Ionospheric differential total electron mass calculation method, device and storage medium

Abstract

The present application discloses a method, device, and storage medium for calculating the total differential electron mass of the ionosphere. The method for calculating the total differential electron mass of the ionosphere includes: obtaining the coordinates of the first puncture point of a user station, the coordinates of the second puncture points of multiple surrounding stations, and a first STEC differential component; obtaining an estimated value of the first STEC differential component of multiple surrounding stations according to a first fitting formula; eliminating the first STEC differential component according to the estimated value and the first STEC differential component; obtaining an estimated value of the second STEC differential component and an estimated value of the third STEC differential component for the eliminated first STEC differential component according to a second fitting formula; calculating the second residual of the estimated value of the second STEC differential component and the first STEC differential component; determining the hyperparameters of the kernel function according to the multiple second puncture point coordinates, the second residual, and the altitude angle of a preset satellite; and determining the STEC differential component of the user station according to the kernel function and the estimated value of the third STEC differential component. According to an embodiment of the present application, the accurate value of the STEC differential component of the user station can be obtained, reducing the error of the ionospheric delay.

Description

Technical Field

[0001] The present application belongs to the field of satellite navigation technology, and in particular relates to a method, device and storage medium for calculating ionospheric differential total electron volume. Background Art

[0002] The Earth's ionosphere is a vital component of the Earth's atmosphere. The plasma formed by a large number of charged particles in the ionosphere affects the propagation of radio waves, causing varying degrees of impact on electromagnetic signals passing through it, including reflection, refraction, scattering, and absorption. This is a major source of spatial ranging errors in satellite navigation signals. The differential Slant Total Electron Content (dSTEC), or STEC differential, is a key parameter describing the characteristics and variations of the ionosphere. Accurately determining the STEC differential allows the determination of the corresponding ionospheric delay, enabling precise positioning based on this ionospheric delay.

[0003] However, in the related art, there is a lack of a model that can accurately reflect the STEC difference, making it difficult to effectively ensure positioning accuracy. Summary of the Invention

[0004] The embodiments of the present application provide a method, device, and storage medium for calculating the ionospheric differential total electron mass, which can solve the technical problem of low accuracy in the existing method of calculating the STEC differential amount.

[0005] In a first aspect, an embodiment of the present application provides a method for calculating ionospheric differential total electron mass, the method comprising:

[0006] Obtaining coordinates of a first puncture point of a line connecting the user station and a preset satellite, coordinates of second puncture points of lines connecting multiple peripheral stations and the preset satellite, and first STEC difference values ​​of the multiple peripheral stations corresponding to the preset satellite and a reference satellite;

[0007] Fitting the first STEC difference component according to a first fitting formula of a preset function to obtain first STEC difference component estimates of multiple surrounding stations and corresponding preset satellites and reference satellites;

[0008] Eliminating the first STEC difference component according to the first STEC difference component estimate and a first residual of the first STEC difference component;

[0009] Fitting the first STEC difference component after elimination according to a second fitting formula of a preset function to obtain estimated second STEC difference components between the plurality of surrounding stations and the corresponding preset satellite and the reference satellite, and estimated third STEC difference components between the user station and the corresponding preset satellite and the reference satellite;

[0010] Calculating a second residual of the first STEC difference component before elimination and a second STEC difference estimate;

[0011] Determining a kernel function based on a geometric relationship between coordinates of the plurality of second puncture points, the second residual, and an altitude angle of a preset satellite;

[0012] Determine the hyperparameters of the kernel function;

[0013] The STEC difference component of the user station is determined according to the kernel function, the second residual, the third STEC difference component estimate, the first puncture point coordinates, and the second puncture point coordinates.

[0014] In a second aspect, an embodiment of the present application provides an ionospheric differential total electron mass calculation device, the device comprising:

[0015] A coordinate acquisition module is used to obtain the coordinates of a first puncture point of the line connecting the user station and the preset satellite, the coordinates of a second puncture point of the line connecting multiple peripheral stations and the preset satellite, and a first STEC difference between the preset satellite and the reference satellite corresponding to the multiple peripheral stations;

[0016] A first fitting module is used to fit the first STEC difference component according to a first fitting formula of a preset function to obtain an estimated value of the first STEC difference component between a plurality of surrounding stations and corresponding preset satellites and a reference satellite;

[0017] a first residual module, configured to eliminate the first STEC difference component according to the first STEC difference component estimated value and a first residual of the first STEC difference component;

[0018] a second fitting module, configured to fit the first STEC difference component after elimination according to a second fitting formula of a preset function to obtain estimated second STEC difference components between a plurality of surrounding stations and corresponding preset satellites and a reference satellite, and estimated third STEC difference components between the user station and corresponding preset satellite and the reference satellite;

[0019] a second residual module, configured to calculate a second residual of a second STEC difference component estimate and the first STEC difference component before elimination;

[0020] a third fitting module, configured to determine a kernel function according to a geometric relationship between coordinates of the plurality of second puncture points, the second residual, and an altitude angle of a preset satellite;

[0021] The training module is used to determine the hyperparameters of the kernel function;

[0022] The calculation module is configured to determine the STEC difference component of the user station according to the kernel function, the second residual, the third STEC difference component estimate, the first puncture point coordinates, and the second puncture point coordinates.

[0023] In a third aspect, an embodiment of the present application provides a computer storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method for calculating the ionospheric differential total electron mass as described in the first aspect is implemented.

[0024] In a fourth aspect, an embodiment of the present application provides a computer program product. When the instructions in the computer program product are executed by a processor of an electronic device, the electronic device executes the ionospheric differential total electron mass calculation method as described in the first aspect.

[0025] Compared to the prior art, the ionospheric differential total electron count calculation method, device, and storage medium provided in the embodiments of the present application can be fitted according to a first fitting formula by obtaining the coordinates of the first puncture point of a user station, the coordinates of the second puncture points of multiple surrounding stations, and the first STEC differential components of the multiple surrounding stations. The multiple first STEC differential components can then be fitted according to a first fitting formula. Substituting the position coordinates of each surrounding station into the first fitting formula, an estimated first STEC differential component value for each surrounding station can be obtained. Based on the estimated first STEC differential component value for each surrounding station and the first residual of the first STEC differential component value, a portion of the multiple first STEC differential components can be eliminated, that is, peripheral stations with significant differences between observed and estimated values ​​among the multiple surrounding stations are eliminated. For the remaining peripheral stations after elimination, the remaining first STEC differential components can be fitted according to a second fitting formula of a preset function. After determining the second fitting formula, the position coordinates of the user station and the position coordinates of each surrounding station are substituted into the second fitting formula to obtain an estimated third STEC differential component value for the user station and an estimated second STEC differential component value for the surrounding stations. After constructing a kernel function model based on the second residual of the first STEC difference component and the estimated second STEC difference component for each surrounding station, the geometric relationship between the coordinates of the second puncture point for each surrounding station, and the elevation angle of the preset satellite, hyperparameters of the kernel function can be calculated based on the surrounding stations, and the difference between the actual STEC difference component of the user station and the estimated third STEC difference component can be calculated based on the kernel function. After determining this difference, the sum of this difference and the estimated third STEC difference component can be calculated to obtain the STEC difference component of the user station. After initially calculating the estimated third STEC difference component for the user station using a fitting formula generated from the observed STEC difference components of the surrounding stations, a kernel function model can be constructed based on the difference between the observed values ​​and the estimated values ​​for the surrounding stations. The kernel function model can then be used to calculate the difference between the actual STEC difference component of the user station and the estimated value, and the actual STEC difference component of the user station can be determined based on the sum of this difference and the estimated third STEC difference component. By processing data from surrounding stations using kernel functions, the complexity of setting up navigation messages can be reduced. Accurate user station STEC differential components can be obtained while ensuring modeling accuracy and low complexity, effectively improving positioning accuracy and convergence time. Furthermore, by screening surrounding stations, the robustness of the calculated results can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 1 is a schematic diagram of the structure of a method for calculating ionospheric differential total electron mass provided in one embodiment of the present application;

[0028] Figure 2 1 is a schematic structural diagram of an ionospheric differential total electron mass calculation device provided in an embodiment of the present application;

[0029] Figure 3 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0030] The features and exemplary embodiments of various aspects of the present application will be described in detail below. In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present application, rather than to limit the present application. For those skilled in the art, the present application can be implemented without the need for some of these specific details. The following description of the embodiments is merely to provide a better understanding of the present application by illustrating the examples of the present application.

[0031] It should be noted that, in this document, relational terms such as first and second, etc., are used only 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 terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, the elements defined by the phrase "comprising..." do not exclude the presence of other identical elements in the process, method, article, or device comprising the elements.

[0032] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The embodiments will be described in detail below with reference to the accompanying drawings.

[0033] The Earth's ionosphere is a vital component of the Earth's atmosphere. The plasma formed by a large number of charged particles in the ionosphere affects the propagation of radio waves, causing varying degrees of impact on electromagnetic signals passing through it, including reflection, refraction, scattering, and absorption. This is a major source of spatial ranging errors in satellite navigation signals. The differential Slant Total Electron Content (dSTEC), or STEC differential, is a key parameter describing the characteristics and variations of the ionosphere. Accurately determining the STEC differential allows the determination of the corresponding ionospheric delay, enabling precise positioning based on this ionospheric delay.

[0034] Currently, existing methods for calculating STEC differentials have low accuracy, resulting in significant discrepancies between the calculated and actual STEC differentials. Furthermore, when STEC differentials deviate, positioning results derived from ionospheric delays can also exhibit significant deviations, significantly reducing positioning accuracy.

[0035] In order to solve the above technical problems, the embodiments of the present application provide a method, device and storage medium for calculating the differential total electron mass of the ionosphere. The following first introduces the method for calculating the differential total electron mass of the ionosphere provided in the embodiments of the present application.

[0036] Figure 1 The following is a schematic diagram of a method for calculating the total differential electron mass of the ionosphere provided by one embodiment of the present application. The method for calculating the total differential electron mass of the ionosphere includes:

[0037] S110, obtaining coordinates of a first puncture point of a line connecting the user station and a preset satellite, coordinates of second puncture points of lines connecting multiple peripheral stations and the preset satellite, and first STEC difference values ​​of the multiple peripheral stations corresponding to the preset satellite and a reference satellite;

[0038] S120, fitting the first STEC difference component according to a first fitting formula of a preset function to obtain first STEC difference component estimates between a plurality of surrounding stations and corresponding preset satellites and a reference satellite;

[0039] S130, eliminating the first STEC difference component according to the first STEC difference component estimated value and a first residual of the first STEC difference component;

[0040] S140, fitting the first STEC difference component after elimination according to a second fitting formula of a preset function to obtain estimated second STEC difference components between the plurality of surrounding stations and the corresponding preset satellite and the reference satellite, and estimated third STEC difference components between the user station and the corresponding preset satellite and the reference satellite;

[0041] S150, calculating a second residual of the second STEC difference component estimated value and the first STEC difference component before elimination;

[0042] S160, determining a kernel function based on the geometric relationship between the coordinates of the plurality of second puncture points, the second residual, and the altitude angle of the preset satellite;

[0043] S170, determining hyperparameters of the kernel function;

[0044] S180 : Determine the STEC difference component of the user station according to the kernel function, the second residual, the third STEC difference component estimate, the first puncture point coordinates, and the second puncture point coordinates.

[0045] The method for calculating the total differential electron mass of the ionosphere provided in the embodiments of the present application can be applied to an electronic device. The electronic device can be a mobile electronic device, such as a smart mobile terminal or a tablet computer, or a non-mobile electronic device, such as a server, an industrial computer, or various edge computing units. The specific form of the electronic device is not limited in this embodiment.

[0046] In a Global Navigation Satellite System (GNSS) application scenario, the GNSS may include satellites and reference stations (e.g., a Ground-Based Augmentation System reference station). The electronic device may be a device within the reference station or a device independent of the reference station, and data can be transmitted between the reference station and the electronic device. To simplify the description, the following describes an embodiment of the present application primarily using an example in which a user station includes an electronic device for executing a method for calculating ionospheric differential total electron mass.

[0047] In S110, the electronic device may determine, based on the location of the user station, multiple reference stations within a preset distance from the user station. The multiple reference stations are respectively multiple peripheral stations corresponding to the user station. The electronic device may obtain the coordinates of a first puncture point of a line connecting the user station and a preset satellite. The electronic device may also obtain the coordinates of a second puncture point of a line connecting each of the multiple peripheral stations and the preset satellite.

[0048] The observation ray emitted by the preset satellite will penetrate the ionosphere in the atmosphere during the process of reaching the base station. The coordinates of the position where the observation ray is located when it penetrates the ionosphere are the puncture point coordinates. For example, the puncture point coordinates can be the position coordinates of the observation ray when it penetrates the ionosphere at an altitude of 450KM. The first puncture point coordinates are the position coordinates of the observation ray when it penetrates the ionosphere during the process of reaching the user station; and the second puncture point coordinates are the position coordinates of the observation ray when it penetrates the ionosphere during the process of reaching the surrounding station. That is, the electronic device can obtain a first puncture point coordinate and multiple second puncture point coordinates, and each second puncture point coordinate represents the position coordinates of the observation ray when it penetrates the ionosphere when the corresponding surrounding station receives the observation ray.

[0049] The geometric characteristics of the observation ray can be determined by the positions of the satellite and the base station receiver. For example, the geometric characteristics of the observation ray can include the altitude angle and azimuth angle of the satellite relative to the base station receiver.

[0050] Each of the plurality of surrounding stations can obtain a STEC observation value corresponding to a preset satellite and a STEC observation value corresponding to a reference satellite. The surrounding station can calculate a first STEC difference value corresponding to the preset satellite and the reference satellite based on the difference between the two STEC observation values. The electronic device can also obtain, from each surrounding station, the first STEC difference value corresponding to the preset satellite and the reference satellite for that surrounding station.

[0051] It can be understood that the above STEC difference represents the difference between the STEC (Slant Total Electron Content) of the preset satellite corresponding to the same station and the STEC of the reference satellite corresponding to the same station. in, is the STEC of the preset satellite s corresponding to the site r, represents the STEC of the reference satellite ref at station r.

[0052] At S120, the electronic device may fit the first STEC difference corresponding to each surrounding station based on a first fitting formula of a preset function to obtain model coefficients in the first fitting formula. The first fitting formula may be a fitting relationship between the location coordinates of the surrounding station and the first STEC difference of the surrounding station, where the location coordinates of the surrounding station may be the coordinates of the second puncture point. After the model coefficients in the first fitting formula are determined, the location coordinates of each surrounding station, i.e., the coordinates of the second puncture point, may be substituted into the first fitting formula to calculate an estimated first STEC difference between each surrounding station and the corresponding preset satellite and reference satellite.

[0053] It can be understood that the first STEC difference value of the surrounding station is calculated based on the difference between the STEC observation value of the corresponding preset satellite and the STEC observation value of the corresponding reference satellite, while the estimated first STEC difference value of the surrounding station is calculated based on the first fitting formula. That is, the first STEC difference value and the estimated first STEC difference value are not exactly the same, and there may be a certain error between the two.

[0054] In some embodiments, the first fitting formula may include:

[0055]

[0056] in, represents the latitude and longitude coordinates of the puncture point of the navigation signal between the preset satellite s and the surrounding station r at the preset ionospheric altitude; p i is the fitting coefficient of the first fitting formula, i∈[1, 2, ..., n], n is the number of fitting coefficients in the first fitting formula; It represents the estimated value of the first STEC difference between the surrounding site r and the corresponding preset satellite s and the reference satellite ref.

[0057] The first and second puncture point coordinates can be the longitude and latitude coordinates of the puncture points, representing the coordinates of the locations when penetrating the ionosphere at a preset altitude. The preset altitude can be 450 km or another altitude within the ionosphere. After obtaining the second puncture point coordinates corresponding to multiple surrounding stations and a preset satellite, as well as the first STEC difference values ​​for the multiple surrounding stations, a preset fitting algorithm can be used to fit the longitude and latitude of the second puncture point coordinates and the first STEC difference values ​​according to a first fitting formula to obtain the fitting coefficients in the first fitting formula. In some examples, the preset fitting algorithm can be a least squares method, for example.

[0058] In S130, after obtaining the first STEC difference component estimate and the first STEC difference component corresponding to each of the multiple surrounding stations, the electronic device can calculate the difference between the first STEC difference component and the first STEC difference component estimate, and use the difference as the first residual for the surrounding station. After calculating the first residual for each surrounding station, the surrounding stations can be screened and eliminated based on the size of the first residual. That is, for surrounding stations with large first residuals, it means that there is a large difference between the STEC observation value of the preset satellite corresponding to the surrounding station and the STEC observation value of the reference satellite, that is, there is a large difference between the first STEC difference component and the first STEC difference component estimate calculated according to the first fitting formula. In order to improve the accuracy of the STEC difference component of the user station, the surrounding stations with large first residuals can be eliminated from the multiple surrounding stations, and the surrounding stations with small first residuals can be retained.

[0059] After the electronic device obtains the first STEC difference corresponding to each surrounding site, the corresponding surrounding site can be eliminated by eliminating the corresponding first STEC difference.

[0060] In some embodiments, the calculation formula of the first residual is as follows:

[0061]

[0062] in, is the first STEC difference corresponding to the surrounding stations, according to and Calculated; is the estimated value of the first STEC difference component calculated based on the first fitting formula and the coordinates of the second puncture points of the surrounding sites.

[0063] After calculating the first residuals corresponding to each peripheral station, the first STEC difference components corresponding to the peripheral stations can be eliminated based on the magnitude of the first residuals. In some examples, this elimination method can include presetting a first residual elimination threshold, retaining first residuals below the elimination threshold, and eliminating peripheral stations corresponding to first residuals above the elimination threshold. Accordingly, the first STEC difference components corresponding to these eliminated peripheral stations are also eliminated.

[0064] Alternatively, the method for eliminating the first STEC difference components can be to pre-set the number of retained first residuals or the number of eliminated first residuals, and to sort the first residuals according to their magnitude. If the number of retained first residuals is pre-set, then a corresponding number of first residuals are retained in ascending order, while the remaining first residuals are eliminated. Accordingly, the first STEC difference components corresponding to the eliminated peripheral stations are eliminated. If the number of eliminated first residuals is pre-set, then a corresponding number of first residuals are eliminated in descending order, and the first STEC difference components corresponding to the eliminated peripheral stations are eliminated.

[0065] In some embodiments, the above elimination method can also be to calculate the corresponding error screening range based on the size of each first residual, and eliminate the first residual that does not meet the error screening range. In some examples, the formula for calculating the error screening range based on the first residual is as follows:

[0066] B=A\{e i ∈A|(e i >E(e)+2(E(e 2 )-E(e) 2 ))∪(ei <E(e)-2(E(e 2 )-E(e) 2 ))};

[0067] e={e i},i=1,…,n;

[0068] Where A is the set of surrounding sites consisting of all surrounding sites; B is the set of surrounding sites consisting of the remaining surrounding sites after elimination based on the first residual; E(e) is the mathematical expectation of all first residuals, E(e 2 ) is the mathematical expectation of the square of the first residual.

[0069] In the above formula, E(e)+2(E(e 2 )-E(e)) and E(e)-2(E(e 2 )-E(e)) is the error screening range calculated based on the magnitude of each first residual. Each first residual can be compared with the error screening range to classify the first residuals into first residuals smaller than the error screening range and first residuals larger than the error screening range.

[0070] It can be understood that when screening surrounding sites based on the first residual, surrounding sites with a small difference between the first STEC difference component and the estimated first STEC difference component, i.e., those with a small first residual, should be retained. After dividing surrounding site set A according to the error screening range, first residuals exceeding the error screening range can be eliminated. The remaining surrounding site set B then includes surrounding sites corresponding to first residuals falling within the error screening range. Accordingly, the first STEC difference components corresponding to these eliminated surrounding sites can also be eliminated, retaining the first STEC difference components corresponding to the surrounding sites in surrounding site set B.

[0071] In S140, after removing some of the first STEC difference components based on the first residuals corresponding to each surrounding station, the surrounding stations corresponding to the remaining first STEC difference components are those for which the difference between the actually observed first STEC difference components and the estimated first STEC difference components calculated according to the first fitting formula is relatively small. For these surrounding stations, the corresponding first STEC difference components can be fitted using the second fitting formula of a preset function to obtain model coefficients in the second fitting formula.

[0072] After obtaining the model coefficients of the second fitting formula, the position coordinates of each surrounding station can be substituted into the second fitting formula to obtain an estimated value of the second STEC difference component between each surrounding station and the corresponding preset satellite and reference satellite; the position coordinates of the user station where the electronic device is located can also be substituted into the second fitting formula to obtain an estimated value of the third STEC difference component between the user station and the corresponding preset satellite and reference satellite.

[0073] In some embodiments, the second fitting formula may include:

[0074]

[0075] in, is the distance from the second puncture point coordinate of the surrounding station r to the first puncture point coordinate of the user station user, p i is the fitting coefficient of the second fitting formula, i∈[1, 2, ..., n], and n is the number of fitting coefficients in the second fitting formula.

[0076] The second fitting formula is set with a corresponding weight coefficient relative to the first fitting formula, and the weight coefficient is negatively correlated with the distance between the coordinates of the second puncture point and the coordinates of the first puncture point.

[0077] After calculating the estimated first STEC difference value for each surrounding station using the first fitting formula and calculating the first residual for each surrounding station, multiple surrounding stations can be eliminated based on the first residual. For the remaining surrounding stations after elimination, a preset fitting algorithm can be used to fit the first STEC difference value for these surrounding stations, the coordinates of the second puncture points for these stations, and the distance between the second puncture point coordinates and the first puncture point coordinates according to the second fitting formula to obtain the fitting coefficients in the second fitting formula. The preset fitting algorithm can also be a least squares method, for example.

[0078] It is understandable that the samples used in the second fitting formula are the remaining surrounding stations after elimination based on the first residual. The difference between the first STEC difference component and the estimated first STEC difference component for these surrounding stations is small, resulting in a small error between the estimated STEC difference component calculated using the second fitting formula and the actual STEC difference component. However, since the estimated STEC difference component for each surrounding station still differs from the observed STEC difference component, there is also a certain error between the actual STEC difference component of the user station and the estimated third STEC difference component calculated using the second fitting formula. If the estimated third STEC difference component is used as the actual STEC difference component of the user station, the final calculated positioning result will be offset.

[0079] In S150, after substituting the location coordinates of each peripheral station into the second fitting formula to obtain a second STEC difference component estimated value corresponding to each peripheral station, the difference between the second STEC difference component estimated value and the first STEC difference component of each peripheral station, i.e., a second residual, can be calculated.

[0080] After removing some surrounding stations based on the first residual, a second fitting formula is generated by fitting the first STEC difference components of the remaining surrounding stations. After generating the second fitting formula, the coordinates of all surrounding stations before removal (i.e., the coordinates of the second puncture point) are substituted into the second fitting formula to calculate the estimated second STEC difference component for each surrounding station before removal. Based on the first STEC difference component of each surrounding station, the difference between the first STEC difference component and the estimated second STEC difference component is calculated to obtain the second residual.

[0081] In S160 , after the estimated value of the third STEC difference component of the user station is calculated, a kernel function model may be constructed according to the geometric relationship of the coordinates of each second puncture point, the second residuals of each surrounding station, and the altitude angle of the preset satellite.

[0082] In S170, after constructing the kernel function model, a training set of the kernel function model can be generated according to the second residuals of each surrounding site and the coordinates of the second puncture point, and the kernel function model is trained by a corresponding training method to obtain hyperparameters of the kernel function.

[0083] In some embodiments, the model function set of the kernel function may include:

[0084] f1(x i ,x j )=||x i -x j || 2 ;

[0085]

[0086] f3(e i ,e j )=||e i -e j || 2 ;

[0087]

[0088] f5(θ i ,θ j )=||θ i -θ j || 2 ;

[0089]

[0090] f out (x i ,x j ,e i ,e j ,θ i ,θ j )=f out (f2,f4,f6)=f2+λ1f4+λ2f6;

[0091] Among them, x i 、e i ,θ i is the puncture point coordinates, second residual and altitude angle of the surrounding station i, x j 、e j ,θ j are the puncture point coordinates, second residuals, and elevation angles of the surrounding site j, i, j∈[1, 2, ..., n], n is the number of surrounding sites; λ1, λ2 are the empirical values ​​specified in the model, σ and τ are the hyperparameters of the model function; f out is the output function of the kernel function, and f1, f2, f3, f4, f5 and f6 are intermediate process functions.

[0092] In another embodiment, the function model set of the kernel function may further include:

[0093] f1(x i ,x j )=|x i -x j |;

[0094]

[0095] f5(θ i ,θ j )=||θ i -θ j || 2 ;

[0096]

[0097] f out (x i ,x j ,θ i ,θ j )=f out (f2,f6)=f2+λ2f6;

[0098] Among them, x i ,θ i is the puncture point coordinates and altitude angle of the surrounding station i, xj ,θ j are the puncture point coordinates and altitude angles of the surrounding site j, i, j∈[1, 2, ..., n], n is the number of surrounding sites; λ1, λ2 are the empirical values ​​specified in the model, σ and τ are the hyperparameters of the model function; f out is the output function of the kernel function, and f1, f2, f5 and f6 are intermediate process functions.

[0099] After fitting the second fitting formula, the corresponding second STEC differential component estimate can be calculated based on the second puncture point coordinates of each surrounding station, and the corresponding third STEC differential component estimate can be calculated based on the first puncture point coordinates of the user station.

[0100] After generating training samples of the kernel function model based on the estimated second STEC difference component and the second residual of the surrounding stations and the altitude angle of the preset satellite and training the kernel function model, the hyperparameters σ and τ of the kernel function model can be solved.

[0101] It is understandable that the above x i It can be the coordinates of the puncture point corresponding to the surrounding site i in the ECEF (Earth-Centered Earth-Fixed) coordinate system.

[0102] In S180, after obtaining the hyperparameters of the kernel function model, the estimated third STEC difference component of the user station, the coordinates of the first puncture point, and the coordinates and second residuals of the second puncture points of each surrounding station can be input into the kernel function model to obtain the deviation between the actual STEC difference component of the user station and the estimated third STEC difference component. The sum of this deviation and the estimated third STEC difference component can be used as the STEC difference component of the user station.

[0103] In some embodiments, after obtaining the hyperparameters of the kernel function model, the STEC difference of the user station can be calculated using the following formula:

[0104]

[0105] Among them, dSTEC user is the STEC differential component of the user station, f dstec (·) is the polynomial model of the estimated value, X represents the coordinates of the second puncture point of the surrounding sites, and X user represents the coordinates of the first puncture point of the user station, e user and e represent the second residual corresponding to the user station and the second residual corresponding to the surrounding stations respectively; θ user and θ represent the elevation angle of the satellite corresponding to the user station and the elevation angle of the satellite corresponding to the surrounding stations, respectively; f out(·,·,·,·) represents the matrix obtained using the model function, represents the dSTEC observations at the surrounding stations, λ represents the regularization hyperparameter, and I represents the identity matrix.

[0106] In the above embodiment, f dstec (X user ) may be the estimated value of the third STEC difference component of the user station calculated according to the second fitting formula, and f dstec (·) represents the polynomial of the second fitting formula, It can represent the first STEC difference between the preset satellite and the reference satellite corresponding to each surrounding site.

[0107] In some embodiments, in generating dSTEC user After obtaining the calculation formula, a regional STEC estimation model can be generated according to the calculation formula. When the electronic device of the user station performs the next positioning or other electronic devices perform positioning, if the coordinates of the ionospheric puncture point corresponding to the electronic device are within the regional range of the STEC estimation model of the region, the STEC estimation model of the region can be obtained, and the STEC difference component of the electronic device can be calculated based on the second puncture point coordinates and the second residual of the surrounding stations, as well as the altitude angles of the satellites corresponding to the electronic device and the surrounding stations.

[0108] In this embodiment, by obtaining the coordinates of the first puncture point of the user station, the coordinates of the second puncture points of multiple surrounding stations, and the first STEC difference components of the multiple surrounding stations, the multiple first STEC difference components can be fitted according to a first fitting formula. The location coordinates of each surrounding station are substituted into the first fitting formula to obtain an estimated first STEC difference component value for each surrounding station. Based on the estimated first STEC difference component value for each surrounding station and the first residual of the first STEC difference component value, a portion of the multiple first STEC difference components can be eliminated. Specifically, the portions of the multiple surrounding stations for which the observed values ​​differ significantly from the estimated values ​​are eliminated. For the remaining surrounding stations after elimination, the remaining first STEC difference components can be fitted according to a second fitting formula of a preset function. After determining the second fitting formula, the location coordinates of the user station and the location coordinates of each surrounding station are substituted into the second fitting formula to obtain an estimated third STEC difference component value for the user station and an estimated second STEC difference component value for the surrounding stations. After constructing a kernel function model based on the second residual of the first STEC difference component and the estimated second STEC difference component for each surrounding station, the geometric relationship between the coordinates of the second puncture point for each surrounding station, and the elevation angle of the preset satellite, hyperparameters of the kernel function can be calculated based on the surrounding stations, and the difference between the actual STEC difference component of the user station and the estimated third STEC difference component can be calculated based on the kernel function. After determining this difference, the sum of this difference and the estimated third STEC difference component can be calculated to obtain the STEC difference component of the user station. After initially calculating the estimated third STEC difference component for the user station using a fitting formula generated from the observed STEC difference components of the surrounding stations, a kernel function model can be constructed based on the difference between the observed values ​​and the estimated values ​​for the surrounding stations. The kernel function model can then be used to calculate the difference between the actual STEC difference component of the user station and the estimated value, and the actual STEC difference component of the user station can be determined based on the sum of this difference and the estimated third STEC difference component. By processing data from surrounding stations using kernel functions, the complexity of setting up navigation messages can be reduced. Accurate user station STEC differential components can be obtained while ensuring modeling accuracy and low complexity, effectively improving positioning accuracy and convergence time. Furthermore, by screening surrounding stations, the robustness of the calculated results can be improved.

[0109] In one embodiment, the reference station may obtain the ionospheric delay in the following manner.

[0110] The base station's receiver receives raw dual-frequency observations and navigation message data, and after eliminating gross errors, calculates the position and elevation angle of the preset satellite, as well as the coordinates of the ionospheric penetration points corresponding to the surrounding stations and the preset satellite. Based on the pseudorange observations and carrier phase observations in the raw dual-frequency observations, the ionospheric delay can be obtained using the non-differenced, non-combined PPP algorithm. The calculation formula is as follows:

[0111]

[0112] Where the superscript Q represents the current navigation system, s represents the sth satellite in the Q navigation system (i.e., the preset satellite), the subscript r represents the receiver at the rth surrounding station, j represents the current frequency band, P represents the pseudorange observation, L represents the carrier observation, ρ represents the geometric distance between the satellite and the receiver, c represents the speed of light, dt represents the clock error, ZWD represents the zenith tropospheric delay, Mw represents the scale factor for converting the tropospheric delay to the oblique direction, γ represents the frequency scale factor for the ionospheric delay, I represents the ionospheric delay, d represents the pseudorange hardware delay, and b represents the carrier phase hardware delay, N represents the carrier phase ambiguity, λ represents the carrier phase wavelength, ε and ξ represent other pseudorange and carrier phase errors, respectively, and DCB represents the intersymbol bias. In other words, the ionospheric delay can be expressed using the STEC value.

[0113] As an optional embodiment, the above S170 may include:

[0114] The hyperparameters of the kernel function are determined according to the second residual and the coordinates of the second puncture point.

[0115] When constructing the kernel function, intermediate process functions of the kernel function can be established based on the second puncture point coordinates of the surrounding stations, the second residuals corresponding to the surrounding stations, and the altitude angle corresponding to the preset satellite. Hyperparameters of the kernel function can be set in each intermediate process function. After obtaining the second puncture point coordinates and second residuals corresponding to multiple surrounding stations, as well as the altitude angle corresponding to the preset satellite, the corresponding data of the above-mentioned surrounding stations and preset satellites can be input into the kernel function model as a training set, and the hyperparameters of the kernel function model can be calculated through the corresponding training method.

[0116] In some embodiments, the step of determining the hyperparameters of the kernel function based on the second residual and the second puncture point coordinates may include:

[0117] According to the geometric relationship between the coordinates of the plurality of second puncture points and the coordinates of the first puncture point, a plurality of first peripheral sites that are closest to the coordinates of the first puncture point are selected from the plurality of peripheral sites, and the remaining ones are used as second peripheral sites;

[0118] The second residuals and the second puncture point coordinates of the first peripheral site are used as the validation set, and the second residuals and the second puncture point coordinates of the second peripheral site are used as the training set. The hyperparameters of the kernel function are obtained through the cross-validation training method.

[0119] In the above cross-validation training method, cross-validation can be performed using a k-fold validation method or a bootstrap method.

[0120] After obtaining the first and second puncture point coordinates, a geometric relationship between the second puncture point coordinates and the first puncture point coordinates can be generated. For example, by calculating the distance between the first puncture point coordinate and each second puncture point coordinate, the distance between each second puncture point coordinate and the first puncture point coordinate can be calculated. Based on the distance between the second puncture point corresponding to each peripheral station and the first puncture point coordinate, the nearest peripheral stations can be selected as the first peripheral stations, and the remaining peripheral stations as the second peripheral stations.

[0121] After dividing the plurality of peripheral sites into first peripheral sites and second peripheral sites, the second residuals and second puncture point coordinates of the plurality of first peripheral sites can be used as a validation set, and the second residuals and second puncture point coordinates of the plurality of second peripheral sites can be used as a training set. A cross-validation training method can be used to generate kernel function hyperparameters. In some examples, the cross-validation training method can include an Adam optimization algorithm.

[0122] In this embodiment, the relationship between the coordinates of the second puncture points and the coordinates of the first puncture points corresponding to each peripheral station can be used to identify first peripheral stations that are closer to the first puncture point coordinates and second peripheral stations that are farther away. After constructing the kernel function model, the kernel function model can be trained using a cross-validation method using the first peripheral stations as a validation set and the second peripheral stations as a training set to obtain the kernel function model's hyperparameters.

[0123] In some embodiments, the step of selecting, from the plurality of surrounding sites, a plurality of first surrounding sites that are closest to the first puncture point coordinates based on the geometric relationship between the plurality of second puncture point coordinates and the first puncture point coordinates, may include:

[0124] Calculating the relative position of the first puncture point coordinates and each second puncture point coordinate according to the plurality of second puncture point coordinates, the first puncture point coordinates, and a preset convex hull algorithm;

[0125] When the coordinates of the first puncture point are on or outside the convex hull, a first error screening range is calculated using a first screening rule; the convex hull is the minimum convex polygon containing all the coordinates of the second puncture points;

[0126] When the coordinates of the first puncture point are within the convex hull, a second error screening range is calculated using a second screening rule; the screening accuracy of the second screening rule is greater than the screening accuracy of the first screening rule;

[0127] The second residual is screened and updated according to the error screening range, and the corresponding first peripheral site is determined according to the screened second residual.

[0128] After obtaining the second puncture point coordinates corresponding to each peripheral site and the first puncture point coordinates corresponding to the user site, the convex hull algorithm can be used to calculate the position of the first puncture point coordinates relative to the convex hull formed by all the second puncture point coordinates, and determine the corresponding number of first peripheral sites based on the position of the first puncture point coordinates relative to the convex hull.

[0129] In some embodiments, the convex hull algorithm may be a Graham Scan algorithm. After inputting each second puncture point coordinate into the convex hull algorithm model, a convex hull polygon consisting of the plurality of second puncture point coordinates may be generated. It is understood that the convex hull polygon is the smallest convex polygon that contains all the second puncture point coordinates, and all the second puncture point coordinates are located on or within the convex hull polygon.

[0130] By comparing the coordinates of the first puncture point with the convex hull polygon generated using a preset convex hull algorithm, the position of the first puncture point coordinates relative to the convex hull polygon can be determined. For example, the coordinates of the first puncture point can be located within, on, or outside the convex hull polygon.

[0131] When the coordinates of the first puncture point are located on or outside the convex hull polygon, a first screening rule may be used to calculate a first error screening range. The second residuals of each surrounding station may be screened according to the first error screening range to screen out multiple second residuals whose second residual values ​​are within the first error screening range. The surrounding stations corresponding to each of the multiple second residuals are the first surrounding stations.

[0132] Similarly, when the coordinates of the first puncture point are within the convex hull polygon, the second screening rule can be used to calculate the second error screening range, and the second residuals that meet the second error screening range can be screened out from multiple second residuals based on the second error screening range. The peripheral stations corresponding to these second residuals are the first peripheral stations.

[0133] It can be understood that when the coordinates of the first puncture point are within the convex hull polygon, it means that the ionospheric puncture point of the user station is within the convex hull polygon composed of the ionospheric puncture points of each surrounding station. At this time, when the kernel function model is trained using a cross-validation training method, the number of samples in the training set can be appropriately reduced. After the first surrounding station is screened out from multiple surrounding stations using the corresponding screening rules, the data of the remaining surrounding stations, i.e., the second surrounding stations, are used as the training set of the kernel function model. By reducing the screening accuracy of the first screening rule, the number of first surrounding stations that meet the first error screening range can be increased, thereby reducing the number of second surrounding stations and reducing the number of training set samples.

[0134] Conversely, when the first puncture point is outside the convex hull polygon, the number of training set samples can be appropriately increased to ensure the accuracy of the kernel function model. By increasing the precision of the second screening rule, the number of first surrounding sites that meet the second error screening range can be reduced, thereby increasing the number of second surrounding sites and increasing the number of training set samples.

[0135] By setting the second filtering rule's precision to be greater than that of the first, the number of first peripheral sites filtered out by the first filtering rule can be increased compared to the number of first peripheral sites filtered out by the second filtering rule. Based on the geometric relationship between the convex hull polygons formed by the coordinates of the first puncture point and each of the second puncture points, the corresponding filtering rule can be selected to adjust the number of samples in the training and validation sets, thereby improving the accuracy of the kernel function model.

[0136] In some embodiments, the first screening rule may include:

[0137] C=A\{e i ∈A|(e i >E(e)+3(E(e 2 )-E(e) 2 ))∪(e i <E(e)-3(E(e 2 )-E(e) 2 ))};

[0138] The second screening rule may include:

[0139] C=A\{e i ∈A|(e i >E(e)+2(E(e 2 )-E(e) 2 ))∪(e i <E(e)-2(E(e 2 )-E(e) 2 ))};

[0140] Here, C represents the first surrounding site set remaining after the second residual is filtered according to the first filtering rule or the second filtering rule.

[0141] According to the first and second screening rules, for the same number of second residuals, the first error screening range calculated using the first screening rule is larger than the second error screening range calculated using the second screening rule. Therefore, the number of surrounding sites that meet the first error screening range should be larger than the number of surrounding sites that meet the second error screening range. In other words, the screening accuracy of the first screening rule is lower than the screening accuracy of the second screening rule.

[0142] It is understandable that the first screening rule and the second screening rule may also be determined in other ways, as long as the screening accuracy of the first screening rule is less than the screening accuracy of the second screening rule.

[0143] like Figure 2 As shown, the embodiment of the present application further provides an ionospheric differential total electron quantity calculation device, the device comprising:

[0144] A coordinate acquisition module 201 is configured to acquire the coordinates of a first puncture point of a line connecting the user station and a preset satellite, the coordinates of second puncture points of lines connecting multiple peripheral stations and the preset satellite, and first STEC difference values ​​of the multiple peripheral stations corresponding to the preset satellite and the reference satellite;

[0145] A first fitting module 202 is configured to fit the first STEC difference component according to a first fitting formula of a preset function to obtain first STEC difference component estimates between a plurality of surrounding stations and corresponding preset satellites and a reference satellite;

[0146] a first residual module 203 for eliminating the first STEC difference component according to the first STEC difference component estimate and a first residual of the first STEC difference component;

[0147] The second fitting module 204 is configured to fit the first STEC difference component after the elimination according to a second fitting formula of a preset function to obtain estimated second STEC difference components between the plurality of surrounding stations and the corresponding preset satellites and the reference satellite, and estimated third STEC difference components between the user station and the corresponding preset satellite and the reference satellite;

[0148] A second residual module 205 is used to calculate a second residual between the second STEC difference component estimate and the first STEC difference component before elimination;

[0149] A third fitting module 206 is configured to determine a kernel function based on the geometric relationship between the coordinates of the plurality of second puncture points, the second residual, and the altitude angle of the preset satellite;

[0150] A training module 207 is used to determine the hyperparameters of the kernel function;

[0151] The calculation module 208 is configured to determine the STEC difference component of the user station according to the kernel function, the second residual, the third STEC difference component estimate, the first puncture point coordinates, and the second puncture point coordinates.

[0152] It should be noted that the ionospheric differential total electron count calculation device is a device corresponding to the above-mentioned ionospheric differential total electron count calculation method. All implementation methods in the above-mentioned method embodiments are applicable to the embodiments of the device and can achieve the same technical effects.

[0153] Figure 3 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application is shown.

[0154] The electronic device may include a processor 301 and a memory 302 storing computer program instructions.

[0155] Specifically, the processor 301 may include a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

[0156] The memory 302 may include a large capacity memory for data or instructions. By way of example and not limitation, the memory 302 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 302 may include removable or non-removable (or fixed) media. Where appropriate, the memory 302 may be inside or outside the integrated gateway disaster recovery device. In a specific embodiment, the memory 302 is a non-volatile solid-state memory.

[0157] In certain embodiments, the memory 302 may include read-only memory (ROM), random access memory (RAM), magnetic disk storage media devices, optical storage media devices, flash memory devices, electrical, optical, or other physical / tangible memory storage devices. Thus, in general, the memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to an aspect of the present disclosure.

[0158] The processor 301 reads and executes computer program instructions stored in the memory 302 to implement any one of the ionospheric differential total electron mass calculation methods in the above embodiments.

[0159] In one example, the electronic device may further include a communication interface 303 and a bus 310. Figure 3 As shown, the processor 301 , the memory 302 , and the communication interface 303 are connected via a bus 310 and communicate with each other.

[0160] The communication interface 303 is mainly used to implement communication between various modules, devices, units and / or equipment in the embodiments of the present application.

[0161] Bus 310 includes hardware, software or both, and the components of online data flow metering equipment are coupled to each other. For example, but not limitation, bus can include accelerated graphics port (AGP) or other graphics bus, enhanced industry standard architecture (EISA) bus, front side bus (FSB), hypertransport (HT) interconnection, industry standard architecture (ISA) bus, infinite bandwidth interconnection, low pin count (LPC) bus, memory bus, micro channel architecture (MCA) bus, peripheral component interconnection (PCI) bus, PCI-Express (PCI-X) bus, serial advanced technology attachment (SATA) bus, video electronics standard association local (VLB) bus or other suitable bus or two or more of these combinations. In appropriate cases, bus 310 can include one or more buses. Although the present application embodiment describes and shows specific bus, the application considers any suitable bus or interconnection.

[0162] In addition, in conjunction with the ionospheric differential total electron count calculation method in the above-mentioned embodiment, embodiments of the present application may provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when the computer program instructions are executed by a processor, any of the ionospheric differential total electron count calculation methods in the above-mentioned embodiments is implemented.

[0163] It should be understood that the present application is not limited to the specific configurations and processes described above and illustrated in the figures. For the sake of brevity, a detailed description of known methods is omitted here. In the above embodiments, several specific steps are described and illustrated as examples. However, the method process of the present application is not limited to the specific steps described and illustrated. Those skilled in the art can make various changes, modifications, and additions, or change the order of the steps after understanding the spirit of the present application.

[0164] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of the present application are programs or code segments that are used to perform the required tasks. Programs or code segments can be stored in machine-readable media, or transmitted on a transmission medium or a communication link by a data signal carried in a carrier wave. "Machine-readable media" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROMs, flash memories, erasable ROMs (EROMs), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, etc. The code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0165] It should also be noted that the exemplary embodiments mentioned in this application describe some methods or systems based on a series of steps or devices. However, this application is not limited to the order of the above steps. In other words, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0166] Aspects of the present disclosure have been described above with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer or other programmable data processing device to produce a machine so that these instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the function / action specified in one or more boxes of the flowchart and / or block diagram. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor or a field programmable logic circuit. It is also understood that each box in the block diagram and / or flowchart and the combination of the boxes in the block diagram and / or flowchart can also be implemented by dedicated hardware that performs the specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0167] The above is only a specific implementation method of the present application. Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, modules and units described above can refer to the corresponding processes in the aforementioned method embodiments, and will not be repeated here. It should be understood that the scope of protection of the present application is not limited to this. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in this application, and these modifications or replacements should be included in the scope of protection of this application.

Claims

1. A method for calculating the total differential electron mass in the ionosphere, characterized in that: The method comprises: Obtaining coordinates of a first puncture point of a line connecting the user station and the preset satellite, coordinates of second puncture points of lines connecting multiple peripheral stations and the preset satellite, and first STEC difference values ​​of the multiple peripheral stations corresponding to the preset satellite and the reference satellite; Fitting the first STEC difference component according to a first fitting formula of a preset function to obtain first STEC difference component estimates of multiple surrounding stations and corresponding preset satellites and reference satellites; Eliminating the first STEC difference component according to the first STEC difference component estimate and a first residual of the first STEC difference component; Fitting the first STEC difference component after elimination according to a second fitting formula of a preset function to obtain estimated second STEC difference components between the plurality of surrounding stations and the corresponding preset satellite and the reference satellite, and estimated third STEC difference components between the user station and the corresponding preset satellite and the reference satellite; Calculating a second residual of the first STEC difference component before elimination and a second STEC difference estimate; Determining a kernel function based on a geometric relationship between coordinates of the plurality of second puncture points, the second residual, and an altitude angle of a preset satellite; Determine the hyperparameters of the kernel function; The STEC difference component of the user station is determined according to the kernel function, the second residual, the third STEC difference component estimate, the first puncture point coordinates, and the second puncture point coordinates.

2. The method for calculating the total differential electron mass of the ionosphere according to claim 1, wherein: The step of determining the hyperparameters of the kernel function further includes: Determine the hyperparameters of the kernel function according to the second residual and the second puncture point coordinates.

3. The method for calculating the total differential electron mass of the ionosphere according to claim 2, wherein: The step of determining the hyperparameters of the kernel function according to the second residual and the second puncture point coordinates further includes: According to the geometric relationship between the coordinates of the plurality of second puncture points and the coordinates of the first puncture point, a plurality of first peripheral sites closest to the coordinates of the first puncture point are selected from the plurality of peripheral sites, and the remaining ones are used as second peripheral sites; The second residuals and the second puncture point coordinates of the first peripheral site are used as a validation set, and the second residuals and the second puncture point coordinates of the second peripheral site are used as a training set, and the hyperparameters of the kernel function are obtained through a cross-validation training method.

4. The method for calculating the total differential electron mass in the ionosphere according to claim 3, wherein: The method of selecting, from the plurality of surrounding sites, a plurality of first surrounding sites that are closest to the first puncture point coordinates based on the geometric relationship between the plurality of second puncture point coordinates and the first puncture point coordinates, includes: Calculating the relative positions of the first puncture point coordinates and each of the second puncture point coordinates according to the plurality of second puncture point coordinates, the first puncture point coordinates, and a preset convex hull algorithm; When the coordinates of the first puncture points are located on or outside the convex hull, a first error screening range is calculated using a first screening rule; the convex hull is the smallest convex polygon containing all the coordinates of the second puncture points; When the coordinates of the first puncture point are within the convex hull, a second error screening range is calculated using a second screening rule; the screening accuracy of the second screening rule is greater than the screening accuracy of the first screening rule; The second residual is screened and updated according to the error screening range, and the corresponding first peripheral site is determined according to the screened second residual.

5. The method for calculating ionospheric differential total electron mass according to claim 1, wherein: The first fitting formula is: in, represents the latitude and longitude coordinates of the puncture point of the navigation signal between the satellite s and the surrounding station r at the preset ionospheric altitude; p i is the fitting coefficient of the first fitting formula, i∈[1, 2, ..., n], n is the number of fitting coefficients in the first fitting formula; It represents the estimated value of the first STEC difference between the surrounding site r and the corresponding preset satellite s and the reference satellite ref.

6. The method for calculating the total differential electron mass in the ionosphere according to claim 5, wherein: The second fitting formula is: in, is the distance from the second puncture point coordinate of the surrounding station r to the first puncture point coordinate of the user station user, p i is the fitting coefficient of the second fitting formula, i∈[1, 2, ..., n], and n is the number of fitting coefficients in the second fitting formula.

7. The method for calculating ionospheric differential total electron mass according to claim 1, wherein: A kernel function is determined according to the geometric relationship of the coordinates of the plurality of second puncture points, the second residual, and the altitude angle of the preset satellite, where the kernel function is: f1(x i ,x j )=||x i -x j || 2 ; f3(e i ,e j )=||e i -e j || 2 ; f5(θ i ,i j )=||θ i -θ j || 2 ; f out (x i ,x j ,e i ,e j ,θ i ,θ j )=f out (f2,f4,f6)=f2+λ1f4+λ2f6; Among them, x i 、e i ,θ i is the puncture point coordinates, second residual and altitude angle of the surrounding station i, x j 、e j ,θ j are the puncture point coordinates, second residuals, and elevation angles of the surrounding site j, i, j∈[1, 2, ..., n], n is the number of surrounding sites; λ1, λ2 are the empirical values ​​specified in the model, σ and τ are the hyperparameters of the model function; f out is the output function of the kernel function, and f1, f2, f3, f4, f5 and f6 are intermediate process functions.

8. An ionospheric differential electron mass calculation device, characterized in that: The device comprises: A coordinate acquisition module is used to obtain the coordinates of a first puncture point of the line connecting the user station and the preset satellite, the coordinates of a second puncture point of the line connecting multiple peripheral stations and the preset satellite, and a first STEC difference between the preset satellite and the reference satellite corresponding to the multiple peripheral stations; A first fitting module is used to fit the first STEC difference component according to a first fitting formula of a preset function to obtain an estimated value of the first STEC difference component between a plurality of surrounding stations and corresponding preset satellites and a reference satellite; a first residual module, configured to eliminate the first STEC difference component according to the first STEC difference component estimated value and a first residual of the first STEC difference component; a second fitting module, configured to fit the first STEC difference component after elimination according to a second fitting formula of a preset function to obtain estimated second STEC difference components between a plurality of surrounding stations and corresponding preset satellites and a reference satellite, and estimated third STEC difference components between the user station and corresponding preset satellite and the reference satellite; a second residual module, configured to calculate a second residual of a second STEC difference component estimate and the first STEC difference component before elimination; a third fitting module, configured to determine a kernel function according to a geometric relationship between coordinates of the plurality of second puncture points, the second residual, and an altitude angle of a preset satellite; The training module is used to determine the hyperparameters of the kernel function; The calculation module is configured to determine the STEC difference component of the user station according to the kernel function, the second residual, the third STEC difference component estimate, the first puncture point coordinates, and the second puncture point coordinates.

9. A computer storage medium, characterized in that The computer storage medium stores computer program instructions, which, when executed by a processor, implement the ionospheric differential total electron mass calculation method according to any one of claims 1 to 7.

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