Modeling method of ionospheric TEC empirical model in low latitude region of China based on multi-source data fusion

Abstract

The application belongs to the technical field of ionospheric physics, and particularly relates to a Chinese low-latitude region ionospheric TEC empirical model based on multi-source data fusion, and a modeling process comprises the following steps: selecting multi-source TEC data in a solar activity week in the Chinese low-latitude region as a multi-source data set; determining the weight of each kind of data by weighting each kind of data through a Helmer mode variance component estimation method; obtaining a modeling data set by fusing various data in the multi-source data set through a 15th order 15th time spherical harmonic function and the determined weight; setting a component of the TEC empirical model, establishing a nonlinear mathematical expression to represent all components; calculating the to-be-estimated parameters in the nonlinear mathematical expression of each component through a nonlinear least square fitting calculation to form the TEC empirical model and complete the final modeling. The application effectively improves the modeling accuracy in the Chinese low-latitude region, and can more accurately describe the temporal and spatial variation law of TEC.

Description

Technical Field

[0001] This invention belongs to the field of ionospheric physics technology, specifically involving a modeling method for an empirical model of the TEC (Temperature and Temperature) of the ionosphere in the low latitude region of China based on multi-source data fusion. Background Technology

[0002] With the continuous improvement of the Global Navigation Satellite System (GNSS), the network of regional and global GNSS tracking stations is becoming increasingly dense. This widespread distribution of GNSS tracking stations provides new avenues for acquiring TEC data globally. GNSS service organizations utilize GNSS tracking station data to calculate and provide Global Ionospheric Maps (GIMs). Currently, over 23 years of GIMs TEC time series are available. GIMs TEC data not only provides new approaches to studying the time-varying characteristics of the global ionosphere but also provides a reliable database for establishing empirical TEC models. In recent years, empirical ionospheric TEC models based on GIMs TEC or GPS-TEC data and grounded in the modeling of TEC spatiotemporal variation characteristics have been developed.

[0003] Global ionospheric empirical models, built upon multi-year observations of global ionospheric TEC data, can comprehensively reflect the spatiotemporal variations of ionospheric TEC. However, influenced by various global factors such as ionospheric anomalies, polar ionospheric time-varying characteristics, and uneven distribution of IGS stations, they often fail to achieve ideal accuracy in certain regions. Compared to the global scale, TEC exhibits uniform variation characteristics within a given region, making it easier to model. Regional TEC empirical models generally have higher accuracy than global TEC empirical models and are more valuable for engineering applications. Therefore, it is essential to study methods for establishing regional (especially anomalous regions) ionospheric empirical models. However, most existing regional ionospheric empirical models are located in non-anomalous regions, somewhat avoiding the modeling process of ionospheric anomalies (especially equatorial anomalies). Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide a modeling method for an empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion, which effectively improves the modeling accuracy of low-latitude regions of China and can more accurately describe the spatiotemporal variation patterns of TEC.

[0005] To achieve the above objectives, this invention provides a modeling method for an empirical TEC model of the ionosphere in the low latitude region of China based on multi-source data fusion. The modeling process includes the following steps:

[0006] S1. Select multi-source TEC data from one solar activity cycle in the low-latitude region of China as the multi-source dataset;

[0007] S2. Using the Hull model variance component estimation method, weights are assigned to each data point in the multi-source dataset to determine the weight of each data point.

[0008] S3. Using a 15th-order spherical harmonic function with defined weights, data fusion is performed on various data from multiple source datasets to obtain the modeling dataset.

[0009] S4. Based on the modeling dataset, set the components of the TEC empirical model, including diurnal variation components, seasonal variation components, geomagnetic components, solar activity components, and EIA correction components, and establish nonlinear mathematical expressions to represent all components;

[0010] S5. Calculate the parameters to be estimated in the nonlinear mathematical expressions of each component through nonlinear least squares fitting, form the TEC empirical model, and complete the final modeling.

[0011] As a preferred embodiment of the present invention, in S1, the multi-source TEC data includes GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC data.

[0012] As a preferred embodiment of the present invention, in S2, the process of weighting each type of data in the multi-source dataset is as follows: the estimated unit weight variance of each type of observation is calculated according to the Helmert approximation formula, i.e., equation (1), and then the weights of each type of observation are re-determined according to equation (2). Each type of observation is each type of data in the multi-source dataset. Equations (1) and (2) are respectively:

[0013] (1);

[0014] (2);

[0015] In the formula, This represents the estimated unit weight variance of the i-th type of observation; Let P represent the sum of squared residuals of the i-th class of observations, where P represents the weight matrix of the observations. This represents the residual vector of the i-th type of observation, with the superscript T indicating transpose; This represents the weight of the i-th type of observation; Represents the number of redundant observations for the i-th type of observation; c represents an arbitrary constant; This represents the weight matrix after weighting the observations of the i-th class;

[0016] When determining the weights, iterative calculations are performed based on equations (1) and (2), and the process is as follows:

[0017] S2.1 For each type of observation, first determine its initial weights;

[0018] S2.2, Perform the first adjustment and obtain... ;

[0019] S2.3. Based on equation (1), perform a first-order variance component estimation to obtain the first estimate of the unit weight variance of each type of observation. Then, the weights are determined according to formula (2);

[0020] S2.4 Repeat S2.2 and S2.3, that is, repeat the adjustment, variance component estimation, weighting and then adjustment, until... until.

[0021] As a preferred embodiment of the present invention, in S3, for any given time, GPS TEC, CODE TEC, Jason TEC, COSMIC TEC and IRI2020 TEC of that time and its adjacent times are selected to participate in data fusion.

[0022] As a preferred embodiment of the present invention, in S3, the data fusion process is as follows: based on the weight of each type of data, data of corresponding proportions are selected to form a fusion dataset, the time resolution is set to 2 hours, the longitude interval is 5°, and the latitude interval is 2.5°. Data fusion is performed using a 15th-order spherical harmonic function model, expressed as:

[0023] (3);

[0024] (4);

[0025] (5);

[0026] (6);

[0027] In the formula, VTEC represents the fused data; Let represent the normalized Legendre function of order n and degree m, where n ranges from 0 to n and 15, and for each n, m ranges from 0 to m and n. N is the maximum order of the spherical harmonic function, i.e., N=15; β is the latitude of the ionospheric puncture point, and s is the longitude of the ionospheric puncture point. Represents the normalization constant; Kronek function; , The coefficients of the spherical harmonic function are unknown parameters estimated through the data fusion process.

[0028] As a preferred embodiment of the present invention, in S4, the following is defined: Indicates the diurnal variation component, Indicates the amount of seasonal variation. Represents geomagnetic components, Indicates the components of solar activity, This represents the EIA correction component, where EIA stands for Equatorial Ionization Anomaly; where:

[0029] When set to local A function of longitude and latitude, expressed as:

[0030] (7);

[0031] (8);

[0032] (9);

[0033] In the formula, The TEC diurnal variation curve function is represented by h; the solar altitude angle is represented by h. , for The parameters to be estimated in the model are modeled using four harmonics, with each harmonic corresponding to a specific parameter. , , Used to determine the amplitude of the daily variation function, Used to determine the phase of the diurnal variation function, j is Index of the parameters to be estimated; Indicates latitude; Indicates the solar declination; Indicates the hour angle;

[0034] Set as annual day The function is represented as:

[0035] (10);

[0036] In the formula, , for The parameters to be estimated in the model are modeled using four harmonics, with each harmonic corresponding to a specific parameter. , , This indicates the magnitude of the harmonic's contribution to seasonal variation. This represents the phase shift of the harmonic, where z is... Index of the parameters to be estimated;

[0037] Set based on corrected magnetic inclination latitude The function is represented as:

[0038] (11);

[0039] (12);

[0040] In the formula, I represents the magnetic tilt angle; g represents... The parameters to be estimated in the data;

[0041] Set as a second-order Taylor expansion of F10.7p and its linear rate of change, it is expressed as:

[0042] (13);

[0043] In the formula, This represents the constant term to be estimated. The parameters to be estimated in the data; The solar activity intensity index F10.7p represents... for The linear rate of change; for The coefficients of the linear terms; for The coefficients of the linear terms; for The coefficient of the quadratic term; for and The cross term coefficient; for The coefficient of the quadratic term;

[0044] The function set to fit the north and south humps of the EIA using two Gaussian functions respectively is expressed as:

[0045] (14);

[0046] (15);

[0047] (16);

[0048] In the formula, The exponential part of the Gaussian function representing the northern hump of the EIA indicates the shape of the northern hump. The exponential part of the Gaussian function representing the southern hump of the EIA represents the shape of the southern hump. , These are the parameters to be estimated in the data, used to determine the intensity of the north and south humps; The latitude of the observation point; The latitude of the center of the North Camel Hump; The latitude range parameter for the North Camel Hump; The latitude of the center of the South Camel Hump; This refers to the latitude range parameter of the southern camel hump.

[0049] As a preferred embodiment of the present invention, in step S5, the parameters to be estimated in the nonlinear mathematical expressions of each component are calculated by nonlinear least squares fitting, including... , , , g , , .

[0050] As a preferred embodiment of the present invention, in S5, the TEC empirical model is expressed as:

[0051] ;

[0052] In the formula, This represents the TEC empirical model, whose input is the year-to-date period. Local time ,longitude ,latitude and solar activity parameters .

[0053] The algorithm involved in this invention can be executed by an electronic device, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The processor executes the software to implement the above-mentioned algorithm calculation.

[0054] The beneficial effects of this invention are:

[0055] This invention integrates five different TEC data sources (GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC), performs precise weighting through Hull model variance component estimation, and uses a 15th-order spherical harmonic function model for data fusion, effectively improving the modeling accuracy of low-latitude regions in China and enabling a more accurate description of the spatiotemporal variation patterns of TEC.

[0056] This invention presents refined function models for diurnal variation components, seasonal variation components, geomagnetic components, and three different modeling schemes for EIA anomaly components, ensuring the prediction accuracy of the proposed model. Residual analysis after model establishment shows that the residuals conform to a normal distribution, with 95.01% of the residuals falling between -10 TECU and 10 TECU. Furthermore, in single-station prediction capability assessment, out-of-region consistency accuracy assessment, and in-region consistency accuracy assessment, the TECM model demonstrates superior prediction capabilities compared to models such as IRI2020, providing a more reliable basis for ionospheric TEC prediction in low-latitude regions of China. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the principle of this invention;

[0058] Figure 2 This is a schematic diagram of the diurnal variation curve of the solar activity index F10.7 from 2003 to 2022 during the verification process of this invention;

[0059] Figure 3 This is a schematic diagram of the residuals after the TECM model was established during the verification process of this invention. Detailed Implementation

[0060] The embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0061] like Figure 1 As shown, the modeling method of the empirical model of ionospheric TEC in the low latitude region of China based on multi-source data fusion includes the following steps:

[0062] S1. Select multi-source TEC data from one solar activity cycle in the low-latitude region of China as the multi-source dataset;

[0063] S2. Using the Hull model variance component estimation method, weights are assigned to each data point in the multi-source dataset to determine the weight of each data point.

[0064] S3. Using a 15th-order spherical harmonic function with defined weights, data fusion is performed on various data from multiple source datasets to obtain the modeling dataset.

[0065] S4. Based on the modeling dataset, set the components of the TEC empirical model, including diurnal variation components, seasonal variation components, geomagnetic components, solar activity components, and EIA correction components, and establish nonlinear mathematical expressions to represent all components;

[0066] S5. Calculate the parameters to be estimated in the nonlinear mathematical expressions of each component through nonlinear least squares fitting, form the TEC empirical model, and complete the final modeling.

[0067] In S1, the multi-source TEC data includes GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020TEC data.

[0068] In S2, the process of weighting each type of data in the multi-source dataset is as follows: the estimated unit weight variance of each type of observation is calculated according to the Helmert approximation formula, i.e., equation (1), and then the weights of each type of observation are re-determined according to equation (2). Each type of observation is the data in the multi-source dataset. Equations (1) and (2) are as follows:

[0069] (1);

[0070] (2);

[0071] In the formula, This represents the estimated unit weight variance of the i-th type of observation; Let P represent the sum of squared residuals of the i-th class of observations, where P represents the weight matrix of the observations. This represents the residual vector of the i-th type of observation, with the superscript T indicating transpose; This represents the weight of the i-th type of observation; Represents the number of redundant observations for the i-th type of observation; c represents an arbitrary constant; This represents the weight matrix after weighting the observations of the i-th class;

[0072] When determining the weights, iterative calculations are performed based on equations (1) and (2), and the process is as follows:

[0073] S2.1 For each type of observation, first determine its initial weights;

[0074] S2.2, Perform the first adjustment and obtain... ;

[0075] S2.3. Based on equation (1), perform a first-order variance component estimation to obtain the first estimate of the unit weight variance of each type of observation. Then, the weights are determined according to formula (2);

[0076] S2.4 Repeat S2.2 and S2.3, that is, repeat the adjustment, variance component estimation, weighting and then adjustment, until... until.

[0077] In S3, for any given time, GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC at that time and its adjacent times are selected to participate in data fusion.

[0078] The data fusion process involves selecting a corresponding proportion of data based on the weight of each data type to form a fusion dataset. The time resolution is set to 2 hours, with a longitude interval of 5° and a latitude interval of 2.5°. A 15th-order spherical harmonic function model is used for data fusion, as shown below:

[0079] (3);

[0080] (4);

[0081] (5);

[0082] (6);

[0083] In the formula, VTEC represents the fused data; Let represent the normalized Legendre function of order n and degree m, where n ranges from 0 to n and 15, and for each n, m ranges from 0 to m and n. N is the maximum order of the spherical harmonic function, i.e., N=15; β is the latitude of the ionospheric puncture point, and s is the longitude of the ionospheric puncture point. Represents the normalization constant; Kronek function; , The coefficients of the spherical harmonic function are unknown parameters estimated through the data fusion process.

[0084] The solution can be obtained using the least squares method. , , is represented as:

[0085] ;

[0086] In the formula, , , , , These represent the GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC data that participated in the fusion, respectively. Because they are in a 15x15 format, for a set of... , There are a total of 256 model parameters to be estimated, which are respectively used as to This is indicated by calculation using spherical harmonic functions; This indicates the systematic bias between ocean altimeter satellite and GNSS observation data; This indicates the systematic bias between occultation data and GNSS observation data;

[0087] In S4, the definition is... Indicates the diurnal variation component, Indicates the amount of seasonal variation. Represents geomagnetic components, Indicates the components of solar activity, This represents the EIA correction component, where EIA stands for Equatorial Ionization Anomaly; where:

[0088] When set to local A function of longitude and latitude, expressed as:

[0089] (7);

[0090] (8);

[0091] (9);

[0092] In the formula, The TEC diurnal variation curve function is represented by h; the solar altitude angle is represented by h. , for The parameters to be estimated in the model are modeled using four harmonics, with each harmonic corresponding to a specific parameter. , , Used to determine the amplitude of the daily variation function, Used to determine the phase of the diurnal variation function, j is Index of the parameters to be estimated; Indicates latitude; Indicates the solar declination; Indicates the hour angle. ;

[0093] Harmonics refer to the sinusoidal components whose frequencies are integer multiples of the fundamental frequency of a periodic non-sinusoidal signal, obtained by performing Fourier series decomposition on the original signal. For example, if the fundamental period of a phenomenon is one day (like the daily variation of TEC, with a period of 24 hours), then the frequency of the "fundamental wave" corresponds to repeating once a day; the frequency of the "second harmonic" corresponds to repeating once every half day (24 hours / 2 = 12 hours); the frequency of the "third harmonic" corresponds to an 8-hour period, and so on. For example, corresponding to j=1, 2, 3, 4:

[0094] j=1: Fundamental wave (24-hour period), describing the most important daily variation trend;

[0095] j=2: Second harmonic (period 12 hours), describing the variation pattern on a semi-diurnal scale;

[0096] j=3: Third harmonic (period 8 hours);

[0097] j=4: Fourth harmonic (period 6 hours).

[0098] By using these four harmonic components of different frequencies, we can more precisely fit the actual shape of the TEC diurnal variation curve, and the same applies to subsequent curves.

[0099] Set as annual day The function is represented as:

[0100] (10);

[0101] In the formula, , for The parameters to be estimated in the model are modeled using four harmonics, with each harmonic corresponding to a specific parameter. , , This indicates the magnitude of the harmonic's contribution to seasonal variation. This represents the phase shift of the harmonic, where z is... Index of the parameters to be estimated;

[0102] Set based on corrected magnetic inclination latitude The function is represented as:

[0103] (11);

[0104] (12);

[0105] In the formula, I represents the magnetic tilt angle; g represents... The parameters to be estimated in the data;

[0106] Set as a second-order Taylor expansion of F10.7p and its linear rate of change, it is expressed as:

[0107] (13);

[0108] In the formula, This represents the constant term to be estimated. The parameters to be estimated in the data; The solar activity intensity index F10.7p represents... for The linear rate of change; for The coefficients of the linear terms; for The coefficients of the linear terms; for The coefficient of the quadratic term; for and The cross term coefficient; for The coefficient of the quadratic term;

[0109] The function set to fit the north and south humps of the EIA using two Gaussian functions respectively is expressed as:

[0110] (14);

[0111] (15);

[0112] (16);

[0113] In the formula, The exponential part of the Gaussian function representing the northern hump of the EIA indicates the shape of the northern hump. The exponential part of the Gaussian function representing the southern hump of the EIA represents the shape of the southern hump. , These are the parameters to be estimated in the data, used to determine the intensity of the north and south humps; The latitude of the observation point; The latitude of the center of the North Camel Hump; The latitude range parameter for the North Camel Hump; The latitude of the center of the South Camel Hump; This refers to the latitude range parameter of the southern camel hump.

[0114] The northern and southern humps of the Equatorial Ionization Anomaly (EIA) refer to regions of maximum electron density that appear within a certain latitude range on both sides of the magnetic equator. At the magnetic equator, under the influence of EXB drift (caused by the combined effects of the eastward electric field and the Earth's magnetic field of the ionosphere), plasma rises to a certain height and then diffuses along the magnetic field lines to the north and south sides of the magnetic equator, thus forming two regions of maximum electron density: the northern one is called the northern hump, and the southern one is called the southern hump.

[0115] In S5, the parameters to be estimated in the nonlinear mathematical expressions of each component are calculated through nonlinear least squares fitting, including... , , , g , , .

[0116] The TEC empirical model is represented as follows:

[0117] ;

[0118] In the formula, This represents the TEC empirical model, whose input is the year-to-date period. Local time ,longitude ,latitude And solar activity parameters (mainly referring to F10.7p) .

[0119] The verification process is as follows:

[0120] GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC data from 2009 to 2020 were selected as modeling data.

[0121] CODE GIM, as the most accurate final product (2-8 TECU) among IGS ionospheric products, is widely used in ionospheric research. The data comes from the CODE center, and the longitude, latitude, and TEC of all grid points in the low-latitude region of China are extracted from this ionospheric product as input data for the spherical harmonic function.

[0122] Jason TEC data was acquired using the JASON series altimeter satellite data products provided by the Radar Altimeter Database System (RADS). First, smoothed dual-frequency ionospheric correction values ​​were extracted from the product, and the total vertical electron content was calculated based on the Ku-band frequency. Second, outlier data with TEC values ​​less than zero were removed. Then, the JASON TEC data was resampled with a resampling time resolution of 10 seconds. Finally, [the data was then analyzed]. The criteria eliminate gross errors. For the JASON series products, the time ranges for JASON-1, JASON-2, and JASON-3TEC data are January 15, 2002 to July 4, 2008, July 4, 2008 to February 12, 2016, and February 12, 2016 to June 30, 2020, respectively.

[0123] Because the raw COSMIC observation data (which can be downloaded from the COSMIC Data Analysis and Archive Center) is affected by various factors such as instruments, meteorology, and space environment, the quality of some electron density profile products is not ideal. Therefore, in order to ensure data quality, quality control of COSMIC TEC data is required. Electron density profiles in the following two cases are removed: (1) Let D1 be the line connecting the bottom and top of the electron density profile, and draw a perpendicular line from D1 through the peak point of electron density. This perpendicular line is D2. If D2 / D1>0.1, the electron density profile is removed; (2) When the altitude is greater than 120km, if there is a point where the electron density is less than 0, the electron density profile is removed. The gradient method is used to integrate the electron density profile to obtain STEC (tilted total electron content). The transformation from measured STEC to vertical total electron content is realized by the projection function. The selected projection function is the SLM mapping function.

[0124] Download the TEC data for the IRI2020 model from 2009 to 2020 using the Fortran program provided by CCMC (The Community Coordinated Modeling Center). The time resolution is 2 hours. Calculate the longitude, latitude, and TEC of all grid points in the IRI2020 data product as input data for the spherical harmonic function (IRI2020 TEC).

[0125] GPS TEC data was obtained from the official website of the National Earthquake Science Data Center.

[0126] Solar extreme ultraviolet (EUV) radiation is the best parameter for studying the time-varying characteristics of solar radiation and the solar-ionospheric effect. However, space-based EUV observation records lack continuity and have a relatively short observation history. Therefore, the solar activity index F10.7 is often used as a proxy for EUV when measuring solar activity levels (Liu et al. 2006). Figure 2 The diurnal variation curves for F10.7 (F10.7p is smoothed F10.7 data) from 2003 to 2022 are shown. Figure 2 The dashed line in the diagram represents the boundary between the rising and falling phases of the solar activity cycle, and also the modeling time period for this validation example. The unit for F10.7 is sfu. From... Figure 2 It can be seen that 2003 to 2007 was the descending phase of the 23rd solar cycle; 2008 to 2018 was the 24th solar cycle, with July 1, 2013 being the dividing point between the ascending and descending phases; and 2019 to 2022 was the ascending phase of the 25th solar cycle.

[0127] Using the grid point locations of IGS GIMs data, the globe was divided into 5183 grid points. After obtaining the modeling dataset, a nonlinear mathematical expression was established to represent all components, the parameters to be estimated were calculated, and the TEC empirical model (TECM model) was formed.

[0128] TECU stands for total electron content unit, used to represent the number of electrons. 1 TECU represents 10 to the power of 16 electrons.

[0129] The residuals after the TECM model is established are as follows Figure 3 (The vertical axis, frequency, represents the number of times the corresponding residual value occurs.) From... Figure 3 It can be seen that the mean of the model residuals is -0.34, the standard deviation is 5.54, and the root mean square error (RMS) is 5.55. The model residuals follow a normal distribution, with approximately 95.01% of the model residuals falling between -10 TECU and 10 TECU.

[0130] Table 1. Accuracy assessment of data from four GPS observation stations and predictions from the TECM model.

[0131]

[0132] In terms of single-station prediction capability evaluation, the accuracy of the predictions was assessed using data from four existing GPS observation stations in low latitudes of China (referred to as fjpt, jxja, kmin, and yong) and the predicted values ​​of the TECM model, as shown in Table 1. The data in the table are the mean values ​​after subtraction; data marked with * indicate smaller mean values, closer to GPS-TEC. Table 1 shows that the TECM model outperforms the IRI2020 model, demonstrating better predictive ability. However, the TECM model also exhibits the same problem as the IRI2020 model: overestimating TEC values. With sufficient data and by dividing solar activity into low, medium, and high levels, the model accuracy would be further improved. TECM minus GPS refers to subtracting the GPS-TEC TEC data from the total electron content data calculated by the TECM model, and evaluating the model's prediction accuracy by calculating the difference (the table shows the mean of the subtraction). The same principle applies to other parameters.

[0133] Table 2 External Consistency Accuracy Evaluation of TECM Model

[0134]

[0135] Regarding the external conformity accuracy assessment, TEC data from the IGS GIMs, IRI2020, and NTCM models (existing broadcast ionospheric models) at 14:00 on January 1, 2008 and 2021 were used to assess the external conformity accuracy of the models, as shown in Table 2. Table 2 shows that the TECM model exhibits significantly better predictive ability than the other models.

[0136] Table 3. Regional compliance accuracy assessment of the TECM model

[0137]

[0138] Regarding the intra-regional conformity accuracy assessment, the TEC data of the IGS GIMs, IRI2020, and NTCM models at 14:00 on January 1, 2016 and 2020 were used to assess the intra-regional conformity accuracy of the models, as shown in Table 3. Table 3 shows that the TECM model exhibits significantly better predictive ability than the other models.

Claims

1. A modeling method for an empirical TEC model of the ionosphere in the low latitude region of China based on multi-source data fusion, characterized in that, The modeling process includes the following steps: S1. Select multi-source TEC data from one solar activity cycle in the low-latitude region of China as the multi-source dataset; S2. Using the Hull model variance component estimation method, weights are assigned to each data point in the multi-source dataset to determine the weight of each data point. S3. Using a 15th-order spherical harmonic function with defined weights, data fusion is performed on various data from multiple source datasets to obtain the modeling dataset. S4. Based on the modeling dataset, set the components of the TEC empirical model, including diurnal variation components, seasonal variation components, geomagnetic components, solar activity components, and EIA correction components, and establish nonlinear mathematical expressions to represent all components; definition Indicates the diurnal variation component, Indicates the amount of seasonal variation. Represents geomagnetic components, Indicates the components of solar activity, This represents the EIA correction component, where EIA stands for Equatorial Ionization Anomaly; where: When set to local A function of longitude and latitude, expressed as: （7）； （8）； （9）； In the formula, The TEC diurnal variation curve function is represented by h; the solar altitude angle is represented by h. , for The parameters to be estimated in the model are modeled using four harmonics, with each harmonic corresponding to a specific parameter. , , Used to determine the amplitude of the daily variation function, Used to determine the phase of the diurnal variation function, j is Index of the parameters to be estimated; Indicates latitude; Indicates the solar declination; Indicates the hour angle; Set as annual day The function is represented as: （10）； In the formula, , for The parameters to be estimated in the model are modeled using four harmonics, with each harmonic corresponding to a specific parameter. , , This indicates the magnitude of the harmonic's contribution to seasonal variation. This represents the phase shift of the harmonic, where z is... Index of the parameters to be estimated; Set based on corrected magnetic inclination latitude The function is represented as: （11）； （12）； In the formula, I represents the magnetic tilt angle; g represents... The parameters to be estimated in the data; Set as a second-order Taylor expansion of F10.7p and its linear rate of change, it is expressed as: （13）； In the formula, This represents the constant term to be estimated. The parameters to be estimated in the data; The solar activity intensity index F10.7p represents... for The linear rate of change; for The coefficients of the linear terms; for The coefficients of the linear terms; for The coefficient of the quadratic term; for and The cross term coefficient; for The coefficient of the quadratic term; The function set to fit the north and south humps of the EIA using two Gaussian functions respectively is expressed as: （14）； （15）； （16）； In the formula, The exponential part of the Gaussian function representing the northern hump of the EIA indicates the shape of the northern hump. The exponential part of the Gaussian function representing the southern hump of the EIA represents the shape of the southern hump. , These are the parameters to be estimated in the data, used to determine the intensity of the north and south humps; The latitude of the observation point; The latitude of the center of the North Camel Hump; This refers to the latitude range parameter of the North Camel Hump; The latitude of the center of the South Camel Hump; This refers to the latitude range parameter of the southern camel hump; S5. Calculate the parameters to be estimated in the nonlinear mathematical expressions of each component through nonlinear least squares fitting, form the TEC empirical model, and complete the final modeling.

2. The modeling method for the empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion according to claim 1, characterized in that, In S1, the multi-source TEC data includes GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC data.

3. The modeling method for the empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion according to claim 1, characterized in that, In S2, the process of weighting each type of data in the multi-source dataset is as follows: the estimated unit weight variance of each type of observation is calculated according to the Helmert approximation formula, i.e., equation (1), and then the weights of each type of observation are re-determined according to equation (2). Each type of observation is the data in the multi-source dataset. Equations (1) and (2) are as follows: （1）； （2）； In the formula, This represents the estimated unit weight variance of the i-th type of observation; Let P represent the sum of squared residuals of the i-th class of observations, where P represents the weight matrix of the observations. This represents the residual vector of the i-th type of observation, with the superscript T indicating transpose; This represents the weight of the i-th type of observation; Represents the number of redundant observations for the i-th type of observation; c represents an arbitrary constant; This represents the weight matrix after weighting the observations of the i-th class; When determining the weights, iterative calculations are performed based on equations (1) and (2), and the process is as follows: S2.1 For each type of observation, first determine its initial weights; S2.2, Perform the first adjustment and obtain... ; S2.

3. Based on equation (1), perform a first-order variance component estimation to obtain the first estimate of the unit weight variance of each type of observation. Then, the weights are determined according to formula (2); S2.4 Repeat S2.2 and S2.3, that is, repeat the adjustment, variance component estimation, weighting and then adjustment, until... until.

4. The modeling method for the empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion according to claim 2, characterized in that, In S3, for any given time, GPS TEC, CODE TEC, Jason TEC, COSMIC TEC, and IRI2020 TEC at that time and its adjacent times are selected to participate in data fusion.

5. The modeling method for the empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion according to claim 4, characterized in that, In S3, the data fusion process involves selecting a corresponding proportion of data based on the weight of each data type to form a fusion dataset. The time resolution is set to 2 hours, with a longitude interval of 5° and a latitude interval of 2.5°. A 15th-order spherical harmonic function model is used for data fusion, as shown below: （3）； （4）； （5）； （6）； In the formula, VTEC represents the fused data; Let represent the normalized Legendre function of order n and degree m, where n ranges from 0 to n and from 15 to n. For each n, m ranges from 0 to m and from n to n. N is the maximum order of the spherical harmonic function, i.e., N=15. β is the latitude of the ionospheric puncture point, and s is the longitude of the ionospheric puncture point. Represents the normalization constant; Kronek function; , The coefficients of the spherical harmonic function are unknown parameters estimated through the data fusion process.

6. The modeling method for the empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion according to claim 1, characterized in that, In S5, the parameters to be estimated in the nonlinear mathematical expressions of each component are calculated through nonlinear least squares fitting, including... , , , g , , .

7. The modeling method for the empirical model of ionospheric TEC in low-latitude regions of China based on multi-source data fusion according to claim 1, characterized in that, In S5, the TEC empirical model is expressed as: ； In the formula, This represents the TEC empirical model, whose input is the year-to-date period. Local time ,longitude ,latitude and solar activity parameters .

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