A method for three-dimensional modeling and data assimilation of ionospheric electron density

Abstract

The application discloses a three-dimensional modeling and data assimilation method for ionospheric electron density, belongs to the field of space environment monitoring and information technology, and comprises the following steps: constructing a hybrid basis function system based on spherical harmonics and empirical orthogonal functions and establishing a state space model, independently perturbing through key geophysical driving parameters, combining a physical empirical model to construct a physical-statistical dynamic model, fusing multi-source heterogeneous observation data, obtaining an analysis state vector set through a set Kalman filtering algorithm and an asynchronous assimilation window, and reconstructing a three-dimensional electron density field and uncertainty products through the hybrid basis function system based on the analysis state vector set.

Description

Technical Field

[0001] This invention relates to the field of space environment monitoring and information technology, and in particular to a method for three-dimensional modeling and data assimilation of ionospheric electron density. Background Technology

[0002] As the part of the Heliospheric space environment most closely related to human activities, accurate perception and modeling of the ionosphere's state are of paramount importance to national strategic infrastructure. Radio signals traversing the ionosphere, especially Global Navigation Satellite System (GNSS) signals, are significantly affected by the ionospheric electron density distribution, resulting in physical effects such as propagation delay and phase lead—a phenomenon known as "ionospheric delay." This effect is one of the most significant sources of error in GNSS applications, particularly in high-precision fields such as air navigation, precise point positioning, and disaster monitoring, where precise correction of ionospheric delay is crucial. Furthermore, satellite communication, over-the-horizon radar, and space target surveillance systems urgently require real-time, accurate three-dimensional ionospheric structure information to ensure their operational reliability and accuracy. Therefore, developing high-precision, high-resolution real-time ionospheric monitoring and modeling technologies has become a strategic requirement for enhancing the capabilities of national PNT (Positioning, Navigation, and Timing) systems and the level of space weather support.

[0003] Currently, ionospheric modeling mainly relies on empirical climatological models and GNSS observation-based inversion techniques. However, these methods all face limitations when dealing with the demands of real-time, high-precision applications. Empirical models, such as the International Reference Ionosphere (IRI) and NeQuick, can characterize the climatological distribution of the ionosphere across geographical, temporal, and solar activity dimensions. However, their reliance on long-term statistical averages makes it difficult to capture instantaneous disturbances and irregular structures at the synoptic scale, leading to systematic biases in real-time scenarios and failing to meet the need for accurate descriptions in dynamically changing environments. On the other hand, while traditional ionospheric tomography can invert electron density distribution using GNSS and other observational data, its pixelated discretization method results in extremely high state vector dimensions, causing not only a heavy computational burden but also ill-posedness in the inversion problem itself. Strong smoothing constraints introduced to force stable solutions, while suppressing numerical oscillations, inevitably smooth out the true gradient characteristics and fine structures of the ionosphere, causing key physical phenomena such as equatorial anomalies and irregularities to be over-smoothed and distorted in the model. Furthermore, even with the introduction of ensemble Kalman filtering within the data assimilation framework to dynamically update the error covariance, the gap between the high-dimensional state space and the finite number of set members still introduces spurious correlations, necessitating manual localization. This increases the uncertainty of subjective intervention and limits the model's adaptive capability while maintaining physical consistency. These factors collectively constitute the fundamental contradiction that current ionospheric modeling techniques face in reconciling real-time performance, resolution, and physical realism. Summary of the Invention

[0004] The purpose of this invention is to provide a three-dimensional modeling and data assimilation method for ionospheric electron density to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, this invention provides a method for three-dimensional modeling and data assimilation of ionospheric electron density, comprising the following steps: S1. Based on spherical harmonic functions and empirical orthogonal functions, a hybrid basis function system for characterizing the three-dimensional structure of the ionosphere is constructed. A state space model with the expansion coefficients of the hybrid basis functions as state vectors is established. Based on the state space model, a set of state vectors is constructed and initialized. S2. By generating independent perturbations for the key geophysical driving parameters of each member in the state vector set and calling the physical empirical model to generate an independent three-dimensional electron density background field, the background state coefficients of each member in the state vector set are obtained, thereby constructing a physical-statistical dynamic model for driving the evolution of the state vector. S3. Call the physical-statistical dynamic model to integrate and advance the set of state vectors from the previous analysis time to the current analysis time, and obtain the predicted state vector set at the current analysis time; acquire multi-source heterogeneous ionospheric observation data, and use the ensemble Kalman filter algorithm and asynchronous assimilation window to assimilate and update the predicted state vector set, and obtain the analysis state vector set at the current analysis time; use this analysis state vector set as the initial state for the next assimilation cycle to achieve continuous assimilation; S4. Based on the analysis of the state vector set, the three-dimensional ionospheric electron density field is reconstructed through a hybrid basis function system, and data products including the three-dimensional ionospheric electron density field are output.

[0006] Preferably, the hybrid basis function system in S1 is constructed by combining spherical harmonic functions and empirical orthogonal functions through tensor product.

[0007] Preferably, in the state-space model of S1, the three-dimensional ionospheric electron density field is defined as a linear expansion of the mixed basis function system, as shown in the following formula: ; in, For height ,longitude ,latitude electron density at that location, The expansion coefficients of the mixed basis functions are . Let be the order of the spherical harmonic function. For a series of spherical harmonic functions, Let be the highest order of the spherical harmonic function. Let be the number of empirical orthogonal functions. It is a spherical harmonic function. For the first An empirical orthogonal function.

[0008] Preferably, the specific steps of S2 are as follows: S21. Independently perturb the key geophysical driving parameters (mainly the solar radiation flux index F10.7 and the geomagnetic Ap index) to form the state vector set. Each member Generate a set of independent perturbation values; S22. Invoke the selected physical empirical model, such as NeQuick or IRI, input the key geophysical driving parameters after independent perturbations, and generate the model with members. Corresponding three-dimensional electron density background field ; S23. Use the least squares method to generate Projecting onto the mixed basis function system, we obtain the members. At the present moment Background state coefficient ; S24, Background State Coefficient Superimposed process noise Generate each member Forecast state vector To construct a physical-statistical dynamic model ; ; in, The process noise covariance matrix is... This is process noise.

[0009] Preferably, the specific steps of S3 are as follows: S31. Call the physical-statistical dynamic model to generate a set of predicted state vectors for the current analysis time; S32. Acquire multi-source heterogeneous ionospheric observation data, including ground-based GNSS oblique total electron content, radio occultation ionospheric observation data, and low-orbit satellite-borne GNSS observation data; S33. Using the ensemble Kalman filter algorithm and asynchronous assimilation window, multi-source heterogeneous ionospheric observation data are fused to assimilate and update the predicted state vector set, thus obtaining the analysis state vector set at the current analysis time. S34. Use the obtained set of analytical state vectors as the initial state for the next assimilation cycle, and iteratively execute steps S31 to S33 to achieve continuous assimilation.

[0010] Preferably, the specific steps of S31 are as follows: S311, Read the previous analysis time. Analysis of the set of state vectors ,in, For the current analysis time, For the assimilation period, To analyze the state vector; S312. For each member in the analysis state vector set Calling the physical-statistical dynamic model In the previous analysis time The analysis state is advanced to the current analysis time. The predicted state vector is obtained. The process is specifically represented as follows: ; in, This is process noise; S313. The forecast state vectors of all members constitute the set of forecast state vectors at the current analysis time. .

[0011] Preferably, the specific steps of S33 are as follows: S331, Set asynchronous assimilation window At the current moment of analysis Collect all observation times satisfy Multi-source heterogeneous ionospheric observation data, among which This is the length of the asynchronous assimilation window; S332. For each observation data within the asynchronous assimilation window The ensemble Kalman filter algorithm is used for iterative updates to obtain the analysis state vector; S333. Repeat S332 until all observation data within the asynchronous assimilation window has been processed, obtaining the final set of analysis state vectors. ,in This represents the total number of observed data.

[0012] Preferably, the specific steps of S332 are as follows: a. Calculate each member based on the forecast state vector set and the mixture basis function. Forecast observations Forecast observation mean and observation anomaly matrix The calculation formula is as follows: ; ; ; in, For the first The set member in the th ... The analysis state vector after the next iteration. For the number of iterations, For the observation operator, The total number of members in the set; The initial analysis state vector is obtained from the set of predicted state vectors, and the expression is as follows: ; b. Calculate the mean of the set of predicted state vectors. and state anomaly matrix The calculation formula is as follows: ; ; c. Calculate the ensemble Kalman gain The calculation formula is as follows: ; in, The observation error covariance matrix; d. Generation and observation of data Related perturbation observation set The calculation formula is as follows: ; in, For random perturbations; e. Update each member of the predicted state vector set using the ensemble Kalman gain and the set of perturbation observations. The analysis state vector is obtained. The calculation formula is as follows: .

[0013] Therefore, the present invention employs the above-mentioned three-dimensional modeling and data assimilation method for ionospheric electron density, which has the following beneficial effects: (1) This invention reduces the state vector representing the three-dimensional structure of the ionosphere from millions of grid points to hundreds of physically or statistically significant basis function coefficients by employing a hybrid basis function system composed of "spherical harmonic functions" and "empirical orthogonal functions". This key transformation converts the ill-posed high-dimensional inversion problem into a low-dimensional, well-posed optimization problem, thereby ensuring real-time computational efficiency while avoiding the distortion of fine structures (such as plasma bubbles) caused by imposing smoothing constraints in traditional methods, and significantly improving the accuracy and resolution of the model.

[0014] (2) The present invention adopts the strategy of "physical model driving + process noise perturbation". The NeQuick / IRI model is used to provide background evolution trend, while the process noise covariance matrix with physical correlation is used to quantify the uncertainty of the model (including driving parameter error and unmodeled physical process). This design makes the model have a solid physical foundation, while also acknowledging its own shortcomings and expressing them clearly through set discreteness, providing the correct direction and reasonable weight for subsequent observation correction.

[0015] (3) This invention has the ability to capture and characterize the irregular structure of the ionosphere. Since the empirical orthogonal function (EOF) in the mixed basis function is learned from data containing historical perturbation structures, some basis function modes are naturally associated with irregular structures such as plasma bubbles. During the assimilation process, when such characteristic signals are observed, the corresponding basis function coefficients can be adaptively adjusted. Thus, not only can irregular bodies be detected, but their three-dimensional morphology, intensity and dynamic evolution can be accurately described with a set of compact coefficients, providing a brand-new tool for fine monitoring of space weather and research on physical mechanisms.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart of a three-dimensional modeling and data assimilation method for ionospheric electron density according to the present invention; Figure 2 This is a general framework diagram of a three-dimensional modeling and data assimilation method for ionospheric electron density according to the present invention. Detailed Implementation

[0018] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely illustrates selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0019] Example like Figure 1 and Figure 2 As shown, this invention provides a three-dimensional modeling and data assimilation method for ionospheric electron density. By constructing a low-dimensional hybrid basis function state space and combining a physical-statistical hybrid dynamic model with an asynchronous ensemble Kalman filter assimilation window, it achieves efficient fusion of multi-source heterogeneous observation data and real-time high-precision reconstruction of the three-dimensional ionosphere. The method includes the following steps: S1. Based on spherical harmonics and empirical orthogonal functions, a hybrid basis function system is constructed to characterize the three-dimensional structure of the ionosphere. The hybrid basis function system is constructed by combining spherical harmonics and empirical orthogonal functions through tensor product. A state space model is established with the expansion coefficients of the hybrid basis functions as state vectors. Based on the state space model, a set of state vectors is constructed and initialized.

[0020] S11. Construct a horizontal grid globally at set latitude and longitude intervals (e.g., 5° × 2.5°); set basic height layers from 60km to 2000km at 50km intervals in the vertical direction, and use higher resolution (e.g., densification to 20km) for intra-layer subdivision in key areas (especially the F2 layer, with an altitude of about 250-600km), thereby forming a three-dimensional basic grid framework covering the main area of ​​the global ionosphere for data organization and statistical analysis.

[0021] S12. Collect historical ionospheric electron density data for at least one complete solar activity cycle. Data sources may include occultation observations from satellites such as COSMIC and GRACE, vertical instrument data, and reanalysis fields from empirical models (such as IRI). For each horizontal grid point in the three-dimensional basic grid framework, extract its electron density vertical profile that changes with time series, and combine all profiles in a unified format to form a historical data matrix for statistical analysis.

[0022] S13. The dominant vertical modes are extracted through principal component analysis. Singular value decomposition is then performed on the historical data matrix to extract a set of eigenvectors and their corresponding eigenvalues ​​from its covariance structure. Each eigenvector corresponds to an empirical orthogonal basis function, representing a typical morphology of the ionospheric vertical profile. Next, the basis functions are sorted in descending order of eigenvalues, and the top eigenvalues ​​are selected. The basis function with the largest eigenvalue (i.e., the largest variance contribution). , as the dominant vertical mode in model construction.

[0023] S14, the obtained A vertical basis function and a spherical harmonic function used to describe global horizontal spatial variation. By combining these components using tensor products, a complete hybrid basis function system capable of simultaneously characterizing the horizontal and vertical three-dimensional structure of the ionosphere is constructed, denoted as... ; S15. Based on the constructed hybrid basis function system, construct a state-space model, define the three-dimensional ionospheric electron density field as a linear expansion of the hybrid basis function system, and construct and initialize the set of state vectors based on the state-space model.

[0024] The specific formula for the state-space model is as follows: ; in, For height ,longitude ,latitude electron density at that location, The expansion coefficients of the mixed basis functions are . Let be the order of the spherical harmonic function. For a series of spherical harmonic functions, Let be the highest order of the spherical harmonic function. Let be the number of empirical orthogonal functions. It is a spherical harmonic function. For the first An empirical orthogonal function.

[0025] The column vector formed by arranging all the expansion coefficients in a preset order is defined as the state vector describing the dynamic evolution of the three-dimensional structure of the ionosphere. The dimension of the state vector is only... The scale is significantly reduced compared to the millions of grid points, achieving a huge dimensionality reduction.

[0026] S2. By generating independent perturbations for the key geophysical driving parameters of each member in the state vector set and calling the physical empirical model to generate an independent three-dimensional electron density background field, the background state coefficients of each member in the state vector set are obtained. In this way, a physical-statistical dynamic model for driving the evolution of the state vector is constructed. The constructed physical-statistical dynamic model is a state prediction model that includes both physical driving trends and quantifiable model uncertainties.

[0027] S21. For each forecast period, independently perturb the key geophysical driving parameters (mainly the solar radiation flux index F10.7 and the geomagnetic Ap index) to form the state vector set. Each member Generate a set of independent perturbation values; ; ; in, For the first The solar radiation flux index F10.7 for each sample is a key physical quantity for measuring the level of solar activity. For the first The geomagnetic Ap index of a sample is an indicator that characterizes the daily average level of global geomagnetic activity. This serves as the baseline value for the solar radiation flux index. This serves as the baseline value for the geomagnetic Ap index. and The average of the solar radiation flux index F10.7 and the geomagnetic Ap index on the day before assimilation can be taken. and It refers to a random disturbance that is independently drawn from a pre-defined distribution (such as a Gaussian distribution with a mean of zero and a variance that reflects the uncertainty of parameters).

[0028] S22, at the current time For the goal, for each member Call the selected physical empirical model, such as NeQuick or IRI, and input the key geophysical driving parameters after the S21 independent perturbation. and Generation and Members Corresponding three-dimensional electron density background field ; S23. Using the least squares method, the independent three-dimensional electron density background field of each member is... By uniformly projecting onto the mixed basis function system, the membership can be obtained. At the present moment Background state coefficient This completes the transformation from physical space to model state space.

[0029] S24. Uncertainties in the real short-term evolution of the ionosphere (such as sudden disturbances, the influence of specific gravity waves, etc.) that cannot be explained by quantitative physical empirical models and function basis fitting, in the background state coefficients. Superimposed process noise Generate each member Forecast state vector To construct a physical-statistical dynamic model ; ; in, This is the process noise covariance matrix, used to describe the uncertainties in the evolution of physical processes not captured by the NeQuick / IRI model and the fitting stage in the dynamic model. This matrix can be obtained through any of the following methods: first, heuristic setting based on prior knowledge of typical variations in ionospheric parameters; second, generation using statistical estimation methods based on covariance samples from the differences between short-term forecasts and subsequent analysis states in historical assimilation sequences; or third, the use of an online adaptive estimation algorithm dynamically adjusted based on ensemble statistical information. This is process noise.

[0030] Physico-statistical dynamic model The core expression indicates the forecast state at the next moment. A deterministic part driven by physics A statistically described random part Together they constitute.

[0031] S3. Call the physical-statistical dynamic model to integrate and advance the set of state vectors from the previous analysis time to the current analysis time, and obtain the predicted state vector set at the current analysis time; acquire multi-source heterogeneous ionospheric observation data, and use the ensemble Kalman filter algorithm and asynchronous assimilation window to assimilate and update the predicted state vector set, and obtain the analysis state vector set at the current analysis time; use this analysis state vector set as the initial state for the next assimilation cycle to achieve continuous assimilation; S31. Call the physical-statistical dynamic model to generate a set of predicted state vectors for the current analysis time; S311, Read the previous analysis time. Analysis of the set of state vectors ,in, For the current analysis time, The assimilation period is, for example, 15 minutes. To analyze the state vector, The number of members in the set.

[0032] S312. For each member in the analysis state vector set Calling the physical-statistical dynamic model In the previous analysis time The analysis state is advanced to the current analysis time. The predicted state vector is obtained. The process is specifically represented as follows: ; S313. The forecast state vectors of all members constitute the set of forecast state vectors at the current analysis time. .

[0033] S32. Accept and process multi-source heterogeneous ionospheric observation data, including ground-based GNSS oblique total electron content, radio occultation ionospheric observation data, and low-Earth orbit satellite-borne GNSS observation data; S33. Using the ensemble Kalman filter algorithm and asynchronous assimilation window, multi-source heterogeneous ionospheric observation data are fused to assimilate and update the predicted state vector set, thus obtaining the analysis state vector set at the current analysis time. S331, Set asynchronous assimilation window At the current moment of analysis Collect all observation times satisfy Multi-source heterogeneous ionospheric observation data, among which This refers to the asynchronous assimilation window length; multi-source heterogeneous ionospheric observation data may be... Arriving before, at, or after is asynchronous.

[0034] S332. For each observation data within the asynchronous assimilation window The observation time is The covariance matrix is The ensemble Kalman filter algorithm is used for iterative updates to obtain the analysis state vector; a. Calculate each member based on the forecast state vector set and the mixture basis function. Forecast observations Forecast observation mean and observation anomaly matrix The calculation formula is as follows: ; ; ; in, For the first The set member in the th ... The analysis state vector after the next iteration. For the number of iterations, For the observation operator, The total number of members in the set; The initial analysis state vector is obtained from the set of predicted state vectors, and the expression is as follows: ; b. Calculate the mean of the set of predicted state vectors. and state anomaly matrix The calculation formula is as follows: ; ; c. Calculate the ensemble Kalman gain The calculation formula is as follows: ; in, The observation error covariance matrix; d. To maintain the dispersion of the set, generate data similar to the observed data. Related perturbation observation set The calculation formula is as follows: ; in, For random perturbations; e. Update each member of the predicted state vector set using the ensemble Kalman gain and the set of perturbation observations. The analysis state vector is obtained. The calculation formula is as follows: .

[0035] S333. Repeat S332 until all observation data within the asynchronous assimilation window has been processed, obtaining the final set of analysis state vectors. ,in This represents the total number of observed data.

[0036] Calculate and analyze the mean of the set of state vectors. As Optimal state estimation at time step, calculating and analyzing the covariance matrix of the state vector set. It is used to characterize the uncertainty of the estimate and serves as a quantitative indicator of the reliability of the estimate.

[0037] ; ; The diagonal elements of the covariance matrix represent the uncertainty variance of each coefficient.

[0038] S34. Use the obtained set of analytical state vectors as the initial state for the next assimilation cycle, and enter the next assimilation cycle. Repeat steps S31 to S33 to achieve continuous assimilation.

[0039] S4. Based on the analysis of the state vector set, the three-dimensional ionospheric electron density field is reconstructed through a hybrid basis function system, and data products including the three-dimensional ionospheric electron density field are output.

[0040] S41. The optimal estimated state vector Substituting into the state-space model, a complete three-dimensional standard analytical field of electron density is reconstructed. .

[0041] S42. Based on the analysis of the state vector set, generate a product representing uncertainty, as follows: S421. Substitute the members of each analysis state vector set into the state-space model to generate... Standard analysis field of three-dimensional electron density at time t. ; S422. Calculate the standard deviation of electron density at each grid point. (As a representative of uncertain fields), the calculation formula is as follows: ; The standard deviation field quantitatively characterizes the uncertainty of the three-dimensional density estimate. The larger the value, the more dispersed the probability distribution of the true electron density at that location falling near the estimated value, i.e., the lower the certainty.

[0042] S43, Calculate the profile morphology parameters.

[0043] S431. Calculate the peak electron density on the vertical profile of each horizontal grid point. The calculation formula is as follows: ; S432. Calculate the peak electron density height on the vertical profile of each horizontal grid point. The height corresponding to the peak electron density is calculated using the following formula: ; S43. The generated data products are packaged in a standardized scientific data format (such as NetCDF format) and published in real time via network protocols for use by various applications.

[0044] Therefore, this invention employs the aforementioned three-dimensional modeling and data assimilation method for ionospheric electron density, achieving a technological leap from static climatological empirical models to highly dynamic real-time digital reconstruction. The resulting high-precision, high-resolution three-dimensional ionospheric electron density product with uncertainty quantification can significantly improve the reliability and performance of national strategic infrastructures such as GNSS precise positioning, satellite communication, and space environment monitoring and early warning.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for three-dimensional modeling and data assimilation of ionospheric electron density, characterized in that, Includes the following steps: S1. Based on spherical harmonic functions and empirical orthogonal functions, a hybrid basis function system for characterizing the three-dimensional structure of the ionosphere is constructed. A state space model with the expansion coefficients of the hybrid basis functions as state vectors is established. Based on the state space model, a set of state vectors is constructed and initialized. S2. By generating independent perturbations for the key geophysical driving parameters of each member in the state vector set and calling the physical empirical model to generate an independent three-dimensional electron density background field, the background state coefficients of each member in the state vector set are obtained, thereby constructing a physical-statistical dynamic model for driving the evolution of the state vector. S3. Call the physical-statistical dynamic model to integrate and advance the set of state vectors from the previous analysis time to the current analysis time, and obtain the predicted state vector set at the current analysis time; acquire multi-source heterogeneous ionospheric observation data, and use the ensemble Kalman filter algorithm and asynchronous assimilation window to assimilate and update the predicted state vector set, and obtain the analysis state vector set at the current analysis time; use this analysis state vector set as the initial state for the next assimilation cycle to achieve continuous assimilation; S4. Based on the analysis of the state vector set, the three-dimensional ionospheric electron density field is reconstructed through a hybrid basis function system, and data products including the three-dimensional ionospheric electron density field are output.

2. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 1, characterized in that: The mixed basis function system in S1 is constructed by combining spherical harmonic functions and empirical orthogonal functions through tensor product.

3. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 1, characterized in that, In the state-space model of S1, the three-dimensional ionospheric electron density field is defined as a linear expansion of the mixed basis function system, as shown in the following formula: ； in, For height ,longitude ,latitude electron density at that location, The expansion coefficients of the mixed basis functions are . Let be the order of the spherical harmonic function. For a series of spherical harmonic functions, Let be the highest order of the spherical harmonic function. Let be the number of empirical orthogonal functions. It is a spherical harmonic function. For the first An empirical orthogonal function.

4. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 1, characterized in that, The specific steps of S2 are as follows: S21. Independently perturb the key geophysical driving parameters to form the state vector set. Each member Generate a set of independent perturbation values; S22. Call the selected physical empirical model, input the key geophysical driving parameters after independent perturbation, and generate the model with members. Corresponding three-dimensional electron density background field ; S23. Use the least squares method to generate Projecting onto the mixed basis function system, we obtain the members. At the present moment Background state coefficient ; S24, Background State Coefficient Superimposed process noise Generate each member Forecast state vector To construct a physical-statistical dynamic model ; ； in, The process noise covariance matrix is... This is process noise.

5. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 1, characterized in that, The specific steps for S3 are as follows: S31. Call the physical-statistical dynamic model to generate a set of predicted state vectors for the current analysis time; S32. Acquire multi-source heterogeneous ionospheric observation data, including ground-based GNSS oblique total electron content, radio occultation ionospheric observation data, and low-orbit satellite-borne GNSS observation data; S33. Using the ensemble Kalman filter algorithm and asynchronous assimilation window, multi-source heterogeneous ionospheric observation data are fused to assimilate and update the predicted state vector set, thus obtaining the analysis state vector set at the current analysis time. S34. Use the obtained set of analytical state vectors as the initial state for the next assimilation cycle, and iteratively execute steps S31 to S33 to achieve continuous assimilation.

6. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 5, characterized in that, The specific steps of S31 are as follows: S311, Read the previous analysis time. Analysis of the set of state vectors ,in, For the current analysis time, For the assimilation period, To analyze the state vector; S312. For each member in the analysis state vector set Calling the physical-statistical dynamic model In the previous analysis time The analysis state is advanced to the current analysis time. The predicted state vector is obtained. The process is specifically represented as follows: ； in, This is process noise; S313. The forecast state vectors of all members constitute the set of forecast state vectors at the current analysis time. .

7. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 6, characterized in that, The specific steps of S33 are as follows: S331, Set asynchronous assimilation window At the current moment of analysis Collect all observation times satisfy Multi-source heterogeneous ionospheric observation data, among which This is the length of the asynchronous assimilation window; S332. For each observation data within the asynchronous assimilation window The ensemble Kalman filter algorithm is used for iterative updates to obtain the analysis state vector; S333. Repeat S332 until all observation data within the asynchronous assimilation window has been processed, obtaining the final set of analysis state vectors. ,in This represents the total number of observed data.

8. The method for three-dimensional modeling and data assimilation of ionospheric electron density according to claim 7, characterized in that, The specific steps of S332 are as follows: a. Calculate each member based on the forecast state vector set and the mixture basis function. Forecast observations Forecast observation average and observation anomaly matrix The calculation formula is as follows: ； ； ； in, For the first The set member in the th ... The analysis state vector after the next iteration. For the number of iterations, For the observation operator, The total number of members in the set; The initial analysis state vector is obtained from the set of predicted state vectors, and the expression is as follows: ； b. Calculate the mean of the set of predicted state vectors. and state anomaly matrix The calculation formula is as follows: ； ； c. Calculate the ensemble Kalman gain The calculation formula is as follows: ； in, The observation error covariance matrix; d. Generation and observation of data Related perturbation observation set The calculation formula is as follows: ； in, For random perturbations; e. Update each member of the predicted state vector set using the ensemble Kalman gain and the set of perturbation observations. The analysis state vector is obtained. The calculation formula is as follows: 。

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