A method for reconstructing the three-dimensional electron density of the ionosphere during magnetic storms based on diffusion models

Abstract

The present invention discloses a method for reconstructing the three-dimensional electron density of the ionosphere during magnetic storms based on a diffusion model. This method is based on the principles of the diffusion model and the three-dimensional electron density reconstruction technology of the ionosphere, which can alleviate the ill-posed problem of three-dimensional ionospheric inversion caused by the limited number of ground-based observation stations and the geometric line of sight between the stations and satellites; the method for reconstructing the three-dimensional ionospheric electron density based on the diffusion model can significantly improve the accuracy and resolution of three-dimensional ionospheric inversion during magnetic storms; it can achieve high-efficiency three-dimensional reconstruction efficiency of the ionosphere and reveal the spatial dynamic change process of the ionosphere during magnetic storms.

Description

Technical Field

[0001] The present invention relates to the technical field of ionospheric research and its data processing, and particularly relates to a method for reconstructing the three-dimensional electron density of the ionosphere during magnetic storms based on a diffusion model. Background Art

[0002] The ionosphere is an important part of the near-Earth space layer of the Earth. Affected by solar activities, the Earth's magnetic field, and atmospheric fluctuations, the spatio-temporal movement characteristics of the ionosphere are extremely complex. On the one hand, it has a significant impact on radio communication and navigation positioning. On the other hand, there is a complex coupling mechanism between the ionosphere and the crust layer. The reconstruction of the three-dimensional electron density of the ionosphere is an advanced detection technology for revealing the spatial structure of the ionosphere. High-precision three-dimensional electron density of the ionosphere can construct an accurate ionospheric delay model, thereby improving the accuracy of navigation and positioning, especially in the mid-low latitude regions where the ionosphere is very active. In addition, by studying the relationship between crustal activities such as earthquakes, tsunamis, and volcanic eruptions and ionospheric disturbances, a new technology can be provided for the field of geological disaster warning.

[0003] Magnetic storms are strong disturbances of the Earth's magnetic field caused by solar activities such as coronal mass ejections and solar flares. Such disturbances can cause drastic changes in the electron density of the ionosphere. In addition, magnetic storms may also cause abnormal phenomena such as ionospheric scintillation and plasma irregularities, which will all affect the stability and reliability of satellite signals. Existing methods for reconstructing the three-dimensional electron density of the ionosphere mainly rely on traditional algorithms (iterative reconstruction algorithms, singular value decomposition, and function models, etc.) and limited observational data. Especially, the ill-posed inversion problem caused by limited ground observation stations and restricted observation perspectives leads to insufficient reconstruction accuracy and resolution. The method based on the diffusion model can effectively handle the three-dimensional ill-posed inversion problem under extreme magnetic storm conditions and improve the reconstruction accuracy and resolution, providing a new technical means for improving the real-time monitoring and prediction of the three-dimensional ionospheric electron density.

[0004] The diffusion model is a mathematical model used to describe the diffusion process of particles, energy, or substances in space. In recent years, the diffusion model has shown great potential and superiority in image reconstruction, text processing, and 3D reconstruction, etc. However, this technology has not been used to describe the spatial structure of the ionosphere. In ionospheric research, the diffusion model is mainly used to simulate the movement and distribution of electrons in the ionosphere. The method for reconstructing the three-dimensional electron density of the ionosphere based on the diffusion model can effectively and accurately reconstruct the spatial structure of the ionosphere. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a method for reconstructing the three-dimensional electron density of the ionosphere during magnetic storms based on a diffusion model; this method can effectively alleviate the three-dimensional ill-posed inversion problem and improve the reconstruction accuracy of the three-dimensional electron density of the ionosphere during magnetic storms.

[0006] To achieve the above technical effects, the present invention is realized through the following technical solutions: A method for reconstructing the three-dimensional electron density of the ionosphere during magnetic storms based on a diffusion model, characterized by comprising the following steps:

[0007] S1. Obtain the original observation data of ground-based observation stations and satellite navigation messages in the reconstruction area, and use the carrier phase smoothed pseudorange algorithm to calculate the slant total electron content (STEC) on the line of sight from the station to the satellite;

[0008] S2. Discretize the ionosphere in the reconstruction area to form a three-dimensional spatial voxel grid;

[0009] S3. Eliminate the geometric lines of sight with low elevation angles between the ground-based observation stations and the satellites, and simultaneously construct an observation intercept matrix between the lines of sight and the voxel grid;

[0010] S4. Use the International Reference Ionosphere (IRI) to obtain the three-dimensional electron density of the ionosphere in the inversion area and at the inversion time; further, match the electron density at the center of each voxel grid as the initial value for iterative reconstruction;

[0011] S5. Use the efficient multiplicative algebraic reconstruction technique (MART) to preliminarily reconstruct the three-dimensional electron density of the ionosphere in the inversion area;

[0012] S6. Use the electron density data obtained from the IRI2020 model as the benchmark for forward training of the diffusion model. The voxel grids not penetrated by the rays during the MART reconstruction process will be regarded as measurement noise and denoised during the reverse process to improve the overall reconstruction accuracy and quality;

[0013] S7. Use ionosonde data as the true value to measure the accuracy of the reconstruction result of the three-dimensional electron density of the ionosphere based on the diffusion model; if the expected effect is not achieved, adjust the parameters of the diffusion model in S6 until finally achieving a high-quality reconstruction of the three-dimensional electron density of the ionosphere.

[0014] Further, the formula for calculating the STEC on the line of sight from the station to the satellite using the carrier phase smoothed pseudorange in S1 is as follows:

[0015]

[0016] In the formula, f1 and f2 are the carrier frequencies of the L1 band and the L2 band respectively, usually 1.57542 GHz and 1.2276 GHz; P sm is the smoothed pseudorange combined observation value, which reduces the influence of noise and multipath; DCB i and DCB j are the hardware delay biases of the station and the satellite respectively; the unit of STEC is TECU, and 1 TECU = 10 16Ne / m 2 ;

[0017] STEC refers to the total amount of electrons from the satellite to the receiver in the satellite signal propagation path; its integral expression is:

[0018]

[0019] In the formula, Ne is the electron density, indicating the number of electrons in the ionosphere at a certain position on the path ;

[0020] When performing 3D inversion, the above formula is usually discretized, and its discretized expression is:

[0021]

[0022] In the formula, A ij is the intercept matrix between the ray and the voxel, indicating the length of the path i passing through the j-th voxel; ∈ i is the measurement error or noise; x j is the electron density of the j-th voxel, which is the unknown quantity to be solved.

[0023] Furthermore, the intercept matrix in S3 adopts the following calculation formula:

[0024]

[0025] In the formula, d is the intercept value of the ray passing through the voxel grid, X1, Y1, Z1 are the spatial positions of the ray entering a certain surface of the voxel; X2, Y2, Z2 are the spatial positions of the ray exiting the other surface of the voxel. The unit of d is generally m.

[0026] Furthermore, the formula of the iterative reconstruction algorithm MART in S5 is as follows:

[0027]

[0028] In the formula, x j k+1 is the electron density of the j-th voxel after the (k + 1)-th iteration, x j k is the estimated value at the k-th iteration; <a i T ,x k > is the TEC calculated according to the estimated value at the k-th iteration; λ is the relaxation factor, and its value range is 0 < λ < 1; a ij is the intercept value of the i-th ray and the j-th voxel; ||a|| is the sum of the intercepts of all voxels passed through by the i-th ray.

[0029] Further, in S6, the forward process of the diffusion model transforms the original electron density data into noise approaching a normal distribution by gradually adding noise to the empirical model electron density data; subsequently, in the reverse process, the voxel electron densities with low reconstruction quality and accuracy due to the ill-posed three-dimensional inversion problem in the MART reconstruction process are treated as noise, and the global voxel electron densities with high precision and quality are gradually reconstructed.

[0030] Further, in S7, the root mean square error (RMSE) is used as the accuracy measurement index; the specific index value can be adjusted according to actual requirements; the root mean square error formula is as follows:

[0031]

[0032] In the formula, x i is the true electron density extracted by an ionosonde or an incoherent scatter radar, and x^ i is the electron density value after denoising by the diffusion model.

[0033] The beneficial effects of the present invention are as follows:

[0034] The present invention alleviates the ill-posed problem of ionospheric three-dimensional inversion caused by the limited number of ground-based observation stations and the limited geometric line of sight between the stations and the satellite;

[0035] The three-dimensional ionospheric electron density reconstruction method based on the diffusion model of the present invention significantly improves the three-dimensional ionospheric inversion accuracy and resolution during magnetic storms;

[0036] The high-efficiency ionospheric three-dimensional reconstruction efficiency of the present invention can reveal the ionospheric spatial dynamic change process during magnetic storms. Description of the Drawings

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of 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, other drawings can be obtained based on these drawings without creative efforts.

[0038] Figure 1 is the high-precision ionospheric electron density reconstruction technical flow chart of the present invention during magnetic storms;

[0039] Figure 2 is the Kp and Dst index chart on March 17, 2015;

[0040] Figure 3 is the electron density distribution diagram of different altitude layers over Europe under magnetic storm conditions at 08:00, 10:00, and 12:00 UT on March 17, 2015;

[0041] Figure 4 It is a comparison chart of the vertical profiles of electron densities derived from IRI2020, MART, and the diffusion model at the same longitude and latitude under the geomagnetic storm environment in the European region on March 17, 2015. Detailed implementation manners

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0043] Embodiment 1

[0044] As Figure 1 shown, the present invention provides a method for reconstructing the three-dimensional electron density of the ionosphere during geomagnetic storms based on a diffusion model, which mainly includes the following steps.

[0045] Step 1: In order to calculate the geometric line of sight and STEC, here, the present invention example obtains the observation data and navigation message of the European region with a longitude range of -10° to 30° and a latitude range of 35° to 70° on March 17, 2015. And the STEC on the line of sight from the station to the satellite is solved using the carrier phase smoothed pseudorange algorithm. The main calculation formula is:

[0046]

[0047] In formula (1), f1 and f2 are the carrier frequencies of the L1 band and the L2 band respectively, usually 1.57542 GHz and 1.2276 GHz respectively; P sm is the smoothed pseudorange combined observation value, which reduces the influence of noise and multipath; DCB i and DCB j are the hardware delay biases of the station and the satellite respectively. The unit of STEC is TECU, and 1 TECU = 10 16 Ne / m 2 .

[0048] STEC usually refers to the total amount of electrons from the satellite to the receiver on the satellite signal propagation path. Its integral expression is:

[0049]

[0050] In formula (2), Ne is the electron density, indicating on the path The number of electrons in the ionosphere at a certain position above. When performing 3D inversion, the above formula is usually discretized, so its discretized expression is:

[0051]

[0052] In formula (3), A ij is the intercept matrix between the ray and the voxel, representing the length of path i passing through the j-th voxel; ∈ i is the measurement error or noise; x j is the electron density of the j-th voxel, which is the unknown quantity to be solved.

[0053] Step 2: The reconstruction range is from longitude -10° to 30°, latitude 35° to 70°, and altitude 90 to 1000 km. The discretized spatial resolution is voxels of size 1° * 1° * 30 km, with a total of 42000 voxels.

[0054] Step 3: Geometric lines of sight with an elevation angle less than 15° between the ground-based observation station and the satellite are excluded, and at the same time, an observation intercept matrix A between the line of sight and the voxel model is constructed. The formula for calculating the intercept is as follows:

[0055]

[0056] In formula (4), d is the intercept value of the ray passing through the voxel, X1, Y1, Z1 are the spatial positions of the ray entering a certain surface of the voxel; X2, Y2, Z2 are the spatial positions of the ray exiting the other surface of the voxel. The unit of d is generally m.

[0057] Step 4: The international ionospheric reference model IRI2020 is used to obtain the three-dimensional electron density in the inversion area and at the corresponding time, and further match the electron density at the center of each voxel as the initial value for iterative reconstruction.

[0058] Step 5: The efficient multiplicative algebraic reconstruction technique (MART) is used to preliminarily reconstruct the three-dimensional electron density of the ionosphere with a certain accuracy. The expression of MART is as follows:

[0059]

[0060] In formula (5), x j k+1 is the electron density of the j-th voxel after the (k + 1)-th iteration, x j k is the estimated value at the k-th iteration; <a i T ,x k > is the TEC calculated based on the estimated value at the k-th iteration; λ is the relaxation factor, and its value range is 0 < λ < 1. In the example of the present invention, λ = 0.2; aij is the intercept value of the i-th ray and the j-th voxel; ||a|| is the sum of the intercepts of all voxels passed through by the i-th ray; the maximum number of iterations using MART is set to 30 times.

[0061] Step 6: Use the electron density data obtained from the IRI2020 model as the benchmark for the forward training of the diffusion model. The voxels not penetrated by the rays during the MART reconstruction process will be regarded as measurement noise and denoised during the reverse process to improve the overall reconstruction accuracy and quality; the main algorithm process of this invention example is as follows in the table:

[0062] Table 1 Ionospheric three-dimensional electron density reconstruction algorithm based on diffusion model

[0063]

[0064]

[0065] Step 7: Use ionosonde data as the true value to measure the accuracy of the ionospheric three-dimensional electron density reconstruction result based on the diffusion model. If the expected effect is not achieved, adjust the diffusion model parameters in Step 6 until high-quality ionospheric three-dimensional electron density reconstruction is finally realized. In this example, the root mean square error (RMSE) is used as the accuracy measurement index. The specific index conditions can be adjusted according to actual needs.

[0066]

[0067] In Equation (6), x i is the true electron density extracted by the ionosonde or incoherent scatter radar, and x^ i is the electron density value after denoising by the diffusion model.

[0068] As Figure 2 shown, on March 17, 2015, the Earth's magnetic field experienced a severe disturbance, the geomagnetic Kp index exceeded 7, and at the same time, the Dst index dropped below -200 nT. This strong geomagnetic disturbance was triggered by the arrival of a coronal mass ejection on March 15, resulting in a strong geomagnetic interference in the ionosphere over the European region.

[0069] As Figure 3 shown, on the left Figure 3 (a), Figure (c), and Figure (e) are the reconstruction results of the traditional MART iterative reconstruction method; on the right Figure 3 (b), Figure (d), and Figure (f) are the reconstruction results of the method based on the diffusion model. Comparing the images on both sides, it is obvious that the image quality reconstructed by the diffusion model method is higher. Figure 3Clearly shows the distribution of ionospheric electron density in the European region at 08:00, 10:00, and 12:00 UTC on March 17, 2015. The data shows that the electron density is mainly concentrated at an ionospheric altitude of approximately 380 km, especially in the low-latitude region where the density is more significant. In contrast, the electron density in the ionospheric regions of 100 - 200 km and above 700 km is relatively low.

[0070] As Figure 4 shown, this example verifies the vertical profiles of the electron density derived from IRI2020, traditional MART, diffusion model-based, and ionosonde at UT08:00 and 10:00 on March 17, and compares the ionosonde profile as the true value. From Figure 4 the cross-sectional comparison diagram, it can be seen that the reconstruction method of the present invention is closer to the true profile of the ionospheric electron density. Compared with the traditional MART iterative reconstruction method, the reconstruction result of the method of the present invention is smoother and can effectively reflect the distribution of the three-dimensional electron density in the ionosphere under the strong geomagnetic storm environment.

Claims

1. A three-dimensional ionospheric electron density reconstruction method during magnetic storms based on a diffusion model, characterized in that, It includes the following steps: S1. Obtain the original observation data of the ground-based observation stations and satellite navigation messages in the reconstruction area, and use the carrier phase smoothed pseudorange algorithm to calculate the slant total electron content STEC on the line of sight from the station to the satellite; S2. Discretize the ionospheric space in the reconstruction area to form a three-dimensional voxel grid; S3. Eliminate the geometric lines of sight with low elevation angles between the ground-based observation stations and the satellites, and simultaneously construct an observation intercept matrix between the lines of sight and the voxel model; S4. Use the International Reference Ionosphere Model IRI to obtain the three-dimensional electron density of the ionosphere in the inversion area and at the inversion time; further, match the electron density at the center of each voxel as the initial value for iterative reconstruction; S5. Use the efficient multiplicative algebraic reconstruction technique MART to preliminarily reconstruct the three-dimensional electron density of the ionosphere in the inversion area; The formula of the iterative reconstruction algorithm MART in S5 is as follows: where x j k+1 is the electron density of the j-th voxel after the (k + 1)-th iteration, and x j k is the estimated value at the k-th iteration; <a i T , x k > is the TEC calculated based on the estimated value at the k-th iteration; λ is the relaxation factor, with a value range of 0 < λ < 1; a ij is the intercept value of the i-th ray and the j-th voxel; ||a|| is the sum of the intercepts of all voxels traversed by the i-th ray; S6. Use the electron density data obtained from the IRI2020 model as the benchmark for the forward training of the diffusion model. The voxels not penetrated by the rays during the MART reconstruction process will be regarded as measurement noise and denoised during the reverse process to improve the overall reconstruction accuracy and quality; In the forward process of the diffusion model in S6, the original electron density data is transformed into noise close to a normal distribution by gradually adding noise to the empirical model electron density data; Subsequently, in the reverse process, the electron density of the voxels with low reconstruction quality and accuracy due to the ill-posed problem of three-dimensional inversion during the MART reconstruction process is treated as noise, and the global voxel electron density with high precision and quality is gradually reconstructed; S7. Use the ionosonde data as the true value to measure the accuracy of the reconstructed result of the three-dimensional electron density of the ionosphere based on the diffusion model; if the expected effect is not achieved, adjust the parameters of the diffusion model in S6, and finally achieve a high-quality reconstruction of the three-dimensional electron density of the ionosphere.

2. The three-dimensional electron density reconstruction method of the ionosphere during magnetic storms based on the diffusion model according to claim 1, characterized in that The formula for calculating the STEC on the line of sight from the station to the satellite using the carrier phase smoothed pseudorange in S1 is as follows: Where f1 and f2 are the carrier frequencies of the L1 band and the L2 band, usually 1.57542 GHz and 1.2276 GHz respectively; P sm is the smoothed pseudorange combination observation value, reducing the influence of noise and multipath; DCB i and DCB j are the hardware delay biases of the station and the satellite respectively; the unit of STEC is TECU, and 1 TECU = 10 16 Ne / m 2 ; STEC refers to the total amount of electrons from the satellite to the receiver along the satellite signal propagation path; Its integral expression is: where Ne is the electron density, representing the number of electrons in the ionosphere at a certain position on the path ; When performing 3D inversion, the above formula is usually discretized, and its discretized expression is: Where, A ij is the intercept matrix between the ray and the voxel, representing the length of the path i passing through the j-th voxel; ∈ i is the measurement error or noise; x j is the electron density of the j-th voxel, which is the unknown quantity to be solved for.

3. A method for reconstructing the three-dimensional electron density of the ionosphere during magnetic storms based on a diffusion model according to claim 1, characterized in that The intercept matrix in S3 adopts the following calculation formula: In the formula, d is the intercept value of the ray passing through the voxel, X1, Y1, Z1 are the spatial positions of the ray entering a certain surface of the voxel; X2, Y2, Z2 are the spatial positions of the ray exiting the other surface of the voxel, and the unit of d is generally m.

4. A three-dimensional electron density reconstruction method of the ionosphere during magnetic storms based on a diffusion model according to claim 1, characterized in that, In S7, the root mean square error RMSE is used as the accuracy measurement index; the specific index value can be adjusted according to actual needs; the root mean square error formula is as follows: where x i is the true electron density extracted by an ionosonde or an incoherent scatter radar, is the electron density value after denoising by a diffusion model.

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