Troposphere delay model construction method based on Gaussian function vertical correction

Abstract

The invention relates to the technical field of crossing of satellite navigation positioning and InSAR (Interferometric Synthetic Aperture Radar), and discloses a troposphere delay model construction method based on Gaussian function vertical correction, which introduces a Gaussian function to express the vertical change of ZTD, and constructs a ZTD vertical correction model by using ERA5 atmosphere reanalysis data. And then a 0.25 degree * 0.25 degree (latitude * longitude) ZTD vertical correction grid model considering Gaussian coefficient seasonal variation is constructed. And based on the ZTD vertical correction grid model considering the Gaussian coefficient seasonal change, constructing a ZTD empirical model considering seasonal oscillation and fine daily change by using ERA5 atmosphere reanalysis data, storing Gaussian coefficients and ZTD periodic coefficients in an ERA5 grid point form, and constructing a real-time high-precision ZTD grid model suitable for any spatial position in a Chinese region. The troposphere delay model based on Gaussian function vertical correction constructed by the invention has important significance for satellite navigation positioning and InSAR troposphere delay correction service performance and high-precision application.

Description

Technical Field

[0001] The invention relates to the technical field of satellite navigation positioning and InSAR intersection, and in particular to a method for constructing a tropospheric delay model based on Gaussian function vertical correction. Background Art

[0002] The signal delay caused by the troposphere when the satellite signal passes through the atmosphere is called tropospheric delay, which is one of the error sources of satellite navigation positioning and InSAR deformation monitoring. Due to the existence of signal delay, GNSS will inevitably produce errors in the process of navigation positioning and other services, seriously affecting the accuracy of applications such as navigation positioning, synthetic aperture radar interferometry and very long baseline interferometry.

[0003] Due to the particularity of the tropospheric medium, the correction of tropospheric delay is generally carried out using models. Commonly used tropospheric delay models are mainly divided into two categories: one is the meteorological parameter model, which requires the input of meteorological parameters when using this type of model; the other is the non-meteorological parameter model, which does not require the input of meteorological parameters when using this type of model. Generally, only the time and space information needs to be input to calculate the target value.

[0004] Non-meteorological parameter models are tropospheric delay models that do not rely on measured meteorological parameters. For example, the UNB3 model and the EGNOS model are both non-meteorological parameter models established earlier. Such models make up for the defects of meteorological parameter models to a certain extent, but their temporal and spatial resolutions are relatively low. These models provide meteorological parameter tables at intervals of 15 degrees latitude. They can reflect the general picture of the spatiotemporal changes of the global tropospheric atmosphere, but it is difficult to reflect the regional characteristics of tropospheric atmospheric changes, especially in China where the terrain is undulating.

[0005] In view of the shortcomings of the above models, many scholars have constructed global grid models such as the TropGrid series, GPT series, IGGtrop series and GZTD. These models have improved the temporal resolution, but their applicability, spatial resolution, semi-annual periodic changes and fine daily changes under special natural geographical conditions need to be further improved. In addition, since the elevation of the grid points of the atmospheric reanalysis data used as the data source for modeling is inconsistent with the user's elevation, directly interpolating the tropospheric delay of the grid points to the user's position will result in large errors, especially in high-altitude areas. The errors caused by large elevation differences are more significant. It is urgent to use high-precision functions to accurately express the vertical changes of tropospheric delays. At the same time, constructing a vertical correction model for tropospheric delays is also the key to the construction of a high-precision tropospheric delay model.

[0006] Through the above analysis, the problems and defects of the existing technology are: the spatial resolution of the tropospheric delay model needs to be provided; the model does not take into account the fine time changes; the regional applicability of the model is poor; and the vertical correction model is not accurate.

[0007] The difficulty of solving the above problems and defects is: constructing a tropospheric delay model that takes into account seasonal oscillations and fine daily variations; selecting high-precision functions to construct a tropospheric delay vertical correction model.

[0008] The significance of solving the above problems and defects is to provide an important reference for the construction of a high-precision tropospheric delay model in the Chinese region, and at the same time, provide real-time tropospheric delay services at any spatial location for satellite navigation positioning and InSAR tropospheric delay correction. Summary of the invention

[0009] The purpose of the present invention is to provide a method for constructing a tropospheric delay model based on Gaussian function vertical correction, so as to solve the problems proposed in the above background technology that the spatial resolution of the tropospheric delay model needs to be provided; the model does not take into account the fine time changes; the regional applicability of the model is poor; and the vertical correction model has low accuracy.

[0010] To achieve the above object, the present invention provides the following technical solutions: the method for constructing a tropospheric delay model based on Gaussian function vertical correction includes introducing a Gaussian function to express the vertical change of ZTD and calculating the Gaussian coefficient, constructing a ZTD vertical correction grid model taking into account the seasonal change of the Gaussian coefficient, using ERA5 ZTD with a time resolution of 1h to construct a ZTD empirical model taking into account seasonal oscillations and fine daily changes, storing the Gaussian coefficient and the periodic coefficient of ZTD in the form of ERA5 grid points, and constructing a tropospheric delay model based on Gaussian function vertical correction;

[0011] Specifically include:

[0012] S1. Perform data preprocessing to obtain the latest ERA5 atmospheric reanalysis data provided by the ECMWF Center, including meteorological data and the potential height corresponding to the standard pressure layer;

[0013] S2, calculate the grid point stratified ZTD with a resolution of 0.25°×0.25° (latitude×longitude) by the integration method based on the ERA5 grid point surface and stratified meteorological data;

[0014] S3, using Gaussian function to express the vertical variation of ZTD of each ERA5 grid point in China, and calculating Gaussian coefficient;

[0015] S4. Perform Fourier transform analysis on the multi-year Gaussian coefficients to obtain the periodic characteristics of the Gaussian coefficients, calculate the periodic coefficients of the Gaussian coefficients using the least square method, store the obtained periodic coefficients in the form of a 0.25°×0.25° grid, and obtain a ZTD vertical correction grid model with a horizontal resolution of 0.25°×0.25° that takes into account the seasonal changes of the Gaussian coefficients;

[0016] S5. Extract the grid point surface ZTD information from the ERA5 grid point layered ZTD, and extract the first layer of ZTD data above the surface in the layered ZTD as the grid point surface ZTD.

[0017] S6. Perform Fourier transform analysis on the surface ZTD of multi-year grid points to obtain the periodic characteristics of the surface ZTD, calculate the periodic coefficient of the surface ZTD using the least squares method, store the obtained periodic coefficient in the form of a 0.25°×0.25° grid, and obtain a ZTD empirical model with a horizontal resolution of 0.25°×0.25° that takes into account seasonal oscillations and fine diurnal variations.

[0018] S7. The Gaussian coefficients and the periodic coefficients of ZTD are stored in the form of ERA5 grid points with a horizontal resolution of 0.25°×0.25°, and a real-time, high-precision tropospheric delay model based on Gaussian function vertical correction is constructed for any spatial location in China.

[0019] Preferably, in step S1, the data source and data preprocessing method include:

[0020] The latest ERA5 atmospheric reanalysis data provided by the ECMWF Center include surface and layered data, of which the surface data include air pressure, temperature, dew point temperature and geopotential height; the layered data include standard pressure layer, geopotential height, temperature and specific humidity corresponding to the standard pressure layer. The horizontal resolution of the ERA5 grid point is 0.25°×0.25°, the vertical resolution is 37 layers, and the time resolution is 1h.

[0021] The data preprocessing method is to calculate the surface specific humidity according to the surface air pressure and the surface dew point temperature. The calculation formula includes:

[0022]

[0023] Where, T dew represents the surface dew point temperature, in K; P represents the surface air pressure, in hPa; e sat represents saturated water vapor pressure, in hPa; Sph represents specific humidity; a1 = 611.21, a3 = 17.502, a4 = 32.19, T0 = 273.16K, R d =287.0597, R v =461.5250 are all constants.

[0024] Preferably, in step S2, the ZTD integral calculation formula includes:

[0025]

[0026] Where, e is the water vapor pressure, in hPa; N is the total refractive index; Sph is the specific humidity; T is the temperature, in K; H is the altitude, in km; h low and h to p represents the lowest and highest elevations; k1, k2, k3 represent refractive constants;

[0027] Since there is residual ZHD at the top of the troposphere, the Saastamonen model is used to estimate the ZHD at the top of the troposphere to correct the integral result of ZTD. The calculation formula of the Saastamonen model is as follows:

[0028]

[0029] In the formula, ZHD top represents the ZHD of the tropospheric layer, in meters; P top It represents the pressure at the top of the troposphere in hPa; Indicates latitude.

[0030] Preferably, in step S3, the Gaussian function expression is as follows:

[0031]

[0032] Where h is the elevation in km; ZTD is the ZTD value at mean sea level in m; b and c are Gaussian coefficients.

[0033] Preferably, in step S4, the horizontal resolution is 0.25°×0.25°. The ZTD vertical correction grid model expression taking into account the seasonal variation of the Gaussian coefficient is as follows:

[0034]

[0035] In the formula, h r and h t Indicates the starting elevation and target elevation in km; ZTD r and ZTD t Indicates the ZTD value at the starting elevation and target elevation, in meters;

[0036] The periodicity of the Gaussian coefficients is expressed as:

[0037]

[0038] In the formula, cof i represents the Gaussian coefficient b or c; i represents the i-th grid point; represents the average value of Gaussian coefficients; to represents the period amplitude coefficient; doy represents the accumulated days per year.

[0039] Preferably, in step S6, the horizontal resolution is 0.25°×0.25°. The ZTD empirical model expression taking into account seasonal oscillations and fine diurnal variations is:

[0040]

[0041] In the formula, Indicates the surface ZTD. The unit is m; represents the average ZTD; to represents the period amplitude coefficient; doy represents the annualized day; hod represents UTC time.

[0042] Preferably, in step S7, the Gaussian coefficients and the periodic coefficients of ZTD are stored in the form of ERA5 grid points with a horizontal resolution of 0.25°×0.25°, and each grid point stores 10 periodic coefficients of Gaussian coefficients and 9 periodic coefficients of ZTD, and each grid point stores a total of 19 model coefficients.

[0043] Preferably, the method for constructing a tropospheric delay model based on Gaussian function vertical correction further comprises:

[0044] According to the user coordinates, four surrounding grid points are searched to obtain 19 model coefficients of the four grid points; the Gaussian coefficient and surface ZTD are calculated according to the target time doy and hod, and the surface ZTD is vertically corrected to the height of the user's position using the Gaussian function; the four ZTDs at the same height are horizontally interpolated to the user's position using the inverse distance weighted method.

[0045] Another object of the present invention is to provide a method for evaluating the accuracy of the tropospheric delay model based on the Gaussian function vertical correction, the method for evaluating the accuracy of the tropospheric delay model based on the Gaussian function vertical correction comprising:

[0046] Taking the bias and root mean square error as the accuracy criteria, the accuracy of the tropospheric delay model based on Gaussian function vertical correction is evaluated by combining the ZTD of 297 GNSS stations with a time resolution of 1 hour in China in 2018 and the ZTD of 88 sounding stations with a time resolution of 12 hours in China in 2018 that are not involved in the modeling.

[0047] Another object of the present invention is to provide a tropospheric delay model construction system based on Gaussian function vertical correction, comprising:

[0048] Grid point meteorological data acquisition module, obtains surface pressure, temperature, dew point temperature and potential height of ERA5 grid points in China, and obtains stratified pressure, temperature, specific humidity and potential height of ERA5 grid points;

[0049] The ZTD integral calculation module calculates the layered ZTD using the integral method based on the ERA5 grid point surface and layered meteorological data;

[0050] Gaussian coefficient calculation module, which uses Gaussian function to express the vertical change of ZTD and calculates Gaussian coefficient according to the ERA5 grid point stratified ZTD and its corresponding potential height;

[0051] The tropospheric delay model acquisition module based on Gaussian function vertical correction calculates the Gaussian coefficient and ZTD periodic coefficient of each ERA5 grid point in China by the least squares method, stores the model coefficients in the form of 0.25°×0.25° ERA5 grid points, and obtains the tropospheric delay model based on Gaussian function vertical correction.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention introduces a Gaussian function to express the vertical variation of ZTD, uses ERA5 atmospheric reanalysis data to construct a ZTD vertical correction model, and then constructs a ZTD vertical correction grid model that takes into account the seasonal variation of the Gaussian coefficient. Based on the ZTD vertical correction grid model that takes into account the seasonal variation of the Gaussian coefficient, the ERA5 atmospheric reanalysis data is used to construct a ZTD empirical model that takes into account seasonal oscillations and fine daily variations, and the Gaussian coefficient and the periodic coefficient of ZTD are stored in the form of ERA5 grid points with a horizontal resolution of 0.25°×0.25° (latitude×longitude), so as to construct a real-time high-precision ZTD grid model suitable for any spatial position in China. The tropospheric delay model based on the vertical correction of the Gaussian function constructed by the present invention solves the shortcomings of the current model, such as poor applicability in China with complex climate and large terrain undulations, low temporal and spatial resolution of the model, failure to take into account fine time variations, and low vertical correction accuracy. The tropospheric delay model based on Gaussian function vertical correction constructed in the present invention has a simple usage method, few model parameters and can calculate the real-time ZTD of any spatial position, which is of great significance to the satellite navigation positioning and InSAR tropospheric delay correction service performance and high-precision application. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of a method for constructing a tropospheric delay model based on Gaussian function vertical correction in Example 1 of the present invention;

[0055] Figure 2 is a schematic diagram of the vertical correction of the Gaussian function in Embodiment 1 of the present invention;

[0056] Figure 3 This is a statistical chart of the accuracy interval of the tropospheric delay model based on the vertical correction of the Gaussian function using the ZTD provided by 88 sounding stations in China in Example 2 of the present invention. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] Embodiment 1:

[0059] Reference Figure 1-Figure 2 , which is the first embodiment of the present invention, such as Figure 1 FIG. 1 is a flow chart of a method for constructing a tropospheric delay model based on Gaussian function vertical correction. This embodiment provides a method for constructing a tropospheric delay model based on Gaussian function vertical correction, comprising the following steps:

[0060] S1. Perform data preprocessing to obtain the latest ERA5 atmospheric reanalysis data from 2014 to 2018 provided by the ECMWF Center, including meteorological data and the potential height corresponding to the standard pressure layer;

[0061] Furthermore, the data source and data preprocessing method include:

[0062] The latest ERA5 atmospheric reanalysis data provided by the ECMWF Center includes surface and layered data, of which the surface data includes air pressure, temperature, dew point temperature and geopotential height; the layered data includes standard pressure layer, geopotential height, temperature and specific humidity corresponding to the standard pressure layer. The horizontal resolution of the ERA5 grid point is 0.25°×0.25°, the vertical resolution is 37 layers, and the time resolution is 1h.

[0063] The data preprocessing method is to calculate the surface specific humidity based on the surface air pressure and surface dew point temperature. The calculation formula includes:

[0064]

[0065] Where, T dew represents the surface dew point temperature, in K; P represents the surface air pressure, in hPa; e sat represents saturated water vapor pressure, in hPa; Sph represents specific humidity; a1 = 611.21, a3 = 17.502, a4 = 32.19, T0 = 273.16K, R d =287.0597, R v =461.5250 are all constants;

[0066] S2. Calculate the grid point stratified ZTD with a resolution of 0.25°×0.25° (latitude×longitude) from 2014 to 2018 by the integration method based on the ERA5 grid point surface and stratified meteorological data;

[0067] Furthermore, the ZTD integral calculation formula includes:

[0068]

[0069] Where, e is the water vapor pressure, in hPa; N is the total refractive index; Sph is the specific humidity; T is the temperature, in K; H is the altitude, in km; h low and h top Indicates the lowest and highest elevations; k1, k2, k3 indicate refractive constants;

[0070] Since there is residual ZHD at the top of the troposphere, the Saastamonen model is used to estimate the ZHD at the top of the troposphere to correct the integral result of ZTD. The calculation formula of the Saastamonen model is as follows:

[0071]

[0072] In the formula, ZHD top represents the ZHD of the tropospheric layer, in meters; P top It represents the pressure at the top of the troposphere in hPa; Indicates latitude.

[0073] S3. Use Gaussian function to express the vertical change of ZTD of each ERA5 grid point in China, and calculate the Gaussian coefficient of the grid points from 2014 to 2017;

[0074] Furthermore, the Gaussian function expression is as follows:

[0075]

[0076] Where h is the elevation in km; ZTD is the ZTD value at mean sea level in m; b and c are Gaussian coefficients.

[0077] S4. Perform Fourier transform analysis on the Gaussian coefficients obtained from 2014 to 2017 to obtain the periodic characteristics of the Gaussian coefficients, calculate the periodic coefficients of the Gaussian coefficients using the least squares method, store the obtained periodic coefficients in the form of a 0.25°×0.25° grid, and obtain a ZTD vertical correction grid model with a horizontal resolution of 0.25°×0.25° that takes into account the seasonal changes of the Gaussian coefficients;

[0078] Furthermore, the expression of the ZTD vertical correction grid model with a horizontal resolution of 0.25°×0.25° and taking into account the seasonal variation of the Gaussian coefficient is as follows:

[0079]

[0080] In the formula, h r and h t Indicates the starting elevation and target elevation in km; ZTD r and ZTD t Indicates the ZTD value at the starting elevation and target elevation, in meters; Figure 2 The figure shows a schematic diagram of Gaussian function vertical correction. In the figure, A1, A2, A3, and A4 are four ERA5 grid points around user P. When the tropospheric delays of these four grid points are interpolated to user P, the tropospheric delays of these four grid points need to be vertically corrected to the same height as the position of user P, that is, B1, B2, B3, and B4.

[0081] The periodicity of the Gaussian coefficients is expressed as:

[0082]

[0083] In the formula, cof i represents the Gaussian coefficient b or c; i represents the i-th grid point; represents the average value of Gaussian coefficients; to represents the period amplitude coefficient; doy represents the accumulated days per year.

[0084] S5. Extract the grid point surface ZTD information from the ERA5 grid point stratified ZTD, and extract the first layer of ZTD data above the surface in the stratified ZTD from 2014 to 2017 as the grid point surface ZTD;

[0085] S6. Perform Fourier transform analysis on the surface ZTD of the grid points from 2014 to 2017 to obtain the periodic characteristics of the surface ZTD, calculate the periodic coefficient of the surface ZTD using the least square method, store the obtained periodic coefficient in the form of a 0.25°×0.25° grid, and obtain a ZTD empirical model with a horizontal resolution of 0.25°×0.25° that takes into account seasonal oscillations and fine diurnal variations;

[0086] Furthermore, the empirical model expression of ZTD with a horizontal resolution of 0.25°×0.25° taking into account seasonal oscillations and fine diurnal variations is:

[0087]

[0088] In the formula, Indicates the surface ZTD. The unit is m; represents the average ZTD; to represents the period amplitude coefficient; doy represents the yearly day; hod represents UTC time.

[0089] S7. The Gaussian coefficients and the periodic coefficients of ZTD are stored in the form of 42021 ERA5 grid points in China with a horizontal resolution of 0.25°×0.25°, and a real-time high-precision tropospheric delay model based on Gaussian function vertical correction applicable to any spatial position in China is constructed.

[0090] In this embodiment: Gaussian coefficients and ZTD periodic coefficients are stored in the form of ERA5 grid points with a horizontal resolution of 0.25°×0.25°. Each grid point stores 10 periodic coefficients of Gaussian coefficients and 9 periodic coefficients of ZTD. Each grid point stores a total of 19 model coefficients.

[0091] In this embodiment: the specific steps of the method for constructing a tropospheric delay model based on Gaussian function vertical correction are as follows: introduce Gaussian function to express the vertical change of ZTD, use the layered ZTD calculated by integrating the ERA5 atmospheric reanalysis data from 2014 to 2017 to construct a ZTD vertical correction model, calculate the Gaussian coefficient of each grid point in the Chinese region, and then construct a 0.25°×0.25° (latitude×longitude) ZTD vertical correction grid model that takes into account the annual cycle and semi-annual cycle of the Gaussian coefficient. Based on the ZTD vertical correction grid model that takes into account the seasonal change of the Gaussian coefficient, the ERA5 atmospheric reanalysis data from 2014 to 2017 is used to construct a ZTD empirical model that takes into account seasonal oscillations and fine daily changes, and the Gaussian coefficient and the periodic coefficient of ZTD are stored in 42021 ERA5 grid points in the Chinese region, so as to construct a real-time, high-precision tropospheric delay model based on Gaussian function vertical correction that is suitable for any spatial position in the Chinese region.

[0092] The method for using the tropospheric delay model based on Gaussian function vertical correction provided by the embodiment of the present invention includes:

[0093] According to the user coordinates, four surrounding grid points are searched to obtain 19 model coefficients of the four grid points; the Gaussian coefficient and surface ZTD are calculated according to the target time doy and hod, and the surface ZTD is vertically corrected to the height of the user's position using the Gaussian function; the four ZTDs at the same height are horizontally interpolated to the user's position using the inverse distance weighted method.

[0094] This embodiment also provides a tropospheric delay model construction system based on Gaussian function vertical correction, including:

[0095] Grid point meteorological data acquisition module, obtains surface pressure, temperature, dew point temperature and potential height of ERA5 grid points in China, and obtains stratified pressure, temperature, specific humidity and potential height of ERA5 grid points;

[0096] The ZTD integral calculation module calculates the layered ZTD using the integral method based on the ERA5 grid point surface and layered meteorological data;

[0097] The Gaussian coefficient calculation module uses Gaussian function to express the vertical change of ZTD and calculates the Gaussian coefficient based on the ERA5 grid point stratified ZTD and its corresponding potential height.

[0098] The tropospheric delay model acquisition module based on Gaussian function vertical correction calculates the Gaussian coefficient and ZTD periodic coefficient of each ERA5 grid point in China by the least squares method, stores the model coefficients in the form of 0.25°×0.25° ERA5 grid points, and obtains the tropospheric delay model based on Gaussian function vertical correction.

[0099] This embodiment also provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for constructing a tropospheric delay model based on Gaussian function vertical correction as proposed in the above embodiment; the storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof.

[0100] Embodiment 2:

[0101] Reference Figure 3 , which is the second embodiment of the present invention. This embodiment is different from the first embodiment in that, in order to verify its beneficial effects, scientific demonstration is carried out through real data.

[0102] like Figure 3 The figure shows the accuracy of the tropospheric delay model based on the vertical correction of the Gaussian function, using the tropospheric delay data of 88 radiosonde stations in China as reference values. Figure 3 We can see that the tropospheric delay model based on Gaussian function vertical correction has the largest RMSE ratio in the range of 2–3 cm, accounting for 30%. In the range of RMSE < 2 cm, the tropospheric delay model based on Gaussian function vertical correction accounts for 2%. From the above accuracy verification results, the RMSE of the model is mostly distributed within 4 cm, showing good stability.

[0103] In the above example, the ZTD data calculated by integrating the ERA5 grid points in China for many years is used to construct a tropospheric delay model based on Gaussian function vertical correction. The model is suitable for providing real-time high-precision ZTD information to users at any spatial location in China, and the model is simple and efficient to use.

[0104] In summary: Compared with Example 2, this embodiment 1 introduces a Gaussian function to express the vertical change of ZTD for satellite navigation positioning and InSAR tropospheric delay correction services, uses ERA5 atmospheric reanalysis data to build a ZTD vertical correction model, and then builds a 0.25°×0.25° (latitude×longitude) ZTD vertical correction grid model that takes into account the seasonal change of the Gaussian coefficient. Based on the ZTD vertical correction grid model that takes into account the seasonal change of the Gaussian coefficient, the ERA5 atmospheric reanalysis data is used to build a ZTD empirical model that takes into account seasonal oscillations and fine daily changes, and the Gaussian coefficient and the periodic coefficient of ZTD are stored in the form of ERA5 grid points. A real-time, high-precision tropospheric delay model based on Gaussian function vertical correction that is suitable for any spatial position in China is built, which is of great significance to the performance and high-precision application of satellite navigation positioning and InSAR tropospheric delay correction services.

[0105] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0106] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a tropospheric delay model based on Gaussian function vertical correction, characterized in that: The method for constructing a tropospheric delay model based on Gaussian function vertical correction includes: The Gaussian function is introduced to express the vertical variation of ZTD and the Gaussian coefficient is calculated. A ZTD vertical correction grid model taking into account the seasonal variation of the Gaussian coefficient is constructed. The ERA5 ZTD with a time resolution of 1h is used to construct a ZTD empirical model taking into account seasonal oscillations and fine daily variations. The Gaussian coefficient and the periodic coefficient of ZTD are stored in the form of ERA5 grid points, and a tropospheric delay model based on the vertical correction of the Gaussian function is constructed. The tropospheric delay model method based on Gaussian function vertical correction further includes: S1. Perform data preprocessing to obtain the latest ERA5 atmospheric reanalysis data provided by the ECMWF Center, including meteorological data and the potential height corresponding to the standard pressure layer; S2, calculate the grid point stratified ZTD with a resolution of 0.25°×0.25° (latitude×longitude) by the integration method based on the ERA5 grid point surface and stratified meteorological data; S3, using Gaussian function to express the vertical variation of ZTD of each ERA5 grid point in China, and calculating Gaussian coefficient; S4. Perform Fourier transform analysis on the multi-year Gaussian coefficients to obtain the periodic characteristics of the Gaussian coefficients, calculate the periodic coefficients of the Gaussian coefficients using the least square method, store the obtained periodic coefficients in the form of a 0.25°×0.25° grid, and obtain a ZTD vertical correction grid model with a horizontal resolution of 0.25°×0.25° that takes into account the seasonal changes of the Gaussian coefficients; S5. Extract the grid point surface ZTD information from the ERA5 grid point layered ZTD, and extract the first layer of ZTD data above the surface in the layered ZTD as the grid point surface ZTD. S6. Perform Fourier transform analysis on the surface ZTD of multi-year grid points to obtain the periodic characteristics of the surface ZTD, calculate the periodic coefficient of the surface ZTD using the least squares method, store the obtained periodic coefficient in the form of a 0.25°×0.25° grid, and obtain a ZTD empirical model with a horizontal resolution of 0.25°×0.25° that takes into account seasonal oscillations and fine diurnal variations. S7. The Gaussian coefficients and the periodic coefficients of ZTD are stored in the form of ERA5 grid points with a horizontal resolution of 0.25°×0.25°, and a real-time, high-precision tropospheric delay model based on Gaussian function vertical correction is constructed for any spatial location in China.

2. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: In step S1, the data source and data preprocessing method include: The latest ERA5 atmospheric reanalysis data provided by the ECMWF Center include surface and layered data, of which the surface data include air pressure, temperature, dew point temperature and geopotential height; the layered data include standard pressure layer, geopotential height, temperature and specific humidity corresponding to the standard pressure layer. The horizontal resolution of the ERA5 grid point is 0.25°×0.25°, the vertical resolution is 37 layers, and the time resolution is 1h. The data preprocessing method is to calculate the surface specific humidity according to the surface air pressure and the surface dew point temperature. The calculation formula includes: Where, T dew represents the surface dew point temperature, in K; P represents the surface air pressure, in hPa; e sat represents saturated water vapor pressure, in hPa; Sph represents specific humidity; a1 = 611.21, a3 = 17.502, a4 = 32.19, T0 = 273.16K, R d =287.0597, R v =461.5250 are all constants.

3. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: In step S2, the ZTD integral calculation formula includes: Where, e is the water vapor pressure, in hPa; N is the total refractive index; Sph is the specific humidity; T is the temperature, in K; H is the altitude, in km; h low and h to p represents the lowest and highest elevations; k1, k2, k3 represent refractive constants; Since there is residual ZHD at the top of the troposphere, the Saastamonen model is used to estimate the ZHD at the top of the troposphere to correct the integral result of ZTD. The calculation formula of the Saastamonen model is as follows: In the formula, ZHD top represents the ZHD of the tropospheric layer, in meters; P top It represents the pressure at the top of the troposphere in hPa; Indicates latitude.

4. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: In step S3, the Gaussian function expression is as follows: Where h is the elevation in km; ZTD is the ZTD value at mean sea level in m; b and c are Gaussian coefficients.

5. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: In step S4, the horizontal resolution is 0.25°×0.25° and the ZTD vertical correction grid model expression taking into account the seasonal variation of the Gaussian coefficient is as follows: In the formula, h r and h t Indicates the starting elevation and target elevation in km; ZTD r and ZTD t Indicates the ZTD value at the starting elevation and target elevation, in meters; The periodicity of the Gaussian coefficients is expressed as: In the formula, cof i represents the Gaussian coefficient b or c; i represents the i-th grid point; represents the average value of Gaussian coefficients; to represents the period amplitude coefficient; doy represents the accumulated days per year.

6. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: In step S6, the horizontal resolution is 0.25°×0.25°, and the ZTD empirical model expression taking into account seasonal oscillations and fine diurnal variations is: In the formula, Indicates the surface ZTD. The unit is m; represents the average ZTD; to represents the period amplitude coefficient; doy represents the annualized day; hod represents UTC time.

7. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: In step S7, the Gaussian coefficients and ZTD periodic coefficients are stored in the form of ERA5 grid points with a horizontal resolution of 0.25°×0.25°. Each grid point stores 10 periodic coefficients of Gaussian coefficients and 9 periodic coefficients of ZTD. Each grid point stores a total of 19 model coefficients.

8. The method for constructing a tropospheric delay model based on Gaussian function vertical correction according to claim 1, characterized in that: The method for constructing a tropospheric delay model based on Gaussian function vertical correction further comprises: According to the user coordinates, four surrounding grid points are searched to obtain 19 model coefficients of the four grid points; the Gaussian coefficient and surface ZTD are calculated according to the target time doy and hod, and the surface ZTD is vertically corrected to the height of the user's position using the Gaussian function; the four ZTDs at the same height are horizontally interpolated to the user's position using the inverse distance weighted method.

9. A system for constructing a tropospheric delay model based on Gaussian function vertical correction according to the method for constructing a tropospheric delay model based on Gaussian function vertical correction according to any one of claims 1 to 8, characterized in that: The tropospheric delay model construction system based on Gaussian function vertical correction includes: Grid point meteorological data acquisition module, obtains surface pressure, temperature, dew point temperature and potential height of ERA5 grid points in China, and obtains stratified pressure, temperature, specific humidity and potential height of ERA5 grid points; The ZTD integral calculation module calculates the layered ZTD using the integral method based on the ERA5 grid point surface and layered meteorological data; Gaussian coefficient calculation module, which uses Gaussian function to express the vertical change of ZTD and calculates Gaussian coefficient according to the ERA5 grid point stratified ZTD and its corresponding potential height; The tropospheric delay model acquisition module based on Gaussian function vertical correction calculates the Gaussian coefficient and ZTD periodic coefficient of each ERA5 grid point in China by the least squares method, stores the model coefficients in the form of 0.25°×0.25° ERA5 grid points, and obtains the tropospheric delay model based on Gaussian function vertical correction.

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