A function-based ionospheric tomography modeling method

Abstract

The present invention discloses a function-based ionospheric tomography modeling method, which includes: obtaining the longitude and latitude grid information of the research area, and calculating the electron content of the plasma layer at a preset height at the center point of each grid by using the IRI-plas model. These data are fitted by a third-order polynomial, and the ionospheric delay observation value is corrected accordingly. Then, the grid without ray penetration is identified based on GNSS data, virtual rays are added and their observation values are calculated. The model coefficients are solved by combining the corrected ionospheric delay and the observation values of virtual rays, and an initial ionospheric tomography model based on spherical harmonic functions is constructed. Finally, the ionospheric residual value is calculated, and the initial model is corrected for residuals to obtain a corrected ionospheric tomography model. The technical solution of the present invention has the advantages of high modeling accuracy and low computational complexity, and the corrected electron density value is closer to the actual measurement data.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS atmospheric inversion, and particularly relates to a functional basis ionospheric tomography modeling method. Background Art

[0002] The ionosphere is located in the range of 60 km to 2000 km above the ground. It is one of the important components of the atmosphere and is also a research hotspot in the field of satellite navigation. Under the action of solar radiation and cosmic rays, neutral atmospheric molecules in the atmosphere are ionized to generate freely moving electrons, and the region where a large number of free electrons exist constitutes the ionosphere. The ionosphere is closely related to human production and life. On the one hand, the ionosphere absorbs ultraviolet radiation and the action of cosmic high-energy ions, avoiding the direct radiation of the sun and harmful rays to the earth, and also providing a propagation medium for long-distance radio transmission; on the other hand, when electromagnetic waves propagate through the ionosphere, refraction and other effects will occur, resulting in changes in signal speed and propagation path. When drastic changes occur, it will even cause communication interruption between satellites and ground equipment, greatly affecting the development of fields such as navigation, communication, and aerospace. Therefore, studying the ionosphere not only has important application value for ensuring the normal progress of space activities, improving satellite navigation and positioning accuracy, and radio long-distance communication performance, but also has important scientific significance for studying the variation characteristics of the space atmospheric environment including the ionosphere.

[0003] Traditional ionospheric monitoring means, such as GNSS satellites, occultation, ionosondes, incoherent scatter radars, etc., can only obtain one-dimensional or two-dimensional ionospheric parameters and are difficult to study the three-dimensional spatio-temporal changes of the ionosphere. Ionospheric tomography technology overcomes the limitations of two-dimensional ionospheric models and provides the possibility for studying three-dimensional ionospheric structures and perturbations. However, affected by the geometric distribution of GNSS satellites and the density of ground observation stations, ionospheric tomography imaging inversion faces ill-posed problems caused by insufficient observation data, uneven ray distribution, limited observation perspectives, etc.

[0004] Existing ionospheric tomography inversion technologies still have the following deficiencies: 1) To solve ill-posed problems, empirical models such as IRI2020 and NeQuick are often used as prior values in areas lacking data. However, the accuracy of these empirical models is limited, which will affect the accuracy of the inverted electron density; 2) In functional basis ionospheric tomography imaging, it is usually assumed that the electron content of the plasmasphere is a fixed constant, such as 3 TECU. However, the electron content of the plasmasphere is not constant and varies with latitude, longitude, time, and solar activity. Summary of the Invention

[0005] The purpose of the present invention is to provide a functional basis ionospheric tomography modeling method to solve the problems existing in the above-mentioned prior art.

[0006] To achieve the above object, the present invention provides a function-based ionospheric tomography modeling method, including:

[0007] Obtain the longitude and latitude grid division information of the research area, and calculate the electron content of the plasma layer at the preset height at the center point of each grid based on the IRI-plas model; fit the calculated electron content of the plasma layer based on a third-order polynomial function, and perform plasma layer correction on the ionospheric delay observation values based on the fitted data to obtain the corrected ionospheric delay observation values;

[0008] Identify the grids without ray penetration based on GNSS observation data, add virtual rays to the grids without ray penetration, and calculate the virtual ray observation values;

[0009] Solve the model coefficients based on the corrected ionospheric delay observation values and the virtual ray observation values;

[0010] Construct an initial ionospheric tomography model based on spherical harmonic functions based on the model coefficients, calculate the ionospheric residual values between the corrected ionospheric delay observation values and the predicted values of the initial ionospheric tomography model, and perform residual correction on the initial ionospheric tomography model based on the ionospheric residual values to obtain the corrected ionospheric tomography model.

[0011] Optionally, the process of obtaining the longitude and latitude grid division information specifically includes:

[0012] Divide the research area horizontally to obtain a number of grids.

[0013] Optionally, the specific calculation formula for performing plasma layer correction on the ionospheric delay observation values based on the fitted data is:

[0014]

[0015] In the formula, is the corrected ionospheric delay observation value, STEC is the original ionospheric delay observation value, VPEC is the electron content of the plasma layer, and Z ' is the zenith distance at the piercing point.

[0016] Optionally, the process of calculating the virtual ray observation values specifically includes:

[0017] Calculate the electron content of the plasma layer at the preset height at the center point of the grid corresponding to the grid after adding the virtual ray to obtain the virtual ray observation values.

[0018] Optionally, the specific calculation formula for solving the model coefficients based on the corrected ionospheric delay observation values and the virtual ray observation values is:

[0019]

[0020] In the formula, is the corrected ionospheric delay observation value, VTEC is the added virtual ray observation value, A1 and A2 are matrices composed of the intercepts of the rays within the pixel, B is the coefficient matrix related to the horizontal and vertical direction functions, x is the column vector of coefficients to be solved, and e is the observation noise.

[0021] Optionally, the calculation process of the ionospheric residual value specifically includes:

[0022]

[0023] In the formula, is the ionospheric delay observation value, STEC' is the inverted ionospheric delay, and STEC res is the ionospheric residual value.

[0024] Optionally, the residual correction of the initial ionospheric tomography model based on the ionospheric residual value specifically includes:

[0025] Based on the ionospheric residual value, perform residual correction on the ionospheric delay and electron density corresponding to each layer of each ray in the initial ionospheric tomography model to obtain the corrected ionospheric tomography model.

[0026] Optionally, the calculation formula for performing residual correction specifically includes:

[0027]

[0028] In the formula, STEC i is the ionospheric delay of the ray in the i-th layer, STEC cor(i) is the correction value of the ionospheric delay of the ray in the i-th layer, D(i) is the intercept of the ray within the grid of the i-th layer, and ELEC cor(i) is the correction value of the electron density of a certain ray in the i-th layer. and are the final ionospheric delay value and electron density final value of the ray in the i-th layer, and ELEC i is the electron density value of the ray in the i-th layer.

[0029] The technical effects of the present invention are:

[0030] After the present invention uses a cubic polynomial to remove the electron content in the plasmasphere, the ionospheric tomography imaging result has higher accuracy than the direct modeling without eliminating the plasmasphere; in the present invention, the initial model adopts a function-based ionospheric tomography model, which significantly reduces the calculation amount; the present invention adjusts the electron density in each voxel based on the STEC residual, and the corrected electron density value is closer to the actual measurement data. Description of the Drawings

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0032] The drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0033] Figure 1 Schematic diagram of the ionospheric tomography model in the embodiments of the present invention;

[0034] Figure 2 Electron content of the plasmasphere more than 2000 km in the research area at a certain moment in the embodiments of the present invention;

[0035] Figure 3 Schematic diagram of the plasmasphere correction in the embodiments of the present invention;

[0036] Figure 4 Distribution diagram of the observed rays at a certain moment in the embodiments of the present invention;

[0037] Figure 5 Result diagram of the internal consistency accuracy of the ionospheric tomography in the embodiments of the present invention;

[0038] Figure 6 Result diagram of the external consistency accuracy of the ionospheric tomography in the embodiments of the present invention;

[0039] Figure 7 Schematic diagram of the comparison result between the tomography inversion result and the digital ionosonde hmF2, NmF2 in the embodiments of the present invention;

[0040] Figure 8 Schematic diagram of the comparison result between the electron density obtained by tomography inversion on August 22, 2021 and the occultation data in the embodiments of the present invention;

[0041] Figure 9 Schematic diagram of the comparison result between the electron density obtained by tomography inversion on August 27, 2021 and the occultation data in the embodiments of the present invention;

[0042] Figure 10 Flowchart of the modeling in the embodiments of the present invention. Detailed implementation manners

[0043] The various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and implementation manners of the present invention.

[0044] It should be understood that the terms described in the present invention are only for describing specific embodiments and are not used to limit the present invention. Additionally, for the numerical ranges in the present invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Each intermediate value within any stated value or stated range, as well as each smaller range between any other stated value or intermediate value within the stated range, is also included in the present invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0045] Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention pertains. Although the present invention only describes preferred methods, any method similar or equivalent to those described herein may also be used in the implementation or testing of the present invention. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In case of conflict with any incorporated document, the content of this specification shall prevail.

[0046] Without departing from the scope or spirit of the present invention, various improvements and changes can be made to the specific embodiments of the present invention specification, which are obvious to those skilled in the art. Other embodiments obtained from the specification of the present invention are obvious to those skilled in the art. The specification and examples of this application are merely exemplary.

[0047] Regarding the use of "comprising", "including", "having", "containing", etc. herein, they are all open-ended terms, meaning including but not limited to.

[0048] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine with the embodiments to detail this application.

[0049] Example 1

[0050] Such as Figure 1 - Figure 10As shown in the figure, in this embodiment, a function-based ionospheric tomography modeling method is provided, including: obtaining the longitude and latitude grid division information of the research area, calculating the electron content of the plasma layer at the center points of each grid at a preset height based on the IRI-plas model; fitting the calculated electron content of the plasma layer with a third-order polynomial function, and performing plasma layer correction on the ionospheric delay observation values based on the fitted data to obtain the corrected ionospheric delay observation values; identifying the grids without ray penetration based on the GNSS observation data, adding virtual rays in the grids without ray penetration, and calculating the virtual ray observation values; solving the model coefficients based on the corrected ionospheric delay observation values and the virtual ray observation values; constructing an initial ionospheric tomography model based on spherical harmonic functions based on the model coefficients, calculating the ionospheric residual values between the corrected ionospheric delay observation values and the predicted values of the initial ionospheric tomography model, and performing residual correction on the initial ionospheric tomography model based on the ionospheric residual values to obtain the corrected ionospheric tomography model.

[0051] In this embodiment, by deeply studying the high-precision function-based ionospheric tomography modeling, it is not only possible to effectively reduce the influence of ionospheric errors on the navigation system, improve the accuracy and reliability of positioning, but also helpful to provide more accurate ionospheric information for multimodal navigation systems, promoting the integration of satellite navigation and other navigation technologies, such as inertial navigation, visual navigation, etc., to further improve the robustness and global applicability of the navigation system. The ionosphere may undergo abnormal changes due to factors such as solar activity, which have a serious impact on the navigation system. High-precision ionospheric modeling research helps to timely identify and respond to these abnormal events, and also provides valuable data support for fields such as early warning of disaster-related geoscience events and space weather forecasting.

[0052] STEC is the integral of the ionospheric electron density from the receiver position to the satellite position, and the expression is as follows:

[0053]

[0054] where r and s are the positions of the receiver and the satellite respectively, Ne is the electron density, and λ, φ, h are the longitude, latitude, and height respectively.

[0055] In this embodiment, the horizontal distribution of the electron density is represented by spherical harmonic functions, and the vertical direction is characterized by 3 EOFs. Then the electron density at any point above the earth's surface can be expressed as:

[0056]

[0057] In ionospheric tomography, the research area is usually divided into pixels of the same size, assuming that the electron density in each pixel remains constant. The STEC value on each ray can be considered equal to the sum of the products of the intercepts of the ray in the corresponding pixels it passes through and the electron density in these pixels. For example, Figure 1 Suppose the total number of pixels after the ionospheric area to be inverted is gridded is, and there are a total of observation rays passing through the area to be inverted. The intercept of the th ray in each pixel is a i (i = 1, 2, 3, … n), and the electron density of each corresponding pixel is x i (i = 1, 2, 3, … n),, and its TEC value is STEC i , that is, it can be expressed as:

[0058]

[0059] where, e i is the observation noise.

[0060] Written in matrix form as:

[0061] STEC m×1 = A m×n X n×1 + e m×1 (4)

[0062] where, A is the matrix composed of the intercepts of each ray in the pixels, and X is the electron density matrix. If the electron density is expressed by mathematical functions in the horizontal and vertical directions, the above formula can be written as:

[0063] STEC m×1 = A m×n B n×u x u×1 + e m×1 (5)

[0064] where, B is the coefficient matrix related to the horizontal and vertical direction functions, m is the number of rays, n is the number of pixels in the tomography area, u is the number of coefficients to be solved, and x is the column vector of coefficients to be solved.

[0065] (1) Correction of the electron content in the plasmasphere: Under normal circumstances, the electron content in the plasmasphere is considered to be a fixed constant of 3 TECU. This constant is divided by the sine of the elevation angle as the correction of the plasma electron content on the slant path. However, the electron content in the plasmasphere varies with latitude, longitude, time, and solar activity. Therefore, in this embodiment, the horizontal direction of the study area is divided into 10 * 13 grids (10 in the latitude direction and 13 in the longitude direction). The IRI-plas 2020 model of assimilating CODE-GIM is used to calculate the electron content in the plasmasphere in the zenith direction above 2000 km at the center point of each grid, denoted as VPEC. IRI-plas extends the International Reference Ionosphere (IRI) to the plasmasphere, and the height can reach the GPS orbital height of 20200 km. IRI-plas can input external information such as the critical frequency of the F2 layer (foF2), the maximum ionization height (hmF2), and the total electron content (TEC) to update the ionospheric state. Research shows that after inputting external TEC, the TEC and foF2 of IRI-plas will be more accurate. The daily VPEC data is fitted with a third-order polynomial function, as Figure 2 shown.

[0066] After obtaining the VPEC at a certain moment, the ionospheric delay observation value can be corrected for the plasmasphere:

[0067]

[0068] where, is the corrected ionospheric delay observation value, STEC is the original ionospheric delay observation value, VPEC is the electron content in the plasmasphere, and Z ' is the zenith distance at the piercing point, as Figure 3 shown.

[0069] In this embodiment, the IRI-plas model is introduced into ionospheric tomography for the first time, and the spatio-temporal characteristics of the electron content above 2000 km are analyzed based on the IRI-plas model. Plasma layer correction is carried out before ionospheric tomography modeling to eliminate the contribution of the plasmasphere to the total electron content and improve the modeling accuracy.

[0070] (2) Enhancement of the virtual rays of IRI-plas by assimilating GIM: Limited by the location distribution of GNSS observation stations and the satellite observation angles, GNSS rays often cannot penetrate all grids within the area to be inverted. At the same time, the electron density distribution in the ionosphere is changing all the time, and ionospheric tomography is often based on the assumption that the ionosphere remains unchanged for a period of time. Therefore, the GNSS observation time interval for ionospheric tomography cannot be too long. This results in the electron density of many grids without ray penetration in ionospheric tomography not being effectively corrected, thus affecting the modeling accuracy. As Figure 4The observed ray distribution for 30 minutes at UT 14:00 on August 20, 2021 is shown as follows.

[0071] As can be seen from Figure 4 even after accumulating 30 minutes of observational data, there are still a large number of grids without ray penetration. The reason for the lack of ray penetration in the grids is that there are few observation stations in the areas near these grids. Therefore, the distribution of observation stations is a major factor affecting the accuracy of ionospheric tomography modeling. If some virtual rays are added to the areas lacking observation stations on the ground, the grids without ray penetration can be covered.

[0072] The total electron content (VTEC) in the vertical direction from 80 - 2000 km in the area lacking observational data is calculated by integrating the IRI - plas 2020 model assimilating GIM, and it is used together with the corrected ionospheric delay observational value to participate in the solution. Then formula (5) can be expressed as:

[0073]

[0074] where is the corrected ionospheric delay observational value, VTEC is the observational value of the added virtual ray, A1 and A2 are matrices composed of the intercepts of the rays within the pixels, B is the coefficient matrix related to the horizontal and vertical direction functions, and x is the column vector of the coefficients to be solved. The weighted least - squares method is used to solve the model coefficients x, where the weight ratio of the observational value and the VTEC observational value is taken as 2:1, and e is the observational noise.

[0075] By setting up virtual observation stations and adding a series of virtual rays in the areas lacking observation stations on the ground, on the one hand, it can effectively correct the voxels that originally had no ray passing through, and on the other hand, it can increase the number of voxels penetrated by the intersecting rays, alleviating the rank deficiency and ill - conditioning problems of the tomography equation. This method can effectively invert the three - dimensional ionospheric electron density, and the inversion accuracy in the areas lacking ray penetration has been significantly improved.

[0076] (3) Tomography model residual correction: Since the spherical harmonic function is a relatively smooth function model, it can only describe relatively gentle ionospheric delay changes. If the ionospheric delay changes violently or has a large amplitude, such as during a magnetic storm, the value of the slant - total electron content (STEC) of the ionospheric delay may be several times that in quiet times. At this time, it is difficult to accurately describe the change trend of STEC with only one spherical harmonic function. Therefore, an initial functional basic analysis model is first established, and then the model is corrected. The correction method is as follows:

[0077] is the ionospheric delay observational value, denote STEC' as the inverted ionospheric delay, and STEC res is the ionospheric residual value, as shown in formula (7).

[0078]

[0079] The ionospheric delay and electron density of each layer of each ray are corrected successively according to formulas (8), (9), (10), and (11):

[0080]

[0081] Among them, STEC i is the ionospheric delay of a certain ray in the i-th layer, STEC cor(i) is the correction value of the ionospheric delay of a certain ray in the i-th layer, D(i) is the intercept of a certain ray within the grid of the i-th layer, and ELEC cor(i (i) is the correction value of the electron density of a certain ray in the i-th layer. and are the final values of the ionospheric delay and electron density of a certain ray in the i-th layer, respectively.

[0082] After removing the electron content of the plasmasphere using a cubic polynomial in this embodiment, the ionospheric tomography imaging result has a higher accuracy than the direct modeling without eliminating the plasmasphere; in this embodiment, the initial model adopts a function-based ionospheric tomography model, which significantly reduces the computational amount; in this embodiment, the electron density in each voxel is adjusted based on the STEC residual, and the corrected electron density value is closer to the actual measurement data.

[0083] A function-based ionospheric tomography modeling method with additional plasma correction and virtual ray enhancement proposed in this embodiment realizes high-precision ionospheric modeling in the region. The results show that the new method can significantly improve the accuracy of ionospheric regional modeling. Comparing the results after modeling with ionosonde and COSMIC2 occultation data shows that this method can effectively reconstruct the three-dimensional electron density and improve the inversion accuracy in the region where ray penetration is limited.

[0084] (1) Internal and external consistency accuracy of the ionospheric tomography model: The average value of the root mean square errors of 48 inversion periods within one day is taken as the overall internal consistency accuracy evaluation index for one day. The internal consistency accuracy results are as shown in Figure 5 . In the figure, the black columns represent the internal consistency accuracy of the ionospheric tomography model established using only the spherical harmonic function in the horizontal direction and the empirical orthogonal decomposition function in the vertical direction, and the red columns represent the internal consistency accuracy after ionospheric residual correction on the basis of the previous step. If only the first step is adopted, the average internal consistency accuracy for 30 days is 3.38 TECU. If the ionospheric residual correction in the second step is carried out on the basis of the first step, the average internal consistency accuracy for 30 days is 1.34 TECU, and the accuracy of the tomography model is significantly improved.

[0085] To objectively evaluate the overall accuracy of the inverted ionospheric tomography model, the inversion results are compared and evaluated with the observation data not involved in ionospheric tomography to evaluate its external consistency accuracy. The root mean square error of all time periods within a day is statistically calculated and averaged as the evaluation index for the overall external consistency accuracy of the day. In this embodiment, the average value of the external consistency accuracy from August 1st to 30th, 2021, for a total of 30 days is statistically calculated. As Figure 6 shown

[0086] Figure 6 in, the blue bars represent the external consistency accuracy of the ionospheric tomography model established using only horizontal spherical harmonic functions and vertical empirical orthogonal decomposition functions. The green bars represent the external consistency accuracy after ionospheric residual correction based on the previous step. If only the first step is adopted, the average external consistency accuracy for 30 days is 2.83 TECU. If ionospheric residual correction is performed in the second step based on the first step, the average external consistency accuracy for 30 days is 1.55 TECU, and the fluctuation of the external consistency accuracy within 30 days is small, all below 2 TECU.

[0087] (2) Digital ionosonde verification: Since the peak density (NmF2) and peak height (hmF2) of the ionospheric F2 layer are important parameters reflecting the electron density profile of the ionosphere, if both NmF2 and hmF2 of the inverted electron density are close to the true values, it can be proved that the inversion result has a high enough accuracy and the algorithm is relatively reliable. Therefore, it can be used as an important reference index for evaluating the accuracy of the ionospheric tomography inversion results. The absolute error between NmF2 and hmF2 obtained by ionospheric tomography inversion at the same time and the data of the digital ionosonde is statistically calculated, and the daily average root mean square error RMSE of the absolute error of all time periods within a day is calculated. The results are as Figure 7 shown

[0088] shown Figure 7 It can be seen that after using the second-step ionospheric residual correction, the root mean square error of the peak density NmF2 from August 1st to 30th, 2021, is significantly reduced, and the peak density is closer to the true value. The change in the peak height hmF2 is not obvious. It is proved that the model accuracy is improved after using residual correction.

[0089] (3) COSMIC2 Occultation Data Verification: The COSMIC series of atmospheric sounding satellites are jointly developed by the United States and the Taiwan region of China. They are equipped with instruments such as GNSS receivers and ionospheric photometers, which can provide parameters such as atmospheric humidity, refractive index, and electron density profiles. They are mainly used for meteorological environment monitoring, ionospheric sounding, and weather forecasting. IonPrfs is a level-2 atmospheric inversion product of COSMIC 1 / 2, which mainly provides electron density data obtained by the Abel transformation method at the moment of occultation events. The COSMIC2 occultation data has the characteristics of large data volume, high precision, all-weather, and being unaffected by the distribution of observation sites. Its measured data can better reflect the small-scale daily variation of the ionosphere. Therefore, the electron density obtained by ionospheric tomography inversion can be compared with the occultation data to verify the inversion results.

[0090] On August 22, 2021, the geomagnetic activity was relatively quiet. There were a total of 4721 occultation events on this day. After removing inaccurate electron density files, there were 4506 left. Among them, there were 38 occultation events occurring over the study area. Compare the electron density profile of each event with the electron density inverted at the same time and the same location. At an interval of 20 km in height, compare the difference between the electron density inverted at each height from 80 to 560 km and the occultation electron density, and calculate the root mean square error of all events at the same height. The results are as Figure 8 shown. Above an altitude of 200 km, the root mean square error after using the second-step residual correction decreases, and the result is more obvious above 300 km, indicating that the electron density inverted using the two-step method has higher precision.

[0091] On August 27, 2021, the geomagnetic activity was relatively active. There were a total of 4893 occultation events on this day. After removing inaccurate electron density files, there were 4650 left. Among them, there were 38 occultation events occurring over the study area. Calculate the root mean square error of this day according to the previous method. The results are as Figure 9 . The root mean square error after using the second-step residual correction decreases, and the result is more obvious above 300 km, indicating that whether the ionosphere is relatively quiet or active, the electron density inverted using this method is closer to the true value, and the model has good robustness.

[0092] As described above, it is only the preferred specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by this application should be covered by the protection scope of this application. Therefore, the protection scope of this application should be subject to the protection scope of the claims.

Claims

1. A function-based ionospheric tomography modeling method, characterized in that, Including: Obtain the longitude and latitude grid division information of the research area, calculate the electron content of the plasmasphere at the center point of each grid at a preset height based on the IRI-plas model; fit the calculated electron content of the plasmasphere based on a third-order polynomial function, and perform plasmasphere correction on the ionospheric delay observation values based on the fitted data to obtain the corrected ionospheric delay observation values; Identify the grids without ray penetration based on the GNSS observation data, add virtual rays to the grids without ray penetration, and calculate the virtual ray observation values; Solve the model coefficients based on the corrected ionospheric delay observation values and the virtual ray observation values; Construct an initial ionospheric tomography model based on spherical harmonic functions based on the model coefficients, calculate the ionospheric residual values between the corrected ionospheric delay observation values and the predicted values of the initial ionospheric tomography model, and perform residual correction on the initial ionospheric tomography model based on the ionospheric residual values to obtain the corrected ionospheric tomography model.

2. The function-based ionospheric tomography modeling method according to claim 1, wherein The process of obtaining the longitude and latitude grid division information specifically includes: Perform horizontal division on the research area to obtain a number of grids.

3. A function-based ionospheric tomography modeling method according to claim 1, characterized in that The specific calculation formula for performing plasmasphere correction on the ionospheric delay observation values based on the fitted data is: In the formula, is the corrected ionospheric delay observation value, STEC is the original ionospheric delay observation value, VPEC is the plasmaspheric electron content, and Z ' is the zenith distance at the piercing point.

4. A function-based ionospheric tomography modeling method according to claim 1, characterized in that The calculation process of the virtual ray observation values specifically includes: Calculate the electron content of the plasmasphere at the center point of the grid corresponding to the grid after adding virtual rays at a preset height to obtain the virtual ray observation values.

5. A method for function-based ionospheric tomography modeling according to claim 1, characterized in that, The specific calculation formula for solving the model coefficients based on the corrected ionospheric delay observation values and the virtual ray observation values is: In the formula, is the corrected ionospheric delay observation value, VTEC is the added virtual ray observation value, A1 and A2 are matrices composed of the intercepts of the rays within the pixel, B is the coefficient matrix related to the horizontal and vertical direction functions, x is the column vector of coefficients to be solved, and e is the observation noise.

6. A function-based ionospheric tomography modeling method according to claim 1, characterized in that The calculation process of the ionospheric residual values specifically includes: In the formula, is the observed value of ionospheric delay, STEC' is the inverted ionospheric delay, and STEC res is the ionospheric residual value.

7. A method for function-based ionospheric tomography modeling according to claim 1, characterized in that The specific process of performing residual correction on the initial ionospheric tomography model based on the ionospheric residual values includes: Perform residual correction on the ionospheric delay and electron density corresponding to each layer of each ray in the initial ionospheric tomography model based on the ionospheric residual values to obtain the corrected ionospheric tomography model.

8. A method for ionospheric tomography modeling based on function basis according to claim 7, characterized in that The calculation formula for performing residual correction specifically includes: where STEC i is the ionospheric delay of the ray in the i-th layer, and STEC cor(i) is the correction value of the ionospheric delay of the ray in the i-th layer. D(i) is the intercept of the ray within the grid of the i-th layer, and ELEC cor(i) is the correction value of the electron density of the ray in the i-th layer, and are the final values of the ionospheric delay and the final value of the electron density of the ray in the i-th layer, respectively. ELEC i is the electron density value of the ray in the i-th layer.

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