VTEC value prediction method based on LSTM-Transformer model

Abstract

SOLUTION: A regional ionospheric delay prediction method based on an LSTM-Transformer model includes a step 1 for collecting ionospheric layer TEC values and acquires a VTEC value by performing calculation by a projection function, a step 2 for dividing the VTEC value into a low frequency and a high frequency by a pair of conjugate filters using wavelet transformation, a step 3 for making a solar radiation index and geomagnetic index information high frequency partial information training data, a step 4 for training data of the step 2 and the step 3 by the LSTM-Transformer model to acquire a LSTM-Transformer combination prediction model, and a step 5 for training a training set to a prediction model of the step 4, optimizing a loss function, and predicting the VTEC value.EFFECT: The accuracy of a VTEC value acquired by a method of this invention is more excellent than a conventional ionospheric layer experiment model and a general neural network model and has a faster prediction speed.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to the field of ionospheric delay prediction technology, and in particular to a regional ionospheric delay prediction method based on LSTM-Transformer model. [Background technology]

[0002] Earth's ionospheric delay is the propagation delay caused by changes in the concentration of electrons in the Earth's ionosphere (a part of the atmosphere located between approximately 60 and 1,000 kilometers above the Earth's surface) as an electromagnetic signal passes through it. Ionospheric delay typically affects the accuracy and reliability of applications such as radio communications, satellite navigation, and geodetic measurements.

[0003] Total electron content (TEC) is a characteristic of the ionosphere, and its main expression is the vertical total electron content (VTEC). Forecasting ionospheric TEC values ​​is important for radio propagation and navigation positioning. Previously, researchers have established empirical ionospheric models, such as the IRI model, Bent model, and Klobuchar model, by examining and utilizing numerous observational data sets. While these empirical ionospheric models can accurately describe the average behavior of global changes, they lack accuracy for small-scale regional changes. Scholars have also proposed autoregressive models based on time series analysis, which can accurately fit periodicity and trends. However, the ionosphere is significantly affected by environmental factors such as geomagnetic disturbances, solar activity, and the relative distance between the Earth and the Sun, which can affect the accuracy of autoregressive models to some extent, resulting in poor performance.

[0004] The IGS center also issues ionospheric products in the form of a grid. The grid products cover the entire globe, but the products issued by different mechanisms all have corresponding system errors and are not very accurate.

[0005] Based on the above analysis, the prior art ionospheric delay prediction has the following shortcomings: 1) The traditional empirical model has low accuracy and is significantly affected by environmental changes. 2) The ionospheric products issued by IGS are also not highly accurate and have hysteresis. 3) The time series model ionospheric forecast solution has low accuracy, is difficult to consider long-term changes and special circumstances, and has poor interference resistance.

[0006] In recent years, neural networks, as an emerging technology, have been able to establish effective models for complex, nonlinear data, which have had a certain effect on the prediction of data sets. They can more accurately represent the dynamic change rules of time series, providing a new method for ionospheric delay forecasting. The LSTM-Transformer model combination can process ionospheric series, simultaneously consider long-term change rules and global information, and has higher model training efficiency. Summary of the Invention [Problem to be solved by the invention]

[0007] The present invention provides a regional ionospheric delay prediction method based on an LSTM-Transformer model, which combines an LSTM model and a Transformer model to process ionospheric sequences, and can simultaneously consider long-term change rules and global information. This makes the model training more efficient, and the accuracy of the obtained VTEC value is superior to that of traditional ionospheric empirical models and general neural network models, and the forecast speed is faster. [Means for solving the problem]

[0008] The technical solutions adopted by the present invention are as follows:

[0009] The regional ionospheric delay prediction method based on the LSTM-Transformer model is Step 1: collecting ionospheric TEC values ​​and calculating them with a projection function to obtain VTEC values; Step 2, using a wavelet transform to process the VTEC values ​​and separate them into two parts: low frequency and high frequency, using a pair of conjugate low-pass and high-pass filters; Step 3: introducing solar radiation index and geomagnetic index information as high frequency partial information training data; Step 4: The data from Step 2 and Step 3 are trained in an LSTM-Transformer model to obtain a combined LSTM-Transformer prediction model. Step 5 includes training the LSTM-Transformer combined prediction model in step 4 using the training set, optimizing it using a loss function, and predicting the VTEC value.

[0010] In step 1, historical ionospheric delay data is collected, and the ionospheric TEC value calculated by the global navigation satellite system (GNSS) is collected. The VTEC value is calculated using a projection function as shown in the following equation:

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[0011] In step 2, the VTEC value is processed using a pair of conjugate low-pass and high-pass filters using a wavelet transform, as shown in the following equation:

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[0012] In step 3, the solar radiation index F 10.7 and geomagnetic index D st , K. p are constructed as the corresponding datasets.

[0013] 1).F 10.7 The index indicates the intensity of solar activity, and is the radiant flux of solar radiation at a wavelength of 10.7 cm. It is divided into three levels: strong, medium, and weak, depending on the magnitude of the index value. The solar radiation index is compiled daily and compiled into the solar radiation index dataset F m Establishing

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[0014] 2) Dst is a time-based geomagnetic index used to describe the process of magnetic storms. It reflects the change of the loop current from the west of the equator and monitors the intensity and spatial-temporal extent of magnetic storms. It is usually obtained by using the horizontal component of the geomagnetic field from four platforms in the middle and low latitudes, and calculating the loop current with latitude correction and elimination. The obtained geomagnetic index is called the dataset Dst. m where each subscript indicates a time of modeling selection, and there are a total of c times.

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[0015] 3).K p The index is calculated based on magnetic field change data from multiple geomagnetic observatories and indicates the impact of solar activity on the geomagnetic field. The calculation method is as follows:

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[0016] Step 4 specifically includes the following steps:

[0017] 1]. LSTM can capture long-term dependencies in time series, so it can be used to measure low-frequency sequences after wavelet transformation. L The model is trained using the following inputs: longitude, latitude, time, and VTEC. L The feature is to perform feature zoom (normalization), build an LSTM model, and construct an input layer, an LSTM layer, and an output layer. After the model training is completed, it is evaluated. Among them, the feature zoom is as follows:

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[0018] Further analysis is performed using principal components to reduce the dimension of the model data, specifically including:

[0019] a) defining the initial matrix X, i.e. the parameters that may affect the VTEC value;

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[0020] c) Characteristic equation |λI P -R|=0, where λ is the feature value, and I P denotes the identity matrix, R denotes the correlation coefficient matrix, arrange the feature values ​​in descending order, and select the principal components you actually need according to your needs.

[0021] The LSTM model has input gates, forget gates, and output gates to control the flow of information, thereby achieving effective time memory function and preventing the problem of vanishing gradients. The input gate is similar to the brain's attention, which determines which part of new input data should be added to the current state; the forget gate is similar to a sieve, which determines which information in the current state should be retained and which information should be forgotten; and the output gate determines which information in the current state should be propagated to the next state and the network output.

[0022] The structure of the LSTM model is shown in Figure 2. The input layer represents the feature values ​​at each time point, and C t-1 indicates the state information of the memory cell at the previous time, and C t indicates the state information of the memory cell at that time, and f t denotes the forget gate, and i t denotes the output of the input gate, and c t indicates the state information of the memory cell after updating, and o t denotes the output of the output gate, σ and tanh denote the activation functions, and H t-1 indicates the output at the previous time, and H t indicates the output at that time.

[0023] Construct the input layer, LSTM layer, and output layer of the LSTM model. (i) Create one input layer and match the feature dimension of the data dimension; (ii) add one LSTM layer, which is used to capture the modes and dependencies in the time series, and set the number of LSTM units and other superparameters; (iii) In the output layer, we add one fully connected layer to combine the features and VTEC L The mapping relationship f(x1,x2,…,x p ) is output.

[0024] 2]. High frequency series after wavelet transformation JPEG2025157074000014.jpg15170 is used as the model input, and high-frequency information JPEG2025157074000015.jpg15170, Geomagnetic index Dst m , K. p,m , solar radiation index F m The data is integrated to form a high-frequency feature matrix H, where each row represents a time step and each column represents a feature, to train a Transformer model and evaluate the training effect. The feature matrix is ​​shown below:

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[0025] A transformer model was constructed, and the structural schematic of the transformer model is shown in Figure 3.

[0026] (i) In the input layer, the feature matrix and Enter JPEG2025157074000017.jpg15170, (ii) In the encoder and decoder layer, multiple encoder layers are created, each of which includes a self-attention mechanism and a feedforward neural network, where the self-attention mechanism serves to grasp the relationship between different positions in the sequence, and the feedforward neural network is used to process the features of each position, and the encoder takes the received features such as solar radiation index and geomagnetic index as input and codes them into a context vector, which includes an indication of the input features; The decoder receives the context vector generated by the received encoder as input, predicts the high frequency part of the TEC based on this context vector, and outputs a prediction for the high frequency part of the TEC.

[0027] (iii) In the output layer, one fully connected layer is added after the encoder layer, which is used to output the features, and the size and activation function of the output layer are adjusted according to the task needs.

[0028] In step 4, the high frequency feature matrix H and the observed JPEG2025157074000018.jpg15170 is input to the encoder. Through multi-attention layers and normalization, the model can dynamically focus on information between different features in the input feature sequence, understand the modes and trends between features, and capture the complex relationships between solar radiation index, geomagnetic index, and noise.

[0029] In the multi-attention layer, the solar radiation index F m,u , geomagnetic index Dst m,u and K. m,u , noise S u are linearized to obtain the query vector Q i , Key vector K i , Value vector V i and p idenotes the i-th feature,

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[0030] Next, the feature information extracted by the encoder and the previous output sequence are input to the decoder, and only the generated sequence is accessed by the mask multi-attention layer restriction, and the feature information and Establish a mapping relationship F(H) with JPEG2025157074000028.jpg15170, as shown below:

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[0031] The training set data is used to train the Transformer model, and the model parameters are optimized by minimizing an appropriate loss function. The model is used to better predict ionospheric delay high-frequency information. The performance of the model is then evaluated using the validation set, and the accuracy of the model is judged based on the difference between the predicted results and the actual values. According to needs, operations such as superparameter adjustment and model structure adjustment are performed to optimize the model performance.

[0032] In step 4, the specific structure of the Transformer combined forecasting model is shown in Figure 4. The Transformer combined forecasting model is based on the relationship between low-frequency and high-frequency feature sequences, and on the solar activity intensity and geomagnetic intensity of the day, and trains the relationship between the feature sequences using a feedforward neural network in the fully connected layer, combines the results, and finally outputs the predicted VTEC value.

[0033] In step 5, the LSTM-Transformer combined prediction model in step 4 is trained using the training set and optimized by a loss function;

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[0034] As shown in Figure 5, in step 5, by inputting the GNSS-VTEC value, the VTEC is subjected to wavelet transformation to obtain low-frequency and high-frequency parts, and then the LSTM-Transformer model is trained to obtain the mapping relationship between the VTEC and the feature information, so that the VTEC can be predicted.

[0035] In step 5, the historical VTEC value and the solar radiation index F m , geomagnetic activity index Dst m , K. p,m The future VTEC value is predicted using the model and the model-predicted VTEC value is output. [Effects of the Invention]

[0036] The regional ionospheric delay prediction method based on the LSTM-Transformer model of the present invention has the following technical advantages:

[0037] 1) The structure of ionospheric delay data is complex, and it is affected by various factors, such as geomagnetic index, solar radiation, latitude and longitude, and also has annual, monthly and day-of-the-week variations, making it difficult to directly use it as the initial value for model training. Therefore, the present invention uses wavelet transform to process the VTEC value, and wavelet decomposition can effectively separate and extract the periodicity, nonlinearity and change trend of the time series data, allowing the forecasting model to better fit and model the periodic change point information and trend items of the time series data, thereby achieving accurate forecasting results.

[0038] 2) The method of the present invention has the advantages of high accuracy and fast solution, and this model combines the advantages of both and can simultaneously consider long-term change rules and global information, resulting in higher model training efficiency.

[0039] 3) The accuracy of the VTEC value obtained by the method of the present invention is superior to that of the traditional ionospheric empirical model and the general neural network model, and the forecast speed is faster.

[0040] 4) The method of the present invention does not require extra investment, does not require building a new observation station based on the existing GNSS observation station and collecting data using extra equipment, and can obtain predicted VTEC data by processing and training the data. [Brief explanation of the drawings]

[0041] Specific embodiments of the present invention will be further described below with reference to the drawings and examples. [Figure 1] 1 is a flow chart of the method of the present invention. [Figure 2] 1 is a schematic diagram of an LSTM model according to the present invention. [Figure 3] FIG. 1 is a schematic diagram of a Transformer model of the present invention. [Figure 4] FIG. 1 is a schematic diagram of the LSTM-Transformer combined prediction model of the present invention. [Figure 5] 1 is a schematic diagram of step 5 of the present invention; DETAILED DESCRIPTION OF THE INVENTION

[0042] A regional ionospheric delay prediction method based on an LSTM-Transformer model uses GNSS observation data, takes into account the influence of solar activity, and forecasts short-term VTEC values ​​in a region. This model can simultaneously consider long-term change patterns and global information, making model training more efficient. The accuracy of the obtained VTEC values ​​is superior to that of traditional ionospheric empirical models and general neural network models, and the forecast speed is faster.

[0043] As shown in Figure 1, the specific implementation steps are as follows:

[0044] 1) Collect historical ionospheric delay data, collect the TEC values ​​calculated by GNSS, and calculate the VTEC value using a projection function as shown in the following equation.

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[0045] 2) The structure of ionospheric delay data is complex, and it is affected by various factors, such as geomagnetic index, solar radiation, latitude and longitude, and also has annual, monthly and day-of-the-week variations, making it difficult to directly use it as the initial value for model training. Therefore, wavelet transform is used to process the VTEC value. Wavelet decomposition can effectively separate and extract the periodicity, nonlinearity and change trend of the time series data, allowing the forecasting model to better fit and model the periodic change point information and trend items of the time series data, thereby achieving accurate forecasting results. Step 2) is completed by computer.

[0046] Using a pair of conjugate low-pass and high-pass filters, as shown in the equation below,

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[0047] Information such as the solar radiation index and geomagnetic index is introduced as high-frequency partial information training data, and step 3) is completed by computer.

[0048] solar radiation index F 10.7 and geomagnetic indices Dst and K p are constructed as the corresponding datasets.

[0049] F 10.7The index indicates the intensity of solar activity, and is the radiant flux of solar radiation at a wavelength of 10.7 cm. It is divided into three levels: strong, medium, and weak, depending on the magnitude of the index value. The solar radiation index is compiled daily and compiled into the solar radiation index dataset F m The following table shows the number of days to respond.

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[0050] 4) The data in 2) and 3) are fed into the LSTM-Transformer model and trained. The specific steps are as follows:

[0051] 1] LSTM can capture long-term dependencies in time series, so it can be used to measure low-frequency sequences after wavelet transformation. L The input of the model is as follows. First, the longitude and latitude, time, and VTEC L is used as a feature, and feature zoom (normalization) is performed as shown in the following equation.

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[0052] Further analysis is performed using principal components to reduce the dimension of the model data, avoid data redundancy, eliminate the influence between related elements, and facilitate subsequent modeling. The principal component analysis steps are as follows:

[0053] a) Define the initial matrix X, i.e., the parameters that may affect the VTEC value, including but not limited to time characteristics year, month, day, hour, longitude, latitude, altitude, etc.;

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[0054] c) Characteristic equation |λI P The feature vector is calculated based on -R|=0, the feature values ​​are arranged in descending order, and the principal components actually required are selected according to the needs, thereby completing the dimension reduction for the features.

[0055] Moreover, the data is classified into subsets based on different features, improving the training effect of the model on the subsets.

[0056] LSTM has input gates, forget gates, and output gates to control the flow of information, thereby realizing effective time memory function and preventing the problem of vanishing gradient. The input gate is similar to the brain's attention, which determines which part of new input data should be added to the current state; the forget gate is similar to a sieve, which determines which information in the current state should be retained and which information should be forgotten; and the output gate determines which information in the current state should be propagated to the next state and the network output.

[0057] Construct the input layer, LSTM layer, and output layer.

[0058] (i) In the input layer, we create one input layer, match the feature dimension of the data dimension, and perform VTEC L Input each feature vector associated with

[0059] (ii) In the LSTM layer, we add one LSTM layer, which is used to capture the mode and dependency in the time series, and set the number of LSTM units and other superparameters.

[0060] (iii) In the output layer, we add one fully connected layer to combine the features and VTEC L The mapping relationship f(x1,x2,…,x p ) and fitting the VTEC periodicity and trend.

[0061] 2) High frequency information using a Transformer model JPEG2025157074000045.jpg15170 was modeled and processed. High Frequency Information JPEG2025157074000046.jpg15170, Geomagnetic index Dst m , K. p,m , solar radiation index F m The data is integrated to form a high-frequency feature matrix H, where each row represents a time step and each column represents a feature, to train a Transformer model and evaluate the training effect. The feature matrix is ​​shown below.

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[0062] Build a Transformer model.

[0063] (i) In the input layer, a feature matrix is ​​input.

[0064] (ii) In the encoder and decoder layer, multiple encoder layers are created, and each encoder layer includes a self-attention mechanism and a feedforward neural network. The self-attention mechanism serves to understand the relationship between different positions in the sequence, and the feedforward neural network is used to process the features of each position.

[0065] (iii) In the output layer, one fully connected layer is added after the encoder layer, which is used to output the features, and the size and activation function of the output layer are adjusted according to the task needs.

[0066] The training set data is used to train the Transformer model, and the model parameters are optimized by minimizing an appropriate loss function. The model is used to better predict ionospheric delay high-frequency information. The performance of the model is then evaluated using the validation set, and the accuracy of the model is judged based on the difference between the predicted results and the actual values. According to needs, operations such as superparameter adjustment and model structure adjustment are performed to optimize the model performance.

[0067] 3] In model feature fusion, A fully connected layer is established to fuse the features of the LSTM model and the Transformer model, and the fused features are input. Based on the geomagnetic activity and solar activity intensity, different weights are assigned to the features using a feedforward neural network to establish a total mapping relationship, and an LSTM-Transformer combined prediction model is obtained. The output result is the predicted VTEC value.

[0068] Step 4) above is completed by computer.

[0069] 5) For the LSTM-Transfomer model in 4), the entire combined model is trained using the training set, and the VTEC value calculated by GNSS and the predicted VTEC value are combined to establish a loss function to optimize the model parameters, and the absolute error and the root mean square error are set as the loss function. Step 5) is completed by a computer;

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[0070] 6) For the model in 5), the historical VTEC value and solar radiation index F m , geomagnetic activity index Dst m , K. p,m The future VTEC value is predicted using the model, and the model-predicted VTEC value is output. Step 6) is completed by a computer.

[0071] During the entire training process, the model parameters are updated using backpropagation and optimization algorithms to minimize the loss function. After the model prediction accuracy reaches a satisfactory level, an accuracy threshold can be set as needed to meet the needs of practical applications. Once the model reaches this accuracy threshold, training can be completed, and a regional ionospheric model will be established.

[0072] The present invention uses high-precision GNSS data and uses an LSTM-Transformer combined model to predict ionospheric delay data, and trains the ionospheric delay by dividing it into low-frequency and high-frequency parts, which can simultaneously consider long-term change rules and global information, resulting in higher model training efficiency and higher accuracy.

[0073] Regarding the verification example, This invention selects the representations of five sites in years A and B, where year A is a year of strong solar activity and year B is a year of weak solar activity. The five sites and their latitudes and longitudes are shown in Table 1 below.

[0074] [Table 1]

[0075] [Table 2]

[0076] [Table 3]

[0077] Tables 2 and 3 show the accuracy of the LSTM model compared to the LSTM-Transformer model and the Transformer model in years of strong and weak solar activity. The MAE and RMS are calculated using the model predictions and the VTEC calculated by GNSS, and are expressed in tecu. As can be seen, the accuracy of the three models in years of strong solar activity A is lower than in years of weak solar activity. Overall, the LSTM-Transformer model provides some improvement over the accuracy of the single models, and also provides some improvement in years of strong solar activity.

Claims

1. Step 1 involves collecting ionospheric TEC values ​​and calculating VTEC values ​​using a projection function, Step 2 involves using wavelet transform to process the VTEC value and separating it into two parts, low frequency and high frequency, using a pair of conjugate low-pass and high-pass filters. Step 3 involves introducing solar radiation index and geomagnetic index information as high-frequency partial information training data, Step 4 involves training the LSTM model with the low-frequency portion of the VTEC value after wavelet transform on the data from Steps 2 and 3, and training the Transformer model with the high-frequency portion of the VTEC value after wavelet transform, thereby obtaining an LSTM-Transformer combined prediction model. A method for predicting VTEC values ​​based on an LSTM-Transformer model, characterized by including step 5: training the LSTM-Transformer combination prediction model in step 4 using a training set, optimizing it using a loss function, and predicting the VTEC value.

2. In step 1, hysteresis ionospheric delay data is collected, ionospheric TEC values ​​obtained by calculation using the Global Navigation Satellite System (GNSS) are collected, and VTEC values ​​are obtained by calculation using a projection function as shown in the following equation. 【Number 1】 The VTEC value prediction method based on the LSTM-Transformer model according to claim 1, characterized in that Z is the elevation angle, R is the radius of the Earth, and H is the height of the puncture point, and the latitude, longitude, and time-related information of the puncture point are stored at this time, and the data is divided into a training set and a validation set in an 8:2 ratio.

3. In step 2 above, the VTEC value is processed using the wavelet transform as shown in the following equation, and a pair of conjugate low-pass and high-pass filters are used. [Math 2] In the above formula, the VTEC value is divided into two parts, which are then decomposed into an approximate value and a detailed value, of which the approximate value is the low-frequency portion of VTEC. Ｌ The detailed values ​​are in the high-frequency portion. 【number】 The VTEC value prediction method based on the LSTM-Transformer model according to claim 1, characterized in that the low-frequency portion includes trend information and long-period information, the high-frequency portion includes information on the effects of solar activity, geomagnetic activity, and magnetic storms, and m indicates the number of signals in the VTEC high-frequency portion.

4. In step 3, the solar radiation index F １０．７ and the geomagnetic index Dst, K ｐ This is configured as the corresponding dataset, 1) F １０．７ The index indicates the intensity of solar activity, and solar radiation is the radiant flux at a wavelength of 10.7 cm. Depending on the magnitude of the index value, it is divided into three levels: strong, medium, and weak. The daily solar radiation index is compiled, and the solar radiation index dataset F is created. ｍ Establish, [Math 3] And, In the above formula, F １０．７，１ , F １０．７，２ , ···, F １０．７，ｉ , ···, F １０．７，ｎ respectively represent the solar radiation index on the i-th day, where i represents the corresponding number of days, and n represents the total number of days. 2) Dst is the geomagnetic index per hour, used to explain the magnetic storm process, reflecting the change in loop current from the west of the equator, monitoring the intensity and spatiotemporal range of the magnetic storm, utilizing the horizontal geomagnetic component of four platforms in the mid- and low latitudes, and obtained by performing latitudinal correction and latitudinal correction and removal calculations on the loop current. The resulting geomagnetic index is then used as the dataset Dst. ｍ It is constructed as follows, where each subscript indicates the time of model selection, and there are a total of c times. [Math 4] And, In the above formula, Dst １ , Dst ２ , Dst ３ , ..., Dst ａ , ..., Dst ｃ The values ​​of the geomagnetic index at time a are shown, where a represents time a and c represents the total number of time points. 3) K ｐ The index is calculated based on magnetic field change data from multiple geomagnetic observatories and shows the influence of solar activity on the Earth's magnetic field. The calculation method is as follows: [Math 5] And, [Math 6] And, Eventually, K ｐ，１ , K ｐ，２ , K ｐ，３ , ..., K ｐ，ｋ , ..., K ｐ，ｓ The kth K ｐ The indices are shown, where s represents the total number of observations, k represents the kth time, and K ｐ，ｍ is K ｐ The VTEC value prediction method based on the LSTM-Transformer model according to claim 1, characterized in that it shows the time series of the index, and n represents the total number of geomagnetic stations involved in the calculation.

5. Step 4 includes, specifically, the following steps: Low-frequency sequence VTEC after wavelet transform Ｌ The LSTM model is trained using the following inputs: longitude, latitude, time, and VTEC. Ｌ This process involves feature zooming, constructing an LSTM model, building input layers, LSTM layers, and output layers, and evaluating the model after training is complete. The feature zooms are as follows: [Number 7] [Number 8] Eventually, x ｔ represents the t-th value in the initial data, μ ｔ σ represents the average value of the original time series. ｔ This is the standard deviation of the original time series, and VTEC ｉ is the VTEC value of the i-th puncture site at time t, 【number】 is the VTEC average value at time t, x' represents each normalized data point, time information is converted to an appropriate code, time is converted to features such as year, month, and hour, and n represents the total number of observations. Furthermore, the dimensionality of the model data is reduced by analyzing it using principal components, specifically including the following: a) Define the initial matrix X, i.e., parameters that may affect the VTEC value, [Number 9] And, Eventually, x １ This indicates the first influencing factor, x ２ This indicates the second influencing factor, x ｐ This indicates the p-th influencing factor, In matrix X, x １１ ...x １ｐ This shows the characteristics corresponding to the first influencing factor, x ｐ１ ...x ｐｐ This shows the characteristics corresponding to the p-th influencing factor, b) Calculate the correlation coefficient matrix, [Number 10] And, Eventually, r １１ This shows the correlation coefficient between the first parameter and the second parameter, r １２ This shows the correlation coefficient between the first parameter and the second parameter, r １ｐ This shows the correlation coefficient between the first parameter and the pth parameter, r ２１ This shows the correlation coefficient between the second parameter and the first parameter, r ２２ This shows the correlation coefficient between the second parameter and the second parameter, r ２ｐ This shows the correlation coefficient between the second parameter and the p-th parameter, r ｐ１ This shows the correlation coefficient between the pth parameter and the first parameter, r ｐ２ This shows the correlation coefficient between the p-th parameter and the second parameter, r ｐｐ This shows the correlation coefficient between the p-th parameter and the p-th parameter. c) Characteristic equation | λI Ｐ Based on -R|=0, the feature vector is obtained, λ represents the feature value, and I Ｐ The VTEC value prediction method based on the LSTM-Transformer model according to claim 1, characterized in that R represents the identity matrix, R represents the correlation coefficient matrix, feature values ​​are arranged in descending order, and the principal components actually required are selected according to the needs.

6. The input layer, LSTM layer, and output layer of the LSTM model are constructed. (i) Create one input layer and match the feature dimension of the data dimension, (ii) Add one LSTM layer, used to take the mode and dependencies in the time series, set the number of LSTM units and other superparameters, (iii) In the output layer, one full connection layer is added, and the features and VTEC Ｌ Mapping relationship f(x １ , x ２ , ..., x ｐ ) outputs, High-frequency sequence after wavelet transform 【number】 The model uses high-frequency information as input. 【number】 , geomagnetic index Dst ｍ _K ｐ，ｍ , solar radiation index F ｍ The data is integrated to construct a single high-frequency feature matrix H, where each row represents one time step and each column represents one feature. A Transformer model is then trained, and the training effect is evaluated. The feature matrix is ​​as follows: [Math 11] Of these, F represents the solar radiation index, Dst and K represent the geomagnetic index, S represents random noise, and F ｍ，ｕ This shows the solar radiation index series for the u-th time step, Dst ｍ，ｕ and K ｍ，ｎ The u-th time step shows the geomagnetic index, where Dst is the loop current index of the magnetic storm, Kp is the 3-hour magnetic information index, and S ｕ The VTEC value prediction method based on the LSTM-Transformer model according to claim 5, characterized in that represents a random noise sequence of the u-th time step, and N represents the total number of time steps.

7. Construct a Transformer model, (i) In the input layer, the feature matrix and Enter the following: (ii) In the encoder and decoder layer, multiple encoder layers are created, each encoder layer including a self-attention mechanism and a feedforward neural network, the self-attention mechanism helps to take relationships between different positions in the sequence, the feedforward neural network is used to process the features of each position, the encoder takes the received solar radiation index and geomagnetic index features as input, codes them as a single context vector, the vector includes an indication of the input features, The decoder takes the context vector generated by the received encoder as input, predicts the high-frequency portion of the TEC based on this context vector, and the decoder's output is the prediction for the high-frequency portion of the TEC. (iii) A VTEC value prediction method based on the LSTM-Transformer model according to claim 6, characterized in that in the output layer, one full connection layer is added after the encoder layer and used to output feature representations, and the size of the output layer and the activation function are adjusted according to the task needs.

8. In step 4, the high-frequency feature matrix H and the observed 【number】 By inputting this into the encoder, and using multiple attention layers and normalization, the model can dynamically focus on information between different features in the input feature sequence. In the multi-attention layer, the solar radiation index F at each time point ｍ，ｕ , geomagnetic index Dst ｍ，ｕ and K ｍ，ｕ Noise S ｕ Linearizing each of them gives the Query vector Q ｉ Key vector K ｉ , Value vector V ｉ obtain, p i This indicates the i-th feature, [Math 12] And, [Number 13] And, [Number 14] And, Eventually, 【number】 This is the weight matrix of the linear transformation, which is the model parameter and is updated incrementally during model training. Normalization involves applying the following process to each feature, where x is the feature, μ is the feature mean, and σ is the feature standard deviation. 【number】 This is the normalized result, The original feature information is retained, and in the subsequent synthesis process, each feature has the same scale. [Number 15] And, After inputting three vectors for each feature into the normalized result, the attention score `scores` is calculated, of which `softmax` is the normalization function, and d ｋ This is a vector dimension, and it is further weighted and added to the value vector to obtain attention output A. ｐ，ｉ This output embodies the weight information between different features, and these are further combined to form the total attention output A. ｐ Obtained, f ｃｏｎｃａｔ It is a composite function, [Number 16] And, [Number 17] And, [Number 18] And, Next, the encoder's extracted feature information and the previous output sequence are input to the decoder, and due to the mask's multi-attention layer restriction, only the generated sequence is accessed, and the feature information and 【number】 A mapping relationship F(H) is established and shown below, [Number 19] And, Eventually, １ ,・・・, l ｋ The method for predicting VTEC values ​​based on the LSTM-Transformer model described in claim 7, characterized by a new feature of model training.

9. In step 5, the LSTM-Transformer combination prediction model from step 4 is trained using the training set and optimized using the loss function. [Number 20] And, [Math 21] And, Eventually, LOSS ｂｉａｓ This shows the loss function with bias as the indicator, LOSS Ｒｍｓ This shows the loss function with Rms as the indicator, and VTEC ＧＮＳＳ This indicates the GNSS-VTEC value, and VTEC ｍ The VTEC value prediction method based on the LSTM-Transformer model according to claim 8, characterized in that represents the VTEC value predicted by the model, i represents the i-th puncture point, and n is the total number of puncture points.

10. In step 5, the historical VTEC value and the solar radiation index F ｍ , geomagnetic activity index DSt ｍ _K ｐ，ｍ A VTEC value prediction method based on an LSTM-Transformer model according to claim 8, characterized by using to predict future VTEC values ​​and outputting model-predicted VTEC values.

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