal gradient grid modeling is performed based on the Kriging interpolation method. The total atmospheric curvature angle, collision parameters, and occultation tangency point are obtained using occultation inversion methods, and the atmospheric refractive index is determined simultaneously. For ERA5, the atmospheric curvature angle and refractive index are solved using ray tracing. The atmospheric curvature angle and refractive index determined using the spherical symmetry assumption are compared and analyzed to investigate the influence of the spherical symmetry assumption on the occultation inversion error. The optimal spherical occultation inversion method is determined. After calculating the total curvature angle, the atmospheric refractive index is solved using the Abel transform. The accuracy of the Abel inverse transform atmospheric inversion method, which incorporates prior gradient information, is verified using simulated new space-based occultation events. If the accuracy verification fails, the space-based occultation experiment is resimulated, incorporating new prior gradient information to seek the optimal spherical occultation inversion method that incorporates prior information. This process continues until the accuracy verification is successful, and finally, the optimal spherical occultation inversion method that incorporates prior information is determined.

2. The method of claim 1, wherein, In the process of calculating the signal bending angle using GNSS phase and amplitude observations, the atmospheric refraction center is first corrected using an atmospheric gradient model so that the local atmosphere roughly conforms to the balloon symmetry assumption on both sides of the line connecting the corrected atmospheric refraction center and the occultation tangent point. Then, the total atmospheric bending angle, collision parameters, and occultation tangent point are obtained using the occultation inversion method.

3. The method of claim 2, wherein, By adding atmospheric horizontal gradient information to the integral formula for atmospheric curvature angle, the inverse Abel transform formula containing this prior information is derived, resulting in the atmospheric refractive index calculation formula that incorporates prior gradient information.

4. The method according to any one of claims 1 to 3, characterized in that, The specific analysis method for modeling and analyzing the horizontal gradient characteristics based on ERA5 atmospheric reanalysis data is as follows: The ray-tracing method is used to solve for the oblique path atmospheric delay and the total zenith delay at different observation elevations and azimuths above the station using ERA5 data. The first-order gradient parameters are solved using least squares for the equations containing the gradient model, oblique path delay, and zenith delay. The accuracy of the first-order gradient model, which ignores higher-order gradient parameters, is analyzed. A higher-order gradient parameter model is introduced based on this first-order gradient, and the accuracy of the first-order gradient model and the higher-order model are compared, along with their applicability under different weather and topographic conditions. The determined optimal atmospheric horizontal gradient model is then used to analyze the spatiotemporal variation characteristics of the atmospheric horizontal gradient under different topographic and weather conditions.

5. The method of claim 4, wherein, The specific process for estimating the atmospheric horizontal gradient parameters of ground-based GNSS is as follows: Modify the atmospheric gradient model in the existing GNSS data processing software; based on the regional CORS network, estimate the atmospheric gradient parameters over the stations in the region using the selected optimal time resolution; study the method for directly calculating the atmospheric slant path delay of BeiDou GEO satellites, compare the results with those calculated by ERA5, and analyze the advantages of GEO satellite observation characteristics in inverting slant path delay; use atmospheric reanalysis data to obtain regional atmospheric gradient parameters as reference values, comprehensively analyze the accuracy differences of atmospheric gradient parameters calculated by different data processing strategies, and determine the optimal method for inverting the atmospheric horizontal gradient based on ground-based GNSS.

6. The method of claim 5, wherein, A grid model of gradient parameters is established using atmospheric gradient parameter values ​​retrieved from GNSS. The accuracy of the grid model is verified using atmospheric gradient values ​​retrieved from GNSS stations not involved in the modeling. If the accuracy verification fails, a suitable data processing strategy is selected again, and the ground-based GNSS atmospheric horizontal gradient parameters are repeatedly estimated to determine the optimal method for ground-based GNSS inversion of the atmospheric horizontal gradient. This process continues until the accuracy verification is successful, and finally, the optimal method for GNSS horizontal gradient inversion and modeling is determined.

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