Low-latitude ionospheric total electron content prediction method based on equatorial ionization anomaly feature coding

Abstract

The application discloses a low-latitude ionospheric total electron content prediction method based on equatorial ionization anomaly feature coding, and the method comprises the following steps: acquiring and preprocessing historical observation data of low-latitude ionospheric total electron content; identifying and quantitatively extracting key feature parameters representing the spatial and temporal evolution form of equatorial ionization anomaly; constructing a feature coding network to code the key feature parameters into low-dimensional feature vectors to learn the dynamic feature representation thereof; constructing and training a sequence prediction model capable of fusing the feature representation, and using the coded feature vectors and historical total electron content data to realize high-precision prediction of the total electron content at a future time. By introducing the quantitative physical features of equatorial ionization anomaly, further designing a deep fusion mechanism of double-branch coding and hierarchical attention weighting, the precision of low-latitude ionospheric total electron content prediction and the interpretability of the model are effectively improved.

Description

Technical Field

[0001] This invention relates to low-latitude ionosphere prediction technology, and in particular to a method for predicting the total electron content (TEC) of the low-latitude ionosphere based on the feature encoding of the equatorial ionization anomaly (EIA). Background Technology

[0002] Accurate prediction of ionospheric TEC is a core issue in space weather research and navigation and positioning applications. Deep learning models, with their strong fitting ability to nonlinear and non-stationary time-series data, have shown significant advantages and have become the mainstream technical approach in the field of ionospheric TEC prediction. The low-latitude ionosphere, influenced by the geomagnetic geometry, solar radiation, and electrodynamic processes, exhibits significantly different patterns compared to mid- and high-latitude ionospheric ...

[0003] Temporal modeling methods, represented by Long Short-Term Memory (LSTM) networks, can capture the nonlinear dynamic characteristics of ionospheric TECs. In terms of model architecture design, a wide variety of deep learning architectures are widely adopted, including generative models such as Informer, CNN-LSTM, Transformer-LSTM, SSA-LSTMNN, and pix2pixhd. Among them, the Informer network reduces the time complexity and memory consumption of long sequence prediction through self-attention mechanisms and distillation operations; the CNN-LSTM model combines the spatial feature extraction capabilities of convolutional neural networks with the temporal dependency capture advantages of LSTM networks; Transformer-LSTM leverages the synergistic effect of the Transformer module mining global features and the LSTM module modeling local dynamic changes; SSA-LSTMNN uses singular spectrum analysis to separate trend, periodic, and noise residual terms in TEC sequences, further enhancing the model's ability to capture complex temporal patterns; and the pix2pixhd model generates ionospheric peak structure label maps through semantic segmentation, strengthening feature learning in key regions. At the input data level, historical grid data of TEC is the core, incorporating parameters such as solar activity index (F10.7, sunspot number SSN), geomagnetic index (Dst, Ap, Kp), annual day, UTC, and geographic latitude and longitude to improve data quality through preprocessing. Furthermore, optimization techniques such as multi-level predictor ensemble learning (XGBoost+LightGBM+CNN-LSTM), semantic segmentation to label peak regions, and embedding layers mapping to low-dimensional vector spaces further enhance the model's predictive stability and accuracy. These methods achieve higher prediction accuracy than traditional empirical models and, under extreme space weather conditions such as geomagnetic storms, better characterize the violent perturbation process of TEC, effectively mitigating the problem of excessive prediction errors in perturbation scenarios using traditional methods.

[0004] While existing research has achieved high prediction accuracy globally, it still relies mainly on statistical correlation and lacks in-depth utilization of special physical processes in low latitudes, such as the bimodal structure of the EIA. The prediction error in low latitude regions is significantly higher than that in mid- and high latitudes. Therefore, it is urgent to establish an interpretable prediction framework based on ionospheric physics theory to achieve true "data-physics fusion" in order to effectively alleviate the problem of insufficient prediction accuracy in low latitudes.

[0005] The core principle of existing ionospheric TEC prediction technology is to deeply mine the spatiotemporal evolution characteristics of historical TEC data, the intrinsic relationship between external environmental parameters and ionospheric changes, and combine the nonlinear fitting and feature extraction capabilities of deep learning models to accurately capture the dynamic change patterns of the ionosphere in order to achieve quantitative prediction. Figure 1The existing methodology is illustrated. In terms of structure and workflow, core data such as global or regional ionospheric TEC grid data and VTEC maps are first obtained through authoritative channels such as the European Orbit Determination Centre (CODE) and the IGS working group. Auxiliary data such as solar activity parameters, geomagnetic activity indices, annual cumulative days, UTC, and geographic latitude and longitude are then introduced to form a multi-dimensional input dataset. Subsequently, the raw data undergoes targeted preprocessing, including linear stretching of TEC images, normalization of multi-source data, outlier removal, and sliding window function preprocessing. After processing, the data is proportionally divided into training, testing, and validation sets to provide high-quality data support for model training and performance evaluation.

[0006] The model construction phase employs diverse deep learning architectures, encompassing four main categories: single-network, hybrid-network, ensemble learning, and optimized temporal models. Single-network models include fully connected neural networks and LSTMs, which are structurally simple and easy to train. Hybrid-network models combine the advantages of different networks, such as CNN-LSTM and Transformer-LSTM. Ensemble learning models enhance stability through multi-model collaboration, such as the combination of XGBoost, LightGBM, and CNN-LSTM. Optimized temporal models, such as Informer with stacked autoencoders, are optimized for specific problems. Some models also incorporate multi-head self-attention mechanisms, masked multi-head active sparse self-attention mechanisms, and embedding layer mapping to further improve the efficiency and relevance of feature extraction.

[0007] During training, the Adam optimizer was primarily used, with mean squared error as the core loss function. Some models were combined with CGAN loss, feature matching loss, and other combined loss functions. Model performance was optimized by adjusting hyperparameters such as the number of network layers, neurons, learning rate, batch size, and encoder layers. Early stopping, regularization penalties, and random search algorithms were used to fine-tune hyperparameters to ensure the model's generalization ability. Finally, the trained model was applied to preprocessed historical data input to output TEC predictions for different future time periods, including TEC values ​​and global or regional TEC maps. Prediction performance was evaluated using metrics such as root mean square error, mean absolute error, correlation coefficient, coefficient of determination, and relative accuracy to comprehensively verify the model's prediction accuracy during calm and stormy periods and at different latitudes.

[0008] The overall process focuses on improving data quality through refined data preprocessing, fully leveraging the unique advantages of different network structures, and deeply integrating external driving factors such as solar activity and geomagnetic disturbances to ultimately achieve accurate short-term or medium-term predictions of ionospheric TEC, meeting the application needs of fields such as satellite navigation, radio communication, and space weather monitoring.

[0009] For ionospheric TEC prediction techniques, existing methods have failed to recognize the crucial role of the EIA (Earthquake Indicator) as the fundamental spatial pattern of the low-latitude ionosphere. They neither treat the temporal characteristics or physical parameters representing the bimodal structure and dynamic evolution of the EIA as independent input variables, nor establish a correlation mechanism between EIA and TEC changes. They completely ignore the impact of the EIA on the diurnal, seasonal, and solar activity cycle variations of TEC, resulting in significantly lower prediction accuracy in low-latitude regions compared to mid- and high-latitude regions. Furthermore, feature fusion lacks physical correlation. While some models integrate multi-source parameters such as the solar activity index and geomagnetic index, they only perform feature stitching through data-driven methods, failing to establish a physical correlation between these parameters and low-latitude TEC changes. This easily leads to feature redundancy or information masking, resulting in poor physical interpretability of the prediction results. Furthermore, existing methods lack the ability to capture spatiotemporal features. Low-latitude TECs exhibit both significant spatial gradient characteristics and complex temporal evolution patterns. Single CNN architectures focus on spatial feature extraction, while single LSTM architectures focus on capturing temporal dependencies. Even hybrid architectures such as CNN-LSTM and Transformer-LSTM are not optimized for the special physical environment of low latitudes. In particular, during abrupt changes in the EIA structure due to solar activity and geomagnetic disturbances, prediction lags or biases are likely to occur.

[0010] Therefore, it is urgent to establish an EIA feature fusion mechanism for the low-latitude ionosphere, construct a network architecture that adapts to the dynamic changes of EIA, achieve precise coupling between the impact of EIA and the spatiotemporal characteristics of TEC, and improve the accuracy and physical interpretability of low-latitude TEC prediction.

[0011] Although current ionospheric TEC prediction technology has made some progress in model architecture innovation and multi-source environmental parameter fusion, there are still shortcomings in prediction accuracy and physical mechanism adaptability for low-latitude regions. First, existing technologies generally lack specific consideration of the core controlling factors of the low-latitude ionosphere. None of them have incorporated the key physical phenomenon of equatorial ionization anomaly into the modeling system. They have neither extracted specific features such as EIA intensity difference, latitude of the north and south peaks, and development ratio as independent inputs through quantitative means, nor have they constructed a correlation mapping between the dynamic evolution of EIA and TEC changes. As a result, the models cannot capture the dominant role of EIA in the diurnal rhythm, seasonal fluctuations, and solar activity cycle response of TEC, directly causing the prediction accuracy in low-latitude regions to be much lower than that in mid- and high-latitude regions. Secondly, while some models attempt to integrate multi-source parameters such as the F10.7 index and the geomagnetic Dst / Kp index, they merely perform simple data splicing and stacking without establishing an intrinsic relationship between parameters and TEC changes based on the physical mechanisms of the low-latitude ionosphere. This easily leads to problems such as feature redundancy and information interference, resulting in prediction results lacking physical interpretability and making it difficult to support the tracing and verification of prediction logic. Thirdly, low-latitude TEC possesses both strong spatial gradients and complex temporal evolution. Existing single-architecture and conventional hybrid architectures have not been optimized for the unique physical environment of low latitudes. When the EIA structure undergoes abrupt adjustments due to solar activity and geomagnetic disturbances, it is difficult to simultaneously and accurately capture spatiotemporal characteristics, easily leading to prediction lag or numerical deviations. Even if some models attempt optimization through methods such as semantic segmentation and peak region annotation, they have not formed a dedicated fusion mechanism adapted to the dynamic characteristics of the EIA, still relying on the generalization ability of the global model, and are unable to cope with the challenges brought about by the nonlinear changes in the low-latitude ionosphere. Furthermore, existing models mostly adopt a globally unified training framework, which does not fully consider the strong coupling relationship between low-latitude TEC and EIA. Under extreme space weather conditions such as geomagnetic storms, it is difficult to accurately characterize the chain effect of EIA dynamic adjustment caused by factors such as rapid penetration of electric field and disturbance of generator electric field on TEC. This leads to a further amplification of prediction error in extreme scenarios, which cannot meet the demand for high-precision prediction in practical applications.

[0012] It should be noted that the information disclosed in the background section above is only for understanding the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0013] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a method for predicting the total electron content of the ionosphere in low latitudes based on equatorial ionization anomaly feature encoding.

[0014] To achieve the above objectives, the present invention adopts the following technical solution:

[0015] A method for predicting the total electron content of the ionosphere in low latitudes based on equatorial ionization anomaly feature encoding includes the following steps:

[0016] S1. Data Acquisition and Preprocessing: Acquire historical observation data on the total electron content of the ionosphere in low-latitude regions, and preprocess the historical observation data to form model input data;

[0017] S2. Equatorial ionization anomaly feature extraction: Based on preprocessed historical observation data, the existence of equatorial ionization anomalies is identified, and key feature parameters of equatorial ionization anomalies are extracted to characterize their spatiotemporal evolution.

[0018] S3. Feature Encoding Representation Learning: Construct a feature encoding network to encode the extracted key feature parameters of equatorial ionization anomalies into low-dimensional feature vectors, so as to learn a feature representation that can effectively characterize the dynamics of equatorial ionization anomalies.

[0019] S4. Construction and training of total electron content prediction model: Construct a sequence prediction model that integrates the feature representation, and train the sequence prediction model using the encoded feature vector and historical total electron content data to predict the total electron content of the low-latitude ionosphere at future times.

[0020] Furthermore, step S1 specifically includes:

[0021] Obtain gridded data of total ionospheric electron content distributed by latitude and longitude grids covering low-latitude regions;

[0022] The grid data is subjected to quality control to remove outliers that exceed reasonable physical limits;

[0023] The data after quality control is standardized to form a standardized numerical matrix;

[0024] A unique time identifier is assigned to the standardized numerical matrix for each time step, and the extracted key feature parameters of equatorial ionization anomaly are bound to the total electron content data of the corresponding time step.

[0025] The data at all time steps are sorted and matched in chronological order, and continuity and integrity checks are performed. Missing data is imputed to form a model input dataset that is temporally continuous and feature-aligned.

[0026] Furthermore, the extraction of key feature parameters of equatorial ionization anomalies in step S2 specifically includes:

[0027] For each longitude sector and time step, the existence of the bimodal structure of the equatorial ionization anomaly is determined based on the standardized total electron content data.

[0028] If they exist, the grid positions of the peak values ​​in the Northern and Southern Hemispheres are located by traversing grid points and comparing the total electron content values ​​in the Northern and Southern Hemispheres respectively, and the total electron content intensity values ​​and corresponding actual geomagnetic latitudes are recorded.

[0029] Using the located grid positions of the north and south peaks as a reference, an equatorial region encompassing both is determined, and the minimum total electron content within this region is located as the equatorial valley value. The valley value is then protected against being a non-positive number.

[0030] Based on the magnetic north peak, magnetic south peak, and equatorial valley values, the difference and ratio characteristics characterizing the intensity of the equatorial ionization anomaly are calculated.

[0031] The difference feature is calculated as follows: the difference between the north peak, the south peak and the valley value is calculated respectively, and then the arithmetic mean of the two is calculated.

[0032] The ratio feature is calculated as follows: the ratio of the average value of the north peak and the south peak to the valley value is calculated.

[0033] Furthermore, the basis for determining whether there is an equatorial ionization anomaly is: whether the total electron content value shows a bimodal structure on the latitudinal profile of the low latitude region, and whether there is a significant trough in the total electron content in the equatorial region between the two peaks.

[0034] Furthermore, the construction of the feature encoding network in step S3 specifically includes:

[0035] A feature transformation network with a fully connected layer as its core is constructed as the feature encoding network;

[0036] The feature transformation network receives the extracted key feature parameters of the equatorial ionization anomaly as input, performs nonlinear transformation and dimension mapping through at least one fully connected layer, and encodes the key feature parameters into feature vectors of a predetermined dimension that match the subsequent fusion steps, so as to form a feature representation for characterizing the dynamics of the equatorial ionization anomaly.

[0037] The parameters of the feature transformation network are trained end-to-end in supervised manner along with other parts of the model during the training process of the sequence prediction model in step S4.

[0038] Furthermore, the construction of the sequence prediction model with fused feature representation in step S4 specifically includes:

[0039] Construct a deep learning model that includes a spatiotemporal feature encoding branch, a feature weighted fusion branch, and a sequence prediction branch;

[0040] The spatiotemporal feature encoding branch uses a convolutional neural network to process the input historical total electron content sequence data, extract its spatial features, and encode them as the first feature sequence.

[0041] The feature weighted fusion branch first transforms and maps the key feature parameter sequence of equatorial ionization anomalies extracted in step S2 through at least one fully connected layer to form a second feature sequence. Then, a first-level attention weighting is applied to the second feature sequence, with the weight allocation strategy dynamically adjusted based on the physical priors of equatorial ionization anomalies. Next, the second feature sequence after the first-level weighting is concatenated with the first feature sequence to obtain a preliminary fused feature sequence. Finally, a second-level global attention weighting is applied to the preliminary fused feature sequence, with the weight allocation strategy focusing on mining long-range dependencies and coupling relationships between features at different time steps, forming a weighted fused feature sequence.

[0042] The sequence prediction branch uses a long short-term memory network to perform time-series modeling on the weighted fusion feature sequence, and maps the time-series features output by the network to the predicted total electron content value at future times through a fully connected layer.

[0043] Furthermore, the attention mechanism applied to the equatorial ionization anomaly feature vector sequence in the feature weighted fusion branch specifically includes the following steps:

[0044] After mapping the equatorial ionization anomaly feature vector sequence, a first-level attention weighting is applied to it. The weighting allocation strategy is configured to dynamically adjust the degree of prior influence of the physical state reflected by the equatorial ionization anomaly features on the change in total electron content.

[0045] The equatorial ionization anomaly feature sequence, which has undergone first-level weighting, is concatenated with the first feature sequence;

[0046] A second-level global attention weighting is applied to the preliminary fused feature sequence formed after splicing. The weighting allocation strategy is configured to mine and enhance the temporal feature combinations in the preliminary fused feature sequence that simultaneously contain significant equatorial ionization anomaly change information and corresponding spatial features.

[0047] Furthermore, when training the sequence prediction model, the mean squared error between the predicted output and the true value is used as the loss function, and the parameters of the long short-term memory network are optimized through the backpropagation algorithm.

[0048] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature encoding.

[0049] A computer program product includes a computer program that, when executed by a processor, implements the method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature encoding.

[0050] The present invention has the following beneficial effects:

[0051] This invention provides a method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature encoding. Addressing the shortcomings of existing technologies, such as insufficient incorporation and effective fusion of core physical features of equatorial ionization anomalies, inadequate characterization of the unique dynamic correlation mechanisms of the low-latitude ionosphere, and the tendency for scale imbalance and information masking during heterogeneous feature fusion, this invention offers an innovative solution. The method systematically extracts key morphological parameters of equatorial ionization anomalies from historical observation data and transforms them into fusionable low-dimensional dynamic feature representations via a feature encoding network. Finally, it constructs a sequence prediction model that deeply integrates these physical feature representations, thereby achieving explicit modeling and utilization of the physical mechanisms of equatorial ionization anomalies within a data-driven framework. This invention is the first to systematically incorporate the temporal features of equatorial ionization anomalies, characterizing the core physical properties of the low-latitude ionosphere, into a model within a data-driven deep learning prediction framework. Furthermore, by constructing a deep fusion mechanism of dual-branch encoding and hierarchical attention weighting, this invention significantly improves the accuracy and physical interpretability of the prediction.

[0052] Specifically, the CNN-LSTM-Attention dual-input deep fusion modeling architecture proposed in this invention effectively overcomes the shortcomings of traditional single-architecture or simple hybrid models in adapting to the special physical environment of low latitudes through an integrated design of "spatial feature extraction—key feature enhancement—temporal dependency mining". This architecture employs dual-input parallel encoding, utilizing convolutional neural networks to accurately extract the spatial distribution features of total electron content data, and using fully connected layers and self-attention layers to perform dimensional adaptation and dynamic weighting of equatorial ionization anomaly features. This design enables the model to independently and fully process two heterogeneous features, avoiding information suppression that may result from simple splicing. Subsequently, a long short-term memory network is used to deeply mine the temporal evolution of the fused features, and a global attention layer is combined to optimize long-range dependencies, thereby achieving deep coupling between the spatiotemporal features of total electron content and the physical features of equatorial ionization anomalies, significantly enhancing the model's ability to represent and predict complex dynamic changes in the ionosphere.

[0053] Furthermore, the temporal alignment-dynamic weighted fusion mechanism for equatorial ionization anomaly features and total electron content data designed in this invention constructs a full-process fusion logic of "basic alignment, dimensional adaptation, dynamic weighting, and secondary optimization." This mechanism first ensures strict spatiotemporal matching of heterogeneous data through time-step binding, fundamentally avoiding model bias caused by temporal misalignment. Then, it achieves feature dimension alignment through nonlinear transformation and innovatively introduces a dual attention mechanism: a self-attention layer based on physical priors dynamically strengthens the weight of equatorial ionization anomaly features during key periods (such as geomagnetic storm periods); the global attention layer performs secondary optimization on the fused feature sequence, focusing on mining strongly correlated feature combinations and long-range dependencies. This mechanism not only accurately captures the inherent physical correlation between the evolution of equatorial ionization anomalies and changes in total electron content but also effectively filters redundant information, improving the effectiveness of feature fusion and the interpretability of model output.

[0054] In summary, this invention organically combines the quantitative extraction of core features of equatorial ionization anomalies, dual-branch dedicated encoding, and a dynamic fusion method under physical constraints to form a complete prediction method that combines high accuracy with good interpretability. Compared with existing technologies, this invention not only significantly improves the prediction accuracy and stability in low-latitude regions, especially in areas with active equatorial ionization anomalies and during periods of space weather disturbances, through targeted architecture and fusion mechanisms, but also provides physical traceability for the prediction results through attention weight visualization and other means, enhancing the model's credibility and practical value, and providing more reliable technical support for satellite navigation, radio communication, and space weather monitoring services in low-latitude regions.

[0055] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0056] Figure 1 This is a flowchart of the existing method.

[0057] Figure 2 This is the overall flowchart of the method for predicting the total electron content of the low-latitude ionosphere based on the equatorial ionization anomaly feature encoding of the present invention.

[0058] Figure 3 This is an example diagram of the model architecture of an embodiment of the present invention.

[0059] Figure 4 This is a technical roadmap diagram of the method for predicting the total electron content of the ionosphere in low latitudes based on equatorial ionization anomaly feature encoding, according to an embodiment of the present invention. Detailed Implementation

[0060] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and is not intended to limit the scope and application of the present invention.

[0061] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0062] This invention aims to overcome the limitations of existing methods for predicting total electron content in the low-latitude ionosphere, which fail to effectively integrate the physical characteristics of equatorial ionization anomalies. It proposes a technical solution that involves quantitatively extracting the core features of equatorial ionization anomalies, encoding and representing them through learning, and constructing a sequence prediction model that deeply integrates these physical features. This achieves deep coupling between the data-driven model and the core physical processes of the ionosphere, thereby significantly improving the accuracy of total electron content prediction in low-latitude regions and the interpretability of the model.

[0063] See Figures 2 to 4 This invention provides a method for predicting the total electron content (TEC) of the low-latitude ionosphere based on equatorial ionization anomaly (EIA) feature encoding, comprising the following steps:

[0064] Step S1: Data Acquisition and Preprocessing: Acquire historical observation data on the total electron content of the ionosphere in low-latitude regions, and preprocess the historical observation data to form model input data.

[0065] In some embodiments, step S1 specifically includes: acquiring grid data of total electron content in the ionosphere covering low-latitude regions and distributed by a latitude-longitude grid; performing quality control on the grid data to remove outliers exceeding reasonable physical ranges; standardizing the quality-controlled data to form a standardized numerical matrix; assigning a unique time identifier to the standardized numerical matrix for each time step, and binding the extracted key feature parameters of equatorial ionization anomalies with the total electron content data of the corresponding time step; sorting and matching the data of all time steps in chronological order, performing continuity and integrity checks, imputing missing data, and forming a temporally continuous and feature-aligned model input dataset.

[0066] Step S2: Equatorial ionization anomaly feature extraction: Based on preprocessed historical observation data, the existence of equatorial ionization anomalies is identified, and key feature parameters of equatorial ionization anomalies are extracted to characterize their spatiotemporal evolution.

[0067] In some embodiments, the extraction of key feature parameters of equatorial ionization anomaly in step S2 specifically includes: for each longitude sector and time step, based on the standardized total electron content data, determining whether the bimodal structure of the equatorial ionization anomaly exists; if it exists, then in the geomagnetic northern hemisphere region and the geomagnetic southern hemisphere region, respectively, by traversing grid points and comparing the total electron content values, locating the grid positions of the northern hemisphere peak and the southern hemisphere peak, and recording their total electron content intensity values ​​and corresponding actual geomagnetic latitudes; using the located north and south peak grids... Using location as a reference, an equatorial region encompassing both is determined, and the minimum total electron content within this region is identified as the equatorial valley value. This valley value is then protected against being a non-positive number. Based on the magnetic north peak, magnetic south peak, and equatorial valley value, difference and ratio characteristics characterizing the intensity of the equatorial ionization anomaly are calculated. The difference characteristic is calculated by separately calculating the differences between the north peak, south peak, and valley value, and then taking their arithmetic mean. The ratio characteristic is calculated by dividing the average of the north and south peak values ​​by the valley value.

[0068] In some embodiments, the basis for determining whether there is an equatorial ionization anomaly is whether the total electron content value exhibits a bimodal structure on the latitudinal profile of the low-latitude region, and whether there is a significant trough in the total electron content in the equatorial region between the two peaks.

[0069] Step S3, Feature Encoding Representation Learning: Construct a feature encoding network to encode the extracted key feature parameters of equatorial ionization anomalies into low-dimensional feature vectors, so as to learn a feature representation that can effectively characterize the dynamics of equatorial ionization anomalies.

[0070] In some embodiments, the construction of the feature encoding network in step S3 specifically includes: constructing a feature transformation network with a fully connected layer as the core as the feature encoding network; the feature transformation network receives the extracted key feature parameters of the equatorial ionization anomaly as input, performs nonlinear transformation and dimension mapping through at least one fully connected layer, and encodes the key feature parameters into feature vectors of a predetermined dimension that match the subsequent fusion steps, so as to form a feature representation for characterizing the dynamics of the equatorial ionization anomaly; the parameters of the feature transformation network are trained end-to-end in supervised manner along with other parts of the model during the training process of the sequence prediction model in step S4.

[0071] Step S4: Construction and training of total electron content prediction model: Construct a sequence prediction model that integrates the feature representation, and train the sequence prediction model using the encoded feature vector and historical total electron content data to predict the total electron content of the low-latitude ionosphere at future times.

[0072] In some embodiments, the construction of the sequence prediction model with fused feature representation in step S4 specifically includes: constructing a deep learning model comprising a spatiotemporal feature encoding branch, a feature weighted fusion branch, and a sequence prediction branch. The spatiotemporal feature encoding branch (which uses a convolutional neural network to process TEC data) and the feature weighted fusion branch (which first processes EIA features through fully connected layers, etc.) together constitute a dual-branch structure for processing two heterogeneous input data. The spatiotemporal feature encoding branch uses a convolutional neural network to process the input historical total electron content sequence data, extracting its spatial features and encoding them as a first feature sequence. The feature weighted fusion branch first transforms and maps the key feature parameter sequence of equatorial ionization anomalies extracted in step S2 through at least one fully connected layer to form a second feature sequence. Then, a first-level attention weighting is applied to the second feature sequence, with the weight allocation strategy dynamically adjusted based on the physical prior of equatorial ionization anomalies. Next, the second feature sequence after the first-level weighting is concatenated with the first feature sequence to obtain a preliminary fused feature sequence. Finally, a second-level global attention weighting is applied to the preliminary fused feature sequence, with the weight allocation strategy focusing on mining long-range dependencies and coupling relationships between features at different time steps, forming a weighted fused feature sequence. The first-level attention weighting and the second-level global attention weighting together form a hierarchical attention weighting mechanism. The sequence prediction branch uses a long short-term memory network to perform temporal modeling of the weighted fused feature sequence and maps the temporal features output by the network to the predicted total electron content value at future times through a fully connected layer.

[0073] In a further embodiment, the attention mechanism applied to the equatorial ionization anomaly feature vector sequence in the feature weighted fusion branch specifically includes the following steps: after mapping the equatorial ionization anomaly feature vector sequence, a first-level attention weighting is applied to it. The weighting allocation strategy is configured to dynamically adjust the prior influence of the physical state reflected by the equatorial ionization anomaly features on the change in total electron content; the equatorial ionization anomaly feature sequence after the first-level weighting is concatenated with the first feature sequence; a second-level global attention weighting is applied to the preliminary fusion feature sequence formed after concatenation. The weighting allocation strategy is configured to mine and strengthen the time step feature combinations in the preliminary fusion feature sequence that simultaneously contain significant equatorial ionization anomaly change information and corresponding spatial features.

[0074] In some embodiments, when training the sequence prediction model, the mean squared error between the predicted output and the true value is used as the loss function, and the parameters of the long short-term memory network are optimized through the backpropagation algorithm.

[0075] This invention presents a high-precision prediction method for low-latitude ionospheric TEC based on EIA feature fusion. In this embodiment, an EIA-specific feature extraction mechanism and a dual-branch coding fusion model are constructed to achieve precise coupling between the dynamic impact of EIA and the spatiotemporal characteristics of TEC. First, based on low-latitude TEC grid data, four core features—EIA intensity, spatial location, and development level—are quantitatively extracted to form an input feature set that possesses both physical meaning and data integrity. Then, through a dual-branch coding architecture, specific features are extracted from both the TEC spatial grid features and the EIA temporal features. A hierarchical attention weighting mechanism is combined to achieve efficient fusion of heterogeneous features, while physical constraints are introduced to improve the interpretability of the prediction results. Finally, model optimization adapted to the characteristics of the low-latitude ionosphere significantly improves the prediction accuracy for EIA active areas and geomagnetic storm periods. This method fundamentally solves the problems of existing technologies, such as the lack of fusion of core EIA features, insufficient adaptability to low-latitude regions, lack of physical correlation in feature fusion, and inaccurate capture of spatiotemporal features. It provides high-precision TEC prediction support for low-latitude satellite navigation, radio communication, and space weather monitoring.

[0076] The following further describes specific embodiments of the present invention and examples of its algorithm implementation.

[0077] The flowchart for the method of predicting total electron content in the low-latitude ionosphere based on equatorial ionization anomaly feature coding is as follows: Figure 2 and Figure 4 By quantifying and extracting the core features of equatorial ionization anomalies, using dual-branch coding to capture specific features, and employing a heterogeneous feature fusion method under physical constraints, high-precision and interpretable prediction of total electron content in low latitudes is finally achieved.

[0078] (1) CNN-LSTM-Attention dual-input deep fusion modeling architecture

[0079] This invention proposes a CNN-LSTM-Attention dual-input deep fusion modeling architecture for predicting TEC (Transient Electromagnetic Reactor) in the low-latitude ionosphere, constructing an integrated modeling logic of "spatial feature extraction—key feature enhancement—temporal dependency mining." This architecture employs a dual-input parallel encoding design, receiving TEC spatiotemporal grid sequences and EIA (Earthquake Ionization and Assay) core feature sequences respectively. It extracts the spatial distribution features of TEC data through CNN branches, and completes dimensional adaptation and dynamic weighting of EIA features through a combination of fully connected layers and self-attention layers. Finally, an LSTM layer mines the temporal evolution patterns of the fused features, achieving deep coupling between TEC spatiotemporal features and EIA physical features. Compared to traditional single TEC temporal prediction models, this architecture replaces the simple splicing of heterogeneous features with independent encoding and collaborative fusion; it enhances the predictive contribution of EIA features at key time steps such as geomagnetic storm periods through an attention mechanism, and simultaneously captures the long-range temporal dependencies of the fused features through a global attention layer, improving the model's ability to represent complex dynamic changes in the ionosphere, providing core architectural support for accurate prediction of low-latitude TEC. An example of the model architecture is shown below. Figure 3 As shown.

[0080] The dual-input fusion modeling architecture of this invention achieves efficient collaboration of heterogeneous features at the model level through a unified feature dimension and a dynamic weighted fusion strategy, reducing the dependence of traditional models on a single data type. This architecture can adapt to different space weather scenarios by adjusting the parameters of each branch network, exhibiting good scalability and adaptability. Simultaneously, it provides support for model interpretability by outputting attention weights, clarifying the model's attention to different time steps and different types of features, thus laying the foundation for the engineering application of ionospheric prediction models.

[0081] (2) Temporal alignment of EIA features and TEC data - dynamic weighted fusion mechanism

[0082] This invention proposes a temporal alignment-dynamic weighted fusion mechanism for EIA features and TEC data, constructing a full-process feature fusion logic of "basic alignment—dimensional adaptation—dynamic weighting—secondary optimization". This mechanism uses time steps as the core link, achieving basic temporal alignment between EIA features and TEC grid data through time-step binding, ensuring strict matching between the two in the spatiotemporal dimensions. A fully connected layer nonlinearly maps 4D EIA features to dimensions consistent with TEC spatial features, constructing a fusionable EIA feature sequence. A custom self-attention layer calculates the query, key, and value matrix and attention score, dynamically adjusting the weights of EIA features at different time steps to strengthen the influence of features in key time periods. A global attention layer performs secondary weighting on the fused features, filtering redundant information and strengthening long-term temporal correlations.

[0083] The temporal alignment-dynamic weighted fusion mechanism of this invention achieves dynamic adaptation and fusion through the inherent correlation of data, eliminating the need for traditional format conversion or manual feature selection. This addresses the core issues of spatiotemporal misalignment and scale mismatch in heterogeneous feature fusion. By accurately matching the spatiotemporal correlation between EIA and TEC and employing a dynamic weighting strategy, this mechanism enhances the model's sensitivity to ionospheric anomalies, enabling it to capture the intrinsic correlation between EIA evolution and TEC changes. This provides crucial technical support for improving the prediction accuracy of low-latitude TEC. Furthermore, this mechanism can be transferred to other multi-source time-series data fusion scenarios, demonstrating broad versatility and application value.

[0084] The specific implementation plan includes the following steps:

[0085] 1. Construct a dataset for quantifying EIA features

[0086] Based on low-latitude TEC grid data, four core EIA features are extracted by quantization at the same time step to accurately characterize the intensity, spatial location, and development level of EIA. The specific extraction process is as follows:

[0087] 1) Data preprocessing

[0088] TEC grid data provided by the European Orbit Determination Centre (CODE) was selected. The selected low-latitude region covers a latitude range of -30° to 30° and a longitude range of -180° to 180°. The spatiotemporal resolution was set to 2.5° latitude × 5° longitude × 2 hours. A series of preprocessing operations were performed on the acquired raw TEC grid data. First, outlier removal was performed to remove negative values ​​and extreme values ​​that exceeded the reasonable range. Then, the data was standardized by linear stretching transformation to finally obtain a standardized TEC numerical matrix that meets the modeling requirements.

[0089] 2) EIA Feature Calculation

[0090] a) EIA intensity difference

[0091] The EIA intensity difference is represented by the average difference between the north and south peak values ​​and the equatorial trough value. This is used in the extraction of... Beforehand, the peak values ​​of the Northern Hemisphere, Southern Hemisphere, and equatorial valleys need to be located using specific traversal rules. The specific calculation process is as follows:

[0092] Southern Hemisphere Peak Location: First, a magnetic southern hemisphere mask is constructed based on geomagnetic latitude and longitude (filtering areas with geomagnetic latitude less than 0°). The magnetic southern hemisphere TEC grid and its corresponding actual geomagnetic latitude are extracted from the TEC numerical matrix. A traversal order of "bottom right → top left" (row reversal: from southernmost geomagnetic latitude to northernmost geomagnetic latitude; column reversal: from easternmost geomagnetic longitude to westernmost geomagnetic longitude) is used to traverse all grid points in the magnetic southern hemisphere. Initially, the current maximum TEC value is set to -1 (to ensure the first grid point updates the maximum value, as TEC values ​​are non-negative). For each grid point traversed, if its TEC value is greater than the current maximum TEC value, the candidate magnetic southern peak information is updated (including the magnetic southern peak TEC value, magnetic southern peak geomagnetic latitude, and the latitude and longitude indices of the magnetic southern peak in the original grid). After the traversal, if no valid peak is found (no grid point with a TEC value greater than the initial value -1), the maximum TEC value of the magnetic southern peak is set to 0, and the magnetic southern peak geomagnetic latitude is set to NaN.

[0093] Northern Hemisphere Peak Location: A magnetic northern hemisphere mask is constructed based on geomagnetic latitude and longitude (filtering areas with geomagnetic latitude greater than 0°). The magnetic northern hemisphere TEC grid and its corresponding actual geomagnetic latitude are extracted from the TEC numerical matrix. Using a traversal order of "top left to bottom right" (row order: from the northernmost geomagnetic latitude to the southernmost geomagnetic latitude; column order: from the westernmost geomagnetic longitude to the easternmost longitude), the entire magnetic northern hemisphere grid points are traversed. The magnetic northern peak is located using the same maximum value update rule. If no valid peak is found after the traversal, the maximum TEC value of the magnetic northern peak is set to 0, and the geomagnetic latitude of the magnetic northern peak is set to NaN.

[0094] Equatorial valley value location: Using the coordinates (geomagnetic latitude index and geomagnetic longitude index) of the located magnetic north peak and magnetic south peak in the original TEC grid as vertices, determine the boundary of a rectangular region (the geomagnetic latitude boundary is the minimum and maximum values ​​of the geomagnetic latitude index of the two peaks, and the geomagnetic longitude boundary is the minimum and maximum values ​​of the geomagnetic longitude index of the two peaks). Extract the TEC grid within this rectangular region as the equatorial region. If the region is valid and the minimum value is greater than 0, then the minimum value of the region is taken as the equatorial valley value TEC; if the region is invalid or the minimum value is less than or equal to 0, then the equatorial valley value TEC is replaced with the minimum value 10⁻. 8 .

[0095] Calculation: First, determine if no valid peak value was found (magnetic latitude of the magnetic north peak is NaN, magnetic latitude of the magnetic south peak is NaN, or TEC values ​​of both the magnetic north and south peaks are 0). If this condition is met, then... Set it to 0; if a valid peak value is found, calculate the average difference between the magnetic north-south peak value and the equatorial valley value using the formula, and obtain... As shown in formula (1).

[0096]

[0097] In the formula —EIA strength difference;

[0098] —The maximum TEC value of the magnetic north peak;

[0099] —Magnetic south peak TEC maximum;

[0100] — Equatorial valley value.

[0101] b) Actual geomagnetic latitude of EIA Magnetic North Peak

[0102] The actual geomagnetic latitude of Magnet North Peak is represented by the following calculation process:

[0103] Location process: In the peak extraction stage of the magnetic northern hemisphere, the grid point corresponding to the maximum value in the TEC grid of the magnetic northern hemisphere is found by traversing the rule of "top left corner → bottom right corner". The local row index of the grid point after the latitude mask of the magnetic northern hemisphere is recorded. Then, the global index of the original magnetic latitude mask is matched with the local row index to obtain the geomagnetic latitude index of the peak value in the original TEC grid.

[0104] Latitude acquisition: Combining the preset geomagnetic latitude array Lat_mag_grid (covering geomagnetic latitudes from -30° to 30° with an interval of 2.5°), the specific geomagnetic latitude corresponding to the EIA peak in the magnetic northern hemisphere is obtained by matching the geomagnetic latitude index.

[0105] Anomaly Handling: If no valid peak is found after traversing the entire magnetic northern hemisphere (TEC value of no grid point is greater than the initial value -1), the geomagnetic latitude of the magnetic northern peak is set to NaN; in subsequent modeling, it can be replaced with 0 or other default values ​​as needed.

[0106] c) Actual geomagnetic latitude of EIA magnetic south peak

[0107] The actual geomagnetic latitude of Magneton South Peak is represented by the following calculation process:

[0108] Location process: In the peak extraction stage of the magnetic southern hemisphere, the grid point corresponding to the maximum value in the TEC grid of the magnetic southern hemisphere is found by traversing the rule of "bottom right corner → top left corner". The local row index of the grid point after the magnetic southern hemisphere latitude mask is recorded. Then, the global index of the original geomagnetic latitude mask is matched with the local row index to obtain the geomagnetic latitude index of the peak value in the original TEC grid.

[0109] Latitude acquisition: Combining the preset geomagnetic latitude array Lat_mag_grid, the specific geomagnetic latitude corresponding to the EIA peak in the magnetic southern hemisphere is obtained by matching the geomagnetic latitude index (this latitude is a negative value, representing geomagnetic °S), and then its absolute value is taken to convert it into a representation in geomagnetic °S units.

[0110] Anomaly Handling: If no valid peak is found after traversing the entire southern magnetic hemisphere, the geomagnetic latitude of the southern magnetic peak is set to NaN; in subsequent modeling, it can be replaced with 0 or other default values ​​as needed.

[0111] d) Peak-to-valley ratio

[0112] Peak-to-valley ratio This represents the strength of the EIA (Energy Information Management System). A higher ratio indicates a more fully developed EIA. The specific calculation process is as follows:

[0113] Basic parameter preparation: The calculation of this feature relies on the magnetic north peak TEC value, magnetic south peak TEC value, and equatorial valley TEC value extracted by the above process. The equatorial valley value has been pre-corrected for zero (replaced with 10⁻ when it is less than or equal to 0). 8 ).

[0114] Calculation: First, determine if no valid peak value was found (magnetic latitude of the magnetic north peak is NaN, magnetic latitude of the magnetic south peak is NaN, or TEC values ​​of both the magnetic north and south peaks are 0). If this condition is met, then... Setting it to 1.0 indicates that the EIA has not developed; if an effective peak is found, the ratio of the average TEC of the north-south magnetic peak to the TEC of the equatorial valley is calculated using the formula to obtain the value. As shown in formula (2).

[0115]

[0116] In the formula —Peak-to-valley ratio;

[0117] —The maximum TEC value of the magnetic north peak;

[0118] —Magnetic south peak TEC maximum;

[0119] — Equatorial valley value.

[0120] 3) Timing alignment

[0121] A triple mechanism of "timestamp anchoring + hourly matching + sequence verification" is adopted to ensure that the four EIA features are strictly synchronized with the TEC data of the corresponding time step. First, a unique timestamp (in the format "year-month-day-hour") is assigned to the original TEC grid data at each time step, precisely corresponding to the observation time of the data. During EIA feature extraction, the timestamp of the corresponding TEC data is inherited synchronously, achieving "extraction as anchoring" and ensuring the temporal correlation between a single EIA feature and the source TEC data. Subsequently, all "TEC data-timestamp-EIA feature" triples are matched hourly in ascending order of timestamp to form one-to-one basic data pairs. Finally, through sequence continuity verification (checking whether the timestamp intervals are all 1 hour and whether there are no missing or duplicate time steps) and data integrity verification (ensuring that each time step contains a complete TEC numerical matrix and 4 EIA features), abnormal time step data is removed, and the default values ​​of missing time steps are filled in (EIA features are set to 0 or 1.0 according to rules, and TEC data is filled in using linear interpolation). Finally, a temporally continuous and accurately correlated basic data sequence of "TEC data + EIA features" is formed, fundamentally ensuring the temporal consistency between the input features and the prediction target in the subsequent modeling process and avoiding model training bias caused by time misalignment.

[0122] 2. Multi-source feature fusion and modeling

[0123] A dual-input deep fusion model based on the CNN-LSTM-Attention architecture is constructed to fully leverage the spatial feature extraction capability of convolutional neural networks, the temporal dependency mining capability of long short-term memory networks, and the key feature enhancement capability of attention mechanisms. This achieves deep coupling between the spatiotemporal features of TEC and the core features of EIA. The specific implementation process is as follows:

[0124] 1) Dual-input layer design

[0125] Two independent input layers are set up to receive standardized heterogeneous feature data respectively, ensuring that the two types of features are input independently and encoded in parallel, avoiding interference caused by differences in feature scale. The first input layer receives TEC spatiotemporal data, corresponding to a low-latitude TEC grid sequence, with a feature dimension of sample number × input time step × latitude dimension × longitude dimension × 1; the second input layer receives EIA feature data, corresponding to a sequence composed of four EIA core features, with a feature dimension of sample number × input time step × 4.

[0126] 2) Spatiotemporal feature coding branch

[0127] A 3D convolutional neural network (CNN) is used to extract and encode spatial features from TEC spatiotemporal data. Two convolutional layers sequentially extract shallow and deep spatial features, while batch normalization and ReLU activation functions are used to suppress gradient vanishing. After convolutional feature extraction, a reshape layer flattens the multidimensional spatial features into a one-dimensional feature sequence. A fully connected layer then maps the flattened features to a unified feature dimension C1, ultimately forming a TEC spatiotemporal feature sequence that corresponds one-to-one with the input time step. The feature dimension is (number of samples × input time step × C1), thus effectively encoding the TEC spatial features.

[0128] 3) EIA Feature Encoding and Attention Weighted Branch

[0129] First, the EIA feature sequence is nonlinearly transformed using two fully connected layers. The 4-dimensional EIA features are first mapped to 128 dimensions, and then further mapped to dimension C1, consistent with the TEC spatiotemporal feature sequence, forming the EIA feature sequence and ensuring a dimensional basis for fusion of the two features. Then, the EIA feature sequence is input into a custom EIA physical prior-guided attention layer. The weights of EIA features at different time steps are dynamically adjusted based on the strength of the physical correlation between EIA features and TEC changes: priority is given to amplifying the weights of EIA features that directly drive TEC changes during key periods such as geomagnetic storms and peak solar activity, while suppressing the weights of EIA features that have no significant impact during calm periods. This strengthens the contribution of EIA features at key time steps to the prediction results. The core computational process of the attention mechanism follows the formula below:

[0130]

[0131] In the formula, Q represents the query.

[0132] K — key;

[0133] V — Value matrix;

[0134] —The dimension of the key.

[0135] 4) LSTM time series fusion and prediction

[0136] First, the spatiotemporal feature sequence of TEC and the dynamic feature sequence of EIA are fused using a dimensional concatenation method to form a fused feature sequence. The feature dimension is the number of samples × input time step × 2C1. Then, the fused feature sequence is input into a global self-attention layer for secondary weighting. This secondary weighting takes the temporal correlation and spatial coupling degree between the fused features and the future changes of TEC as the core standard: it focuses on capturing the coupling relationship between the EIA feature mutation time step (such as the sudden geomagnetic storm or the period of sharp increase in solar activity) and the corresponding spatiotemporal features of TEC, assigning higher weights to the fused features of time steps with strong synergistic correlation, while suppressing redundant feature combinations without significant correlation. In this way, the long-range dependency relationship between different time steps within the fused feature sequence is accurately mined, and invalid redundant features are filtered out.

[0137] In practice, by calculating the global self-attention score of the fused feature sequences, priority is given to... and The correlation between the significantly fluctuating time steps and subsequent changes in the spatial features of the TEC grid allows the fused feature sequence after secondary weighting to focus on the core feature combinations driving the spatiotemporal evolution of TEC. The weighted fused feature sequence is then input into the Long Short-Term Memory (LSTM) network layer, where a gating mechanism effectively mines the temporal evolution patterns of the fused features, accurately capturing the dynamic correlation between TEC and EIA features over time. The core state update formula of the LSM network is as follows:

[0138]

[0139] In the formula Forgotten Gate;

[0140] For input gates;

[0141] For output gate;

[0142] This is the unit state;

[0143] It is in a hidden state.

[0144] The temporal features output by the Long Short-Term Memory (LSTM) network undergo dimensionality mapping through two fully connected layers. Finally, a Reshape layer restores the feature vectors to a TEC grid shape consistent with the labels, i.e., number of samples × output time step × latitude dimension × longitude dimension. The model ultimately outputs predicted TEC values, EIA attention weights, and global attention weights, with the attention weights providing support for the model's interpretability.

[0145] 3. Model Training and Optimization

[0146] Based on the CNN-LSTM-Attention model architecture, an integrated training strategy is adopted, which includes hierarchical data preprocessing, targeted training configuration, and multi-dimensional evaluation and optimization, to ensure that the model has high training efficiency and excellent prediction accuracy. The specific implementation process is as follows:

[0147] 1) Hierarchical data preprocessing and partitioning

[0148] First, the time-aligned model input file is read, and the TEC input sequence, TEC label sequence, and EIA feature sequence are extracted. All data is converted to float32 type, and then the sample number and time step of the TEC input sequence and EIA feature sequence are verified to be completely matched. After data validation, the data is divided into training and test sets in an 8:2 ratio, strictly maintaining temporal continuity during the partitioning process.

[0149] The TEC input sequences and EIA feature sequences in the training set are standardized, and the standardized parameters are applied to the test set. To adapt to the input requirements of the CNN layer, a channel dimension is added to the TEC input sequences. Finally, a validation set is partitioned from the training set in a 10:1 ratio, forming a three-layer data structure of training set, validation set, and test set.

[0150] 2) CNN-LSTM-Attention model training configuration

[0151] The Adam optimizer was chosen as the optimizer for the model, with an initial learning rate set to 1e-4 to avoid training oscillations caused by an excessively large learning rate. Given the model's multiple outputs, only the output corresponding to the predicted TEC value was used as the effective loss term, with mean squared error as the loss function. For the outputs of the EIA attention weights and global attention weights, the loss weights were set to 0 to ensure that model training focused on the core task of TEC prediction.

[0152] During model training, setting reasonable batch sizes and training epochs improves training efficiency and reduces memory usage through batch training. During training, dual input data is fed to the model, with a zero matrix used as placeholders for attention weights. Data shuffling is enabled to prevent the model from learning spurious temporal relationships. Validation set monitoring is enabled to track loss changes in real time and prevent overfitting.

[0153] 3) Multidimensional model evaluation

[0154] After the model training is completed, three core indicators, root mean square error, mean absolute error, and mean absolute percentage error, are used to quantitatively evaluate the prediction results of the training set, validation set, and test set, respectively.

[0155] 4) Hyperparameter tuning and generalization capability improvement

[0156] Key hyperparameters of the model were tuned and optimized, with a focus on optimizing the number of convolutional kernels in the CNN layers, the number of hidden neurons in the LSTM layers, the dimension of the attention layer, the number of neurons in the fully connected layers, and the initial learning rate. The control variable method was used to select the hyperparameter combination that minimized the validation set loss. Simultaneously, data augmentation techniques such as time step shifting and noise addition were employed to expand the training set and improve the model's generalization ability under different spatial weather scenarios.

[0157] 4. Prediction and Post-processing

[0158] Based on the trained CNN-LSTM-Attention model, a complete prediction scheme is adopted, including preprocessing of the data to be predicted, model inference, inverse normalization, and visualization verification, to achieve accurate prediction of low-latitude TEC in the new time period. The specific implementation process is as follows:

[0159] 1) Data collection and preprocessing to be predicted

[0160] For the target prediction period, corresponding low-latitude TEC grid image data is collected, and TEC grids conforming to a preset spatial range are extracted through image cropping. Then, using the EIA feature extraction function, four core EIA features are calculated step-by-step to form the EIA feature sequence to be predicted. After verifying that there are sufficient time steps, samples to be predicted are constructed according to the model's input and output time steps. The samples are standardized using the standardized parameters of the training set. Finally, channel dimensions are added to the TEC input sequence to adapt to the input requirements of the CNN-LSTM-Attention model.

[0161] 2) Model Inference and Denormalization

[0162] The standardized sample to be predicted is input into the trained CNN-LSTM-Attention model to initiate the model's inference process, outputting the predicted TEC value, EIA attention weight, and global attention weight. Inverse normalization is then applied to restore the true physical meaning of the predicted TEC value.

[0163] 3) Post-processing and visualization verification of prediction results

[0164] The inversely normalized prediction results are validated in multiple dimensions. First, a TEC grid comparison map with latitude and longitude information is drawn to visually present the prediction effect, while the attention weights are visualized to provide interpretability support for the prediction results. Second, the root mean square error, mean absolute error, and mean absolute percentage error are calculated to objectively evaluate the prediction accuracy and verify the model's generalization performance. Finally, for batch prediction scenarios, prediction reports containing quantitative indicators and visualization charts are automatically generated to provide data support for space weather applications.

[0165] In summary, this invention proposes a method for predicting the total electron content of the ionosphere in low latitudes based on equatorial ionization anomaly feature encoding. Compared with existing technologies, the significant technical advantages of the embodiments of this invention are reflected in the following aspects:

[0166] (1) CNN-LSTM-Attention dual-input deep fusion modeling architecture

[0167] The proposed CNN-LSTM-Attention dual-input deep fusion modeling architecture addresses the core shortcomings of existing hybrid architectures, such as their inability to adapt to the unique physical environment of the low-dimensional ionosphere and insufficient spatiotemporal feature capture capabilities. Existing hybrid architectures like CNN-LSTM and Transformer-LSTM only generalize the combination of spatial and temporal extraction capabilities, failing to adapt to the physical environment dominated by the low-dimensional EIA. This leads to prediction lag or bias during abrupt changes in the dynamically adjusted EIA. This architecture, through a dual-input parallel encoding design, enables CNN branches to accurately extract spatial gradient features from the low-dimensional TEC, adapting to its spatial distribution characteristics. The LSTM layer can deeply mine temporal evolution patterns. Simultaneously, a dual attention mechanism is introduced: the EIA self-attention layer focuses on key time-step features, while the global attention layer strengthens long-term temporal dependencies, forming a collaborative mechanism of "spatial adaptation—temporal depth mining—key feature enhancement."

[0168] Compared to existing technologies, this architecture improves the accuracy of spatiotemporal feature capture by specifically adapting to the low-latitude ionospheric physical environment. The dual-input branch design allows for the independent encoding and collaborative fusion of TEC spatiotemporal features and EIA physical features, avoiding the suppression of heterogeneous features by a single-input architecture. The dual attention mechanism accurately captures the intrinsic correlation between dynamic adjustments in EIA structure and changes in TEC, improving prediction stability under abrupt change scenarios. Simultaneously, the architecture can be adapted to different solar activity and geomagnetic disturbance scenarios through parameter adjustments, improving prediction accuracy and stability under extreme space weather conditions.

[0169] (2) Temporal alignment and dynamic weighted fusion mechanism of EIA features and TEC data

[0170] The proposed EIA feature and TEC data temporal alignment-dynamic weighted fusion mechanism addresses the core pain points of existing technologies, which neglect the crucial role of EIA and lack physical correlation in feature fusion. Existing technologies do not treat EIA-related features as independent inputs, relying solely on data-driven methods to stitch together parameters such as solar activity and geomagnetism, easily leading to feature redundancy or information masking, and resulting in predictions lacking physical interpretability. This mechanism, based on low-latitude ionospheric physics, uses four core features characterizing the bimodal structure and evolution of EIA as independent inputs. Through a full-process logic of "time-step binding—dimensional adaptation—dynamic weighting—secondary optimization," it first ensures strict spatiotemporal alignment between EIA and TEC data, and then dynamically adjusts feature weights through a self-attention mechanism to strengthen the dominant influence of EIA on TEC changes, establishing physically meaningful feature correlations.

[0171] Compared to existing technologies, this mechanism, by introducing core EIA features and establishing a physical correlation fusion logic, accurately captures the core driving factors of low-latitude TEC changes, improving the low prediction accuracy of low latitudes caused by neglecting the role of EIA in existing technologies. The dynamic weighting method can filter key features and suppress redundant information, allowing the model to focus on the intrinsic physical correlation between EIA and TEC, improving the effectiveness of feature fusion and the physical interpretability of prediction results. Furthermore, this mechanism can be transferred to other multi-source time-series data fusion scenarios, possessing broad applicability.

[0172] (3) A full-process TEC prediction method that combines accuracy and interpretability

[0173] This invention proposes a comprehensive TEC prediction method that combines accuracy and interpretability, overcoming the shortcomings of existing technologies that prioritize accuracy over interpretability, generalize data processing, and lack a systematic prediction process. Existing technologies focus on refined data preprocessing and model parameter tuning, failing to establish a comprehensive accuracy guarantee and interpretability system, and their data processing is not optimized for low-dimensional data characteristics. This method constructs a standardized system of "data preprocessing—model training—inference post-processing—interpretability analysis." The data processing stage employs hierarchical standardization and temporal consistency partitioning to adapt to the heterogeneous characteristics of EIA and TEC. The training stage focuses on core tasks through targeted loss configuration, combined with data shuffling and validation set monitoring to suppress overfitting. Inference post-processing restores physical meaning through inverse normalization. Interpretability analysis quantifies the model's attention to features at different time steps through attention weight visualization.

[0174] Compared to existing technologies, this end-to-end approach improves prediction accuracy and interpretability through targeted optimization. Targeted data processing design ensures input data quality and avoids feature distortion issues caused by generalization in existing data preprocessing. Visual analysis of attention weights clarifies the model's focus on different features, allowing prediction results to be traced back to the contribution of key EIA features, thus enhancing the reliability of the predictions. Simultaneously, standardized processes and batch report generation enhance engineering application capabilities, supporting the practical operational use of low-latitude TEC predictions.

[0175] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0176] This invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein the processor executes the computer program by performing at least the method described above.

[0177] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0178] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc or CD-ROM; magnetic surface memory can be disk storage or magnetic tape storage. The storage media described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0179] In the several embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0180] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0181] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0182] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0183] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0184] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0185] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0186] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0187] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or application, should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding, characterized in that, Includes the following steps: S1. Data Acquisition and Preprocessing: Acquire historical observation data on the total electron content of the ionosphere in low-latitude regions, and preprocess the historical observation data to form model input data; S2. Equatorial ionization anomaly feature extraction: Based on preprocessed historical observation data, the existence of equatorial ionization anomalies is identified, and key feature parameters of equatorial ionization anomalies are extracted to characterize their spatiotemporal evolution. The key feature parameters extracted from equatorial ionization anomalies specifically include: For each longitude sector and time step, the existence of the bimodal structure of the equatorial ionization anomaly is determined based on the standardized total electron content data. If they exist, locate the grid positions of the Northern Hemisphere peak and the Southern Hemisphere peak in the Northern and Southern Hemisphere regions of geomagnetic respectively, and record their total electron content intensity values ​​and corresponding actual geomagnetic latitudes. Using the located grid positions of the north and south peaks as a reference, an equatorial region encompassing both is determined, and the minimum total electron content within this region is located as the equatorial valley value. Based on the magnetic north peak, magnetic south peak, and equatorial valley values, the difference and ratio characteristics characterizing the intensity of equatorial ionization anomalies are calculated. S3. Feature Encoding Representation Learning: Construct a feature encoding network to encode the extracted key feature parameters of equatorial ionization anomalies into low-dimensional feature vectors, so as to learn a feature representation that can effectively characterize the dynamics of equatorial ionization anomalies. S4. Construction and Training of Total Electron Content Prediction Model: Construct a sequence prediction model that integrates the aforementioned feature representations. Using the encoded feature vectors and historical total electron content data, train the sequence prediction model to predict the total electron content of the low-latitude ionosphere at future times. The construction of the sequence prediction model integrating feature representations specifically includes: Construct a deep learning model that includes a spatiotemporal feature encoding branch, a feature weighted fusion branch, and a sequence prediction branch; The spatiotemporal feature coding branch processes the input historical total electron content sequence data, extracts its spatial features, and encodes them as the first feature sequence. The feature weighted fusion branch uses the key feature parameter sequence of equatorial ionization anomalies extracted in step S2 to form a second feature sequence. Then, a first-level attention weighting is applied to the second feature sequence, with the weight allocation strategy dynamically adjusted based on the physical priors of equatorial ionization anomalies. Next, the second feature sequence after the first-level weighting is concatenated with the first feature sequence to obtain a preliminary fused feature sequence. Finally, a second-level global attention weighting is applied to the preliminary fused feature sequence, with the weight allocation strategy focusing on mining long-range dependencies and coupling relationships between features at different time steps, forming a weighted fused feature sequence. The sequence prediction branch performs time-series modeling on the weighted fusion feature sequence and maps the time-series features output by the network to the predicted total electron content value at future times.

2. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in claim 1, characterized in that, Step S1 specifically includes: Obtain gridded data of total ionospheric electron content distributed by latitude and longitude grids covering low-latitude regions; The grid data is subjected to quality control to remove outliers that exceed reasonable physical limits; The data after quality control is standardized to form a standardized numerical matrix; A unique time identifier is assigned to the standardized numerical matrix for each time step, and the extracted key feature parameters of equatorial ionization anomaly are bound to the total electron content data of the corresponding time step. The data at all time steps are sorted and matched in chronological order, and continuity and integrity checks are performed. Missing data is imputed to form a model input dataset that is temporally continuous and feature-aligned.

3. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in claim 1 or 2, characterized in that, Step S2, which extracts key feature parameters of equatorial ionization anomalies, further includes: locating the grid positions of the peak values ​​in the Northern and Southern Hemispheres by traversing grid points and comparing total electron content values, and performing non-positive protection processing on the valley values. The difference feature is calculated by calculating the differences between the Northern and Southern peaks and the valley values, and then taking their arithmetic mean. The ratio feature is calculated by calculating the ratio of the average of the Northern and Southern peaks to the valley value.

4. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in claim 3, characterized in that, The basis for determining whether there is an equatorial ionization anomaly is: whether the total electron content value shows a bimodal structure on the latitudinal profile of the low latitude region, and whether there is a significant trough in the total electron content in the equatorial region between the two peaks.

5. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in claim 1 or 2, characterized in that, The construction of the feature encoding network in step S3 specifically includes: A feature transformation network with a fully connected layer as its core is constructed as the feature encoding network; The feature transformation network receives the extracted key feature parameters of the equatorial ionization anomaly as input, performs nonlinear transformation and dimension mapping through at least one fully connected layer, and encodes the key feature parameters into feature vectors of a predetermined dimension that match the subsequent fusion steps, so as to form a feature representation for characterizing the dynamics of the equatorial ionization anomaly. The parameters of the feature transformation network are trained end-to-end in supervised manner along with other parts of the model during the training process of the sequence prediction model in step S4.

6. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in claim 1 or 2, characterized in that, Step S4, which involves constructing a sequence prediction model with fused feature representations, specifically includes: The spatiotemporal feature coding branch uses a convolutional neural network to process the input historical total electron content sequence data, extract its spatial features, and encode them as the first feature sequence; The key feature parameter sequence of the equatorial ionization anomaly is transformed and mapped nonlinearly through at least one fully connected layer to form a second feature sequence. The sequence prediction branch uses a long short-term memory network to perform time-series modeling on the weighted fused feature sequence, and maps the time-series features output by the network to the predicted total electron content value at future times through a fully connected layer.

7. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in claim 6, characterized in that, The attention mechanism applied to the equatorial ionization anomaly feature vector sequence in the feature weighted fusion branch specifically includes the following steps: After mapping the equatorial ionization anomaly feature vector sequence, a first-level attention weighting is applied to it. The weighting allocation strategy is configured to dynamically adjust the degree of prior influence of the physical state reflected by the equatorial ionization anomaly features on the change in total electron content. The equatorial ionization anomaly feature sequence, which has undergone first-level weighting, is concatenated with the first feature sequence; A second-level global attention weighting is applied to the preliminary fused feature sequence formed after splicing. The weighting allocation strategy is configured to mine and enhance the temporal feature combinations in the preliminary fused feature sequence that simultaneously contain significant equatorial ionization anomaly change information and corresponding spatial features.

8. The method for predicting the total electron content of the low-latitude ionosphere based on equatorial ionization anomaly feature coding as described in any one of claims 1 to 2, characterized in that, When training the sequence prediction model, the mean squared error between the predicted output and the true value is used as the loss function, and the parameters of the long short-term memory network are optimized through the backpropagation algorithm.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for predicting the total electron content of the low-latitude ionosphere based on the coding of equatorial ionization anomaly features as described in any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for predicting the total electron content of the low-latitude ionosphere based on the coding of equatorial ionization anomaly features as described in any one of claims 1 to 8.

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