An ionospheric occultation additional phase correction method and system without auxiliary side data

Abstract

The application discloses a kind of ionosphere occultation additional phase correction method and system of unaided side data, for realizing the accurate inversion of ionospheric electron density under only occultation side observation condition.The method comprises: additional phase and satellite positioning data are preprocessed, are sorted according to collision height and are screened according to interval, and initial quasi-correction is completed;Based on quasi-correction result, the initial total electron content at each collision height is calculated, and the top electron density coefficient and altitude coefficient are iteratively solved;Top electron density parameters, altitude parameters and total electron content compensation items at each height are calculated using the final coefficient;Compensation item is added to initial total electron content to obtain correction result, and further generate electron density profile.The present application can carry out high-precision inversion without auxiliary side data, overcome the limitation of traditional differential correction method, significantly improve the inversion accuracy and stability in low-orbit satellite mission, and expand the application range of occultation technology.

Description

Technical Field

[0001] This application relates to the field of satellite remote sensing technology, and in particular to a method and system for ionospheric occultation additional phase correction without auxiliary side data, which is especially suitable for ionospheric additional phase processing when there is no auxiliary side observation data. Background Technology

[0002] In the field of ionospheric detection, Global Navigation Satellite System (GNSS) radio occultation technology is an important remote sensing method. Its basic principle is that when radio signals transmitted by GNSS satellites pass through the ionosphere and are received by low-Earth orbit (LEO) satellites, the signal path is affected by free electrons in the ionosphere, resulting in additional phase delays and amplitude changes. By processing observational data from dual-frequency signals (such as the L1 and L2 frequencies of GPS), the vertical profile of the ionospheric electron density can be retrieved, which is of great significance for space weather research and applications.

[0003] Currently, one of the core steps in retrieving an accurate electron density profile from raw phase observations is to correct for the observed "excess phase." The purpose of this step is to extract, as accurately as possible, the phase delay introduced solely by the ionosphere near the occultation path, while eliminating errors on other common paths.

[0004] The core idea of ​​the correction method proposed by Schreiner et al. in 1999 is differential correction. It requires that, in a complete occultation event, in addition to the observation data from the main "occultation side" (usually the negative elevation side, i.e., the portion of the signal penetrating the atmosphere), observation data from the "auxiliary side" (usually the positive elevation side) must also be obtained simultaneously. The correction process involves subtracting the ionospheric phase estimate from the occultation side data, obtained through interpolation, from the auxiliary side data at the same impact parameter, from the ionospheric phase addition on the occultation side.

[0005] Under these ideal conditions, differential processing can effectively eliminate errors common to all links from GPS satellites to LEO satellites (e.g., satellite and receiver clock errors, hardware delays, etc.) as well as the influence of the ionosphere above orbital altitude, thus obtaining a relatively "clean" corrected phase that mainly reflects the local ionospheric structure of the occultation path.

[0006] However, this differential correction method still has limitations: it is highly dependent on the completeness of the auxiliary side observation data. In actual satellite missions, due to mission objectives, satellite platform attitude, or receiver hardware settings, effective auxiliary side data cannot always be obtained. A typical example is the CHAMP satellite mission, whose receivers are usually configured to record only occultation event data at negative elevation angles (occultation side), resulting in the complete lack of auxiliary side data.

[0007] To overcome the above problems, those skilled in the art have proposed an approximate correction method, commonly referred to as the "quasi-correction method." This method involves uniformly subtracting the additional phase value observed at the maximum impact altitude (i.e., the point farthest from the Earth's center during the entire occultation event, typically corresponding to the orbital altitude of LEO) from all ionospheric additional phase observations on the occultation side.

[0008] While this method is effective, it is essentially a rough approximation and introduces significant systematic errors. The root cause lies in its oversimplified physical assumptions. This method implicitly assumes that the contribution of the ionosphere to the additional phase in the region at and above the maximum impact altitude is a constant value, or that its effect is negligible. However, in reality, the ionosphere between LEO altitude and GPS satellite altitude—that is, the ionosphere above the LEO satellite orbital altitude—still has an electron density gradient, which introduces a varying phase delay throughout the signal path. Simply subtracting a fixed value cannot accurately characterize this complex, spatially varying effect.

[0009] Therefore, existing technologies face a significant technical challenge when dealing with occultation missions like CHAMP that lack auxiliary side data: how to effectively and relatively accurately correct the additional phase of the ionosphere on the occultation side in the absence of auxiliary side observation data, in order to overcome the inherent biases of simple "quasi-correction methods" and obtain more reliable ionospheric electron density profile inversion results. The difficulty in solving this problem lies in the need to more reasonably estimate and eliminate systematic phase biases through improved algorithm models without direct reference data (auxiliary side), which places higher demands on the robustness and accuracy of the inversion algorithm. Summary of the Invention

[0010] The purpose of this application is to overcome the problem that it is difficult to effectively and relatively accurately correct the ionospheric additional phase on the occultation side and obtain more reliable ionospheric electron density profile inversion results when auxiliary side observation data is lacking. Therefore, this application provides a method for correcting the ionospheric occultation additional phase without auxiliary side data, the steps of which include: The ionospheric additional phase data and satellite positioning data are preprocessed, the additional phase data are rearranged according to the collision height order, the sorted additional phase data are filtered according to the preset collision height range, and the filtering results are initially quasi-corrected. The initial quasi-corrected total electron content at each collision height is calculated based on the quasi-corrected ionospheric additional phase, and the top electron density coefficient and elevation coefficient are iteratively solved; The top electron density parameter and elevation parameter are calculated using the final top electron density coefficient and elevation coefficient, and the final total electron content compensation term for each collision height is calculated based on the top electron density parameter and elevation parameter. The final total electron content compensation term is added to the initial quasi-corrected total electron content to generate the corrected total electron content. An electron density profile is generated based on the corrected total electron content and top electron density.

[0011] The preprocessing steps include: Read the data file containing the ionospheric additional phase, coordinates and velocity information of global navigation satellites and low-Earth orbit satellites, transform the satellite coordinates to the geocentric geofixed coordinate system, and calculate the collision height and tangent latitude and longitude of the occultation rays at each observation time.

[0012] The initial quasi-correction of the screening results includes: Collect all ionospheric additional phase observations on all occultation sides, and subtract the ionospheric additional phase value corresponding to the maximum collision height to obtain the initial quasi-corrected total electron content.

[0013] The top electron density parameter The calculation formula is as follows: ; in, This is the final top electron density coefficient. This is the maximum collision height; The elevation parameters The calculation formula is as follows: ; in, This is the final elevation coefficient.

[0014] The calculation of the final total electron content compensation term The calculation formula is: ; in, For the first The collision height is given by exp, which is an exponential function, and erfc is the complementary error function.

[0015] The corrected total electron content The calculation formula is: ; in, This represents the initial quasi-corrected total electron content.

[0016] The method for generating the electron density profile is as follows: based on the local spherical symmetry assumption and Abel integral transform, the electron density profile is solved by the onion peeling method.

[0017] This application also proposes an ionospheric occultation supplementary phase correction system without auxiliary side data, comprising: Data preprocessing module: Used to preprocess ionospheric observation files containing ionospheric additional phase data and satellite positioning observation data; Data rearrangement and filtering module: used to rearrange the additional phase data according to the collision height order, and filter the sorted additional phase data according to the preset collision height range; Initial quasi-correction module: used to perform initial quasi-correction on the screening results; Iterative compensation and correction module: Based on the quasi-corrected total electron content and collision height parameters near the maximum collision height, iteratively solves for the top electron density coefficient and elevation coefficient; uses the final top electron density coefficient and elevation coefficient to calculate the top electron density parameter and elevation parameter; calculates the final total electron content compensation term at each collision height based on the top electron density parameter and elevation parameter; adds the final total electron content compensation term to the initial quasi-corrected total electron content to generate the corrected total electron content; and Data output module: Generates an electron density profile based on the corrected total electron content and top electron density.

[0018] The advantages of this application are: 1. Solved the data availability problem in specific mission scenarios: This invention, through an improved correction process, enables effective ionospheric inversion even in satellite missions that can only acquire occultation side data, overcoming the absolute dependence of the classical differential correction method on auxiliary side data and expanding the application scope of occultation technology.

[0019] 2. Significantly improved inversion accuracy without auxiliary side data: Compared to the simple "subtract a fixed value" quasi-calibration method, this invention introduces an analytical estimation term based on a physical model to compensate for the total electron content of the quasi-calibration, and optimizes key parameters through an iterative algorithm. This technique directly addresses the systematic bias introduced by the simple quasi-calibration method near the LEO height, effectively reducing the resulting electron density inversion error, especially at the top of the profile, thereby obtaining more reliable information on the vertical structure of ionospheric electron density that better reflects actual physical conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method in this application; Detailed Implementation

[0021] The technical solutions provided in this application are further illustrated below with reference to the embodiments.

[0022] Example 1 like Figure 1 As shown, this application provides a method for ionospheric occultation phase correction without auxiliary side data, including the following steps: Step 1: Acquisition and Preprocessing of Additional Ionospheric Phase Data Read the occultation observation data file (ionPhs) containing the ionospheric additional phase at L1 and L2 frequencies, as well as the coordinates and velocity information of GNSS and low-Earth orbit satellites. Transform the satellite coordinates to the geocentric-ground-fixed coordinate system and calculate the collision height and tangency latitude and longitude of the occultation rays at each observation time.

[0023] Step 2: Ionospheric Additional Phase Data Reshaping and Filtering Using the maximum collision altitude as the boundary, the observed data were divided into occultation side (the main part) and auxiliary side (if any) based on the observation elevation angle. The negative elevation portion is the occultation side data, and the positive elevation portion is the auxiliary side data. The data array was then uniformly rearranged in ascending order of collision altitude. From the occultation side data, data with collision altitudes between 150 km above the Earth's surface and slightly below the orbital altitude of low Earth orbit satellites (1 km below the orbital altitude) were selected for subsequent processing. 150 km is a conservative lower bound to ensure that the data fully enters the ionosphere, and 1 km is a data margin set to avoid interference from satellite platforms.

[0024] Step 3: Initial Quasi-Corrected Ionospheric Additional Phase Determine the maximum collision altitude during the entire occultation event ( The additional phase value of the ionosphere observed at a location near the orbital altitude of a low-Earth orbit satellite. .

[0025] Ionospheric phase observations at L1 and L2 frequencies on all occultation sides and Subtract the corresponding ionospheric additional phase value at the maximum impact height respectively. and The quasi-corrected additional phase is obtained. and Its core relation is: (1) This step aims to eliminate the reference phase offset along the LEO to GNSS altitude path. It utilizes quasi-corrected dual-frequency differential additional phase. The quasi-corrected total electron content is calculated according to the following formula ( ): (2) in, and These are the frequencies of the L1 and L2 carriers, respectively.

[0026] Step 4: Iterative compensation and correction of ionospheric additional phase This step is crucial for improving calibration accuracy, aiming to accurately estimate the top electron density through iterative algorithms. and elevation The parameters are used to systematically compensate for the quasi-corrected total electron content obtained from the additional phase transformation. The execution flow is as follows: Step 4-1: Initialize iteration parameters Set the current iteration index Maximum number of iterations (e.g., 100 times) and convergence threshold (e.g., 0.01).

[0027] Step 4-2: Iteratively solve for the top parameters Enter the iteration loop, in each iteration Perform the following operations in the middle: Based on quasi-corrected total electron content observation data near the top and collision height parameters By using linear correlation, the coefficients related to the top electron density are solved. and coefficients related to elevation superscript This represents the number of iterations.

[0028] Step 4-3: Convergence test If the number of iterations reaches the set maximum number of iterations or coefficient The rate of change is less than the set threshold Then record the final top electron density coefficient. and elevation coefficient And exit the iteration and proceed to step 4-4; otherwise, let Then continue iterating from step 4-1 to step 4-3.

[0029] Step 4-4: Calculate and correct the compensation term. By fusing quasi-corrected total electron content data with several prior pieces of information, correlation coefficients for parameters at the top of the ionosphere were obtained. , A robust estimate, which provides a basis for updating the elevation. With top electron density A reliable and implementable method is provided. After iteration, the final top electron density coefficient obtained through convergence is used. and final elevation parameters The electron density and elevation parameters at the top are calculated as follows: Top electron density parameter: (3) Elevation parameters: (4) And based on the elevation parameters Top electron density parameter calculation is applicable to all collision heights. Final total electron content compensation item:

[0030] in, This indicates the first occultation side data selected in step 2. Collision height. Subscript ( =1,2,...) are data indices, representing data points arranged from low to high collision height. erfc is the complementary error function, and exp is the exponential function.

[0031] The compensation term is added to the initial quasi-corrected total electron content, i.e. The above yields a high-precision corrected total electron content, ultimately used for electron density inversion:

[0032] Thus, the iterative compensation and correction of the additional phase of the ionosphere was completed, and an accurate corrected total electron content sequence was obtained.

[0033] Step 5: Data Output and Post-processing Using the corrected total electron content and electron density at orbital altitude Based on the assumption of local spherical symmetry and Abel integral transform, the electron density profile is solved by the onion peeling method.

[0034] Example 2 This embodiment uses a typical ionospheric occultation event without positive elevation observation data as an example to illustrate the implementation process of the present invention in detail. Those skilled in the art can implement the present invention using general scientific computing platforms (such as Fortran, MATLAB, etc.) combined with necessary satellite orbit and occultation data processing libraries, based on the description of this embodiment.

[0035] Step 1. Data Acquisition and Coordinate Transformation: Retrieve the ionPhs data file for the specified occultation event from the data server. This file contains the following key information: occultation ID, event start and end times, position and velocity vectors of GPS and LEO satellites in the Earth's inertial coordinate system, and the original ionospheric additional phase at GPS L1 and L2 frequencies. , )sequence. Greenwich Mean Time (GMT) is calculated based on the observation time, and then the coordinates of GPS satellites and low-Earth orbit satellites are transformed from the Earth inertial coordinate system to the geocentric coordinate system.

[0036] Based on the satellite coordinates in the Earth-centered Earth-fixed coordinate system, the collision height of each ray is calculated point by point. , and the geographical latitude and longitude (lon, lat) of the tangent point.

[0037] Step 2. Data Reorganization and Range Filtering The collision height sequence and all corresponding observation data (including additional phase, tangent coordinates, etc.) are reversed so that the first element of the sequence corresponds to the lowest collision height. The range of the reshaped tangent height is checked, and the processing range is set to the area where the collision height is between 150 km above the Earth's surface and slightly below the orbital altitude of low Earth orbit satellites (1 km below the orbital altitude). After confirming that the data covers this range, data points outside the boundary are removed, and the valid occultation side data sequence is retained.

[0038] Step 3. Initial Quasi-calibration Locate the maximum collision height within a valid data sequence. This point typically corresponds to the last data point in the sequence (because the data is already sorted in ascending order of collision height). For each data point in the sequence... Its collision height is Read in The additional phase values ​​of the L1 and L2 ionospheric regions observed at the location are denoted as... and ; Read in The additional phase values ​​of the L1 and L2 ionospheric regions observed at the location are denoted as... and Perform the following calculations:

[0039]

[0040] This yields the quasi-corrected additional phase sequence. and Then, the dual-frequency differential additional phase is calculated: .

[0041] Then, the quasi-corrected total electron content value for each data point is calculated using the following formula. :

[0042] in, , .

[0043] Received The unit is TECU ( ).

[0044] Step 4. Iterative compensation and correction This step is the core of improving the accuracy of the additional phase correction, and it compensates for the total electron content of the initial quasi-correction through an iterative process.

[0045] Step 4.1 Initialize iteration parameters: Set the current iteration number Maximum number of iterations (e.g., 100 times), and the convergence threshold. (e.g., 0.01).

[0046] Step 4.2 Iteratively estimate the elevation and top electron density : Based on current quasi-corrected total electron content data An iterative weighted least squares method with prior constraints is used to accurately estimate the top coefficient, and the elevation is calculated accordingly. and top electron density .

[0047] Prepare input data and parameters: : Array of effective collision heights on the occultation side in the current iteration (unit: km).

[0048] :and The corresponding total electron content value near the top after initial quasi-correction ( (Unit: TECU).

[0049] The total number of data points on the occultation side.

[0050] The orbital altitude of a low-Earth orbit satellite, i.e. (Unit: km).

[0051] The assumed standard deviation of the total electron content observations (for weighted fitting) is set to 0.1.

[0052] The assumed standard deviation of the prior values ​​of the elevation parameter (used for constraint fitting) is set to 2.0.

[0053] Elevation parameter factor (initial value set to 5.0).

[0054] : Coefficient related to top electron density (Initial value) The calculation is as follows: after the iteration begins, the value from the previous iteration is used. The superscript indicates the number of iterations.

[0055] coefficient initial value Calculated using the following formula:

[0056] Define basis functions as follows:

[0057] in For the first The collision height value of each data point. This refers to the orbital altitude of a low-Earth orbit satellite. For a range of values Dimensionless parameters within.

[0058] Data preprocessing and normalization: Select a location approximately 5km from the top of the occultation side. Fit the data to a maximum of 100 data points and calculate the following normalized variables: ,

[0059] , It is a sequence of dimensionless basis variables based on the Chapman layer theory model and after normalization and centering. This is a normalized sequence of dimensionless total electron content observations, derived from the initial quasi-corrected total electron content values. Divide by the observed standard deviation of total electron content get; It is related to elevation parameters The relevant normalized auxiliary variable sequence represents the linear correction term for the change in total electron content caused by the elevation effect.

[0060] The occultation side data are arranged in ascending order of collision height from low to high, with a total of [number missing]. To process data from top to bottom, the index... Using reverse order ( Therefore, the first element (index) of each vector. The top data corresponding to the highest collision height is used to achieve the calculation order from high to low.

[0061] At the same time, a priori constraint term is added to the end of the sequence vector. The constraint term at the end of the sequence data will be updated with the coefficient in each iteration. It changes with each update, and its upper right subscript represents the number of iterations.

[0062]

[0063]

[0064]

[0065] Thus, a length of [length missing] has been constructed. vector sequence, Sequence, and initial sequence.

[0066] Iterative solution to obtain the final top electron density coefficient and the final elevation coefficient Set the maximum number of internal iterations. (For example, 100 times), perform the following iterative calculations: Step 4.2.1 Calculate matrix elements: Using the current vector , , Calculate the following summation terms, where the number of array elements in each term is . :

[0067]

[0068]

[0069]

[0070]

[0071] in, It is a normalized observation vector With normalized basis vectors The weighted cross-correlation inner product, It is a normalized observation vector With the normalization correction term vector The weighted cross-correlation inner product, It is a normalized basis vector The weighted autocorrelation inner product, It is a normalized basis vector With the normalization correction term vector The weighted cross-correlation inner product, It is the normalization correction term vector The weighted autocorrelation inner product; These are the normalized basis vectors used in the data preprocessing and normalization process. The observation vector in the data preprocessing and normalization section , The vector of normalization correction terms in the data preprocessing and normalization process. ,because The last term of the sequence will change with the coefficient. It updates with each update, so its vector sequence is represented as . The first data point in the top data point of the occultation side Data points.

[0072] Step 4.2.2. Solve the system of linear equations: and We obtain the following by solving the normal equation:

[0073] Its analytical solution is:

[0074]

[0075]

[0076] in, An auxiliary quantity introduced to solve the normal equation, mathematically equal to the negative value of the determinant of the coefficient matrix, is used to determine the validity of the solution and to calculate the coefficients. and .

[0077] Step 4.2.3. Update nonlinear variables : Use the The newly solved solution in the next iteration Update the next iteration The last value of the vector, i.e., the first... In the next iteration, the vector The Each element (corresponding to prior constraint terms):

[0078] for arrive , Remain unchanged, that is .

[0079] Step 4.2.4. Convergence Judgment: Execute steps 4.2.1-4.2.4 sequentially. If ,or If the value is less than a certain internal threshold (e.g., 0.01), then the internal iteration terminates. Otherwise, let... Return to step 4.2.1 to continue the internal iteration. When the internal iteration ends, record the final coefficients as... and .

[0080] Step 4.3 Calculate the compensation term and update the quasi-corrected total electron content: Based on coefficients and Calculate the updated top electron density:

[0081] in, As a dimensional conversion factor, to ensure the consistency of electron density units (e.g., converting to...). ).

[0082] Calculate the updated elevation :

[0083] For each collision height in the sequence Using the current top ionosphere parameters and Calculate the analytical compensation term for the quasi-corrected total electron content. :

[0084] Where erfc is the complementary error function. Adding the compensation term to the initial quasi-corrected total electron content yields the corrected total electron content: Step 5. Data Output and Post-processing The corrected total electron content value and the top electron density Substituting these values ​​into the onion method inversion formula based on the assumption of spherical symmetry yields the electron density profile.

[0085] Example 3 This embodiment provides an alternative implementation scheme for some steps based on embodiment 2.

[0086] Regarding alternative solutions for the compensation term model: The compensation model in step 4 of this application can be replaced. For example, it can be assumed that the electron density of the top ionosphere follows a Chapman layer distribution or other empirical models, and the corresponding analytical expression for the total electron content compensation term can be derived. This is as long as the model can reasonably describe... The contribution of the electron density in the vicinity to the total electron content is within the scope of protection of this invention.

[0087] Alternative solutions for the iteration strategy: Iteration control: The maximum number of iterations can be adjusted according to computational efficiency and convergence requirements. Furthermore, more complex convergence criteria can be introduced, such as simultaneously monitoring changes in the electron density profile morphology.

[0088] Simulation verification data: To verify the effectiveness of this invention, simulation methods were employed. Using a known, real electron density profile (such as that derived from an IRI model) as the "true value," the additional phase of the ionosphere on the occultation side was simulated using the model without auxiliary side data. The electron density profile was then inverted using both conventional and the method of this invention: Traditional method: namely, the simple quasi-correction method that skips step 4 in Example 3.

[0089] The total electron content value near the top was obtained through initial quasi-correction. ,Right now : ; Then solve the coefficients initial value : ; Thus, the initial top electron density is obtained. : ; Finally, by substituting the initial top electron density (without iteration) and the quasi-corrected TEC at each collision height obtained above into the onion method inversion formula, the electron density profile of the traditional method can be obtained.

[0090] The comparison results show that, in the simulation scenario, the root mean square error (RMSE) of the electron density profile obtained by the method of the present invention compared with the "true value" is significantly reduced compared with the traditional method. Especially in the top region of the profile (>300km), the method of the present invention effectively eliminates the inherent negative bias of the traditional method, making the shape of the electron density profile closer to the real situation.

[0091] Example 4 An ionospheric occultation phase correction system without auxiliary side data, implemented based on the above method, includes: Data preprocessing module: Used to preprocess ionospheric observation files containing ionospheric additional phase data and satellite positioning observation data; Data rearrangement and filtering module: used to rearrange the additional phase data according to the collision height order, and filter the sorted additional phase data according to the preset collision height range; Initial quasi-correction module: used to perform initial quasi-correction on the screening results; Iterative compensation and correction module: Based on the quasi-corrected ionospheric additional phase, the initial quasi-corrected total electron content at each collision height is calculated; the top electron density coefficient and elevation coefficient are iteratively solved; using the final top electron density coefficient and elevation coefficient, the top electron density parameter and elevation parameter are calculated; based on the top electron density parameter and elevation parameter, the final total electron content compensation term for each collision height is calculated; the final total electron content compensation term is added to the initial quasi-corrected total electron content to generate the corrected total electron content; and Data output module: Generates an electron density profile based on the corrected total electron content and top electron density.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for ionospheric occultation phase correction without auxiliary side data, comprising the following steps: The ionospheric additional phase data and satellite positioning data are preprocessed, the additional phase data are rearranged according to the collision height order, the sorted additional phase data are filtered according to the preset collision height range, and the filtering results are initially quasi-corrected. The initial quasi-corrected total electron content at each collision height is calculated based on the quasi-corrected ionospheric additional phase, and the top electron density coefficient and elevation coefficient are iteratively solved; The top electron density parameter and elevation parameter are calculated using the final top electron density coefficient and elevation coefficient, and the final total electron content compensation term for each collision height is calculated based on the top electron density parameter and elevation parameter. The top electron density parameter The calculation formula is as follows: ； in, This is the final top electron density coefficient. This is the maximum collision height; The elevation parameters The calculation formula is as follows: ； in, This is the final elevation coefficient; The final total electron content compensation term is added to the initial quasi-corrected total electron content to generate the corrected total electron content. The final total electron content compensation item The calculation formula is as follows: ； in, For the first The collision height is given by exp, which is an exponential function, and erfc is a complementary error function. An electron density profile is generated based on the corrected total electron content and top electron density.

2. The ionospheric occultation additional phase correction method according to claim 1, characterized in that, The preprocessing steps include: Read the data file containing the ionospheric additional phase, coordinates and velocity information of global navigation satellites and low-Earth orbit satellites, transform the satellite coordinates to the geocentric geofixed coordinate system, and calculate the collision height and tangent latitude and longitude of the occultation rays at each observation time.

3. The ionospheric occultation additional phase correction method according to claim 1, characterized in that, The aforementioned top electron density parameter is the electron density parameter at the maximum collision height.

4. The ionospheric occultation additional phase correction method according to claim 1, characterized in that, The initial quasi-correction of the screening results includes: Collect all ionospheric additional phase observations on all occultation sides, and subtract the ionospheric additional phase value corresponding to the maximum collision height to obtain the initial quasi-corrected total electron content.

5. The ionospheric occultation additional phase correction method according to claim 1, characterized in that, The corrected total electron content The calculation formula is: ； in, This represents the initial quasi-corrected total electron content.

6. The ionospheric occultation additional phase correction method according to claim 1, characterized in that, The method for generating the electron density profile is as follows: based on the local spherical symmetry assumption and Abel integral transform, the electron density profile is solved by the onion peeling method.

7. An ionospheric occultation supplementary phase correction system without auxiliary side data, implemented based on the method described in any one of claims 1-6, characterized in that, include: Data preprocessing module: Used to preprocess ionospheric observation files containing ionospheric additional phase data and satellite positioning observation data; Data rearrangement and filtering module: used to rearrange the additional phase data according to the collision height order, and filter the sorted additional phase data according to the preset collision height range; Initial quasi-correction module: used to perform initial quasi-correction on the screening results; Iterative compensation and correction module: Based on the quasi-corrected ionospheric additional phase, the initial quasi-corrected total electron content at each collision height is calculated, and the top electron density coefficient and elevation coefficient are iteratively solved; the top electron density parameter and elevation parameter are calculated using the final top electron density coefficient and elevation coefficient, and the final total electron content compensation term at each collision height is calculated based on the top electron density parameter and elevation parameter. The final total electron content compensation term is added to the initial quasi-corrected total electron content to generate the corrected total electron content; and Data output module: Generates an electron density profile based on the corrected total electron content and top electron density.

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