Wide-area high-precision troposphere delay model hierarchical modeling method and system

Abstract

The invention provides a wide-area high-precision troposphere delay model hierarchical modeling method and system, and relates to the technical field of satellite navigation. A background model and residual grid coordinated wide-area high-precision troposphere delay model grading modeling method is designed, and the effectiveness of the method is verified by taking the precision single-point positioning precision and the precision single-point positioning convergence time as evaluation criteria on the premise of improving the precision single-point positioning precision. Precise single-point positioning is carried out based on a Saastamoinen model and a wide-area high-precision troposphere delay grading model, the precision of precise single-point positioning is improved, and the convergence time of precise single-point positioning is shortened. The application range of the delay model is wide, the troposphere delay background model is broadcasted through the satellite, the troposphere delay residual error grid is broadcasted through the ground network, the troposphere delay grading service is jointly provided, and the method can also be applied to a blind area which cannot be covered by the Internet. The parameters of the delay model are simple, the broadcast data volume is small, the user can receive the data in real time, and the real-time processing efficiency is high.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite navigation, and particularly relates to a wide-area high-precision tropospheric delay model hierarchical modeling method and system. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) is one of the main technologies of modern space geodesy, which can provide real-time or post-processing positioning, navigation and timing (PNT) services. Due to the change of atmospheric density with height, the propagation speed and path of GNSS signals will change when passing through the troposphere, resulting in time delay, which is called tropospheric delay. Research shows that the tropospheric delay is about 2 m in the zenith direction, and gradually increases to 20 m as the satellite elevation angle decreases, which is one of the main error sources of GNSS precise positioning.

[0003] According to the cause, the zenith tropospheric delay (ZTD) can be divided into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). Among them, ZHD is mainly affected by atmospheric static pressure and is relatively stable, which can be characterized by a model, while ZWD is easily affected by atmospheric water vapor content, but the water vapor content is affected by temperature, pressure, humidity and other environmental factors, and changes complex and unevenly, especially the water vapor content in the wide area or the area with large changes in elevation is more complex, so it is difficult to accurately model ZWD. In the GNSS positioning solution process, the empirical model is usually used to provide the prior value of ZHD, and then the ZWD is estimated as a set of certain process noise parameters. However, the prior value of ZHD must have errors, and the process noise set must not perfectly characterize the change of ZWD, which will affect the separation of tropospheric delay parameters and other estimated parameters, and further affect the accuracy and convergence time of GNSS precise positioning.

[0004] Current tropospheric delay models can be divided into two categories: classic models based on measured meteorological parameters to obtain ZTD information and empirical models without measured meteorological data to obtain ZTD information. Commonly used classic tropospheric delay models include Hopfield model, Saastamoinen model and Black model, etc. Such models are based on the ideal gas state equation and corresponding assumptions, and the accuracy of ZTD obtained under different conditions varies from decimeter to centimeter. Empirical models include UNB series models and GPT series models, etc. Such models can obtain ZTD information by directly inputting station location information and annual accumulated days. However, the above models are mainly used to serve standard navigation and positioning services, and their accuracy is low, which cannot meet the accuracy requirements of tropospheric augmentation positioning. In order to solve the problems of insufficient accuracy and insufficient space-time resolution, many scholars have successively developed many high-precision regional and wide-area tropospheric models, such as IGGtrop model and GZTD series model obtained by directly modeling tropospheric delay based on meteorological elements, and OFC model and MOFC model obtained by directly modeling tropospheric delay based on GNSS positioning solution. These models have their own advantages, but also have certain limitations, such as regional tropospheric models, which are usually only applicable to atmospheric augmentation in the corresponding region, and will produce large deviations if applied to other regions. Wide-area tropospheric models generally use more parameters and have more complex models in order to achieve high accuracy. At the same time, the current existing tropospheric delay models are mostly global models, which will have large deviations in local areas. At the same time, the application of all models at the user end needs to rely on the data transmission of satellite-based or ground-based network, and the data transmission pressure caused thereby cannot be ignored. High-precision wide-area tropospheric models with complex models are generally broadcast to users through the Internet, and users only need to have network access to receive the models. However, there will be a large range of positioning blind areas in high altitude, sea, desert and mountainous areas where communication signals are difficult to cover. In view of the regional limitations of ground-based augmentation systems, developing satellite-based augmentation systems is a solution. However, due to the bandwidth constraints of satellites, it is difficult to broadcast such complex wide-area tropospheric models. SUMMARY

[0005] To solve the above technical problems, the present application provides a wide-area high-precision tropospheric delay model hierarchical modeling method and system.

[0006] The first aspect of the present application discloses a wide-area high-precision tropospheric delay model hierarchical modeling method, wherein the wide-area high-precision tropospheric delay hierarchical model refers to a tropospheric zenith wet delay model, and the tropospheric zenith wet delay model includes a tropospheric zenith wet delay background model and a tropospheric zenith wet delay residual grid model; the method comprises: Step S1, the stations deployed globally by the International GNSS Service are used to observe the GPS satellite, and the pseudorange and carrier phase observation values of the L-band satellite-ground link of each station are obtained, and the zenith wet delay solving value of each station is obtained by using the non-difference non-combination precise point positioning method according to the pseudorange and carrier phase observation values of each station; Step S2, the global is divided into multiple observation regions, for each observation region, according to the zenith wet delay solving value of all stations in the observation region, the coefficient of the tropospheric zenith wet delay background model of the observation region and the tropospheric zenith wet delay residual value of each grid point in the observation region are calculated, and the coefficient of the tropospheric zenith wet delay background model of the observation region is broadcast by the GNSS satellite, and the tropospheric zenith wet delay residual value of each grid point in the observation region is broadcast through the ground Internet; Step S3, the user terminal observes the GNSS satellite, and the pseudorange and carrier phase observation values of the L-band satellite-ground link of the user terminal are obtained; Step S4, the user terminal determines the target observation region where the user terminal is located, receives the coefficient of the tropospheric zenith wet delay background model of the target observation region broadcast by the satellite, and calculates the tropospheric zenith wet delay background model value of the user terminal by using the tropospheric zenith wet delay background model of the target observation region; Step S5, the user terminal receives the tropospheric zenith wet delay residual values of the four grid points around the user terminal in the target observation region broadcast through the ground Internet, calculates the tropospheric zenith wet delay residual value of the user terminal by using the inverse distance interpolation method, and determines the sum of the tropospheric zenith wet delay background model value of the user terminal and the tropospheric zenith wet delay residual value of the user terminal as the tropospheric zenith wet delay value of the user terminal; Step S6, the tropospheric zenith wet delay value of the user terminal is used as the tropospheric virtual observation value in the precise point positioning solution, and the pseudorange and carrier phase observation values of the user terminal are used for additional tropospheric constraint precise point positioning solution.

[0007] According to the method of the first aspect of the application, in step S2, according to the zenith wet delay solving value of all stations in the observation region, the coefficient of the tropospheric zenith wet delay background model of the observation region and the tropospheric zenith wet delay residual value of each grid point in the observation region are calculated, and the method specifically comprises: The zenith wet delay solving value of all stations in the observation region is used as an observation, and the coefficient of the tropospheric zenith wet delay background model of the observation region is solved by using the least square method; The tropospheric zenith wet delay background model value of each station in the observation region is calculated by using the tropospheric zenith wet delay background model of the observation region, and the tropospheric zenith wet delay residual of the station is obtained by subtracting the tropospheric zenith wet delay background model value of the station from the zenith wet delay solving value of the station. A tropospheric zenith wet delay residual grid is determined within the observation area, and the distance radius between the station participating in the calculation of the tropospheric zenith wet delay residual and the grid point is determined. With the grid point as the center, the tropospheric zenith wet delay residuals of the stations within the distance radius of the grid point are all included in the calculation of the tropospheric zenith wet delay residual of the grid point. The tropospheric zenith wet delay residual value of the grid point is obtained by inverse distance interpolation.

[0008] According to the method of the first aspect of the present invention, the tropospheric zenith wet delay background model of the observation area is constructed in the following manner: The central point of the observation area is used as the reference point for the tropospheric zenith wet delay background model, and the tropospheric zenith wet delay background model of the observation area is constructed. The tropospheric zenith wet delay background model for this observation region is as follows: in, For the stations within this observation area The calculated value of the zenith wet delay; These are the coefficients of the tropospheric zenith wet delay background model for this observation region; and These represent the longitude and latitude differences of the stations within the observation area relative to the reference point, respectively. This represents the average elevation of the stations within the observation area.

[0009] According to the method of the first aspect of the present invention, with the grid point as the center, the tropospheric zenith wet delay residuals of stations within the distance radius of the grid point are all included in the calculation of the tropospheric zenith wet delay residual of the grid point. The tropospheric zenith wet delay residual value of the grid point is obtained by inverse distance interpolation, specifically including: In the formula, This represents the tropospheric zenith wet delay residual value for that grid point. This indicates the stations participating in the interpolation of this grid point. i Tropospheric zenith wet delay residual, n This indicates the total number of stations participating in the interpolation of this grid point. This indicates the grid point and the stations participating in the interpolation of this grid point. i The distance.

[0010] According to the method of the first aspect of the present invention, in step S6, the virtual observation equation for the tropospheric delay is as follows: in, Virtual tropospheric observations added for precise single-point positioning solutions. The tropospheric wet delay is a parameter to be estimated in precise point positioning.

[0011] According to the method of the first aspect of the application, the zenith tropospheric delay includes a zenith hydrostatic delay and a zenith wet delay, wherein the Saastamoinen model is used as an empirical model to provide a priori value for the zenith hydrostatic delay.

[0012] According to the method of the first aspect of the application, the longitude and latitude span of the observation area is not more than 20°x20°. The residual grid of the zenith wet delay of the troposphere in the observation area is 1°x1°, and the distance radius is 150km.

[0013] The second aspect of the application discloses a hierarchical modeling system for a wide-area high-precision tropospheric delay model, wherein the hierarchical model for the wide-area high-precision tropospheric delay refers to a zenith wet delay model of the troposphere, and the zenith wet delay model of the troposphere includes a background model of the zenith wet delay of the troposphere and a residual grid model of the zenith wet delay of the troposphere; the system includes: The first processing module is configured to observe GPS satellites by using the global GNSS service stations, obtain pseudorange and carrier phase observation values of L-band satellite-ground links of each station, and obtain zenith wet delay calculation values of each station by using a non-difference non-combination precise point positioning method according to the pseudorange and carrier phase observation values of each station. The second processing module is configured to divide the global area into multiple observation areas, and for each observation area, calculate coefficients of a background model of the zenith wet delay of the troposphere of the observation area and residual values of the zenith wet delay of the troposphere of each grid point in the observation area according to the zenith wet delay calculation values of all stations in the observation area, and broadcast the coefficients of the background model of the zenith wet delay of the troposphere of the observation area by GNSS satellites and broadcast the residual values of the zenith wet delay of the troposphere of each grid point in the observation area through the ground Internet. The third processing module is configured to observe GNSS satellites by a user terminal, and obtain pseudorange and carrier phase observation values of L-band satellite-ground links of the user terminal. The fourth processing module is configured to determine a target observation area in which the user terminal is located, receive coefficients of a background model of the zenith wet delay of the troposphere of the target observation area broadcast by satellites, and calculate a background model value of the zenith wet delay of the troposphere of the user terminal by using the background model of the zenith wet delay of the troposphere of the target observation area. The fifth processing module is configured to receive, by the user terminal, tropospheric zenith wet delay residual values of four grid points around the user terminal in the target observation area broadcast by the ground Internet, calculate the tropospheric zenith wet delay residual value of the user terminal by using the inverse distance interpolation method, and determine the sum of the tropospheric zenith wet delay background model value of the user terminal and the tropospheric zenith wet delay residual value of the user terminal as the tropospheric zenith wet delay value of the user terminal. The sixth processing module is configured to take the tropospheric zenith wet delay value of the user terminal as a tropospheric virtual observation value in precise point positioning calculation, and perform the precise point positioning calculation with additional tropospheric constraint by combining the pseudorange and carrier phase observation values of the user terminal.

[0014] According to the system of the second aspect of the present application, the second processing module specifically comprises: The first processing submodule is configured to take the zenith wet delay calculation value of all stations in the observation area as an observation, and calculate the coefficient of the tropospheric zenith wet delay background model of the observation area by using the least square method. The second processing submodule is configured to calculate the tropospheric zenith wet delay background model value of each station in the observation area by using the tropospheric zenith wet delay background model of the observation area, and obtain the tropospheric zenith wet delay residual of the station by subtracting the tropospheric zenith wet delay background model value of the station from the zenith wet delay calculation value of the station. The third processing submodule is configured to determine the tropospheric zenith wet delay residual grid in the observation area, and determine the distance radius between the station participating in the tropospheric zenith wet delay residual calculation of the grid point and the grid point. The tropospheric zenith wet delay residual of the stations within the distance radius of the grid point from the center of the grid point participates in the tropospheric zenith wet delay residual calculation of the grid point. The tropospheric zenith wet delay residual value of the grid point is calculated by using the inverse distance interpolation method.

[0015] According to the system of the second aspect of the present application, the tropospheric zenith wet delay background model of the observation area is constructed in the following manner: The central point of the observation area is taken as the reference point of the tropospheric zenith wet delay background model, and the tropospheric zenith wet delay background model of the observation area is constructed. The tropospheric zenith wet delay background model of the observation area is as follows: wherein, is the zenith wet delay calculation value of the station in the observation area; is the coefficient of the tropospheric zenith wet delay background model of the observation area; and respectively, the longitude difference and the latitude difference of the station in the observation area relative to the reference point.​ This represents the average elevation of the stations within the observation area.

[0016] According to the system of the second aspect of the present invention, the third processing submodule is specifically used to calculate the tropospheric zenith wet delay residual value of the grid point by using the inverse distance interpolation method, with the grid point as the center and the tropospheric zenith wet delay residual of all stations within the distance radius of the grid point participating in the calculation of the tropospheric zenith wet delay residual of the grid point: In the formula, This represents the tropospheric zenith wet delay residual value for that grid point. This indicates the stations participating in the interpolation of this grid point. i Tropospheric zenith wet delay residual, n This indicates the total number of stations participating in the interpolation of this grid point. This indicates the grid point and the stations participating in the interpolation of this grid point. i The distance.

[0017] According to the system of the second aspect of the present invention, the virtual observation equation for tropospheric delay is as follows: in, Virtual tropospheric observations added for precise single-point positioning solutions. The parameters to be estimated for tropospheric wet delay in precise single-point positioning calculations.

[0018] According to the system of the second aspect of the invention, the zenith tropospheric delay includes zenith static delay and zenith wet delay, wherein the Saastamoinen model is used as an empirical model to provide a priori values ​​for the zenith static delay.

[0019] According to the system of the second aspect of the present invention, the longitude and latitude span of the observation area does not exceed 20°×20°; The tropospheric zenith wet delay residual grid within the observation area is 1°×1° with a distance radius of 150km.

[0020] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps in the wide-area high-precision tropospheric delay model hierarchical modeling method of any one of the first aspects of this disclosure.

[0021] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the wide-area high-precision tropospheric delay model hierarchical modeling method according to any one of the first aspects of this disclosure.

[0022] In summary, the solution proposed in this invention has the following technical effects: This invention designs a hierarchical modeling method for a wide-area, high-precision tropospheric delay model that coordinates a background model and a residual grid. With the premise of improving precise single-point positioning accuracy, the effectiveness of the invention is verified by using precise single-point positioning accuracy and convergence time as evaluation criteria. Based on the classical Saastamoinen model and the wide-area, high-precision tropospheric delay hierarchical model established in this invention, precise single-point positioning was achieved. The convergence times for GPS satellites were 14 minutes and 13.1 minutes, respectively, and the precise single-point positioning accuracies were 4.2 cm and 3.7 cm, respectively. The convergence time was improved by 6.4%, and the positioning accuracy by 12%. This invention improves both precise single-point positioning accuracy and convergence time. The wide-area tropospheric delay model constructed based on this invention has a wider application range compared to current tropospheric delay models. It can provide tropospheric delay hierarchical services by broadcasting the tropospheric delay background model via satellite and the tropospheric delay residual grid via terrestrial networks, and can also be applied to areas such as high altitudes, seas, deserts, and mountains where the internet cannot cover. The wide-area tropospheric delay model constructed based on the hierarchical modeling method of the present invention has simplified model parameters, a small amount of data to be broadcast, and can be received by users in real time. Its real-time processing efficiency is higher than that of the current wide-area tropospheric models. Attached Figure Description

[0023] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 A flowchart illustrating a hierarchical modeling method for a wide-area, high-precision tropospheric delay model according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the geographical distribution of monitoring stations according to an embodiment of the present invention; Figure 3 This is a structural diagram of a wide-area high-precision tropospheric delay model hierarchical modeling system according to an embodiment of the present invention; Figure 4 This is a structural diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] The first aspect of this invention discloses a hierarchical modeling method for a wide-area, high-precision tropospheric delay model. Figure 1 This is a flowchart of a wide-area high-precision tropospheric delay model hierarchical modeling method according to an embodiment of the present invention. The wide-area high-precision tropospheric delay hierarchical model refers to a tropospheric zenith wet delay model, which includes a tropospheric zenith wet delay background model and a tropospheric zenith wet delay residual grid model, such as... Figure 1 As shown, the method includes: Step S1: Use the international GNSS service to observe GPS satellites from stations deployed globally, obtain the pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of each station, and use the non-differential non-combined precise single-point positioning method to calculate the zenith wet delay solution value of each station based on the pseudorange and carrier phase observation values ​​of each station. Step S2: Divide the globe into multiple observation areas. For each observation area, calculate the coefficients of the tropospheric zenith wet delay background model and the tropospheric zenith wet delay residual value of each grid point in the observation area based on the zenith wet delay solution values ​​of all stations in the observation area. Then, broadcast the coefficients of the tropospheric zenith wet delay background model of the observation area via GNSS satellite and broadcast the tropospheric zenith wet delay residual value of each grid point in the observation area via the terrestrial Internet. Step S3: The user terminal observes the GNSS satellite and obtains the pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of the user terminal. Step S4: The user terminal determines its own target observation area, receives the coefficients of the tropospheric zenith wet delay background model of the target observation area broadcast by the satellite, and calculates the tropospheric zenith wet delay background model value of the user terminal using the tropospheric zenith wet delay background model of the target observation area. Step S5: The user terminal receives the tropospheric zenith wet delay residual values ​​of four grid points around the user terminal within the target observation area broadcast by the terrestrial Internet. The user terminal calculates the tropospheric zenith wet delay residual value using the inverse distance interpolation method. The sum of the user terminal's tropospheric zenith wet delay background model value and the user terminal's tropospheric zenith wet delay residual value is determined as the user terminal's tropospheric zenith wet delay value. Step S6: Use the tropospheric zenith wet delay value of the user terminal as the tropospheric virtual observation value in the precise single-point positioning solution, and combine it with the pseudorange and carrier phase observation values ​​of the user terminal to perform a precise single-point positioning solution with additional tropospheric constraints.

[0027] In step S1, GPS satellites are observed using stations deployed globally by the international GNSS service. The pseudorange and carrier phase observations of the L-band satellite-to-ground link of each station are obtained. Based on the pseudorange and carrier phase observations of each station, the zenith wet delay calculation value of each station is obtained by using the non-differential non-combined precise single-point positioning method.

[0028] In some embodiments, the calculation of the zenith wet delay value for each station using the non-differential non-combined precise single-point positioning method is common knowledge to those skilled in the art, and will not be elaborated further in this disclosure.

[0029] In step S2, the globe is divided into multiple observation areas. For each observation area, the coefficients of the tropospheric zenith wet delay background model and the tropospheric zenith wet delay residual value of each grid point in the observation area are calculated based on the zenith wet delay solution values ​​of all stations in the observation area. The coefficients of the tropospheric zenith wet delay background model of the observation area are broadcast via GNSS satellite, and the tropospheric zenith wet delay residual value of each grid point in the observation area is broadcast via the terrestrial Internet.

[0030] In some embodiments, based on the zenith wet delay solution values ​​of all stations within the observation area, the coefficients of the tropospheric zenith wet delay background model for the observation area and the tropospheric zenith wet delay residual value for each grid point within the observation area are calculated, specifically including: The zenith wet delay solution values ​​of all stations in the observation area are used as observations, and the coefficients of the tropospheric zenith wet delay background model for the observation area are obtained by using the least squares method. The tropospheric zenith wet delay background model value of each station in the observation area is calculated using the tropospheric zenith wet delay background model value of the station. The tropospheric zenith wet delay residual of the station is obtained by subtracting the tropospheric zenith wet delay background model value of the station from the zenith wet delay solution value. A tropospheric zenith wet delay residual grid is determined within the observation area, and the distance radius between the station participating in the calculation of the tropospheric zenith wet delay residual and the grid point is determined. With the grid point as the center, the tropospheric zenith wet delay residuals of the stations within the distance radius of the grid point are all included in the calculation of the tropospheric zenith wet delay residual of the grid point. The tropospheric zenith wet delay residual value of the grid point is obtained by inverse distance interpolation.

[0031] Example location, station i Tropospheric zenith wet delay residual ,in, , They are the stations i Zenith wet delay solution, station i The tropospheric zenith wet delay background model value.

[0032] In some embodiments, the tropospheric zenith wet delay background model for the observation region is constructed in the following manner: The central point of the observation area is used as the reference point for the tropospheric zenith wet delay background model, and the tropospheric zenith wet delay background model of the observation area is constructed. The tropospheric zenith wet delay background model for this observation region is as follows: in, For the stations within this observation area The calculated value of the zenith wet delay; These are the coefficients of the tropospheric zenith wet delay background model for this observation region; and These represent the longitude and latitude differences of the stations within the observation area relative to the reference point, respectively. This represents the average elevation of the stations within the observation area.

[0033] Centered on this grid point, the tropospheric zenith wet delay residuals of stations within a radius of this grid point are all included in the calculation of the tropospheric zenith wet delay residuals of this grid point. The inverse distance interpolation method is used to calculate the tropospheric zenith wet delay residual value of this grid point, specifically including: In the formula, This represents the tropospheric zenith wet delay residual value for that grid point. This indicates the stations participating in the interpolation of this grid point. i Tropospheric zenith wet delay residual, n This indicates the total number of stations participating in the interpolation of this grid point. This indicates the grid point and the stations participating in the interpolation of this grid point. i The distance.

[0034] In step S3, the user terminal observes the GNSS satellite and obtains the pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of the user terminal.

[0035] For example, the equations for the pseudorange and carrier phase observations of the user terminal are as follows: in, j Indicates frequency, Indicates satellite, Indicates the user terminal receiver. Indicates a satellite system. and These represent the user terminal receiver. For satellite systems satellites in In the j Pseudorange and phase observations at frequency, Indicates receiver With satellite system China Satellite Geometric distance between them Relative to satellite systems receiver The clock difference, Relative to satellite systems satellite The clock difference, , Indicates satellite system The j The ionospheric delay factor of frequency, Indicates satellite system The j carrier frequency of frequency Indicates user terminal receiver For satellite systems satellites in First frequency oblique path ionospheric delay, Indicates user terminal receiver For satellite systems satellites in The oblique path tropospheric delay, Indicates user terminal receiver For satellite systems satellites in In the j Phase ambiguity at frequency, Indicates satellite system The j Frequency signal at the receiver On pseudo-range hardware delay, Indicates satellite system The j Frequency signals in satellite pseudorange hardware delay, Indicates satellite system The j Frequency signal at the receiver Phase hardware delay on, Indicates satellite system The jFrequency signals in satellite Phase hardware delay, and These represent the user terminal receiver. For satellite systems China Satellite The j Measurement noise in frequency pseudorange and phase observations.

[0036] In step S5, the user terminal receives the tropospheric zenith wet delay residual values ​​of four grid points around the user terminal within the target observation area broadcast by the terrestrial Internet, calculates the tropospheric zenith wet delay residual value of the user terminal using the inverse distance interpolation method, and determines the sum of the tropospheric zenith wet delay background model value and the tropospheric zenith wet delay residual value of the user terminal as the tropospheric zenith wet delay value of the user terminal.

[0037] Specifically, the tropospheric zenith wet delay value of the user terminal ,in, A tropospheric zenith wet delay background model for user terminals; This represents the tropospheric zenith wet delay residual value for the user terminal.

[0038] In step S6, the tropospheric zenith wet delay value of the user terminal is used as the tropospheric virtual observation value in the precise single-point positioning solution, and the pseudorange and carrier phase observation values ​​of the user terminal are combined to perform a precise single-point positioning solution with additional tropospheric constraints.

[0039] In some embodiments, the virtual observation equation for tropospheric delay is as follows: in, Virtual tropospheric observations added for precise single-point positioning solutions. The parameters to be estimated for tropospheric wet delay in precise single-point positioning calculations.

[0040] In some embodiments, the Zenith Tropospheric Delay (ZTD) includes the Zenith Hydrostatic Delay (ZHD) and the Zenith Wet Delay (ZWD), wherein the Saastamoinen model is used as an empirical model to provide prior values ​​for the Zenith Hydrostatic Delay.

[0041] For example, the equation for tropospheric delay is: in, For the station For the zenith tropospheric delay of satellite S in satellite system Q, , They are the stations The troposphere at its location is divided into ZHD and ZWD. , The projection functions are for ZHD and ZWD, respectively, and the Saastamoinen model is used to provide prior values ​​for ZHD for correction.

[0042] In some embodiments, the longitude and latitude span of the observation area does not exceed 20° × 20°. That is, the longitude and latitude span of the observation area required for modeling the tropospheric delay background model does not exceed 20° × 20°.

[0043] In some embodiments, the tropospheric zenith wet delay residual grid in the observation area is 1°×1°, and the distance radius between the station participating in the calculation of the tropospheric zenith wet delay residual and the grid point is 150km.

[0044] The effectiveness of the proposed wide-area, high-precision tropospheric delay model hierarchical modeling method is verified below. All data are from the Australian Continuously Operating Reference Station (CORS) network. Based on the observation data from these stations, the accuracy of the tropospheric hierarchical model is evaluated, and its enhancement effect on PPP solution is verified. The experimental area covers 134°–154°E and 26°–35°S. First, observation data from 329 CORS stations within this region over a three-day period from DOY 182 to 184 in 2024 are selected for a full-area tropospheric delay modeling study. The study area is then divided into three approximately equal sub-regions (regions 1, 2, and 3) according to a west-to-east distribution principle, each containing 95, 136, and 98 stations, respectively. The geographical distribution of these 329 stations is as follows: Figure 2 As shown, all stations support dual-frequency data processing using GPS, Galileo, and BDS-3 systems. Stations in regions 1, 2, and 3 are distinguished by hollow circles (red, green, and blue), respectively. Stations in regions 1, 2, and 3 are distinguished by solid circles (red, green, and blue), respectively. The tropospheric delay modeling data of this invention is obtained based on dual-frequency PPP calculations using GPS, Galileo, and BDS-3 systems.

[0045] Precise single-point positioning experiments were conducted using both the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention. The convergence criterion was that the static positioning error was less than 20 cm horizontally and less than 40 cm vertically within 5 consecutive minutes. The convergence times of precise single-point positioning based on the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention were statistically analyzed, as shown in Table 1. The precision single-point positioning accuracy based on the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention was statistically analyzed, as shown in Table 2.

[0046] Table 1. Convergence time for precise single-point localization based on the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention (unit: min).

[0047] Table 2. Precise single-point positioning accuracy (unit: cm) based on the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention.

[0048] The convergence times for precise single-point localization based on the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention are 14 minutes and 13.1 minutes, respectively. The precise single-point localization accuracies based on the classical Saastamoinen model and the wide-area high-precision tropospheric delay classification model established in this invention are 4.2 cm and 3.7 cm, respectively.

[0049] The second aspect of this invention discloses a wide-area, high-precision tropospheric delay model hierarchical modeling system. Figure 3 This is a structural diagram of a wide-area high-precision tropospheric delay model hierarchical modeling system according to an embodiment of the present invention; the wide-area high-precision tropospheric delay hierarchical model refers to the tropospheric zenith wet delay model, which includes a tropospheric zenith wet delay background model and a tropospheric zenith wet delay residual grid model. Figure 3 As shown, the system 400 includes: The first processing module 401 is used to observe GPS satellites from stations deployed globally using international GNSS services, obtain pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of each station, and calculate the zenith wet delay solution value of each station based on the pseudorange and carrier phase observation values ​​of each station using the non-differential non-combined precise single-point positioning method. The second processing module 402 is used to divide the globe into multiple observation areas. For each observation area, based on the zenith wet delay solution values ​​of all stations in the observation area, it calculates the coefficients of the tropospheric zenith wet delay background model for that observation area and the tropospheric zenith wet delay residual value of each grid point in the observation area. It then broadcasts the coefficients of the tropospheric zenith wet delay background model for that observation area via GNSS satellites and the tropospheric zenith wet delay residual value of each grid point in the observation area via the terrestrial Internet. The third processing module 403 is used for user terminals to observe GNSS satellites and obtain pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of the user terminals. The fourth processing module 404 is used for the user terminal to determine its own target observation area, receive the coefficients of the tropospheric zenith wet delay background model of the target observation area broadcast by the satellite, and calculate the tropospheric zenith wet delay background model value of the user terminal using the tropospheric zenith wet delay background model of the target observation area. The fifth processing module 405 is used to receive the tropospheric zenith wet delay residual values ​​of four grid points around the user terminal in the target observation area broadcast by the terrestrial Internet, calculate the tropospheric zenith wet delay residual value of the user terminal using the inverse distance interpolation method, and determine the sum of the tropospheric zenith wet delay background model value of the user terminal and the tropospheric zenith wet delay residual value of the user terminal as the tropospheric zenith wet delay value of the user terminal. The sixth processing module 406 is used to use the tropospheric zenith wet delay value of the user terminal as the tropospheric virtual observation value in the precise single-point positioning solution, and to perform a precise single-point positioning solution with additional tropospheric constraints in conjunction with the pseudorange and carrier phase observation values ​​of the user terminal.

[0050] According to the system of the second aspect of the present invention, the second processing module specifically includes: The first processing submodule is used to take the zenith wet delay solution values ​​of all stations in the observation area as observations and use the least squares method to solve for the coefficients of the tropospheric zenith wet delay background model of the observation area. The second processing submodule is used to calculate the tropospheric zenith wet delay background model value of each station in the observation area using the tropospheric zenith wet delay background model of the observation area, and to obtain the tropospheric zenith wet delay residual of the station by subtracting the tropospheric zenith wet delay background model value of the station from the zenith wet delay solution value of the station. The third processing submodule is used to determine the tropospheric zenith wet delay residual grid within the observation area, and to determine the distance radius between the station participating in the calculation of the tropospheric zenith wet delay residual and the grid point. With the grid point as the center, the tropospheric zenith wet delay residuals of the stations within the distance radius of the grid point are all included in the calculation of the tropospheric zenith wet delay residual of the grid point. The inverse distance interpolation method is used to calculate the tropospheric zenith wet delay residual value of the grid point.

[0051] According to the system of the second aspect of the present invention, the tropospheric zenith wet delay background model of the observation region is constructed in the following manner: The central point of the observation area is used as the reference point for the tropospheric zenith wet delay background model, and the tropospheric zenith wet delay background model of the observation area is constructed. The tropospheric zenith wet delay background model for this observation region is as follows: in, For the stations within this observation area The calculated value of the zenith wet delay; These are the coefficients of the tropospheric zenith wet delay background model for this observation region; and These represent the longitude and latitude differences of the stations within the observation area relative to the reference point, respectively. This represents the average elevation of the stations within the observation area.

[0052] According to the system of the second aspect of the present invention, the third processing submodule is specifically used to calculate the tropospheric zenith wet delay residual value of the grid point by using the inverse distance interpolation method, with the grid point as the center and the tropospheric zenith wet delay residual of all stations within the distance radius of the grid point participating in the calculation of the tropospheric zenith wet delay residual of the grid point: In the formula, This represents the tropospheric zenith wet delay residual value for that grid point. This indicates the stations participating in the interpolation of this grid point. i Tropospheric zenith wet delay residual, n This indicates the total number of stations participating in the interpolation of this grid point. This indicates the grid point and the stations participating in the interpolation of this grid point. i The distance.

[0053] According to the system of the second aspect of the present invention, the virtual observation equation for tropospheric delay is as follows: in, Virtual tropospheric observations added for precise single-point positioning solutions. The parameters to be estimated for tropospheric wet delay in precise single-point positioning calculations.

[0054] According to the system of the second aspect of the invention, the zenith tropospheric delay includes zenith static delay and zenith wet delay, wherein the Saastamoinen model is used as an empirical model to provide a priori values ​​for the zenith static delay.

[0055] According to the system of the second aspect of the present invention, the longitude and latitude span of the observation area does not exceed 20°×20°; The tropospheric zenith wet delay residual grid within the observation area is 1°×1° with a distance radius of 150km.

[0056] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps in the wide-area high-precision tropospheric delay model hierarchical modeling method of any one of the first aspects of this disclosure.

[0057] Figure 4 This is a structural diagram of an electronic device according to an embodiment of the present invention, such as... Figure 4 As shown, the electronic device includes a processor, memory, communication interface, display screen, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, Near Field Communication (NFC), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0058] Those skilled in the art will understand that Figure 4 The structure shown is merely a structural diagram of the part related to the technical solution of this disclosure and does not constitute a limitation on the electronic device to which the solution of this application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0059] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the wide-area high-precision tropospheric delay model hierarchical modeling method according to any one of the first aspects of this disclosure.

[0060] In summary, the technical solution proposed in this invention has the following technical effects: This invention designs a hierarchical modeling method for a wide-area, high-precision tropospheric delay model that coordinates a background model and a residual grid. With the premise of improving precise single-point positioning accuracy, the effectiveness of the invention is verified by using precise single-point positioning accuracy and convergence time as evaluation criteria. Based on the classical Saastamoinen model and the wide-area, high-precision tropospheric delay hierarchical model established in this invention, precise single-point positioning was achieved. The convergence times for GPS satellites were 14 minutes and 13.1 minutes, respectively, and the precise single-point positioning accuracies were 4.2 cm and 3.7 cm, respectively. The convergence time was improved by 6.4%, and the positioning accuracy by 12%. This invention improves both precise single-point positioning accuracy and convergence time. The wide-area tropospheric delay model constructed based on this invention has a wider application range compared to current tropospheric delay models. It can provide tropospheric delay hierarchical services by broadcasting the tropospheric delay background model via satellite and the tropospheric delay residual grid via terrestrial networks, and can also be applied to areas such as high altitudes, seas, deserts, and mountains where the internet cannot cover. The wide-area tropospheric delay model constructed based on the hierarchical modeling method of the present invention has simplified model parameters, a small amount of data to be broadcast, and can be received by users in real time. Its real-time processing efficiency is higher than that of the current wide-area tropospheric models.

[0061] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A hierarchical modeling method for a wide-area, high-precision tropospheric delay model, characterized in that, The wide-area high-precision tropospheric delay classification model refers to the tropospheric zenith wet delay model, which includes a tropospheric zenith wet delay background model and a tropospheric zenith wet delay residual grid model. The method includes: Step S1: Use the international GNSS service to observe GPS satellites from stations deployed globally, obtain the pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of each station, and use the non-differential non-combined precise single-point positioning method to calculate the zenith wet delay solution value of each station based on the pseudorange and carrier phase observation values ​​of each station. Step S2: Divide the globe into multiple observation areas. For each observation area, calculate the coefficients of the tropospheric zenith wet delay background model and the tropospheric zenith wet delay residual value of each grid point in the observation area based on the zenith wet delay solution values ​​of all stations in the observation area. Then, broadcast the coefficients of the tropospheric zenith wet delay background model of the observation area via GNSS satellite and broadcast the tropospheric zenith wet delay residual value of each grid point in the observation area via the terrestrial Internet. Step S3: The user terminal observes the GNSS satellite and obtains the pseudorange and carrier phase observation values ​​of the L-band satellite-to-ground link of the user terminal. Step S4: The user terminal determines its own target observation area, receives the coefficients of the tropospheric zenith wet delay background model of the target observation area broadcast by the satellite, and calculates the tropospheric zenith wet delay background model value of the user terminal using the tropospheric zenith wet delay background model of the target observation area. Step S5: The user terminal receives the tropospheric zenith wet delay residual values ​​of four grid points around the user terminal within the target observation area broadcast by the terrestrial Internet. The user terminal calculates the tropospheric zenith wet delay residual value using the inverse distance interpolation method. The sum of the user terminal's tropospheric zenith wet delay background model value and the user terminal's tropospheric zenith wet delay residual value is determined as the user terminal's tropospheric zenith wet delay value. Step S6: Use the tropospheric zenith wet delay value of the user terminal as the tropospheric virtual observation value in the precise single-point positioning solution, and combine it with the pseudorange and carrier phase observation values ​​of the user terminal to perform a precise single-point positioning solution with additional tropospheric constraints.

2. The method according to claim 1, characterized in that, In step S2, based on the zenith wet delay solution values ​​of all stations within the observation area, the coefficients of the tropospheric zenith wet delay background model for the observation area and the tropospheric zenith wet delay residual value for each grid point within the observation area are calculated, specifically including: The zenith wet delay solution values ​​of all stations in the observation area are used as observations, and the coefficients of the tropospheric zenith wet delay background model for the observation area are obtained by using the least squares method. The tropospheric zenith wet delay background model value of each station in the observation area is calculated using the tropospheric zenith wet delay background model value of the station. The tropospheric zenith wet delay residual of the station is obtained by subtracting the tropospheric zenith wet delay background model value of the station from the zenith wet delay solution value. A tropospheric zenith wet delay residual grid is determined within the observation area, and the distance radius between the station participating in the calculation of the tropospheric zenith wet delay residual and the grid point is determined. With the grid point as the center, the tropospheric zenith wet delay residuals of the stations within the distance radius of the grid point are all included in the calculation of the tropospheric zenith wet delay residual of the grid point. The tropospheric zenith wet delay residual value of the grid point is obtained by inverse distance interpolation.

3. The method according to claim 2, characterized in that, The tropospheric zenith wet delay background model for this observation region was constructed in the following manner: The central point of the observation area is used as the reference point for the tropospheric zenith wet delay background model, and the tropospheric zenith wet delay background model of the observation area is constructed. The tropospheric zenith wet delay background model for this observation region is as follows: in, For the stations within this observation area The calculated value of the zenith wet delay; These are the coefficients of the tropospheric zenith wet delay background model for this observation region; and These represent the longitude and latitude differences of the stations within the observation area relative to the reference point, respectively. This represents the average elevation of the stations within the observation area.

4. The method according to claim 2, characterized in that, Centered on this grid point, the tropospheric zenith wet delay residuals of stations within a radius of this grid point are all included in the calculation of the tropospheric zenith wet delay residuals of this grid point. The inverse distance interpolation method is used to calculate the tropospheric zenith wet delay residual value of this grid point, specifically including: In the formula, This represents the tropospheric zenith wet delay residual value for that grid point. This indicates the stations participating in the interpolation of this grid point. i Tropospheric zenith wet delay residual, n This indicates the total number of stations participating in the interpolation of this grid point. This indicates the grid point and the stations participating in the interpolation of this grid point. i The distance.

5. The method according to claim 1, characterized in that, In step S6, the virtual observation equation for tropospheric delay is as follows: in, Virtual tropospheric observations added for precise single-point positioning solutions. The parameters to be estimated for tropospheric wet delay in precise single-point positioning calculations.

6. The method according to claim 1, characterized in that, The zenith tropospheric delay includes the zenith static delay and the zenith wet delay. The Saastamoinen model is used as an empirical model to provide prior values ​​for the zenith static delay.

7. The method according to claim 1, characterized in that, The longitude and latitude span of the observation area shall not exceed 20° × 20°; The tropospheric zenith wet delay residual grid within the observation area is 1°×1° with a distance radius of 150km.

8. A wide-area, high-precision hierarchical modeling system for tropospheric delay models, characterized in that, The wide-area high-precision tropospheric delay classification model refers to the tropospheric zenith wet delay model. The tropospheric zenith wet delay model includes a tropospheric zenith wet delay background model and a tropospheric zenith wet delay residual grid model. The system includes: The first processing module is used to observe GPS satellites from stations deployed globally using international GNSS services, obtain pseudorange and carrier phase observations of the L-band satellite-to-ground link of each station, and calculate the zenith wet delay value of each station based on the pseudorange and carrier phase observations of each station using the non-differential non-combined precise single-point positioning method. The second processing module is used to divide the globe into multiple observation areas. For each observation area, based on the zenith wet delay solution values ​​of all stations in the observation area, it calculates the coefficients of the tropospheric zenith wet delay background model for that observation area and the tropospheric zenith wet delay residual value for each grid point in the observation area. The coefficients of the tropospheric zenith wet delay background model for that observation area are broadcast via GNSS satellites, and the tropospheric zenith wet delay residual value for each grid point in the observation area is broadcast via the terrestrial Internet. The third processing module is used for user terminals to observe GNSS satellites and obtain pseudorange and carrier phase observation values ​​of L-band satellite-to-ground links; The fourth processing module is used for the user terminal to determine its own target observation area, receive the coefficients of the tropospheric zenith wet delay background model of the target observation area broadcast by the satellite, and calculate the tropospheric zenith wet delay background model value of the user terminal using the tropospheric zenith wet delay background model of the target observation area. The fifth processing module is used to receive the tropospheric zenith wet delay residual values ​​of four grid points around the user terminal within the target observation area broadcast by the terrestrial Internet, calculate the tropospheric zenith wet delay residual value of the user terminal using the inverse distance interpolation method, and determine the sum of the tropospheric zenith wet delay background model value and the tropospheric zenith wet delay residual value of the user terminal as the tropospheric zenith wet delay value of the user terminal. The sixth processing module is used to use the tropospheric zenith wet delay value of the user terminal as the tropospheric virtual observation value in the precise single-point positioning solution, and to perform a precise single-point positioning solution with additional tropospheric constraints by combining pseudorange and carrier phase observation values.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps in the wide-area high-precision tropospheric delay model hierarchical modeling method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the wide-area high-precision tropospheric delay model hierarchical modeling method according to any one of claims 1 to 7.

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