Sky wave communication F2 layer critical frequency prediction method and system

Abstract

The invention relates to a sky wave communication F2 layer critical frequency prediction (foF2) method and system. Firstly, ionosphere foF2 historical observation data and multi-source environment parameters in the global range are obtained, and the most representative input characteristics are obtained through screening by comprehensively analyzing the correlation between foF2 and multi-source space environment driving factors under the conditions of different latitudes and different local time. Then, a space-time cross gating mechanism is introduced, feature enhancement and dynamic weight adjustment are carried out on space position embedding, a driving parameter sequence and a historical foF2 sequence, and self-adaptive extraction of key change factors of the ionized layer is achieved. And then, by constructing a Transform network structure based on a multi-head self-attention mechanism, carrying out long-time dependence modeling on ionosphere spatio-temporal evolution in a global range so as to obtain a global foF2 distribution prediction result at a future moment. According to the method, the foF2 prediction precision of low-weft, middle-weft and high-weft regions can be remarkably improved, and available frequency planning and reliability evaluation of a sky wave communication link are improved.

Description

Technical Field

[0001] This invention relates to the fields of skywave communication and ionospheric prediction technology, specifically to a method and system for predicting the critical frequency of the F2 layer in skywave communication. This method belongs to the fields of space environment monitoring, ionospheric modeling, and radio communication frequency planning, and can be used for frequency management and link stability assurance in medium- and long-distance skywave communication. Background Technology

[0002] Skywave communication, operating in the 3–30MHz frequency band, is a key technology in medium- to long-range wireless communication. Due to its advantages such as flexible deployment, low infrastructure requirements, and ability to operate independently of terrestrial or satellite networks, skywave communication has significant application value in disaster relief, long-range communication on maritime and air platforms, and beyond-line-of-sight military operations. Skywave signals propagate primarily through two mechanisms: ground waves and sky waves. Skywaves, relying on ionospheric reflection, can achieve long-distance transmission over thousands of kilometers, making them particularly suitable for communication in environments where satellite links are limited or unavailable. However, the ionosphere exhibits significant spatiotemporal dynamics; its electron density distribution is affected by various factors such as diurnal variations, seasonal variations, solar activity, and geomagnetic disturbances, resulting in highly unstable propagation paths and making skywave channels one of the most uncertain wireless propagation environments. Therefore, accurate characterization and real-time forecasting of the ionospheric state, especially the F2 layer critical frequency (foF2), are crucial for frequency management and link reliability in skywave communication. Despite significant advancements in physical layer technologies such as Multiple-Input Multiple-Output (MIMO) in recent years, which have improved skywave link performance, their actual effectiveness still relies on accurate prediction of the highest available frequency (MUF). Under conditions of drastic ionospheric changes, traditional empirical models such as IRI struggle to meet the demands for real-time, high-precision prediction. With the development of artificial intelligence and deep learning, neural network-based models have demonstrated the ability to extract ionospheric nonlinearity and spatiotemporal dependent structures, achieving superior performance to traditional models in foF2 prediction. However, most existing methods are designed for single stations or local areas, lacking the ability to model the spatiotemporal evolution of the ionosphere on a global scale, thus limiting their application in global skywave communication systems. To address this deficiency, it is necessary to construct a global prediction model capable of handling the spatiotemporal dynamics of the ionosphere under different latitudes to support the frequency management needs of skywave communication worldwide. Summary of the Invention

[0003] Purpose of the Invention: The purpose of this invention is to provide a method and system for predicting the critical frequency of the F2 layer in skywave communication, so as to accurately model the complex spatiotemporal changes of the ionosphere, improve the global foF2 prediction accuracy, enhance the generalization ability of foF2 prediction in multi-latitude regions and under disturbance conditions, and solve the problem that existing empirical models and traditional machine learning models are unable to effectively characterize the nonlinear spatiotemporal evolution characteristics of the ionosphere under the combined effects of solar radiation, geomagnetic activity, seasonal changes and geographical factors, which leads to a significant decrease in prediction performance during ionospheric disturbances or strong solar activity, thereby affecting the reliability of skywave communication links.

[0004] Technical Solution: To achieve the above objectives, the present invention provides a method for predicting the critical frequency of the F2 layer in skywave communication, comprising the following steps:

[0005] We acquire historical observation data of the ionosphere foF2 from around the world, as well as multi-source environmental parameters including solar activity index, geomagnetic disturbance index and geographic location information, and construct a multi-source input dataset for spatiotemporal prediction.

[0006] Based on the correlation analysis results between foF2 and various driving factors under different latitudes, the key features that best reflect the spatiotemporal variation characteristics of the ionosphere are selected from multi-source environmental parameters to form the optimal feature input set.

[0007] Geographic embedding vectors are obtained by embedding geographic location information. Time series features are obtained by embedding and location encoding the selected solar and geomagnetic driving parameters and historical foF2 sequences. A spatiotemporal cross-gating mechanism is used to perform cross-attention joint feature extraction on geographic embedding vectors and time series features. The time series features and the cross-attention output of geographic embedding vectors and time series features are dynamically fused through an adaptive weight gating structure to obtain the fused spatiotemporal features.

[0008] A Transformer model based on a self-attention mechanism is constructed. The fused spatiotemporal features are input, and the cross-regional and cross-time correlation information is captured through a multi-head attention structure to generate foF2 prediction results for future time moments.

[0009] Furthermore, based on the correlation analysis results between foF2 and various driving factors under different latitude conditions, the key features that best reflect the spatiotemporal variation characteristics of the ionosphere are selected from multi-source environmental parameters to form an optimal feature input set, including:

[0010] Correlation analysis was conducted on foF2 and each driving factor in different latitudinal regions, including calculating the linear correlation between each driving factor and foF2 using the Pearson correlation coefficient.

[0011] Based on correlation values, in low-latitude regions, foF2 and Solar flux, Radiation is correlated with sunspot number; in mid-latitude regions, foF2 is correlated with the AE index, AL index, and Dst index; in high-latitude regions, foF2 is correlated with the AE index, AL index, AU index, and IMT-Bz index. It is related to solar flux, Kp index, pc index, and ap index;

[0012] The key feature screening results from different latitude regions are merged to form the optimal feature input set.

[0013] Furthermore, the optimal feature input set includes the IMT-Bz index, Kp index, sunspot number, Dst index, and ap index. Solar flux, AE index, AL index, AU index, PC index A set consisting of radiation and the critical frequency of foF2.

[0014] Furthermore, the embedding of geographic location information to obtain a geographic embedding vector includes: embedding a feature vector containing longitude and latitude. Geographic embedding vectors are obtained by projection through a multi-layer feedforward network with hidden layers. in , , , For learnable parameters, , To hide dimensions, For GELU activation function, The normalization operator; the embedding and location encoding of the selected solar and geomagnetic driving parameters and historical foF2 sequences to obtain time series features includes: embedding time series samples containing the selected solar and geomagnetic driving parameters and historical foF2 sequences. The projection is obtained through a multi-layer feedforward network with hidden layers. in , , , For learnable parameters, For the input feature dimension, , To hide the dimension, temporal location encoding is performed to obtain time-series features containing location information. in This is a position encoding function.

[0015] Furthermore, the cross-attention joint feature extraction of geographic embedding vectors and time series features includes: using time series features For query , with geographic embedding vector For key Sum Calculate attention to obtain cross-attention output in It is a vector of all 1s. For the dimension of attention head, The number of heads for multi-head attention. For model dimensions.

[0016] Furthermore, the step of dynamically fusing time-series features and geographic embedding vectors with time-series features across attention output through an adaptive weight gating structure to obtain fused spatiotemporal features includes: defining the adaptive gating as... in It is the Sigmoid activation function. For the gated parameter matrix, As the bias term; the fused spatiotemporal features are represented as follows: Among the symbols This indicates element-wise multiplication.

[0017] Furthermore, the Transformer model based on the self-attention mechanism includes an encoder composed of stacked identical Transformer layers, each layer containing a multi-head self-attention mechanism and a positional feedforward network; the encoder's response to the fused spatiotemporal features of the input... The final hidden representation is generated through a series of sequentially stacked Transformer networks. Each Transformer layer employs a pre-normalization strategy, performing layer normalization before the self-attention module and the feedforward network module. The input and attention output are connected via residual connections, then undergo another layer normalization before being fed into a position feedforward network consisting of two linear transformation layers and intermediate GELU activations. Finally, the output of each Transformer layer is obtained through residual connections. (Encoder output) The input is fed into a lightweight decoder consisting of two multilayer perceptrons, and the decoder output is the foF2 prediction result for the future time.

[0018] The present invention provides a critical frequency prediction system for F2 layer of skywave communication, used to implement the aforementioned critical frequency prediction method for F2 layer of skywave communication, comprising:

[0019] The dataset construction module is used to acquire historical observation data of the ionosphere foF2 from around the world, as well as multi-source environmental parameters including solar activity index, geomagnetic disturbance index and geographic location information, to construct a multi-source input dataset for spatiotemporal prediction.

[0020] The feature selection module is used to select the key features that best reflect the spatiotemporal variation characteristics of the ionosphere from multi-source environmental parameters based on the correlation analysis results between foF2 and various driving factors under different latitude conditions, and form the optimal feature input set.

[0021] The spatiotemporal feature fusion module is used to embed geographic location information to obtain geographic embedding vectors, embed and encode the selected solar and geomagnetic driving parameters and historical foF2 sequences to obtain time series features, and use a spatiotemporal cross-gating mechanism to perform cross-attention joint feature extraction on geographic embedding vectors and time series features. Through an adaptive weight gating structure, the time series features and the cross-attention output of geographic embedding vectors and time series features are dynamically fused to obtain the fused spatiotemporal features.

[0022] The prediction module is used to build a Transformer model based on a self-attention mechanism. It takes the fused spatiotemporal features as input, captures cross-regional and cross-time correlation information through a multi-head attention structure, and generates foF2 prediction results for future time moments.

[0023] Furthermore, the system can be deployed in a ground-based numerical weather prediction center or a skywave communication frequency management system.

[0024] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for predicting the critical frequency of the F2 layer in skywave communication.

[0025] Beneficial Effects: This invention, by introducing a spatiotemporal cross-gating mechanism and combining it with the self-attention structure of Transformer, achieves efficient fusion and long-range dependency modeling of ionospheric spatiotemporal features. It can accurately model complex spatiotemporal variations of the ionosphere, significantly improving the prediction accuracy of foF2 under complex spatial environments. Simultaneously, by performing correlation analysis on the multi-source driving factors of foF2 under different latitudinal conditions, this invention forms an optimal feature input set, enhancing the generalization ability of foF2 prediction in multi-latitudinal regions and under perturbation conditions. It constructs a unified global prediction model, reducing the complexity of traditional models when modeling globally, improving computational efficiency, and thus effectively supporting real-time frequency management and link assurance in high-frequency communication systems. Experiments show that this invention can effectively capture ionospheric behavior, maintain stable prediction performance with fewer model parameters, significantly improve the foF2 prediction accuracy in low, mid, and high latitude regions, improve available frequency planning and reliability assessment of skywave communication links, and reduce dependence on traditional empirical models. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating an embodiment of the present invention.

[0027] Figure 2 This is a correlation analysis diagram of the parameters in an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram of STCGT in an embodiment of the present invention.

[0029] Figure 4 The image shows the results of the ablation experiment of STCGT in this embodiment of the invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] like Figure 1 As shown in the figure, an embodiment of the present invention discloses a method for predicting the critical frequency of the F2 layer in skywave communication, including the following steps:

[0032] S1. Obtain historical observation data of the ionosphere foF2 from around the world, as well as multi-source environmental parameters including solar activity index, geomagnetic disturbance index and geographic location information, and construct a multi-source input dataset for spatiotemporal prediction;

[0033] S2. Based on the correlation analysis results between foF2 and various driving factors under different latitudes, the key features that best reflect the spatiotemporal variation characteristics of the ionosphere are selected from the multi-source environmental parameters to form the optimal feature input set.

[0034] S3. Geographic embedding vectors are obtained by embedding geographic location information. Time series features are obtained by embedding and location encoding the selected solar and geomagnetic driving parameters and historical foF2 sequences. A spatiotemporal cross-gating mechanism is used to perform cross-attention joint feature extraction on geographic embedding vectors and time series features. The time series features and geographic embedding vectors and time series features are dynamically fused through an adaptive weight gating structure to obtain the fused spatiotemporal features.

[0035] S4. Construct a Transformer model based on a self-attention mechanism, input the fused spatiotemporal features, capture cross-regional and cross-time correlation information through a multi-head attention structure, and generate foF2 prediction results for future times.

[0036] The solution of this invention can be applied to frequency management and propagation environment assessment of skywave communication systems. First, this invention constructs a global spatiotemporal prediction modeling problem that integrates solar index, geomagnetic index, geographic features, and historical foF2 data. The input is structured according to the spatiotemporal distribution characteristics of the global ionosphere (e.g., constructing spatial feature vectors containing latitude and longitude) to adapt to subsequent deep learning model processing. Second, under different latitudinal conditions, this invention performs correlation analysis on the multi-source driving factors of foF2. By comparing the linear correlation between each exogenous parameter and foF2, the key input features most relevant to ionospheric changes are selected. Based on the analysis results of the correlation heatmap, an optimal feature set is constructed, providing a physically meaningful and data-driven reliable input for subsequent model learning. Next, this invention employs a spatiotemporal cross-gating mechanism to interactively fuse geographic embeddings, environmental driving parameters, and historical foF2 sequences. This mechanism achieves adaptive adjustment of the importance of temporal and spatial features through dynamic weight gating, enabling the model to effectively capture the complex spatiotemporal evolution of the ionosphere under different latitudes and geomagnetic disturbance levels, improving the effectiveness of input feature representation. Subsequently, a Transformer model based on a multi-head self-attention mechanism is constructed to learn the long-term dependence and cross-regional correlation of global ionospheric ionization degree changes. A multi-layer Transformer encoder captures multi-scale dynamic patterns of ionospheric variation over time and space, generating high-precision predictions of future foF2 changes, achieving comprehensive prediction and highly reliable frequency management of the future ionospheric propagation environment. The following section provides a more detailed explanation of the method in this embodiment using a specific scenario.

[0037] In step S2, the feature selection process specifically includes: performing correlation analysis on foF2 and each driving factor in different latitudinal regions, including calculating the linear correlation between each driving factor and foF2 using the Pearson correlation coefficient; and selecting based on the correlation values. In low-latitude regions, foF2 and... Solar flux, Radiation is correlated with sunspot number; in mid-latitude regions, foF2 is correlated with the AE index, AL index, and Dst index; in high-latitude regions, foF2 is correlated with the AE index, AL index, AU index, interplanetary magnetic field Bz component (IMT-Bz) index, The solar flux, Kp index, pc index, and ap index are correlated; the key feature screening results from different latitudinal regions are merged to form the optimal feature input set, specifically the IMT-Bz index, Kp index, sunspot number, Dst index, and ap index. Solar flux, AE index, AL index, AU index, PC index A set consisting of radiation and the critical frequency of foF2.

[0038] In this embodiment, a correlation heatmap was plotted to select appropriate exogenous parameters for foF2 prediction, showing the relationship between exogenous parameters and foF2. The correlation coefficient quantifies the relationship between variables. The heatmap provides a visual representation of these correlations, making it easier to identify patterns and relationships between variables. Strong correlations may indicate underlying relationships or dependencies between variables. This can help determine which variables in the dataset are most influential or redundant, thus enabling informed feature selection decisions. The Pearson correlation coefficient is shown below. Figure 2 As shown.

[0039] Given that existing empirical models and traditional machine learning models struggle to effectively characterize the nonlinear spatiotemporal evolution of the ionosphere under the combined influence of solar radiation, geomagnetic activity, seasonal variations, and geographical factors, prediction performance significantly degrades during ionospheric disturbances or strong solar activity, thus impacting the reliability of skywave communication links, this embodiment constructs a spatiotemporal cross-gated Transformer (STCGT) prediction model capable of accurately modeling complex spatiotemporal variations of the ionosphere, improving global foF2 prediction accuracy, and enhancing generalization capabilities across multi-latitude regions and under disturbance conditions.

[0040] Specifically, in step S3, the model achieves spatiotemporal information fusion through a spatiotemporal cross-gate mechanism. Its core components include a spatiotemporal cross-attention module and a dynamic gating fusion mechanism. The overall architecture is as follows: Figure 3 As shown. Let the sequence length be... Then define For IMT-Bz index, For Kp index, For the number of sunspots, For Dst index, For AP index, for Solar flux, For AE index, For AL index, For AU index, PC Index for radiation, This is the foF2 critical frequency. The input time series samples... Defined as

[0041]

[0042] in Geographic coordinates respectively and Defined as longitude and latitude. Geographic feature vector. for

[0043]

[0044] Time-based features are projected through a multi-layer feedforward network with hidden layers to capture temporal dependencies, as represented by the equation.

[0045]

[0046] in , , , These are learnable parameters. Input matrix First, it is projected into a hidden dimension. Then Dimensions are mapped to through fully connected layers. Dimension For GELU activation function, This is the normalization operator.

[0047] Similarly, spatial features composed of geographic information are also projected using a similar method.

[0048]

[0049] in , , , These are learnable parameters. Input vector First, it is projected onto the hidden dimension. Then Dimensions are mapped to through fully connected layers. Dimension For GELU activation function, This is the normalization operator.

[0050] Sine and cosine functions are used to construct smooth and periodic position information, so that different positions have unique codes, while ensuring that there is a smooth gradient of change between the codes of adjacent positions.

[0051] For each position and model dimensions Its position encoding is defined as

[0052]

[0053] in Indicates the position index. This serves as a dimensional index. Each dimension of the positional encoding corresponds to a sine function of a different frequency, with its wavelength range varying geometrically, from... Extend to .

[0054] After location encoding, the final input feature containing location information is:

[0055]

[0056] in This is a position encoding function.

[0057] To effectively integrate spatiotemporal information, this invention employs a cross-attention mechanism that uses temporal features as queries and spatial features as keys and values. This mechanism enhances the interaction between temporal and spatial features, helping the model better capture the dynamic relationships between them.

[0058] Cross-attention mechanism is defined as

[0059]

[0060] in Indicates time characteristics, and These represent spatial features. Cross-attention mechanisms enable models to capture long-range dependencies between temporal and spatial features.

[0061] The cross-attention output is calculated as follows:

[0062]

[0063] in It is a vector of all 1s. For the dimension of attention head, The number of heads receiving multi-head attention.

[0064] To control the proportion of spatiotemporal feature fusion, this invention designs an adaptive weight gating mechanism. This dynamic fusion mechanism can autonomously adjust the importance of temporal and spatial features according to the specific context of the input data, thereby improving the model's flexibility and predictive performance.

[0065] The computational definition of adaptive gating is as follows:

[0066]

[0067] in It is the Sigmoid activation function. For the gated parameter matrix, For bias terms,

[0068] The fused features are represented as follows:

[0069]

[0070] symbol This represents element-wise multiplication. This dynamic fusion mechanism enables the model to flexibly adjust the contribution ratio of temporal and spatial features based on the differences in input data, thereby enhancing the effective combination of spatiotemporal information and improving overall prediction accuracy.

[0071] In step S4, the Transformer architecture is used to capture the complex spatiotemporal dependencies in the input data. The core of the model is an encoder composed of stacked identical Transformer layers. Each layer includes a multi-head self-attention mechanism and a positional feedforward network, and training stability and gradient propagation are enhanced through residual connections and layer normalization.

[0072] For the fused input features The encoder generates the final hidden representation through a series of sequentially stacked Transformer networks, as follows:

[0073]

[0074] Each Transformer layer employs a pre-normalization strategy, meaning layer normalization is performed before the self-attention module and the feedforward network module. Specifically, the layer's input is first normalized as follows:

[0075]

[0076] in This is the normalization operator. Then, a learnable parameter matrix is ​​used. Mapped to query ( ),key( ) and value ( )matrix:

[0077]

[0078] The multi-head self-attention mechanism independently computes scaled dot product attention for each attention head:

[0079]

[0080] Then, the outputs of all attention heads are concatenated, and the attention output is obtained through a linear transformation:

[0081]

[0082] Subsequently, a residual connection is used between the input and the attention output:

[0083]

[0084] in Given a learnable linear transformation matrix, the result... After another layer normalization:

[0085]

[0086] It is then fed into a position feedforward network consisting of two layers of linear transformation and intermediate GELU activation:

[0087]

[0088] in , and , Here are the weights and biases for the fully connected layer. Finally, the output of this layer is obtained through residual connections:

[0089]

[0090] The above structure is in the entire encoder The implicit representation is repeated within each layer, and each layer further optimizes the implicit representation based on the output of the previous layer.

[0091] To perform the final prediction, the encoder outputs... The input is fed into a lightweight decoder consisting of two multilayer perceptrons. The final state of the encoder is retrieved. The decoder's calculation process is as follows:

[0092]

[0093] in and The weights and biases of the first fully connected layer. and The weights and biases of the second fully connected layer. For activation function, These are the predicted values. The predicted outputs are used to train the model. Compared with the true value The mean squared error (MSE) between the two losses is defined as follows:

[0094]

[0095] in Indicates the size of the training batch. To calculate the total number of samples, Let be the predicted and true values ​​for the i-th sample. MSE loss enables the model to generate continuous outputs close to the true values ​​in regression tasks.

[0096] The effectiveness and advantages of the present invention are demonstrated below through specific experimental examples.

[0097] The foF2 data in the experiment came from the Global Ionospheric Radio Astronomy Observatory (GIRO) database, while solar activity indicators, including sunspot number and solar flux, came from NASA's Goddard Space Flight Center via the OMNIWeb data service. Modeling and simulation were implemented in Python, with PyCharm used as the primary integrated development environment (IDE). Deep learning models were built and trained using the PyTorch framework. All simulation tasks were performed on high-performance workstations equipped with Intel Core i9 processors and NVIDIA RTX 4090 GPUs, ensuring computational efficiency for large-scale training and parameter evaluation.

[0098] Figure 4 The results of the ablation study are presented, evaluating the relationship between model size and test RMSE under different architectural configurations. The figure compares the baseline model with several variants where key components such as position encoding (no_pos_encoding), cross-attention, spatial features (no_spatial), and fusion gates were removed. The results show that removing position encoding significantly improves RMSE, highlighting its crucial role in maintaining prediction accuracy. Similarly, removing the fusion gate and cross-attention module leads to significant performance degradation. Notably, the baseline model achieves a lower RMSE with fewer parameters, demonstrating its effectiveness and efficiency.

[0099] All models with different input sequence lengths (16, 32, 64, 128) were evaluated using MAE, RMSE, and MAPE, and their performance was assessed at three representative validation points (Boulder (mid-latitude), Cachoeira (low-latitude), and Thule (high-latitude)) to capture geophysical changes.

[0100] Table 1 Comparison of STCGT with other methods

[0101]

[0102] As shown in Table 1, STCFT consistently achieves the lowest error metric across all sites and input lengths, demonstrating higher prediction accuracy compared to baseline models (including Transformer, LSTM, BiLSTM, and IRI2020). Even with short input sequences, STCFT significantly outperforms other models, particularly under complex ionospheric conditions at low and high latitudes. With increasing input sequence length, STCFT maintains robust performance, with only a slight increase in error, still outperforming alternatives. In contrast, baseline models exhibit larger and more variable prediction errors across different locations and sequence lengths. These results collectively confirm the reliability and effectiveness of STCFT in accurate, sequence-length-flexible global foF2 prediction.

[0103] Based on the same inventive concept, this invention discloses a skywave communication F2 layer critical frequency prediction system, used to implement the aforementioned skywave communication F2 layer critical frequency prediction method, comprising: a dataset construction module, used to acquire historical observation data of ionospheric foF2 from around the world and multi-source environmental parameters including solar activity index, geomagnetic disturbance index, and geographic location information, to construct a multi-source input dataset for spatiotemporal prediction; a feature selection module, used to select the key features that best reflect the spatiotemporal variation characteristics of the ionosphere from the multi-source environmental parameters based on the correlation analysis results between foF2 and various driving factors under different latitude conditions, forming an optimal feature input set; and a spatiotemporal feature fusion module, used for... The system embeds geographic location information to obtain geographic embedding vectors. It then embeds and positions selected solar and geomagnetic driving parameters and historical foF2 sequences to obtain time-series features. A spatiotemporal cross-gating mechanism is used to perform cross-attention joint feature extraction on the geographic embedding vectors and time-series features. An adaptive weight gating structure dynamically fuses the time-series features and the cross-attention output of the geographic embedding vectors and time-series features to obtain the fused spatiotemporal features. The prediction module constructs a Transformer model based on a self-attention mechanism. Inputting the fused spatiotemporal features, it captures cross-regional and cross-time correlation information through a multi-head attention structure to generate foF2 prediction results for future times. The system can be deployed in a ground-based numerical weather prediction center or a skywave communication frequency management system.

[0104] This invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for predicting the critical frequency of the F2 layer in skywave communication.

[0105] The program code used to implement the method of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the steps of the method of the present invention to be performed. The program code can be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a standalone software package, or entirely on a remote machine or server. All aspects not detailed in this invention are well-known to those skilled in the art.

[0106] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for predicting the critical frequency of the F2 layer in skywave communication, characterized in that, Includes the following steps: We acquire historical observation data of the ionosphere foF2 from around the world, as well as multi-source environmental parameters including solar activity index, geomagnetic disturbance index and geographic location information, and construct a multi-source input dataset for spatiotemporal prediction. Based on the correlation analysis results between foF2 and various driving factors under different latitudes, the key features that best reflect the spatiotemporal variation characteristics of the ionosphere are selected from multi-source environmental parameters to form the optimal feature input set. Geographic embedding vectors are obtained by embedding geographic location information. Time series features are obtained by embedding and location encoding the selected solar and geomagnetic driving parameters and historical foF2 sequences. A spatiotemporal cross-gating mechanism is used to perform cross-attention joint feature extraction on geographic embedding vectors and time series features. The time series features and the cross-attention output of geographic embedding vectors and time series features are dynamically fused through an adaptive weight gating structure to obtain the fused spatiotemporal features. A Transformer model based on a self-attention mechanism is constructed. The fused spatiotemporal features are input, and the cross-regional and cross-time correlation information is captured through a multi-head attention structure to generate foF2 prediction results for future time moments.

2. The method for predicting the critical frequency of the F2 layer in skywave communication according to claim 1, characterized in that, Based on the correlation analysis results between foF2 and various driving factors under different latitudinal conditions, the key features that best reflect the spatiotemporal variation characteristics of the ionosphere are selected from multi-source environmental parameters to form an optimal feature input set, including: Correlation analysis was conducted on foF2 and each driving factor in different latitudinal regions, including calculating the linear correlation between each driving factor and foF2 using the Pearson correlation coefficient. Based on correlation values, in low-latitude regions, foF2 and Solar flux, Radiation is correlated with sunspot number; in mid-latitude regions, foF2 is correlated with the AE index, AL index, and Dst index; in high-latitude regions, foF2 is correlated with the AE index, AL index, AU index, and IMT-Bz index. It is related to solar flux, Kp index, pc index, and ap index; The key feature screening results from different latitude regions are merged to form the optimal feature input set.

3. The method for predicting the critical frequency of the F2 layer in skywave communication according to claim 1, characterized in that, The optimal feature input set includes the IMT-Bz index, Kp index, sunspot number, Dst index, and ap index. Solar flux, AE index, AL index, AU index, PC index A set consisting of radiation and the critical frequency of foF2.

4. The method for predicting the critical frequency of the F2 layer in skywave communication according to claim 1, characterized in that, The process of embedding geographic location information to obtain a geographic embedding vector includes: embedding a feature vector containing longitude and latitude. Geographic embedding vectors are obtained by projection through a multi-layer feedforward network with hidden layers. in , , , For learnable parameters, , To hide dimensions, For GELU activation function, The normalization operator; the embedding and location encoding of the selected solar and geomagnetic driving parameters and historical foF2 sequences to obtain time series features includes: embedding time series samples containing the selected solar and geomagnetic driving parameters and historical foF2 sequences. The projection is obtained through a multi-layer feedforward network with hidden layers. in , , , For learnable parameters, For the input feature dimension, , To hide the dimension, temporal location encoding is performed to obtain time-series features containing location information. in This is a position encoding function.

5. The method for predicting the critical frequency of the F2 layer in skywave communication according to claim 4, characterized in that, The cross-attention joint feature extraction of geographic embedding vectors and time series features includes: using time series features For query , with geographic embedding vector For key Sum Calculate attention to obtain cross-attention output in It is a vector of all 1s. For the dimension of attention head, The number of heads receiving multi-head attention. For model dimensions.

6. The method for predicting the critical frequency of the F2 layer in skywave communication according to claim 5, characterized in that, The process of dynamically fusing time-series features and geographic embedding vectors with time-series features across attention outputs through an adaptive weight gating structure to obtain fused spatiotemporal features includes: defining the adaptive gating as... in It is the Sigmoid activation function. For the gated parameter matrix, As the bias term; the fused spatiotemporal features are represented as follows: Among the symbols This indicates element-wise multiplication.

7. The method for predicting the critical frequency of the F2 layer in skywave communication according to claim 1, characterized in that, The Transformer model based on the self-attention mechanism includes an encoder composed of stacked identical Transformer layers, each layer containing a multi-head self-attention mechanism and a positional feedforward network; the encoder handles the fused spatiotemporal features of the input. The final hidden representation is generated through a series of sequentially stacked Transformer networks. Each Transformer layer employs a pre-normalization strategy, performing layer normalization before the self-attention module and the feedforward network module. The input and attention output are connected via residual connections, then undergo another layer normalization before being fed into a position feedforward network consisting of two linear transformation layers and intermediate GELU activations. Finally, the output of each Transformer layer is obtained through residual connections. (Encoder output) The input is fed into a lightweight decoder consisting of two multilayer perceptrons, and the decoder output is the foF2 prediction result for the future time.

8. A critical frequency prediction system for F2 layer of skywave communication, used to implement the critical frequency prediction method for F2 layer of skywave communication according to any one of claims 1-7, characterized in that, include: The dataset construction module is used to acquire historical observation data of the ionosphere foF2 from around the world, as well as multi-source environmental parameters including solar activity index, geomagnetic disturbance index and geographic location information, to construct a multi-source input dataset for spatiotemporal prediction. The feature selection module is used to select the key features that best reflect the spatiotemporal variation characteristics of the ionosphere from multi-source environmental parameters based on the correlation analysis results between foF2 and various driving factors under different latitude conditions, and form the optimal feature input set. The spatiotemporal feature fusion module is used to embed geographic location information to obtain geographic embedding vectors, embed and encode the selected solar and geomagnetic driving parameters and historical foF2 sequences to obtain time series features, and use a spatiotemporal cross-gating mechanism to perform cross-attention joint feature extraction on geographic embedding vectors and time series features. Through an adaptive weight gating structure, the time series features and the cross-attention output of geographic embedding vectors and time series features are dynamically fused to obtain the fused spatiotemporal features. The prediction module is used to build a Transformer model based on a self-attention mechanism. It takes the fused spatiotemporal features as input, captures cross-regional and cross-time correlation information through a multi-head attention structure, and generates foF2 prediction results for future time moments.

9. The critical frequency prediction system for the F2 layer of skywave communication according to claim 8, characterized in that, The system is deployed in a ground-based numerical weather prediction center or a skywave communication frequency management system.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the critical frequency prediction method for F2 layer of skywave communication according to any one of claims 1-7.

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