Ionospheric TEC Prediction Model Incorporating Dual Mechanisms of Comprehensive Self-Attention and Self-Correlation

Abstract

The present invention provides an ionospheric TEC prediction model that combines self-attention and self-correlation dual mechanisms, belonging to the technical field of ionospheric delay prediction. The model includes: a trend prediction module, a correlation analysis module, and a sequence fusion module. Among them, the trend prediction module predicts the overall change trends of the ionospheric TEC sequence and the space environment parameters respectively by means of a self-correlation operation mechanism. The correlation analysis module uses the self-attention mechanism to analyze the mutual connections among the ionospheric TEC sequence, the space environment parameters, and the latitude and longitude positions. The sequence fusion module then uses the correlation information obtained by the correlation analysis module to further integrate and optimize the overall trend of the ionospheric TEC sequence, and finally obtains the ionospheric TEC prediction result that fuses the space environment and the latitude and longitude position information. The present invention makes full use of the space environment data and the latitude and longitude position information, greatly improving the accuracy of model prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of ionospheric delay prediction, and in particular relates to an ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms. Background Art

[0002] Ionospheric delay is one of the main factors causing satellite positioning errors, especially having a great impact on pseudorange single point positioning (SPP). The magnitude of ionospheric delay can be approximately expressed by the vertical total electron content (VTEC) of the ionosphere.

[0003] Currently, common classical ionospheric TEC models include: the broadcast ionospheric model (Klobuchar model) applied to GPS, the NeQuick model applied to the Galileo navigation system, and the global ionospheric TEC equivalent grid model, etc. In addition, there are also ionospheric TEC statistical prediction models constructed by means of traditional mathematical statistical methods, such as the linear time series model (LTS), the auto-regressive moving average model (ARMA), etc. In recent years, with the rise of deep learning technology, many new ionospheric TEC prediction models based on deep learning technologies such as RNN, LSTM, GAN, CNN-LSTM, Transformer, etc. have also been widely proposed and applied.

[0004] The prediction accuracy of traditional ionospheric TEC empirical models is relatively low because the traditional models have a small number of parameters and can only describe the changing trend of ionospheric TEC with relatively simple equations, and cannot well reflect the specific laws of ionospheric TEC in various regions and time periods. Many ionospheric TEC deep learning models emerging in recent years have increased the number of parameters of the models, and the accuracy has been improved compared with the traditional solutions. However, due to structural problems, the prediction effects of many models are unstable. They often have good prediction effects in the middle latitudes, but the prediction effects will significantly decline in the low latitudes and high latitudes.

[0005] The global ionospheric TEC equivalent grid model is equivalently generated from the observation results of each global station, but the spatial resolution is relatively low and cannot be specific to more refined grid points. Many model algorithms predict for the global ionospheric TEC equivalent grid. Such models have two disadvantages. One is that the prediction object is extended to two dimensions, significantly increasing the complexity; the other is that they rely on the global ionospheric TEC equivalent grid map and cannot be specific to any longitude and latitude position for the prediction of ionospheric TEC.

[0006] For deep neural network models, model training and prediction efficiency are crucial issues. In the past, many ionospheric TEC prediction models based on deep learning technology have been able to improve the prediction accuracy of ionospheric TEC by continuously increasing the number of parameters and model depth, but the consequence of doing so is that the training and prediction costs of the model have been significantly increased, especially many serial computing architectures based on recurrent neural networks. This type of model has many parameters, large amount of calculations, and low computing efficiency, and the computational cost and time cost are both high. Summary of the invention

[0007] The present invention uses deep learning technology to construct an ionospheric TEC prediction model that integrates the dual mechanisms of self-attention and self-correlation. In view of the ionospheric TEC prediction problem, the objectives of the present invention are mainly reflected in the following aspects:

[0008] 1. Improve prediction accuracy;

[0009] The present invention adopts deep learning technology to construct a model and reasonably increases the number of model parameters, so that the model can explore more complex ionospheric TEC variation laws and prevent the model from overfitting; the model cleverly integrates the dual mechanisms of self-attention and autocorrelation, and extracts the overall variation trend of ionospheric TEC with the help of autocorrelation operation. At the same time, the self-attention mechanism is used to analyze the relationship between ionospheric TEC, space environmental parameters and longitude and latitude positions, and deeply explores the influence of space environmental parameters and longitude and latitude positions on the variation law of ionospheric TEC, thereby improving the accuracy of ionospheric TEC prediction.

[0010] 2. Improve spatial resolution;

[0011] The present invention completely gets rid of the dependence on the global ionospheric TEC equivalent grid map by introducing specific latitude and longitude position information, and can predict the ionospheric TEC for any specified latitude and longitude position. The present invention uses the TEC data of sites distributed at different latitude and longitude positions around the world for model training, so that the model can learn the influence of latitude and longitude positions on the law of ionospheric TEC changes, rather than being limited to fixed grid points, thereby improving the spatial resolution.

[0012] 3. Reduce the amount of calculation and improve the calculation efficiency;

[0013] The present invention uses autocorrelation operation to predict the overall change trend of ionospheric TEC. Different from the serial operation of the general recurrent neural network prediction model, autocorrelation performs parallel operation in the sequence as a whole. This process requires fewer parameters and has higher operation efficiency, which can give full play to the parallel operation acceleration characteristics of GPU. In addition to the autocorrelation operation, the self-attention mechanism and the subsequent sequence fusion process also adopt a parallel operation structure. Therefore, this model will take up less running memory and achieve more accurate prediction results in a shorter operation time.

[0014] The technical solution of the present invention is: an ionospheric TEC prediction model that combines self-attention and self-correlation dual mechanisms. The model includes: a trend prediction module, a correlation analysis module, and a sequence fusion module. Among them,

[0015] The trend prediction module predicts the overall change trends of the ionospheric TEC sequence and space environment parameters respectively by means of a self-correlation operation mechanism. It includes: the trend prediction module receives a matrix composed of historical ionospheric TEC and space environment parameters as input, independently analyzes the change trends of the ionospheric TEC values and space environment parameters respectively by means of self-correlation operation, and outputs their predicted trend matrix ;

[0016] The correlation analysis module uses the self-attention mechanism to analyze the mutual connections among the ionospheric TEC sequence, space environment parameters, and longitude and latitude positions. It includes: the correlation analysis module receives a matrix composed of historical ionospheric TEC sequences, space environment parameters, and longitude and latitude as input, mines the relationships among the ionospheric TEC values, various space environment parameters, and longitude and latitude by means of the self-attention mechanism, and outputs a matrix containing their correlation relationships at each moment ;

[0017] The sequence fusion module then uses the correlation information obtained by the correlation analysis module to further integrate and optimize the overall trend of the ionospheric TEC sequence, and finally obtains the ionospheric TEC prediction result that integrates the space environment and longitude and latitude position information. It includes: the sequence fusion module simultaneously receives the output of the trend prediction module and the output of the correlation analysis module , and by means of the masked self-attention method, reasonably fuses the information contained in and , and finally outputs the predicted time series vector of the ionospheric TEC, with a length of L.

[0018] The present invention has the following beneficial effects:

[0019] 1. The present invention constructs a model by using deep learning technology, innovatively combines self-attention and self-correlation dual mechanisms. On the one hand, it uses self-correlation operation to efficiently predict the overall change trend of the ionospheric TEC. On the other hand, it uses the self-attention mechanism to deeply mine the mutual connections among the ionospheric TEC, space environment parameters, and longitude and latitude positions, and finally further integrates and optimizes the overall trend of the ionospheric TEC by means of the correlation information among the three, thereby making full use of the space environment data and longitude and latitude position information, and greatly improving the prediction accuracy of the model.

[0020] 2. The present invention uses the longitude and latitude position information as one of the model input data, and analyzes the influence of the longitude and latitude position on the variation law of ionospheric TEC by means of the self-attention mechanism, so that the model can perform corresponding ionospheric TEC prediction for any specified longitude and latitude position, thus getting rid of the dependence on the global ionospheric TEC equivalent grid map and improving the spatial resolution of the model prediction.

[0021] 3. The present invention completely abandons the previous scheme of using a recurrent neural network for serial operation to predict ionospheric TEC, and instead uses autocorrelation operation to perform parallel operation with the sequence as a whole unit, which greatly accelerates the prediction process of the overall change trend of ionospheric TEC. Similarly, all subsequent correlation analysis and sequence fusion operations also adopt parallel operation structures, which makes the number of parameters required by the entire model less, and the operation efficiency higher. At the same time, it is also more conducive to using devices such as GPUs for operation acceleration. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is the overall structural framework diagram of the model of the present invention;

[0023] Figure 2 is the detailed structural diagram of the trend prediction module;

[0024] Figure 3 is the detailed structural diagram of the correlation analysis module;

[0025] Figure 4 is the detailed structural diagram of the sequence fusion module. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, the present invention adopts the following technical solutions.

[0027] The present invention proposes an ionospheric TEC prediction model that combines the dual mechanisms of self-attention and autocorrelation. The model takes the preprocessed data of a total of 9 items, namely the ionospheric TEC in the past 24 hours, the geomagnetic index (Dst), the ap index, the F10.7 index, the sunspot number (SSN), the X-ray index (X-ray), the D-region absorption prediction (D-RAP), latitude, and longitude, as inputs, and outputs the ionospheric TEC prediction sequence for the next 24 hours.

[0028] The model consists of three major modules: the Trend Prediction Module, the Relation Analysis Module, and the Series Merging Module. The Trend Prediction Module predicts the overall change trends of the ionospheric TEC and space environment parameters respectively by means of an autocorrelation operation mechanism; the Relation Analysis Module analyzes the interrelationships among the ionospheric TEC, space environment parameters, and latitude and longitude positions using the self-attention mechanism; the Series Merging Module then uses the correlation information obtained by the Relation Analysis Module to further integrate and optimize the overall trend of the ionospheric TEC, and finally obtains the prediction result of the ionospheric TEC that fuses the space environment and latitude and longitude position information.

[0029] 1. Input data

[0030] The data that the model needs to input are: ionospheric TEC, geomagnetic index (Dst), ap index, F10.7 index, sunspot number (SSN), X-ray index (X-ray), D-region absorption prediction data (D-RAP), latitude, and longitude, a total of 9 items of data.

[0031] (1) Data description

[0032] Ionospheric TEC: The average value of the vertical TEC (VTEC) of the ionosphere at the satellite piercing point above the station or within the specified area, with a time resolution of 30 minutes, and the data within one day forms a time series with a length of 48.

[0033] Space environment parameters: geomagnetic index (Dst), ap index, F10.7 index, sunspot number (SSN), X-ray index (X-ray), D-region absorption prediction (D-RAP), a total of 6 items. The spatio-temporal resolutions of the original data are not uniform, and interpolation or mean processing needs to be carried out separately to make their spatio-temporal resolutions consistent with the ionospheric TEC data. These 5 items of data, namely the geomagnetic index, ap index, F10.7 index, sunspot number, and X-ray index, are one-dimensional time series, while the D-region absorption prediction data is given in the form of a global grid, and specific values need to be assigned according to different latitudes and longitudes. The specific spatio-temporal resolutions of the space environment parameters are shown in Table 1.

[0034] Latitude and longitude: The latitude and longitude of the station or the center of the specified area, indicating the geographical location of the area.

[0035] Table 1 Spatio-temporal resolutions of space environment parameters

[0036]

[0037] (2) Data preprocessing

[0038] The units of the seven items of data, namely ionospheric TEC, geomagnetic index, ap index, F10.7 index, sunspot number, X-ray index, and D-region absorption prediction data, are different, and there may be a large numerical gap between them, which affects model inference. Therefore, each item of data needs to be standardized separately so that the mean of each item of data is 0 and the variance is 1. The standardization formula is Equation (1):

[0039] (1)

[0040] where represents the mean value, represents the standard deviation, is the value after standardization, is the data to be processed.

[0041] The longitude and latitude are normalized. The longitude range [-180, 180] and the latitude range [-90, 90] are scaled to the range [-1, 1]. The normalization formula is Equation (2):

[0042] (2)

[0043] where is the value after normalization, is the data to be processed, is the maximum value, is the minimum value. The nine preprocessed time series data are combined into a matrix , Each row represents one item of data, with a total of 9 rows; each column represents the data of each item at a certain moment, with a total of columns. The matrix will be used as the final input data format of this algorithm model. This algorithm recommends setting the first row as the time series data of ionospheric TEC, the last two rows as longitude and latitude data respectively, and the middle six rows as the time series data of various space environment parameters, so as to facilitate the design of subsequent masks.

[0044] 2. Model Structure

[0045] This model is generally divided into three major modules: the Trend Prediction Module, the Relation Analysis Module, and the Series Merging Module. Figure 1 Shows the interconnections between the three major modules of this model.

[0046] The Trend Prediction Module receives the matrix composed of historical ionospheric TEC values and space environment parameters As input, the changing trends of the ionospheric TEC values and the space environment parameters are independently analyzed by means of autocorrelation operation, and their approximate prediction trends are output 。

[0047] The correlation analysis module receives a matrix composed of historical ionospheric TEC values, space environment parameters, and longitude and latitude As input, the relationships among the ionospheric TEC values, various space environment parameters, and longitude and latitude are mined by means of self-attention mechanism, and a matrix containing their correlation relationships at each moment is output 。

[0048] The sequence fusion module simultaneously receives the output of the trend prediction module and the output of the correlation analysis module ,and by means of a special masked self-attention method, the and contained information is reasonably fused together, and finally a predicted time series vector of the ionospheric TEC is output ,with a prediction length of L

[0049] (1) Structural details of the trend prediction module

[0050] The main function of the trend prediction module is to analyze the changing trends of the ionospheric TEC values and various space environment parameters over time. Its core algorithms are autocorrelation operation (Auto-Correlation) and series decomposition (SeriesDecomposition), and at the same time, a feed-forward neural network (Feed-Forward Network) is used to add variable parameters to increase the model complexity. The specific details of the trend module are as Figure 2 shown

[0051] The trend prediction module is composed of N layers in series as a whole, and the internal structure of each layer is the same. The specific process is as follows: the input data first passes through the autocorrelation operation unit, and then through the series decomposition unit to obtain the trend component (Trend) and the periodic component (Season). The periodic component passes through the feed-forward neural network and then undergoes another series decomposition. The trend components obtained from the two series decompositions are weighted and summed, and then the trend component and the periodic component enter the next layer respectively. There is a skip connection addition after the data passes through the autocorrelation operation unit and the feed-forward neural network. The trend component and the periodic component output by the last layer are added to the mean value of the original input data to obtain the final output ,that is

[0052] (3)

[0053] ① Autocorrelation operation

[0054] Input data First, perform three different linear layer mappings to form three data matrices of Q, K, and V respectively, and solve them with the Fast Fourier Transform (FFT) and the Inverse Fourier Transform (IFFT). The autocorrelation function after mapping :

[0055] (4)

[0056] After that, find the time shift amounts corresponding to the top k largest values in :

[0057] (5)

[0058] Among them, arg TopK is to find the top k largest values; calculate the weights corresponding to the vectors after these k time shifts through the Softmax function :

[0059] (6)

[0060] Denote as the time series data V circularly time shifted The output of the autocorrelation operation module can be expressed as:

[0061] (7)

[0062] It should be noted that in the whole process, each row in the three data matrices of Q, K, and V is independent and parallelly operated, and the amount of time shift required for each row in the V matrix is not necessarily the same.

[0063] ② Sequence decomposition

[0064] The sequence decomposition module smooths the input data by means of moving average to obtain the trend component and the periodic component . The moving average process can be completed through the average pooling operation (AvgPool). To keep the time series length unchanged, padding needs to be performed on both sides of the time series first. The process is shown in Equation (8):

[0065] (8)

[0066] (2) Structural details of the correlation analysis module

[0067] The main function of the correlation analysis module is to explore the interrelationships among the ionospheric TEC, various space environment parameters, and the latitude and longitude positions. Its core algorithm is the self-attention mechanism, and a feed-forward neural network is also used to increase the complexity. The specific structure is shown in Figure 3 .

[0068] The correlation analysis module is overall composed of M layers in series. Each layer has the same structure but different specific parameters. The specific execution process of each layer is as follows: Input the data matrix composed of ionospheric TEC values, space environment parameters, and latitude and longitude , First, pass through the Masked Self-Attention unit, and perform skip connection and layer normalization (Add& LayerNorm). Then, pass through the FeedForward neural network. Finally, perform skip connection and layer normalization and output to the next layer. The output of the last layer is the correlation information matrix of each item of data . The overall process of each layer in the correlation analysis module is Equation (9):

[0069] (9)

[0070] Among them, represents the input data of each layer in the correlation analysis module, represents the intermediate variable after passing through the Masked Self-Attention unit and layer normalization, represents the output data of each layer.

[0071] ① Masked Self-Attention unit

[0072] Input data First, perform three different linear layer mappings to form three data matrices of Q, K, and V respectively. Then, calculate the attention matrix A using Q and K. Then, add the mask Mask(A). Then, calculate the weights corresponding to each row of Mask(A) using the Softmax function. Finally, multiply by the V matrix. The process is as Equation (10):

[0073] (10)

[0074] Among them, is the scaling factor, equal to the sequence length. The multi-head structure is adopted in the self-attention unit. The above process is independently executed in each head. The process is the same, but the parameters are different, which improves the model complexity and enables the model to learn more complex structures.

[0075] ② Mask design

[0076] In the self-attention unit, a suitable mask needs to be added. The three assumptions based on which the mask is constructed are as follows: The variation law of the ionospheric TEC value is affected by the latitude and longitude positions and various space environment parameters; various space environment parameters affect each other and are affected by the latitude and longitude positions, but not by the ionospheric TEC value; the latitude and longitude are not affected by any factors because it is a fixed value.

[0077] To ensure that the above three assumptions can be realized, it is necessary to set a suitable mask to mask certain values in the attention matrix A. A certain row in the attention matrix represents the influence of other row data on this row of data. For example, represents the influence of the data in the j-th row on the data in the i-th row. Then, if the data in the j-th row has no influence on the data in the i-th row itself, then needs to be masked with the mask. Generally, the common practice is to mark it as negative infinity, so that the corresponding weight after passing through the Softmax function is 0.

[0078] According to the suggestions in the previous data processing process, assume that the input data The first row is the time series data of the ionospheric TEC, the last two rows are the latitude and longitude data respectively, and the middle 6 rows are the time series data of various space environment parameters. Then, a mask matrix with the same size as the attention matrix A can be designed first . According to the design requirements of the mask matrix, the mask matrix The specific values are as shown in Equation (11):

[0079] (11)

[0080] According to the value of the matrix , the attention matrix is processed in the way of Equation (12):

[0081] (12)

[0082] (3) Structural details of the sequence fusion module

[0083] The main task of the sequence fusion module is to fuse the trend information predicted by the trend prediction module and the correlation information between various data mined by the correlation analysis module together, and finally output the prediction sequence of the ionospheric TEC , where L is the target prediction length. The core structure of the sequence fusion module is the self-attention mechanism, and it fuses various data with the help of a linear fully connected layer, and at the same time adds a skip connection to keep the mean value of the prediction sequence stable. Figure 4 shows the specific structure of the sequence fusion module.

[0084] The trend information predicted by the trend prediction module Concatenate the longitude and latitude data to form so that it has the same dimension as the correlation information output by the correlation analysis module At the same time, as Q and K, they are input into the fusion self-attention unit, while is used as K to input into the fusion self-attention unit. The output of the fusion self-attention unit is denoted as Remove the longitude and latitude two rows of data in to obtain and then add it to to get : :

[0085] (13)

[0086] After that, through layer normalization, and with the help of a linear layer, weighted sum each row of to get :

[0087] (14)

[0088] The initially input trend information In it, the time series corresponding to the ionospheric TEC is denoted as Add to and obtain the final ionospheric TEC prediction sequence through time series smoothing :

[0089] (15)

[0090] In the process of the sequence fusion module, two skip connection operations are performed. The main purpose is to maintain the time series mean, because the fusion self-attention unit may cause a large change in the time series mean, while the layer normalization operation forces the time series mean to be 0.

[0091] ① Fusion self-attention unit

[0092] The fusion self-attention unit is basically the same as the masked self-attention unit in the correlation analysis module, and the added masks are also the same. The difference is that the generation of the V data matrix of the fusion self-attention unit does not require linear mapping.

[0093] Since the added masks of the two modules are the same, so in the output of the fusion self-attention unit: the time series corresponding to the ionospheric TEC is composed of Obtained by weighting all 9 lines of data; the time series corresponding to the space environment parameters is obtained by weighting the remaining 8 lines of data except for the sequence corresponding to the ionospheric TEC; the longitude and latitude data remains unchanged. At this time, the longitude and latitude information has been integrated into each item of data, so the longitude and latitude data does not participate in the fusion during subsequent linear weighted fusion.

[0094] ② Time series smoothing

[0095] The time series smoothing operation is mainly to eliminate high-frequency noise and make the output prediction data smoother. Practice has proved that without adding time series smoothing, there will be more "spiky" phenomena in the prediction sequence.

[0096] 3. Training and prediction

[0097] This algorithm model is a deep neural network model, so it needs to be trained with a large amount of data first, and then the prediction of the ionospheric TEC time series can be carried out.

[0098] The key points in model training are as follows:

[0099] (1) Data selection and processing

[0100] In order to learn the influence of longitude and latitude on the ionospheric TEC, when selecting data, it is necessary to involve data from different longitude and latitude regions around the world as much as possible. If the data in the observation site area is used as the training set, the selected sites should be distributed as evenly as possible.

[0101] Due to the different resolutions of the space environment data, data preprocessing needs to perform interpolation or mean processing on the space environment data. The resolutions of many space environment parameters are 1 day or 1 hour, so the overall resolution should not be too low, preferably in the range of 10 - 30 minutes.

[0102] (2) Model training parameters

[0103] When setting the model hyperparameters, the number of layers in the trend prediction module should preferably be more than that in the correlation analysis module. After testing, when the number of layers in the trend prediction module is 6 and the number of layers in the correlation analysis module is 4, the effect is better. The model is recommended to be optimized using the Adam algorithm, and the learning rate is set to , and an exponentially decaying dynamic learning rate can be used to gradually reduce the learning rate during training. After testing, the model can be trained smoothly and quickly on an NVIDIA RTX3080 graphics card (10G video memory), and the requirements for hardware are not high. The specific parameter details of model training are shown in Table 2.

[0104] Table 2 Details of model training parameters

[0105]

Claims

1. An ionospheric TEC prediction model integrating self-attention and autocorrelation mechanisms, characterized by: The model includes: a trend prediction module, a correlation analysis module and a sequence fusion module; wherein, The trend prediction module uses the autocorrelation operation mechanism to predict the overall change trend of the ionospheric TEC sequence and the space environment parameters; including: the trend prediction module receives the matrix composed of historical ionospheric TEC and space environment parameters As input, the ionospheric TEC value and the space environment parameters are analyzed independently by autocorrelation operation, and their prediction trend matrix is ​​output. ; The trend forecast module consists of The internal structure of each layer is the same. The specific process is as follows: input data , first through the autocorrelation operation unit, and then through the sequence decomposition unit to obtain the trend component Trend and the periodic component Season, the periodic component is decomposed again after passing through the feedforward neural network, the trend components of the two sequence decompositions are weighted summed, and then the trend component and the periodic component enter the next layer respectively. After the data passes through the autocorrelation operation unit and the feedforward neural network, there is a skip connection addition, and the trend component output by the last layer and periodic component , and the mean of the original input data Add together to get the final output ,Right now: (3) The correlation analysis module uses the self-attention mechanism to analyze the relationship between the ionospheric TEC sequence, space environment parameters and longitude and latitude positions; including: the correlation analysis module receives the matrix composed of historical ionospheric TEC sequence, space environment parameters and longitude and latitude As input, the self-attention mechanism is used to mine the relationship between the ionospheric TEC value, various spatial environmental parameters and longitude and latitude, and the matrix containing their correlation at each moment is output. ; The sequence fusion module uses the correlation information obtained by the correlation analysis module to further integrate and optimize the overall trend of the ionospheric TEC sequence, and finally obtains the ionospheric TEC prediction result that integrates the space environment and longitude and latitude position information; including: the sequence fusion module simultaneously receives the output of the trend prediction module Output of the correlation analysis module , using the masked self-attention method, and The information contained is integrated together to finally output the predicted time series vector of ionospheric TEC , the prediction length is L; the model takes 9 pre-processed data of the historical 24-hour ionospheric TEC, geomagnetic index Dst, ap index, F10.7 index, sunspot number SSN, X-ray index X-ray, D-region absorption prediction D-RAP, latitude and longitude as input, and outputs the ionospheric TEC prediction sequence for the next 24 hours; The autocorrelation operation is as follows: Input Data First, three different linear layer mappings are performed to form three data matrices Q, K, and V respectively, and then the fast Fourier transform FFT and inverse Fourier transform IFFT are used to solve Autocorrelation function after mapping : (4) Afterwards, find The time shift corresponding to the largest value of k in the front : (5) Among them, arg TopK is to find the top k largest values; the weights corresponding to these k time-shifted vectors are calculated through the Softmax function : (6) remember Indicates that the time series data V is cyclically shifted The output of the autocorrelation operation module is expressed as follows: (7) During the whole process, each row in the three data matrices Q, K, and V is independent of each other and is calculated in parallel.

2. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 1, characterized in that: Ionospheric TEC is: the average value of the vertical TEC of the ionosphere at the satellite penetration point above the station or in the specified area, with a time resolution of 30 minutes, and the data within one day are formed into a time series of length 48; The space environment parameters include: geomagnetic index Dst, ap index, F10.7 index, sunspot number SSN, X-ray index X-ray, D-region absorption prediction D-RAP; the space environment parameters are processed by difference or mean respectively to make their temporal and spatial resolution consistent with the ionospheric TEC series. The geomagnetic index, ap index, F10.7 index, sunspot number, and X-ray index are all one-dimensional time series, while the D-region absorption prediction data are given in the form of a global grid, and specific values ​​are assigned according to different longitudes and latitudes. Latitude and longitude are: the latitude and longitude of the site or the center of a specified area, indicating the geographical location of the area.

3. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 2, characterized in that: The ionospheric TEC, geomagnetic index, ap index, F10.7 index, sunspot number, X-ray index, and D-region absorption prediction data are standardized so that the mean of each data item is 0 and the variance is 1. The standardized formula is formula (1): (1) in, represents the mean, represents standard deviation; is the standardized value, The data to be processed; The longitude and latitude are normalized, scaling the longitude range [-180, 180] and the latitude range [-90, 90] to the range [-1, 1]. The normalization formula is formula (2): (2) in, is the normalized value, For the data to be processed, is the maximum value, As the minimum value, the preprocessed time series data is merged into a matrix , Each row represents a data, a total of 9 rows; each column represents the data of a moment, a total of List.

4. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 3, characterized in that: The sequence decomposition is as follows: Smoothing input data using the sliding average method , thus obtaining the trend component and periodic component The sliding average process is completed through the average pooling operation AvgPool. Padding is first performed on both sides of the time series. The process is shown in formula (8): (8)。 5. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 4, characterized in that: The correlation analysis module consists of The layers are connected in series, each layer has the same structure but different specific parameters. The specific execution process of each layer is as follows: input the data matrix composed of ionospheric TEC value, space environment parameters and longitude and latitude , First, it passes through the masked self-attention unit Self-Attention, and performs skip connection and layer normalization Add & LayerNorm, then passes through the feedforward neural network FeedForward, and finally performs skip connection and layer normalization before outputting to the next layer. The output of the last layer is the relevant information matrix of each data , the overall process is formula (9): (9) in, Represents the input data of each layer in the correlation analysis module, express Through the masked self-attention unit and the intermediate variable after layer normalization, Represents the output data of each layer.

6. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 5, characterized in that: The masked self-attention unit is specifically: Input Data First, three different linear layer mappings are performed to form three data matrices Q, K, and V respectively. Then, the attention matrix A is calculated using Q and K, and then the mask Mask(A) is added. The Softmax function is used to calculate the weight corresponding to each row of Mask(A), and finally multiplied by the V matrix. The process is as shown in formula (10): (10) in, is the scaling factor, which is equal to the time series length; Add a mask to the self-attention unit and design a mask matrix of the same size as the attention matrix A , according to the design requirements of the mask matrix, the mask matrix The specific values ​​are as shown in formula (11): (11) According to the matrix The value of attention matrix Process it in the way of formula (12): (12)。 7. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 6, characterized in that: Trend information predicted by the trend prediction module Cascade the latitude and longitude data to form , thus the relevant information output by the correlation analysis module The dimensions are the same, At the same time, it is used as the input of Q and K to fuse the self-attention unit, and Then K is used as the input of the fused self-attention unit, and the output of the fused self-attention unit is recorded as , remove The two rows of longitude and latitude data in , and then with Add together to get : (13) Then, it is normalized by layer and transformed into The weighted sum of each row of : (14) Initially entered trend information In the above example, the time series corresponding to the ionospheric TEC is recorded as ,Will and Add and smooth the time series to get the final ionospheric TEC prediction sequence : (15)。 8. The ionospheric TEC prediction model integrating self-attention and autocorrelation dual mechanisms according to claim 7, characterized in that: The fused self-attention unit is the same as the masked self-attention unit in the correlation analysis module, and the added mask is the same, wherein the generation of the V data matrix of the fused self-attention unit does not require linear mapping.

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