Improved GNSS tropospheric delay real-time grid model construction method and system

Abstract

Disclosed are an improved GNSS tropospheric delay (ZTD) real-time grid model construction method and system. Firstly, a global tropospheric delay elevation normalization grid model is constructed using global ERA5 reanalysis data from a plurality of years. Then, elevation normalization and grid horizontal interpolation are performed on GNSS real-time ZTDs to obtain a global tropospheric delay real-time grid model. A user only needs to provide position and time information and use the global tropospheric delay elevation normalization grid model and the global tropospheric delay real-time grid model to be able to obtain a ZTD at a target point. According to the present invention, the high spatial resolution of a numerical weather model (NWM) and the high precision of the GNSS tropospheric product are comprehensively used, and an elevation normalization function form is optimized, so that the construction of a tropospheric delay real-time grid model covering a larger height range is achieved, and high-precision tropospheric delay correction information can be provided for GNSS real-time high-precision data processing, thereby improving the data processing performance.

Description

An improved method and system for constructing a real-time grid model of GNSS tropospheric delay Technical Field

[0001] The present invention belongs to the technical field of GNSS meteorology, and in particular relates to an improved method and system for constructing a real-time grid model of GNSS tropospheric delay. Background Art

[0002] When satellite-transmitted radio signals pass through the neutral atmosphere, atmospheric refraction causes changes in propagation speed and path, resulting in tropospheric delay (ZTD). This delay affects the accuracy of precise positioning. Furthermore, ZTD is strongly coupled with elevation, requiring a long time for the two parameters to converge in precise point positioning (PPP). This severely limits PPP's real-time applications. Therefore, in high-precision, real-time GNSS positioning applications, it is necessary to introduce an accurate prior for ZTD and then estimate the residual along with other parameters. Currently, the most commonly used prior ZTD is provided by traditional empirical models, which fall into three categories: The first type of model relies on measured meteorological parameters as external inputs and combines them with a ZTD correction model to obtain the ZTD, such as the Saastamoinen model; the second type of model embeds meteorological parameters, establishing them as position and time input models, such as the GPT series of models; and the third type of model eliminates meteorological parameters as intermediate variables and directly establishes ZTD as a computational model with position and time inputs, such as the GZTD series of models. However, empirical models have limited accuracy and struggle to capture the high short-term variability of ZTD. Therefore, introducing external data sources, such as epoch-by-epoch discrete tropospheric models like the VMF series built from numerical weather models (NWMs), can provide more accurate a priori ZTD. However, inconsistencies still exist between NWMs and GNSS.

[0003] In summary, integrating the high spatial resolution of NWM with the high precision of GNSS ZTD, which relies on measured atmospheric information, to construct a real-time grid model of tropospheric delay has the potential to effectively enhance real-time precise positioning. However, current research on integrating NWM and GNSS to construct tropospheric delay models has certain limitations. Most models focus only on users near the surface, failing to meet the growing demand for ZTD models applicable to a wide range of altitudes in areas such as drones. To achieve ZTD conversion between different altitudes, an elevation normalization model is crucial. The elevation normalization component of current tropospheric delay models, both in terms of data source and model format, focuses on near-surface users, failing to consider the applicability of models covering a wider altitude range. To address these issues, integrating the strengths of NWM and GNSS data to construct a real-time grid model of tropospheric delay covering a wider altitude range would help meet the urgent need for high-precision real-time positioning. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention provides an improved method for constructing a real-time grid model of GNSS tropospheric delay, comprising the following steps:

[0005] Step 1: Obtain global ERA5 layered meteorological data, divide it into grids, and calculate the ZTD information of each pressure layer at each grid point;

[0006] Step 2: Use the fourth-order exponential function to characterize the change of ZTD in the vertical direction, and obtain the parameters of the fourth-order exponential function at each grid point by least squares fitting;

[0007] Step 3: Use trigonometric functions to fit the time series of the fourth-order exponential function parameters at each global grid point obtained in step 2 to obtain the global tropospheric delay height normalized model coefficients;

[0008] Step 4: storing the global tropospheric delay elevation normalized model coefficients obtained in step 3 in a grid manner to obtain a global tropospheric delay elevation normalized grid model;

[0009] Step 5: Based on the global tropospheric delay elevation normalized grid model obtained in step 4, horizontal interpolation and elevation correction are performed on the GNSS real-time ZTD to obtain a global tropospheric delay real-time grid model;

[0010] Step 6: Based on the target point location provided by the user, obtain the global tropospheric delay elevation normalized grid model coefficients at the four nearest grid points around the target point;

[0011] Step 7: Based on the time information provided by the user, the ZTD of the four nearest grid points around the target point is normalized to the target height by combining the global tropospheric delay elevation normalization grid model coefficients and the global tropospheric delay real-time grid model;

[0012] Step 8: Use the inverse distance weighted interpolation method to horizontally interpolate the target height ZTD at the four nearest grid points around the target point to the target point position.

[0013] Furthermore, the ERA5 layered meteorological data in step 1 includes specific humidity, temperature, pressure, and geopotential height. These data are gridded, and the ZTD value of each pressure layer at the grid point is calculated by integration. The specific calculation formula is as follows:

[0014] Where Q is the specific humidity, T is the temperature, P is the air pressure, g is the acceleration due to gravity, ε is the gas constant ratio, and R d is the gas constant of dry air, R vis the gas constant of water vapor, and k1, k2, and k3 are constants.

[0015] Furthermore, in step 2, a fourth-order exponential function is used to characterize the vertical variation of ZTD, so as to normalize the ZTD at sea level to the target height. The expression is as follows:

[0016] Where ZTD h is the ZTD value at the target height h, ZTD0 represents the tropospheric delay value at sea level, and a1~a4 are the parameters of the fourth-order exponential function.

[0017] Based on the ZTD value and corresponding height of each pressure layer obtained in step 1, the parameters of the fourth-order exponential function at each grid point are obtained using the least squares method.

[0018] Furthermore, in step 3, the time series of the fourth-order exponential function parameters a1 to a4 are fitted in the form of a trigonometric function to obtain the tropospheric delay height normalization model as follows:

[0019] where doy represents the accumulated days per year, π represents the circumference of a circle, B0 represents the annual mean, (B1, B2) and (B3, B4) represent the coefficients of the annual and semi-annual tropospheric delay height normalization models, respectively.

[0020] To enhance the periodicity of the time series and improve computational efficiency, the five coefficients of parameter a4 are fixed with their mean.

[0021] Furthermore, in step 5, for each grid point, the nearest N GNSS stations are found, and the ZTD at the station height is normalized to the grid point height. The specific calculation method is as follows:

[0022] Where ZTD grid 、ZTD sta are the grid point heights h g , measuring station height h s where ZTD0 represents the tropospheric delay at sea level, and a1 to a4 are the parameters of the fourth-order exponential function.

[0023] Then, the ZTDs of N stations normalized to the grid height are horizontally interpolated to the grid points using the inverse distance weighted interpolation method. Finally, the ZTDs of all grid points are uniformly normalized to the sea level using formula (2) to obtain the real-time grid model of global tropospheric delay.

[0024] Moreover, in step 7, the global tropospheric delay height normalized grid model coefficient and the annual cumulative day provided by the user are first substituted into formula (3) to calculate the fourth-order exponential function parameters, and then the sea level heights ZTD at the four nearest grid points around the target point provided by the global tropospheric delay real-time grid model are normalized to the target height using formula (2).

[0025] The present invention also provides an improved GNSS tropospheric delay real-time grid model construction system, which is used to implement the improved GNSS tropospheric delay real-time grid model construction method as described above.

[0026] Furthermore, the system includes a processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the program instructions in the memory to execute the improved method for constructing a real-time grid model of GNSS tropospheric delay as described above.

[0027] Alternatively, it includes a readable storage medium having a computer program stored thereon, and when the computer program is executed, it implements the improved method for constructing a real-time grid model of GNSS tropospheric delay as described above.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] 1) The global tropospheric delay elevation normalization grid model established in the present invention uses a fourth-order exponential function in the vertical direction to characterize the variation of tropospheric delay with altitude, which improves the applicability of the elevation normalization model at different altitudes and can cover the altitude range of 0-15 km.

[0030] 2) The global tropospheric delay real-time grid model established by the present invention comprehensively considers the high spatial resolution of NWM and the high precision of GNSS, and integrates the advantages of both to provide high-precision prior tropospheric delay at global grid points, providing high-precision atmospheric enhancement for wide-area high-precision positioning users.

[0031] 3) The global tropospheric delay real-time grid model established by the present invention can obtain the tropospheric delay at any location. Compared with the currently commonly used traditional models, the tropospheric delay real-time grid model established by the present invention has higher accuracy and stronger real-time performance, and can be applied to different altitudes. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] FIG1 is a flow chart of a real-time tropospheric delay calculation method according to the present invention.

[0033] FIG2 is a flow chart of constructing a real-time grid model of tropospheric delay according to the present invention.

[0034] FIG3 shows the geographical distribution of product errors of different ZTD models according to an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The present invention provides an improved method and system for constructing a real-time grid model of GNSS tropospheric delay. The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0036] Example 1

[0037] As shown in FIG1 , an embodiment of the present invention provides an improved method for constructing a real-time grid model of GNSS tropospheric delay, comprising the following steps:

[0038] Step 1: Obtain the global ERA5 layered meteorological data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), divide it into a grid with a horizontal resolution of 1° × 1° (longitude × latitude), and calculate the ZTD information of each pressure layer at each grid point.

[0039] ERA5 layered meteorological data includes specific humidity, temperature, pressure, and geopotential height. It is divided into a grid with a horizontal resolution of 1°×1° (longitude×latitude). The ZTD value of each pressure layer at the grid point is calculated by integration. The specific calculation formula is as follows:

[0040] Where Q is the specific humidity; T is the temperature; P is the air pressure; g is the acceleration due to gravity; ε is the gas constant ratio, which is 0.622; R d is the gas constant of dry air, which is 287.058; R v is the gas constant of water vapor, which is 461.5; k1, k2, and k3 are constants, k1 = 0.7760 KPa -1 , k2=0.704KPa -1 , k3=0.03739×10 5 K 2 Pa -1 .

[0041] Step 2: Use the fourth-order exponential function to characterize the change of ZTD in the vertical direction, and obtain the parameters of the fourth-order exponential function at each grid point by least squares fitting.

[0042] The fourth-order exponential function is used to characterize the change of ZTD in the vertical direction, which is used to normalize the ZTD at sea level to the target height. Its expression is as follows:

[0043] Where ZTD h is the ZTD value at the target height h (horizontal height), ZTD0 represents the tropospheric delay value at sea level, and a1~a4 are the parameters of the fourth-order exponential function.

[0044] Based on the ZTD value and corresponding height of each pressure layer obtained in step 1, the parameters of the fourth-order exponential function at each grid point are obtained using the least squares method.

[0045] Step 3: Use trigonometric functions to fit the time series of the fourth-order exponential function parameters at each global grid point obtained in step 2 to obtain the global tropospheric delay height normalized model coefficients.

[0046] The time series of the fourth-order exponential function parameters (i.e., a1 to a4) are fitted in the form of trigonometric functions, and the tropospheric delay height normalization model is obtained as follows:

[0047] where doy represents the accumulated days per year, π represents the circumference of a circle, B0 represents the annual mean, (B1, B2) and (B3, B4) represent the coefficients of the annual and semi-annual tropospheric delay height normalization models, respectively.

[0048] In order to enhance the periodicity of the time series and improve the computational efficiency, the present invention fixes the mean of the five coefficients of parameter a4.

[0049] Step 4: Store the model coefficients in a grid format with a horizontal resolution of 1°×1° (longitude×latitude) to obtain a global tropospheric delay height normalized grid model.

[0050] The model coefficients obtained in step 3 are stored in a grid with a horizontal resolution of 1°×1° (longitude×latitude). There are 64,800 grid points in the world, and each grid point has 16 model coefficients (parameters a1 to a3 each have 5 coefficients B0 to B4, and parameter a4 has a fixed average of 1 coefficient). Finally, the global tropospheric delay height normalized grid model is obtained.

[0051] Step 5: Based on the tropospheric delay elevation normalized grid model obtained in step 4, horizontal interpolation and elevation correction are performed on the GNSS real-time ZTD to obtain the tropospheric delay real-time grid model.

[0052] For each grid point, find the 10 nearest GNSS stations and normalize the ZTD at the station height to the grid point height. The specific calculation method is as follows:

[0053] Where ZTD grid 、ZTD sta are the grid point heights h g , measuring station height h s where ZTD0 represents the tropospheric delay at sea level, and a1 to a4 are the parameters of the fourth-order exponential function.

[0054] Then, the ZTDs of the 10 stations normalized to the grid height are horizontally interpolated to the grid points using the inverse distance weighted interpolation method. Finally, the ZTDs of all grid points are uniformly normalized to the sea level using formula (2) to obtain the real-time grid model of global tropospheric delay.

[0055] Step 6: Based on the target point location provided by the user, obtain the global tropospheric delay elevation normalized grid model coefficients at the four nearest grid points around the target point.

[0056] Based on the latitude and longitude of the target point provided by the user, obtain the global tropospheric delay elevation normalized grid model coefficients at the four nearest grid points around the target point.

[0057] Step 7: Based on the time information provided by the user, combined with the global tropospheric delay elevation normalized grid model coefficients and the global tropospheric delay real-time grid model, the sea level heights ZTD at the four nearest grid points around the target point are normalized to the target height.

[0058] First, the global tropospheric delay height normalized grid model coefficient and the user-provided annual cumulative day are substituted into formula (3) to calculate the fourth-order exponential function parameters. Then, the sea level heights ZTD at the four nearest grid points around the target point provided by the global tropospheric delay real-time grid model are normalized to the target height using formula (2).

[0059] Step 8: Use the inverse distance weighted interpolation method to horizontally interpolate the target height ZTD at the four nearest grid points around the target point to the target point position.

[0060] In this embodiment, some GNSS stations in North America were selected for testing, and the bias (Bias) and root mean square (RMS) were used for accuracy assessment. The results are shown in Table 1.

[0061] Table 1 Mean error of products of different ZTD models

[0062] As can be seen from Table 1, the tropospheric delayed real-time grid model (Exp4) constructed based on the fourth-order exponential elevation normalization model of the present invention has an accuracy of less than 7 mm, which is better than the ERA5 reanalysis data, GFS forecast products, the real-time grid model (Exp1) constructed based on the single-exponential elevation normalization model, and the traditional tropospheric models GPT3, UNB3m, and VMF3.

[0063] FIG3 shows the geographical distribution of errors of different ZTD model products. It can be seen from FIG3 that the real-time grid model of tropospheric delay constructed based on the fourth-order exponential elevation normalization model of the present invention has obvious improvements in areas where the accuracy of other model products is poor.

[0064] Example 2

[0065] Based on the same inventive concept, the present invention also provides an improved GNSS tropospheric delay real-time grid model construction system, including a processor and a memory, the memory is used to store program instructions, and the processor is used to call the program instructions in the memory to execute the above-mentioned improved GNSS tropospheric delay real-time grid model construction method.

[0066] Example 3

[0067] Based on the same inventive concept, the present invention also provides an improved GNSS tropospheric delay real-time grid model construction system, including a readable storage medium, on which a computer program is stored. When the computer program is executed, an improved GNSS tropospheric delay real-time grid model construction method as described above is implemented.

[0068] In specific implementation, the method proposed in the technical solution of the present invention can be automatically run by those skilled in the art using computer software technology. System devices that implement the method, such as computer-readable storage media that store the corresponding computer program of the technical solution of the present invention and computer equipment that runs the corresponding computer program, should also be within the scope of protection of the present invention.

[0069] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. An improved method for constructing a real-time grid model of GNSS tropospheric delay, characterized in that: The following steps are involved: Step 1, obtain the global ERA5 layered meteorological data, divide it into grids, and calculate the tropospheric delay ZTD information of each pressure layer at each grid point; Step 2, using the fourth-order exponential function to characterize the change of ZTD in the vertical direction, and obtaining the fourth-order exponential function parameters at each grid point by least squares fitting; The fourth-order exponential function is used to characterize the change of ZTD in the vertical direction, which is used to normalize the ZTD at sea level to the target height. Its expression is as follows: Where ZTD h is the ZTD value at the target height h, ZTD0 represents the tropospheric delay value at sea level, a1, a2, a3 and a4 are the parameters of the fourth-order exponential function; Based on the ZTD value and the corresponding height of each pressure layer obtained in step 1, the fourth-order exponential function parameters at each grid point are obtained using the least squares method; Step 3, using trigonometric functions to fit the time series of the fourth-order exponential function parameters at each global grid point obtained in step 2, to obtain the global tropospheric delay height normalization model coefficients; Step 4, storing the global tropospheric delay elevation normalized model coefficients obtained in step 3 in a grid manner to obtain a global tropospheric delay elevation normalized grid model; Step 5, based on the global tropospheric delay elevation normalized grid model obtained in step 4, horizontal interpolation and elevation correction are performed on the GNSS real-time ZTD to obtain a global tropospheric delay real-time grid model; Step 6, according to the target point location provided by the user, obtain the global tropospheric delay elevation normalized grid model coefficients at the four nearest grid points around the target point; Step 7: According to the time information provided by the user, combined with the global tropospheric delay elevation normalized grid model coefficient and the global tropospheric delay real-time grid model, the sea level height ZTD at the four nearest grid points around the target point is normalized to the target height; Step 8: Use the inverse distance weighted interpolation method to horizontally interpolate the target height ZTD at the four nearest grid points around the target point to the target point position.

2. The improved method for constructing a real-time grid model of GNSS tropospheric delay according to claim 1, characterized in that: In step 1, the ERA5 stratified meteorological data includes specific humidity, temperature, air pressure and potential height. These data are gridded, and the ZTD value of each air pressure layer at the grid point is calculated by integration. The specific calculation formula is as follows: In the formula, Q represents specific humidity, T represents temperature, P represents air pressure, g represents gravitational acceleration, ε represents gas constant ratio, and R represents d is the gas constant of dry air, R v is the gas constant of water vapor, k1, k2, k3 are constants.

3. The improved method for constructing a real-time grid model of GNSS tropospheric delay according to claim 1, characterized in that: In step 3, the time series of the fourth-order exponential function parameters a1, a2, a3 and a4 are fitted in the form of trigonometric functions, and the tropospheric delay height normalization model is obtained as follows: Where doy represents the accumulated days per year, π represents the circumference of a circle, B0 represents the annual mean, (B1, B2) and (B3, B4) represent the coefficients of the annual and semi-annual tropospheric delay height normalization models, respectively; In order to enhance the periodicity of the time series and improve the computational efficiency, the five coefficients of parameter a4 are fixed at their mean values.

4. The improved method for constructing a real-time grid model of GNSS tropospheric delay according to claim 1, characterized in that: In step 5, for each grid point, find the nearest N GNSS stations and normalize the ZTD at the station height to the grid point height. The specific calculation method is as follows: Where ZTD grid 、ZTD sta are the grid point heights h g , station height h s where ZTD0 represents the tropospheric delay value at sea level, and a1, a2, a3, and a4 are the parameters of the fourth-order exponential function; Then, the inverse distance weighted interpolation method is used to horizontally interpolate the ZTDs of N stations normalized to the grid height to the grid points. Finally, formula (2) is used to uniformly normalize the ZTDs of all grid points to the sea level height to obtain the real-time grid model of global tropospheric delay.

5. The improved method for constructing a real-time grid model of GNSS tropospheric delay as claimed in claim 3, characterized in that: In step 7, firstly, the global tropospheric delay elevation normalized grid model coefficient and the annual accumulation day provided by the user are substituted into formula (3) to calculate the fourth-order exponential function parameters, and then the sea level height ZTD at the four nearest grid points around the target point provided by the global tropospheric delay real-time grid model is normalized to the target height using formula (2).

6. An improved GNSS tropospheric delay real-time grid model construction system, characterized in that: It includes a processor and a memory, the memory is used to store program instructions, and the processor is used to call the program instructions in the memory to execute an improved GNSS tropospheric delay real-time grid model construction method as described in any one of claims 1-5.

7. An improved GNSS tropospheric delay real-time grid model construction system, characterized in that: It includes a readable storage medium, on which a computer program is stored. When the computer program is executed, an improved GNSS tropospheric delay real-time grid model construction method as described in any one of claims 1 to 5 is implemented.

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