Differential Ionospheric Modeling Method and System

Abstract

This application relates to the field of positioning, and discloses a differential ionospheric modeling method and system. The method includes: receiving the original observation data and navigation message of a regional base station receiver, and calculating the elevation angle, the geodetic coordinates of the pierce point, and the ionospheric delay observation between each satellite and the base station; selecting a reference satellite, and calculating the difference between the ionospheric delay observations corresponding to other satellites and the reference satellite to obtain the differential ionospheric delay observation at the current epoch; based on the geodetic coordinates of the pierce point and the corresponding differential ionospheric delay observations, using a fitting function to fit a regional differential ionospheric model; taking the model parameters and the satellite hardware delay deviation as parameters to be estimated, and the differential ionospheric delay observations at the current epoch as an observation vector to construct an observation equation; based on the observation equation, performing filtering processing on the parameters to be estimated to solve the model parameters. The ionospheric product obtained by the embodiments of this application significantly improves the positioning accuracy and convergence time of users.

Description

Technical Field

[0001] This application relates to the field of positioning, and particularly to differential real-time ionospheric modeling technology. Background Art

[0002] The Earth's ionosphere is an important part of the Earth's atmosphere. The plasma formed by a large number of charged particles in the ionosphere affects the propagation of radio waves and causes varying degrees of influence on electromagnetic signals passing through it, including reflection, refraction, scattering, and absorption. The ionosphere has an inescapable impact in many fields such as communication, remote sensing, GPS, and interstellar exploration. It is a common key problem faced by high-precision space information systems, restricting the rapid development of space technology and commercial spaceflight, especially in navigation and positioning. Ionospheric delay error is one of the main errors in real-time positioning. Currently, the models used for real-time ionospheric delay correction are mainly broadcast ionospheric models. However, these models are empirical models, such as the Klobuchar model, NeQuick2 model, IRI model, etc. Due to the complex changes in the ionosphere, the empirical models established based on long-term observation data cannot well reflect the ionospheric changes, so the correction accuracy is limited.

[0003] The total electron content (TEC) of the ionosphere is one of the most important parameters for describing the characteristics and variations of the ionosphere. Accurately obtaining TEC information is of great significance for in-depth research on the physical characteristics and variation laws of the ionosphere and improving the positioning accuracy of GNSS. The ionospheric grid model uses GNSS augmentation system data to obtain a distribution model of the vertical total electron content (VTEC) of wide-area grid points, providing ionospheric delay broadcast and correction for users. With the unprecedented development of the global navigation satellite system GNSS and the rapid increase of ground-based observation networks, it provides an effective means for realizing high-precision ionospheric monitoring and forecasting at the regional and even global levels. The International GNSS Service (IGS) has provided ionospheric products since 1998. The IGS ionospheric analysis and calculation of the global ionospheric TEC grid are considered the representative methods for global ionospheric TEC monitoring and modeling at present. Ionospheric analysis centers include the Center for Orbit Determination in Europe (CODE), the Jet Propulsion Laboratory (JPL) of the United States, the European Space Operations Center (ESOC), the Polytechnic University of Catalonia (UPC) in Spain, and other units. Currently, ionospheric analysis centers generally adopt the single-layer model assumption, that is, all free electrons in the ionosphere are evenly distributed on a single-layer spherical shell with a certain height from the ground and an infinitely thin thickness. The international IGS ionospheric model center mainly uses the observation data of the IGS global receiver network to establish a global ionospheric model and generate grid products. The update time is 2 hours, and the spatial grid points are relatively sparse, generally 5 degrees. When this model is applied to a small area, the accuracy is not high and the real-time performance is insufficient. The current development of the ionospheric grid model is gradually moving towards new requirements such as real-time performance and high precision. Summary of the Invention

[0004] The purpose of this application is to provide a differential ionospheric modeling method and system, and the obtained ionospheric products can significantly improve the positioning accuracy of the user terminal and reduce the positioning convergence time.

[0005] This application discloses a differential ionospheric modeling method, including:

[0006] Receiving the original observation data and navigation messages of the regional base station receiver, and calculating the elevation angle, piercing point longitude and latitude, and ionospheric delay observables between each satellite and the base station;

[0007] Selecting a reference star, and calculating the difference between the ionospheric delay observables corresponding to other satellites and the reference star to obtain the differential ionospheric delay observables at the current epoch;

[0008] Based on the piercing point longitude and latitude and the corresponding differential ionospheric delay observables, using a fitting function to fit a regional differential ionospheric model;

[0009] Taking the model parameters and the satellite hardware delay deviation as the parameters to be estimated, and using the differential ionospheric delay observations at the current epoch to form an observation vector, an observation equation is constructed.

[0010] Based on the observation equation, filtering processing is performed on the parameters to be estimated to solve the model parameters.

[0011] In a preferred example, after performing filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters, it further includes:

[0012] Using the solved regional differential ionospheric model to calculate the differential ionospheric delay observations at grid points, saving them in grid form and broadcasting them to regional user terminals.

[0013] In a preferred example, the original observation data is dual-frequency observation data.

[0014] In a preferred example, when calculating the ionospheric delay observations, it further includes:

[0015] Based on the dual-frequency pseudorange observations and carrier observations, using the undifferenced and uncombined PPP algorithm to calculate the ionospheric delay observations, where the calculated ionospheric delay observations are expressed as:

[0016] where a represents the integral constant of the ionospheric propagation path, represents the total electron content on the slant path between base station k and satellite s, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, DCB k represents the hardware delay deviation of receiver k, and DCB s represents the hardware delay deviation of satellite s.

[0017] In a preferred example, when performing filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters, it further includes:

[0018] Establishing a Kalman filter and performing real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters.

[0019] In a preferred example, when establishing the Kalman filter and performing real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters, it further includes:

[0020] Adding the constraint condition "for satellite s not observed at each epoch time, then DCB s = 0" to avoid rank deficiency of the equation, where DCB s represents the hardware delay deviation of satellite s.

[0021] In a preferred example, when calculating the longitude and latitude of the piercing point, it further includes:

[0022] Based on the assumption of the ionospheric single-layer model, calculate the longitude and latitude of the piercing point according to the following formula

[0023]

[0024]

[0025] where α represents the geocentric angular distance of the piercing point, H represents the ionospheric height, E and A respectively represent the satellite altitude angle and azimuth angle, R represents the radius of the earth, λ k represents the receiver longitude, represents the receiver latitude.

[0026] In a preferred example, for the selection of the reference star, calculating the difference between the ionospheric delay observables of other satellites and the reference star to obtain the differential ionospheric delay observable of the current epoch further includes:

[0027] For the same base station, select the satellite with the largest average altitude angle as the reference star, and the differential ionospheric delay observable of the current epoch is equal to the difference between the ionospheric delay observables of other satellites and the reference star respectively. Among them, the differential ionospheric delay observable between base station k and satellite s is expressed as:

[0028] where, is the differential total electron content between base station k and satellite s, represents the integrated amount of the path ionospheric electron density between base station k and satellite s, represents the integrated amount of the slant path ionospheric electron density between base station k and the reference satellite ref, DCB ref represents the hardware delay deviation of the reference star ref, DCB s represents the hardware delay deviation of satellite s.

[0029] In a preferred example, the fitting function is a polynomial function;

[0030] Based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observables, fitting a regional differential ionospheric model using a fitting function, which is expressed as:

[0031] where E mn represents the model parameter, represents the geographical latitude of the center point of the measurement area, S0 represents the center point of the measurement area At the solar hour angle at the central moment t0 of this period, λ represents the geographical longitude of the piercing point, t represents the observation moment, M and N represent the model orders.

[0032] In a preferred example, the fitting function is a spherical harmonic function;

[0033] Based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observables, using the fitting function to fit the regional differential ionospheric model, which is expressed as:

[0034] Among them, A nm 、B nm represent model parameters, n max represents the model order, P nm (cosφ) represents the Legendre function of the nth order and mth degree that is not fully normalized. φ and λ are respectively expressed as:

[0035]

[0036]

[0037] Among them, λ IPP 、 respectively represent the geographical longitude and latitude at the piercing point, t represents the current epoch, λ M 、 respectively represent the geomagnetic longitude and latitude, λ SUN represents the longitude of the meridian passing through the center of the earth and the sun.

[0038] In a preferred example, the observation equation is expressed as:

[0039] Among them, a represents the integral constant of the ionospheric propagation path, MF represents the projection function, z' represents the angle between the line connecting the base station and the satellite at the piercing point IPP and the zenith direction, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, DCB s represents the hardware delay deviation of satellite s, DCB ref represents the hardware delay deviation of the reference star ref, dVTEC IPP represents the differential vertical total electron content of the ionosphere at the piercing point IPP.

[0040] This application also discloses a differential ionospheric modeling system, including:

[0041] A receiving module, configured to receive the original observation data and navigation message of the regional base station receiver, and calculate the elevation angle between each satellite and the base station, the longitude and latitude of the piercing point, and the ionospheric delay observables;

[0042] A calculation module, configured to select a reference satellite, calculate the difference between the ionospheric delay observables corresponding to other satellites and the reference satellite to obtain the differential ionospheric delay observables at the current epoch;

[0043] A fitting module, configured to fit a regional differential ionospheric model by using a fitting function based on the puncture point longitude and latitude and the corresponding differential ionospheric delay observables;

[0044] A solution module, configured to use the model parameters and the satellite hardware delay bias as parameters to be estimated, form an observation vector with the differential ionospheric delay observables at the current epoch, construct an observation equation, and perform filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters.

[0045] In a preferred example, the system further includes a broadcast module, configured to calculate the differential ionospheric delay observables at grid points by using the solved regional differential ionospheric model, save them in a grid form, and broadcast them to regional user terminals.

[0046] In a preferred example, the original observation data is dual-frequency observation data.

[0047] In a preferred example, the receiving module is further configured to calculate the ionospheric delay observables by using a non-differential and non-combined PPP algorithm based on the dual-frequency pseudorange observables and carrier observables, where the calculated ionospheric delay observables are expressed as:

[0048] where a represents the integral constant of the ionospheric propagation path, STEC represents the slant total electron content, represents the total electron content on the slant path between base station k and satellite s, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, DCB k represents the hardware delay bias of receiver k, and DCB s represents the hardware delay bias of satellite s.

[0049] In a preferred example, the solution module is further configured to establish a Kalman filter and perform real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters.

[0050] In a preferred example, the solution module is further configured to add a constraint condition "for satellite s not observed at each epoch, then DCB s = 0" to avoid rank deficiency of the equation, where DCB s represents the hardware delay bias of satellite s.

[0051] In a preferred example, the receiving module is further configured to calculate the puncture point longitude and latitude according to the following formula based on the ionospheric single-layer model assumption

[0052]

[0053]

[0054]

[0055] Among them, α represents the geocentric angular distance of the puncture point, H represents the ionospheric height, E and A respectively represent the satellite altitude angle and azimuth angle, R represents the radius of the Earth, and λ k represents the longitude of the receiver, represents the latitude of the receiver.

[0056] In a preferred example, the calculation module is further configured to select, for the same base station, the satellite with the largest average altitude angle as the reference star, and the differential ionospheric delay observation value of the current epoch is equal to the difference between the ionospheric delay observation values corresponding to other satellites and the ionospheric delay observation value corresponding to the reference star. Among them, the differential ionospheric delay observation value between base station k and satellite s is expressed as:

[0057] Among them, is the total differential electron content between base station k and satellite s, represents the integrated path ionospheric electron density between base station k and satellite s, represents the integrated slant path ionospheric electron density between base station k and reference satellite ref, and DCB ref represents the hardware delay bias of reference star ref, and DCB s represents the hardware delay bias of satellite s.

[0058] In a preferred example, the fitting module is further configured to fit a regional differential ionospheric model based on the longitude and latitude of the puncture point and the corresponding differential ionospheric delay observation values, which is expressed as:

[0059] Among them, E mn represents the model parameter, represents the geographical latitude of the center point of the measurement area, S0 represents the center point of the measurement area at the solar hour angle t0 at the central moment of this time period, λ represents the geographical longitude of the puncture point, t represents the observation time, M and N represent the model order.

[0060] In a preferred example, the fitting module is further configured to fit a regional differential ionospheric model based on the longitude and latitude of the puncture point and the corresponding differential ionospheric delay observation values, using spherical harmonic functions, which is expressed as:

[0061] Among them, A nm and B nm represent model parameters, n max represents the model order, and P nm (cosφ) represents the Legendre function of order n and degree m that is not fully normalized. φ and λ are respectively expressed as:

[0062]

[0063]

[0064] Among them, λ IPP and respectively represent the geographical longitude and latitude at the puncture point. t represents the current epoch, and λ M and respectively represent the geomagnetic longitude and latitude, and λ SUN represents the meridian longitude passing through the center of the earth and the sun.

[0065] In a preferred example, the observation equation is expressed as:

[0066] Among them, a represents the integral constant of the ionospheric propagation path, MF represents the projection function, z' represents the angle between the line connecting the base station and the satellite and the zenith direction at the puncture point IPP, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, DCB s represents the hardware delay deviation of satellite s, and DCB ref represents the hardware delay deviation of the reference star ref, and dVTEC IPP represents the differential vertical total electron content of the ionosphere at the puncture point IPP.

[0067] This application also discloses a differential ionospheric modeling system, including:

[0068] A memory for storing computer-executable instructions; and,

[0069] A processor for implementing the steps in the method described above when executing the computer-executable instructions.

[0070] This application also discloses a computer-readable storage medium. Computer-executable instructions are stored in the computer-readable storage medium, and when the computer-executable instructions are executed by a processor, the steps in the method described above are implemented.

[0071] In the embodiments of this application, compared with the prior art, it includes at least the following advantages and beneficial effects:

[0072] Define the scope of the modeling area, select a reference satellite based on the elevation angles between each satellite and the base station within the defined area, and perform differential calculation on the ionospheric delay observables of each satellite and the reference satellite to eliminate the hardware delay deviation at the base station end, effectively reducing the modeling error. Compared with the prior art, the model accuracy of the differential ionospheric model constructed according to the embodiments of the present application is significantly improved.

[0073] Furthermore, calculate the ionospheric differential delay at grid points using the regional differential ionospheric model obtained by the embodiments of the present application and broadcast it to regional users as the ionospheric constraint condition in the user-side positioning algorithm (such as the PPP algorithm), which can significantly improve the user-side positioning accuracy and reduce the positioning convergence time.

[0074] A large number of technical features are recorded in the description of the present application, distributed in various technical solutions. If all possible combinations of technical features (i.e., technical solutions) of the present application are listed, the description will be too long. To avoid this problem, each technical feature disclosed in the above-mentioned invention content of the present application, each technical feature disclosed in the following embodiments and examples, and each technical feature disclosed in the drawings can be freely combined with each other to form various new technical solutions (these technical solutions are all regarded as having been recorded in this description), unless the combination of such technical features is technically infeasible. For example, in one example, features A+B+C are disclosed, and in another example, features A+B+D+E are disclosed. Features C and D are equivalent technical means that play the same role, and only one of them can be used technically and they cannot be used simultaneously. Feature E can be combined with feature C technically. Then, the solution of A+B+C+D should not be regarded as having been recorded because it is technically infeasible, while the solution of A+B+C+E should be regarded as having been recorded. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a schematic flowchart of a differential ionospheric modeling method according to the first embodiment of the present application.

[0076] Figure 2 It is a schematic structural diagram of a differential ionospheric modeling system according to the second embodiment of the present application.

[0077] Figure 3 It is a schematic flowchart of a differential real-time ionospheric modeling process according to an example of the present application.

[0078] Figure 4 It is a schematic diagram of calculating differential ionospheric delay observables according to an example of the present application.

[0079] Figure 5 It is a comparison chart of non-differential and non-combined PPP positioning errors with or without adding ionospheric dVTEC constraint conditions according to an example of the present application.

[0080] Figure 6 This is a statistical histogram of the RMS of the modeling error of an example regional ionospheric dVTEC distribution model according to the present application. Detailed implementation manners

[0081] In the following description, many technical details are presented for the reader to better understand the present application. However, those of ordinary skill in the art can understand that the technical solutions claimed in the present application can be implemented even without these technical details and various changes and modifications based on the following embodiments.

[0082] To make the objectives, technical solutions, and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0083] The first embodiment of the present application relates to a differential ionospheric modeling method, and its process is as Figure 1 shown. This method includes the following steps:

[0084] In step 101, the original observation data and navigation message of the regional base station receiver are received, and the elevation angle, the longitude and latitude of the piercing point, and the ionospheric delay observation quantity between each satellite and the base station are calculated.

[0085] There is no limitation on the division of each region in step 101. For example, the region can be divided equally by area; or, the region can also be divided according to administrative regions (taking China as an example, the region can be divided according to provincial administrative regions, etc.). For the scope of the regional base station in step 101, it can be all the base stations in the region, or a part of the base stations selected from all the base stations in the region. For the method of selecting part of the base stations, for example, but not limited to, selecting an appropriate number and appropriate positions of base stations according to the distribution of each base station in the region and / or the geographical environment, etc.

[0086] Optionally, in step 101, it further includes the step of eliminating the gross error of the received data. Among them, the specific method of eliminating the gross error can be any existing technology for eliminating gross error, which will not be elaborated here.

[0087] Optionally, the original observation data can be, but not limited to, single-frequency or dual-frequency observation data, etc.

[0088] In one embodiment, when calculating the ionospheric delay observation quantity, the non-differential and non-combination PPP algorithm can be used to calculate the ionospheric delay observation quantity based on the dual-frequency pseudorange observation quantity and the carrier observation quantity. Specifically, the dual-frequency pseudorange observation quantity and the dual-frequency carrier phase observation quantity are respectively expressed as:

[0089]

[0090]

[0091] Among them, s, k, and j respectively represent the satellite, the base station receiver, and the frequency; c represents the speed of light; represents the pseudorange observation value between the satellite s and the base station receiver k at the frequency j; represents the carrier phase observation value between the satellite s and the base station receiver k at the frequency j; represents the geometric distance from the satellite s to the antenna phase center of the base station receiver k; δt k represents the clock error of the base station receiver k; δt s represents the clock error of the satellite s; represents the tropospheric delay; represents the ionospheric delay; α j represents the frequency ratio represents the pseudorange hardware delay of the receiver at the frequency j; represents the pseudorange hardware delay of the satellite at the frequency j; represents the carrier phase deviation (hardware delay) of the receiver at the frequency j; represents the carrier phase deviation (hardware delay) of the satellite at the frequency j; λ j represents the carrier wavelength at the frequency j; N j represents the undifferenced phase integer ambiguity at the frequency j; represents the modelable errors, including antenna phase center correction, antenna phase wrapping, relativistic effects, tidal correction, etc. It is assumed that the above errors have been corrected to the observed values using an empirical model; represents the pseudorange observation value noise at the frequency j; represents the phase observation value noise at the frequency j. The code pseudorange and phase observation values (distance units) on the L1 and L2 carriers are P1, P2, Φ1, and Φ2 in sequence; the ionospheric delay can be represented by the total electron content TEC in the ionosphere. The spatial and temporal variations of TEC reflect the main characteristics of the ionosphere. The ionospheric delay observation value can be expressed in a form containing TEC:

[0092] Among them, a represents the ionospheric propagation path integration constant, with a value of 40.3; STEC (Slant Total Electron Content) represents the slant total electron content; is the total electron content on the slant path between the base station k and the satellite s; f1 is the frequency of the L1 carrier; f2 is the frequency of the L2 carrier; DCB k is the differential code bias of the receiver k; DCB sis the differential code bias of satellite s. In the non-differential and non-combination model, the pseudorange and phase observables, and the hardware delay differences between the receiver and the satellite can be expressed as two parts related to frequency and independent of frequency, as shown in the following formula:

[0093]

[0094]

[0095] where the frequency-dependent term is absorbed by the ionospheric delay Therefore, it is defined that and are the hardware delay biases between the receiver and each satellite, respectively, referring to the difference in hardware delays between different frequencies.

[0096] In other embodiments, when calculating the ionospheric delay observable, the phase-smoothed pseudorange algorithm or the pseudorange single-point positioning algorithm can also be used, etc., and the present application does not make any restrictions.

[0097] Optionally, when calculating the longitude and latitude of the piercing point, the ionospheric single-layer model assumption can be adopted, that is, it is assumed that all free electrons in the ionosphere are concentrated on an infinitely thin single layer at a height of H. The value of H can be equal to 350 km, etc. At this time, when the signal between the satellite and the base station passes through the ionosphere, it can be represented by the ionospheric pierce point (IPP). According to the positions, elevation angles E and azimuth angles A of the satellite and the base station receiver, the longitude and latitude of the piercing point are calculated according to the following formula

[0098]

[0099]

[0100] where α represents the geocentric angular distance of the piercing point, H represents the ionospheric height, E and A represent the satellite elevation angle and azimuth angle respectively, R represents the radius of the earth, and λ k represents the receiver longitude, represents the receiver latitude.

[0101] After that, enter step 102. At a single epoch, select a reference star, and calculate the difference between the ionospheric delay observables corresponding to other satellites and the reference star to obtain the differential ionospheric delay observable of the current epoch.

[0102] Generally, the satellite with the best signal quality is selected as the reference satellite. The judgment criteria usually include elevation angle, signal-to-noise ratio, the fixation situation in the previous epoch, etc. In this embodiment, the elevation angle is selected as the basis for selection. By calculating the average value of the elevation angles between each satellite and multiple base stations, the average elevation angle corresponding to each satellite is obtained, and the satellite with the largest average elevation angle is selected as the reference satellite. It should be understood that the present invention is not limited to using the elevation angle as the basis, and can also be selected according to the signal-to-noise ratio, etc.

[0103] In the embodiment of selecting the reference satellite according to the elevation angle, for example, for the same base station, the satellite with the largest elevation angle with respect to this base station can be selected as the reference satellite, and different base stations correspond to different reference satellites. Alternatively, for each satellite, the average elevation angle between each satellite and each base station can be calculated, and the satellite with the largest calculated average elevation angle is selected as the reference satellite.

[0104] Optionally, in the embodiment of calculating the ionospheric delay observable by using the undifferenced and uncombined PPP algorithm based on dual-frequency pseudorange observables and carrier observables, the differential ionospheric delay observable at the current epoch is equal to the difference between the ionospheric delay observables of other satellites and that of the reference satellite respectively. Then, the differential ionospheric delay observable between base station k and satellite s is constructed It can be expressed as:

[0105] Wherein, is the differential total electron content between base station k and satellite s, represents the integrated path ionospheric electron density between base station k and satellite s, represents the integrated slant path ionospheric electron density between base station k and reference satellite ref, DCB ref represents the hardware delay bias of reference satellite ref, DCB s represents the hardware delay bias of satellite s. In this way, the hardware delay bias at the base station end can be eliminated.

[0106] Furthermore, when the ionospheric delay observable at the obtained piercing point is obtained, for the convenience of calculation, preferably, dSTEC is projected onto the vertical direction dVTEC, and the projection function is as follows:

[0107]

[0108]

[0109] dSTEC = dVTEC·MF

[0110] Wherein, MF (Mapping Function) is the projection function, and z' is the angle between the connection line of the station and the satellite at the piercing point and the zenith direction.

[0111] After that, enter step 103. Based on the longitude and latitude of the piercing point calculated in step 101 and the corresponding differential ionospheric delay observables, use a fitting function to fit the regional differential ionospheric model (i.e., the dVTEC (difference Vertical Total Electron Content) distribution model). The dVTEC value at any piercing point is a function related to the longitude and latitude of the piercing point.

[0112] There are various types of fitting functions used in this step 103, such as but not limited to spherical harmonic functions, polynomial functions, spline functions, or spherical cap harmonic functions, etc.

[0113] For example, when the fitting function uses a polynomial function, this step 103 can be further implemented as: Based on the longitude and latitude of the piercing point, use the polynomial function to fit the regional differential ionospheric model, expressed as:

[0114] where, E mn represents the model parameter, represents the geographical latitude of the center point of the measurement area, S0 represents the center point of the measurement area at the solar hour angle t0 at the central moment of this time period, λ represents the geographical longitude of the piercing point, t represents the observation time, M and N represent the model orders.

[0115] For example, when the fitting function uses a spherical harmonic function, this step 103 can be further implemented as: Based on the longitude and latitude of the piercing point, use the spherical harmonic function to fit the regional differential ionospheric model, expressed as:

[0116] where, A nm , B nm represent the model parameters, n max represents the model order, P nm (cosφ) represents the Legendre function of order n and degree m that is not fully normalized, and φ and λ are respectively expressed as:

[0117]

[0118]

[0119] where, λ IPP , respectively represent the geographical longitude and latitude at the piercing point, t represents the current epoch, λ M , respectively represent the geomagnetic longitude and latitude, λ SUN represents the longitude of the meridian passing through the center of the earth and the sun.

[0120] After that, enter step 104. Take the model parameters and the satellite hardware delay deviation as the parameters to be estimated, and use the differential ionospheric delay observables at the current epoch to form an observation vector, and construct an observation equation.

[0121] Optionally, combine the ionospheric differential observables obtained in step 102 and the regional differential ionospheric model (i.e., the dVTEC distribution model) obtained in step 103 to construct the observation equation as:

[0122]

[0123] Furthermore, taking the example of fitting the model with spherical harmonic functions, the differential ionospheric delay observables can be expressed as:

[0124]

[0125] The observation equation can be further expressed as:

[0126] where a represents the integral constant of the ionospheric propagation path, MF represents the projection function, z' represents the angle between the line connecting the base station and the satellite at the piercing point IPP and the zenith direction, f1 represents the frequency of the L1 carrier wave, f2 represents the frequency of the L2 carrier wave, DCB s represents the hardware delay deviation of satellite s, DCB ref represents the hardware delay deviation of the reference star ref, and dVTEC IPP represents the differential vertical total electron content of the ionosphere at the piercing point IPP.

[0127] After that, enter step 105. Based on the observation equation constructed in step 104, perform filtering processing on the parameters to be estimated to solve the model parameters.

[0128] The methods for solving the model parameters in step 105 are diverse. Optionally, step 105 can be further implemented as: establishing a Kalman filter and performing real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters. Optionally, step 105 can be further implemented as: performing real-time filtering processing on the parameters to be estimated according to algorithms such as least squares to solve the model parameters. And it is not limited to these two methods.

[0129] Furthermore, in the embodiment of establishing a Kalman filter and performing real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters, the parameters to be estimated at the current epoch include the dVTEC model parameters and the hardware delay deviation of the satellite: X = [A 00 , B 00 , A 01 , B 01 ,..., DCB1 , DCB 2 ,...] T , where [DCB 1 , DCB 2 ,...] represents the hardware delay deviation of all visible satellites. Since inter-satellite differencing is performed for each base station, there is no hardware delay deviation of the receiver in the parameters to be estimated.

[0130] Optionally, in step 105, to avoid rank deficiency of the equation, a constraint condition can be added: the DCB of the satellite s not observed at each epoch is set to 0, that is, DCB s = 0, where DCB s represents the hardware delay deviation of satellite s.

[0131] Optionally, after step 105, the following steps can also be included: calculating the differential ionospheric delay observables at the grid points using the solved regional differential ionospheric model, saving them in grid form and broadcasting them to the regional user terminals. Among them, the broadcast format is, for example, but not limited to, using IONEX (The IONosphere Map Exchange, Format), etc. The regional user terminals can, for example, use the received differential ionospheric delay observables at the grid points as the ionospheric constraint conditions in the positioning algorithm, which can significantly improve the positioning accuracy and convergence speed of the algorithm.

[0132] The modeling process of the implementation manner of this application can be real-time differential ionospheric modeling epoch by epoch, or can be differential ionospheric modeling periodically (for example, every preset epoch, etc.).

[0133] The second implementation manner of this application relates to a differential ionospheric modeling system, the structure of which is as Figure 2 shown. This differential ionospheric modeling system includes a receiving module, a calculating module, a fitting module and a solving module.

[0134] Specifically, this receiving module is used to receive the original observation data and navigation messages of the regional base station receivers, and calculate the elevation angle, piercing point longitude and latitude, and ionospheric delay observables between each satellite and the base station.

[0135] Among them, there is no limitation on the division of the region. For example, the region can be divided evenly by area; or, for another example, the region can also be divided by administrative regions (taking China as an example, the region can be divided by provincial administrative regions, etc.). The range of the regional base stations can be all the base stations in the region, or can be part of the base stations selected from all the base stations in the region. For the selection method of part of the base stations, for example, but not limited to, selecting the appropriate number and appropriate locations of base stations according to the distribution of each base station in the region and / or the geographical environment, etc.

[0136] Optionally, the receiving module is further configured to reject outliers in the received data. Specifically, the method for rejecting outliers can be any existing outlier rejection technique, which will not be elaborated herein.

[0137] Optionally, the raw observation data can be, but is not limited to, single-frequency or dual-frequency observation data, etc.

[0138] In one embodiment, the receiving module is further configured to calculate the ionospheric delay observable based on the dual-frequency pseudorange observable and the carrier observable using the undifferenced and uncombined PPP algorithm. In other embodiments, when calculating the ionospheric delay observable, the phase-smoothed pseudorange algorithm or the pseudorange single-point positioning algorithm, etc., can also be used to calculate the ionospheric delay observable, and the present application does not make any restrictions.

[0139] Optionally, the receiving module is further configured to adopt the assumption of the ionospheric single-layer model, that is, assume that all free electrons in the ionosphere are concentrated on an infinitely thin single layer at a height of H. For example, H = 350 km, etc. At this time, when the signal between the satellite and the base station passes through the ionosphere, it can be represented by the Ionospheric Pierce Point (IPP). Given the positions, elevation angles E, and azimuth angles A of the satellite and the base station receiver, the longitude and latitude of the piercing point are calculated according to the following formula

[0140]

[0141]

[0142]

[0143] where α represents the geocentric subtended angle of the piercing point, H represents the ionospheric height, E and A respectively represent the satellite elevation angle and azimuth angle, R represents the radius of the earth, λ k represents the receiver longitude, represents the receiver latitude.

[0144] The calculation module is configured to select a reference satellite and calculate the difference between the ionospheric delay observables corresponding to other satellites and the ionospheric delay observable corresponding to the reference satellite to obtain the differential ionospheric delay observable at the current epoch.

[0145] Generally, the satellite with the best signal quality is selected as the reference satellite. The judgment criteria usually include elevation angle, signal-to-noise ratio, the fixed situation in the previous epoch, etc. In this embodiment, the elevation angle is used as the selection basis. By calculating the average value of the elevation angles between each satellite and multiple base stations, the average elevation angle corresponding to each satellite is obtained, and the satellite with the largest average elevation angle is selected as the reference satellite. It should be understood that the present invention is not limited to using the elevation angle as the basis and can also be selected according to the signal-to-noise ratio, etc.

[0146] In an embodiment of selecting a reference star according to the elevation angle, for example, for the same base station, the satellite with the largest elevation angle with respect to the base station can be selected as the reference star, and different base stations correspond to different reference stars. Alternatively, for each satellite, the average elevation angle between each satellite and each base station can be calculated, and the satellite with the largest calculated average elevation angle can be selected as the reference star.

[0147] For example, in an embodiment of calculating the ionospheric delay observation by using a non-differential and non-combination PPP algorithm based on dual-frequency pseudorange observations and carrier observations, the calculation module is further configured to calculate that the differential ionospheric delay observation is equal to the difference between the ionospheric delay observations of other satellites and the reference star respectively, and construct the differential ionospheric delay observation between base station k and satellite s. It can be expressed as:

[0148] Wherein, is the differential total electron content between base station k and satellite s, represents the integrated path ionospheric electron density between base station k and satellite s, represents the integrated slant-path ionospheric electron density between base station k and reference satellite ref, DCB ref represents the hardware delay bias of reference star ref, DCB s represents the hardware delay bias of satellite s. In this way, the hardware delay bias at the base station end can be eliminated.

[0149] Furthermore, the calculation module calculates the differential ionospheric delay observation at the piercing point For the convenience of calculation, the calculation module is further configured to project dSTEC to the vertical direction dVTEC, and the projection function is as follows:

[0150]

[0151]

[0152] dSTEC = dVTEC · MF

[0153] Wherein, MF (Mapping Function) is the projection function, and z' is the angle between the line connecting the station and the satellite at the piercing point and the zenith direction.

[0154] The fitting module is configured to fit a regional differential ionospheric model by using a fitting function based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observation, and the dVTEC value at any piercing point is a function related to the longitude and latitude of the piercing point.

[0155] The types of fitting functions adopted by the fitting module are diverse, such as but not limited to spherical harmonic functions, polynomial functions, spline functions, or spherical cap harmonic functions, etc.

[0156] For example, when using a polynomial function, the fitting module is also used to fit the regional differential ionospheric model dVTEC based on the longitude and latitude of the piercing point by using the polynomial function, which is expressed as:

[0157] where E mn represents the model parameter, represents the geographical latitude of the center point of the measurement area, S0 represents the center point of the measurement area at the solar hour angle t0 at the central moment of this time period, λ represents the geographical longitude of the piercing point, t represents the observation moment, M and N represent the model orders.

[0158] For example, when using a spherical harmonic function, the fitting module is also used to fit the regional differential ionospheric model dVTEC based on the longitude and latitude of the piercing point by using the spherical harmonic function, which is expressed as:

[0159] where A nm and B nm represent the model parameters, n max represents the model order, P nm (cosφ) represents the Legendre function of the nth order and mth degree that is not fully normalized, and φ and λ are respectively expressed as:

[0160]

[0161]

[0162] where λ IPP and respectively represent the geographical longitude and latitude at the piercing point, t represents the current epoch, λ M and respectively represent the geomagnetic longitude and latitude, and λ SUN represents the longitude of the meridian passing through the center of the earth and the sun.

[0163] The solution module is used to take the model parameters and the satellite hardware delay deviation as the parameters to be estimated, form an observation vector with the differential ionospheric delay observables at the current epoch, construct an observation equation, and perform filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters.

[0164] Optionally, the ionospheric differential observables calculated by the joint calculation module and the regional differential ionospheric model dVTEC fitted by the fitting module are used to construct an observation equation as:

[0165]

[0166] Further, taking the model obtained by fitting with spherical harmonic functions as an example, the differential ionospheric delay observables can be expressed as:

[0167]

[0168] The observation equation can be expressed as:

[0169] where a represents the integral constant of the ionospheric propagation path, MF represents the projection function, z' represents the angle between the line connecting the base station and the satellite at the piercing point IPP and the zenith direction, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, DCB s represents the hardware delay deviation of satellite s, DCB ref represents the hardware delay deviation of the reference star ref, and dVTEC IPP represents the differential vertical total electron content of the ionosphere at the piercing point IPP.

[0170] Optionally, the solution module is further configured to establish a Kalman filter to perform real-time Kalman filtering on the parameter to be estimated to solve the model parameter. Optionally, the solution module is further configured to perform filtering on the parameter to be estimated in real time according to algorithms such as least squares to solve the model parameter. And it is not limited to these two methods.

[0171] For example, in the embodiment of establishing a Kalman filter to perform real-time Kalman filtering on the parameter to be estimated to solve the model parameter, the parameters to be estimated at the current epoch include dVTEC model parameters and the hardware delay deviation of the satellite: X = [A 00 , B 00 , A 01 , B 01 ,..., DCB 1 , DCB 2 ,...] T , where [DCB 1 , DCB 2 ,...] represents the hardware delay deviations of all visible satellites. Since inter-satellite differencing is performed for each base station, there is no hardware delay deviation of the receiver in the parameters to be estimated.

[0172] Optionally, the solution module is further configured to add a constraint condition that "the DCB of the unobserved satellite s at each epoch is set to 0, i.e., DCB s = 0" to avoid rank deficiency of the equation, where DCB s represents the hardware delay deviation of satellite s.

[0173] Optionally, the system further includes a broadcasting module, which is used to calculate the differential ionospheric delay observables at grid points by using the solved regional differential ionospheric model, save them in the form of a grid and broadcast them to regional user terminals. Among them, the broadcast format is, for example but not limited to, IONEX (The Ionosphere Map Exchange Format), etc. The regional user terminal can, for example, use the received differential ionospheric delay observables at grid points as the ionospheric constraint condition in the positioning algorithm, which can significantly improve the positioning accuracy and convergence speed of the algorithm.

[0174] The first implementation manner is a method implementation manner corresponding to this implementation manner. The technical details in the first implementation manner can be applied to this implementation manner, and the technical details in this implementation manner can also be applied to the first implementation manner.

[0175] In order to demonstrate the advantages and effects of this application, a specific example will be described below. The details listed in this example are mainly for easy understanding and do not limit the protection scope of this application.

[0176] This example is a modeling experiment verification based on the data of the Beidou ground-based augmentation system at the regional reference stations in Yunnan. The data was collected on May 1, 2020, from 0:01:00 to 23:59:30 UTC, with a sampling interval of 30 s. A total of 22 base stations in this region were selected, among which 21 base stations were used as the modeling stations for the dVTEC distribution model, and the remaining one base station was used as the model performance verification station. That is, the regional differential ionospheric model was established according to the implementation manner of this application using the data of 21 real-time modeling stations, and the PPP positioning experiment was carried out using the data of the verification station.

[0177] Figure 3 The figure shows the flow chart of the differential ionospheric modeling method for this example, which specifically includes: obtaining or receiving the data of the modeling stations and the verification station, preprocessing the obtained or received data (gross error detection, cycle slip detection and repair, error correction, etc.), filtering the preprocessed data using a non-differential and non-combined PPP filter, selecting reference satellites and calculating differential ionospheric delay observables based on the filtered data, fitting the regional differential ionospheric model and constructing the observation equation, estimating the model parameters of the fitted regional differential ionospheric model using a Kalman filter based on the observation equation, so as to finally obtain the regional differential ionospheric model (i.e., the dVTEC distribution model), and finally generating a grid ionospheric product based on this model and broadcasting it to the user terminals in this region.

[0178] Figure 4 A schematic diagram of a method for calculating differential ionospheric delay observables in an example is given. In the figure, the four surrounding base stations are used as modeling stations, and the red station at the center position is the verification station or the user terminal. For each modeling station, the satellite with the largest average elevation angle is selected as the reference satellite. Figure 4The green satellite represents the selected reference satellite S-REF. For example, Figure 4 As shown, the ionospheric delay observables between base station K01 and satellites S01, S02, and S03 are differentially calculated with the delay corresponding to the reference satellite S-REF to form the differential ionospheric delay observables between the base station and the satellites, which are used as the input observables for dVTEC distribution modeling to construct the model. The dVTEC value at the user location is calculated according to the longitude and latitude and used as the ionospheric constraint in the positioning algorithm.

[0179] Figure 5 The comparison of positioning errors obtained by the dual-frequency non-differential and non-combined PPP algorithm without ionospheric constraint (black line) and the dual-frequency non-differential and non-combined PPP algorithm with the addition of the dVTEC distribution model as the ionospheric constraint (red line) is given. The algorithm converges once per hour.

[0180] The following Table 1 is the statistical table of the convergence time of non-differential and non-combined PPP with or without ionospheric dVTEC constraint in this example, which shows the influence of whether to add the differential ionospheric dVTEC distribution model as a constraint on the positioning convergence time of the PPP algorithm in dual-frequency non-differential and non-combined PPP. According to the statistical results, it can be seen that after accessing the regional differential ionospheric dVTEC distribution model constraint, the convergence speed of dual-frequency PPP can be effectively improved.

[0181] Table 1

[0182]

[0183] The following Table 2 is the statistical table of the positioning errors of non-differential and non-combined PPP with or without ionospheric dVTEC constraint in this example, which shows the influence of whether to add the ionospheric dVTEC distribution model as a constraint on the positioning accuracy of the PPP algorithm in dual-frequency non-differential and non-combined PPP. According to the calculation, the positioning accuracy in the three directions is improved by 24.52%, 26.87%, and 31.16% respectively. After adding the ionospheric dVTEC distribution model, the positioning errors of 2058 out of 2880 epochs throughout the day have decreased, accounting for 71.46%, while the errors of 805 epochs have increased slightly. The possible reason is that the gross errors at these epoch times are relatively large, resulting in large errors in the ionospheric delay observables extracted by the non-differential and non-combined PPP algorithm. This error is further introduced into the dVTEC distribution model, resulting in the failure to improve the positioning accuracy as a constraint.

[0184] Table 2

[0185]

[0186] Figure 6The RMS statistical histogram of the modeling error corresponding to the dVTEC distribution model is given, that is, the RMS value of the dSTEC modeling error is statistically calculated for each satellite. After calculation, the average value of the dSTEC modeling error of this model is about 0.0350 m, that is, 0.2158 TECU. As Figure 6 shown by the dashed line in

[0187] It should be noted that those skilled in the art should understand that the implementation functions of the various modules shown in the above implementation manner of the differential ionospheric modeling system can be understood with reference to the relevant descriptions of the foregoing differential ionospheric modeling method. The functions of the various modules shown in the above implementation manner of the differential ionospheric modeling system can be realized by a program (executable instruction) running on a processor, or can be realized by specific logic circuits. If the differential ionospheric modeling system in the embodiments of the present application is implemented in the form of software function modules and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the embodiments of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in the various embodiments of the present application. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read Only Memory), magnetic disks, or optical discs that can store program codes. In this way, the embodiments of the present application are not limited to any specific combination of hardware and software.

[0188] Accordingly, an embodiment of the present application further provides a computer-readable storage medium, which stores computer-executable instructions. When the computer-executable instructions are executed by a processor, the various method embodiments of the present application are implemented. The computer-readable storage medium includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible by a computing device. As defined herein, computer-readable storage media do not include transitory media such as modulated data signals and carrier waves.

[0189] In addition, an embodiment of the present application further provides a differential ionosphere modeling system, which includes a memory for storing computer-executable instructions and a processor. The processor is configured to implement the steps in the above-mentioned method embodiments when executing the computer-executable instructions in the memory. Among them, the processor can be a central processing unit (Central Processing Unit, abbreviated as "CPU"), or other general-purpose processors, digital signal processors (Digital Signal Processor, abbreviated as "DSP"), application specific integrated circuits (Application Specific Integrated Circuit, abbreviated as "ASIC"), etc. The aforementioned memory can be a read-only memory (abbreviated as "ROM"), random access memory (abbreviated as "RAM"), flash memory, hard disk, or solid-state drive, etc. The steps of the methods disclosed in the embodiments of the present invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules in the processor.

[0190] It should be noted that in the application documents of this patent, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one" does not exclude the existence of additional identical elements in the process, method, article or device comprising said element. In the application documents of this patent, if it is mentioned that an act is performed according to a certain element, it means that the act is performed at least according to that element, including two cases: the act is performed only according to that element, and the act is performed according to that element and other elements. Expressions such as multiple, many times, various, etc. include 2, 2 times, 2 kinds, and more than 2, more than 2 times, more than 2 kinds.

[0191] All the documents mentioned in this application are considered to be integrally included in the disclosure of this application so as to be used as a basis for modification when necessary. In addition, it should be understood that the above description is only a preferred embodiment of this specification and is not used to limit the protection scope of this specification. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of one or more embodiments of this specification shall be included in the protection scope of one or more embodiments of this specification.

Claims

1. A differential ionospheric modeling method, characterized in that, Including: Receiving the original observation data and navigation message of the regional base station receiver, and calculating the elevation angle between each satellite and the base station, the longitude and latitude of the piercing point, and the ionospheric delay observation quantity; Selecting a reference star, and calculating the difference between the ionospheric delay observation quantities corresponding to other satellites and the reference star to obtain the differential ionospheric delay observation quantity of the current epoch; Based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observation quantity, fitting a regional differential ionospheric model by using a fitting function; Taking the model parameters and the satellite hardware delay deviation as parameters to be estimated, and using the differential ionospheric delay observation quantity of the current epoch to form an observation vector, and constructing an observation equation; Based on the observation equation, performing filtering processing on the parameters to be estimated to solve the model parameters; Wherein, the original observation data is dual-frequency observation data; And, when calculating the ionospheric delay observation quantity, it further includes: Based on dual-frequency pseudorange observables and carrier observables, the undifferenced and uncombined PPP algorithm is used to calculate the ionospheric delay observables, where the calculated ionospheric delay observables are expressed as: where a represents the integral constant of the ionospheric propagation path, represents the total electron content on the slant path between base station k and satellite s, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, and DCB k represents the hardware delay deviation of receiver k, and DCB s represents the hardware delay deviation of satellite s; And, the step of selecting a reference star, calculating the difference between the ionospheric delay observation quantities corresponding to other satellites and the reference star to obtain the differential ionospheric delay observation quantity of the current epoch further includes: For the same base station, select the satellite with the largest elevation angle as the reference satellite. The differential ionospheric delay observation value at the current epoch is equal to the difference between the ionospheric delay observation values corresponding to other satellites and the reference satellite respectively. Among them, the differential ionospheric delay observation value between base station k and satellite s is expressed as: wherein, is the differential total electron content between base station k and satellite s, represents the integrated amount of ionospheric electron density along the path between base station k and satellite s, represents the integrated amount of ionospheric electron density along the slant path between base station k and reference satellite ref, DCB ref represents the hardware delay bias of reference satellite ref, DCB s represents the hardware delay bias of satellite s.

2. The differential ionospheric modeling method according to claim 1, wherein After performing filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters, it further includes: Calculating the differential ionospheric delay observation quantity at the grid point by using the solved regional differential ionospheric model, saving it in the form of a grid and broadcasting it to the regional user terminal.

3. The differential ionospheric modeling method according to claim 1, characterized in that The step of performing filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters further includes: Establishing a Kalman filter, and performing real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters.

4. The differential ionospheric modeling method according to claim 3, wherein When establishing the Kalman filter and performing real-time Kalman filtering processing on the parameters to be estimated to solve the model parameters, it further includes: Add the constraint condition "For satellite s not observed at each epoch, then DCB s = 0" to avoid rank deficiency of the equation, where DCB s represents the hardware delay bias of satellite s.

5. The differential ionospheric modeling method according to claim 1, characterized in that When calculating the longitude and latitude of the piercing point, it further includes: Based on the assumption of the ionospheric single-layer model, calculate the longitude and latitude of the piercing point according to the following formula Among them, α represents the geocentric angular distance of the puncture point, H represents the ionospheric height, E and A respectively represent the satellite altitude angle and azimuth angle, R represents the radius of the Earth, and λ k represents the longitude of the receiver, represents the latitude of the receiver.

6. The differential ionospheric modeling method according to claim 1, wherein The fitting function is a polynomial function; Based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observation quantity, fitting a regional differential ionospheric model by using a fitting function, which is expressed as: Among them, E mn represents the model parameters, represents the geographical latitude of the center point of the survey area, S0 represents the center point of the survey area at the solar hour angle at the central moment t0 of the modeling time period, λ represents the geographical longitude of the puncture point, t represents the observation time, and M and N represent the model orders.

7. The differential ionospheric modeling method according to claim 1, characterized in that The fitting function is a spherical harmonic function; Based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observation quantity, fitting a regional differential ionospheric model by using a fitting function, which is expressed as: Among them, A nm , B nm represent model parameters, n max represents the model order, P nm (cosφ) represents the Legendre function of order n and degree m that is not fully normalized. φ and λ are respectively expressed as: Among them, λ IPP , represent the geographical longitude and latitude at the puncture point respectively, t represents the current epoch, λ M , represent the geomagnetic longitude and latitude respectively, and λ SUN represents the meridian longitude passing through the center of the Earth and the Sun.

8. The differential ionospheric modeling method according to claim 6 or 7, characterized in that, The observation equation is expressed as: Among them, a represents the integral constant of the ionospheric propagation path, and MF represents the projection function. z' represents the angle between the line connecting the base station and the satellite at the piercing point IPP and the zenith direction, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, and DCB s represents the hardware delay deviation of satellite s, and DCB ref represents the hardware delay deviation of the reference star ref, and dVTEC IPP represents the differential vertical total electron content of the ionosphere at the piercing point IPP.

9. A differential ionospheric modeling system, characterized in that, Including: A receiving module, configured to receive the original observation data and navigation message of the regional base station receiver, and calculate the elevation angle between each satellite and the base station, the longitude and latitude of the piercing point, and the ionospheric delay observation quantity; A calculation module, configured to select a reference star, and calculate the difference between the ionospheric delay observation quantities corresponding to other satellites and the reference star to obtain the differential ionospheric delay observation quantity of the current epoch; A fitting module, configured to fit a regional differential ionospheric model by using a fitting function based on the longitude and latitude of the piercing point and the corresponding differential ionospheric delay observation quantity; A solution module, configured to take the model parameters and the satellite hardware delay deviation as parameters to be estimated, use the differential ionospheric delay observation quantity of the current epoch to form an observation vector, construct an observation equation, and perform filtering processing on the parameters to be estimated based on the observation equation to solve the model parameters; Wherein, the original observation data is dual-frequency observation data; And, when calculating the ionospheric delay observation quantity, it further includes: Based on dual-frequency pseudorange observables and carrier observables, the undifferenced and uncombined PPP algorithm is used to calculate the ionospheric delay observables, where the calculated ionospheric delay observables are expressed as: where a represents the integral constant of the ionospheric propagation path represents the total electron content on the slant path between base station k and satellite s, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, and DCB k represents the hardware delay deviation of receiver k, and DCB s represents the hardware delay deviation of satellite s; Moreover, the step of selecting a reference satellite and calculating the difference between the ionospheric delay observables of other satellites and the reference satellite to obtain the differential ionospheric delay observables at the current epoch further includes: For the same base station, select the satellite with the largest elevation angle as the reference satellite. The differential ionospheric delay observation at the current epoch is equal to the difference between the ionospheric delay observations corresponding to other satellites and the reference satellite respectively. Among them, the differential ionospheric delay observation between base station k and satellite s is expressed as: Among them, is the differential total electron content between base station k and satellite s, represents the integrated amount of the path ionospheric electron density between base station k and satellite s, represents the integrated amount of the oblique path ionospheric electron density between base station k and reference satellite ref, DCB ref represents the hardware delay bias of reference satellite ref, DCB s represents the hardware delay bias of satellite s.

10. The differential ionospheric modeling system according to claim 9, wherein It further includes a broadcast module, which is configured to calculate the differential ionospheric delay observables at grid points by using the solved regional differential ionospheric model, save them in the form of a grid, and broadcast them to regional user terminals.

11. The differential ionospheric modeling system according to claim 9, wherein The original observation data is dual-frequency observation data.

12. The differential ionospheric modeling system according to claim 11, wherein The receiving module is further configured to calculate the ionospheric delay observable by using a non-differential and non-combination PPP algorithm based on dual-frequency pseudo-range observables and carrier observables, wherein the calculated ionospheric delay observable is expressed as: Among them, a represents the integral constant of the ionospheric propagation path, represents the total electron content on the oblique path between base station k and satellite s, f1 represents the frequency of the L1 carrier wave, f2 represents the frequency of the L2 carrier wave, DCB k represents the hardware delay deviation of receiver k, DCB s represents the hardware delay deviation of satellite s.

13. The differential ionospheric modeling system according to claim 9, wherein, The solving module is further configured to establish a Kalman filter and perform real-time Kalman filtering on the parameters to be estimated to solve the model parameters.

14. The differential ionospheric modeling system according to claim 13, wherein The solution module is further configured to add a constraint condition that "for a satellite s not observed at each epoch, then DCB s = 0", to avoid rank deficiency of the equation, where DCB s represents the hardware delay deviation of satellite s.

15. The differential ionospheric modeling system according to claim 9, wherein The receiving module is further configured to calculate the latitude and longitude of the piercing point based on the assumption of the ionospheric single-layer model according to the following formula Among them, α represents the geocentric angular distance of the puncture point, H represents the ionospheric height, E and A respectively represent the satellite altitude angle and azimuth angle, R represents the radius of the Earth, and λ k represents the longitude of the receiver, represents the latitude of the receiver.

16. The differential ionospheric modeling system according to claim 12, wherein The calculation module is further configured to select, for the same base station, the satellite with the largest elevation angle as the reference satellite, and the differential ionospheric delay observation value of the current epoch is equal to the difference between the ionospheric delay observation values corresponding to other satellites and the reference satellite respectively, where the differential ionospheric delay observation value between base station k and satellite s is expressed as: Among them, is the differential total electron content between base station k and satellite s, represents the integrated amount of the path ionospheric electron density between base station k and satellite s, represents the integrated amount of the slant-path ionospheric electron density between base station k and reference satellite ref, DCB ref represents the hardware delay bias of reference satellite ref, DCB s represents the hardware delay bias of satellite s.

17. The differential ionospheric modeling system according to claim 9, characterized in that The fitting module is further configured to fit a regional differential ionospheric model based on the puncture point longitude and latitude and the corresponding differential ionospheric delay observables by using a polynomial function, which is expressed as: Among them, E mn represents the model parameters, represents the geographical latitude of the center point of the survey area, S0 represents the center point of the survey area at the solar hour angle at the central moment t0 of the modeling time period, λ represents the geographical longitude of the puncture point, t represents the observation time, M and N represent the model orders.

18. The differential ionospheric modeling system according to claim 9, wherein The fitting module is further configured to fit a regional differential ionospheric model based on the puncture point longitude and latitude and the corresponding differential ionospheric delay observables by using a spherical harmonic function, which is expressed as: Among them, A nm , B nm represent model parameters, n max represents the model order, P nm (cosφ) represents the Legendre function of order n and degree m that is not fully normalized. φ and λ are respectively expressed as: where, λ IPP , represent the geographical longitude and latitude at the puncture point respectively, t represents the current epoch, λ M , represent the geomagnetic longitude and latitude respectively, and λ SUN represents the meridian longitude passing through the center of the Earth and the Sun.

19. The differential ionospheric modeling system according to claim 17 or 18, wherein The observation equation is expressed as: Among them, a represents the integral constant of the ionospheric propagation path, and MF represents the projection function. z' represents the angle between the line connecting the base station and the satellite and the zenith direction at the piercing point IPP, f1 represents the frequency of the L1 carrier, f2 represents the frequency of the L2 carrier, and DCB s represents the hardware delay deviation of satellite s, and DCB ref represents the hardware delay deviation of the reference star ref, and dVTEC IPP represents the differential vertical total electron content of the ionosphere at the piercing point IPP.

20. A differential ionospheric modeling system, characterized in that, including: a memory for storing computer-executable instructions; and a processor for implementing the steps in the method according to any one of claims 1 to 8 when executing the computer-executable instructions.

21. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by the processor, the steps in the method according to any one of claims 1 to 8 are implemented.

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