A method and system for low-altitude atmospheric duct analysis for electromagnetic propagation optimization

Abstract

The application discloses a low-altitude atmospheric waveguide analysis method and system for electromagnetic propagation optimization, and relates to the technical field of ocean atmospheric environment detection and electromagnetic propagation. The specific steps of the method are as follows: synchronously collecting multiple types of marine meteorological data of a target sea area, and constructing a standardized data set after processing; constructing a physical constraint deep neural network to generate a mesoscale parameter field; constructing a model with a correction mechanism to generate a small-scale profile model; constructing a multi-scale fusion model to output a spatio-temporal prediction result; analyzing characteristics, outputting an optimization strategy and feeding back reversely to complete whole-process optimization. The application realizes fine waveguide modeling from mesoscale to small scale, and improves the accuracy of atmospheric waveguide feature representation by constructing a physical constraint deep neural network and introducing an interface inclination angle correction mechanism. The application realizes cross-scale adaptive fusion, improves prediction accuracy, establishes a reverse feedback mechanism to promote whole-process optimization, and better adapts to the requirements of a marine electromagnetic system by constructing a multi-scale fusion model.

Description

Technical Field

[0001] This invention relates to the field of marine atmospheric environment detection and electromagnetic propagation technology, specifically to a low-altitude atmospheric waveguide analysis method and system for electromagnetic propagation optimization. Background Technology

[0002] Low-altitude atmospheric waveguides are a unique atmospheric refraction phenomenon at sea, enabling electromagnetic waves to propagate beyond visual range. They play a crucial role in regulating the performance of electromagnetic systems such as maritime radar detection and wireless communication. Atmospheric waveguides in target sea areas are influenced by air-sea coupling, exhibiting distinct mesoscale spatial distribution characteristics and small-scale spatiotemporal variability. Their formation and evolution are closely related to continuous changes in marine meteorological parameters such as temperature, humidity, and ocean currents. Accurate analysis of the spatiotemporal distribution patterns of low-altitude atmospheric waveguides is a core prerequisite for optimizing maritime electromagnetic propagation and improving the beyond-visual-range coverage and anti-interference capabilities of electromagnetic systems, and has become a key research focus in the field of marine electromagnetic engineering.

[0003] Existing technologies for analyzing low-altitude atmospheric waveguides suffer from several shortcomings: Traditional mesoscale numerical models' air-sea coupling parameterization schemes, due to simplified physical assumptions, struggle to accurately characterize the complexities of air-sea turbulence, resulting in insufficient prediction accuracy for atmospheric waveguide characteristic parameter fields; small-scale waveguide profile modeling often employs conventional spatial interpolation methods, failing to consider the influence of waveguide interface tilt, thus failing to accurately simulate the spatial distribution characteristics of non-uniform waveguides, leading to distortion in fine-grained interpolation results; waveguide prediction models lack effective cross-scale feature fusion mechanisms, making it difficult to integrate multi-source features from mesoscale global, small-scale local, and radiosonde measurements, resulting in poor spatiotemporal resolution and continuity of prediction results; furthermore, existing methods lack a closed-loop feedback mechanism between electromagnetic propagation measurements and waveguide analysis, resulting in insufficient adaptability and dynamic adjustment capabilities of electromagnetic propagation optimization strategies, making it difficult to meet the practical application requirements of marine electromagnetic systems.

[0004] The operational efficiency of marine electromagnetic systems places stringent demands on the accuracy, spatiotemporal resolution, and dynamic optimization capabilities of low-altitude atmospheric waveguide analysis. However, existing technologies, due to limitations in areas such as air-sea coupling parameterization, small-scale modeling, multi-scale feature fusion, and closed-loop optimization, cannot achieve high-precision spatiotemporal continuous forecasting of atmospheric waveguides and accurate optimization of electromagnetic propagation. Currently, the field of marine electromagnetic engineering urgently needs an analytical method that integrates the physical laws of atmospheric waveguides with deep learning techniques to solve the technical challenges of multi-scale waveguide modeling and cross-scale feature fusion, and to establish a full-process closed-loop optimization mechanism. This would improve the accuracy and timeliness of low-altitude atmospheric waveguide analysis, providing reliable technical support for the optimization of marine electromagnetic propagation. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a low-altitude atmospheric waveguide analysis method and system for electromagnetic propagation optimization. This method involves collecting and processing various types of marine meteorological data to construct a standardized dataset; building a physically constrained deep neural network to generate a mesoscale parameter field; introducing an interface tilt angle correction mechanism to construct a small-scale profile model; constructing a multi-scale Transformer fusion model to output spatiotemporal forecast results; and finally performing characteristic analysis, outputting optimization strategies, and providing back-feedback optimization.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: On one hand, a low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization, the method comprising:

[0007] S100. Data Processing: Synchronously collect various types of marine meteorological data from the target sea area, complete data cleaning, spatiotemporal alignment and normalization processing, and construct a unified spatiotemporal dimension multi-source meteorological standardized dataset.

[0008] S200, Parameter Optimization: Using a multi-source meteorological standardized dataset as input, a physically constrained deep neural network embedded with atmospheric waveguide physical prediction equations is constructed to replace the traditional ocean-atmosphere coupling parameterization scheme of mesoscale numerical models and generate a mesoscale atmospheric waveguide characteristic parameter field for the target sea area.

[0009] S300, Small-scale waveguide modeling: Using the characteristic parameter field of the mesoscale atmospheric waveguide as the boundary constraint, a two-dimensional coupled Markov chain model with an interface tilt angle correction mechanism is constructed to complete fine-grained spatial interpolation and non-uniform waveguide profile simulation, and generate a small-scale atmospheric waveguide profile model of the target sea area.

[0010] S400, waveguide spatiotemporal forecast: Simultaneously input mesoscale atmospheric waveguide characteristic parameter field, small-scale atmospheric waveguide profile model and radiosonde data in multi-source meteorological standardized dataset, construct multi-scale Transformer fusion model with hierarchical attention mechanism, complete cross-scale feature extraction and adaptive fusion, and output spatiotemporal continuous forecast results of low-altitude atmospheric waveguide in target sea area;

[0011] S500, Characteristic Analysis and Closed-Loop Optimization: Based on the spatiotemporal continuous forecast results of low-altitude atmospheric waveguides, an atmospheric refractive index profile is constructed and electromagnetic wave propagation characteristics are simulated. Combined with the working parameters of the target marine electromagnetic system, an electromagnetic propagation optimization strategy is output. At the same time, the deviation between the measured and predicted electromagnetic propagation is fed back to the preceding models to complete the full-process iterative optimization.

[0012] Furthermore, the specific process of data processing is as follows: three types of marine meteorological data are collected simultaneously: mesoscale numerical model meteorological data covering multiple heights of the target sea area, radiosonde observation meteorological data covering the entire low-altitude region, and sea surface observation meteorological data collected by fixed sea surface stations and buoys. All three types of data include basic meteorological parameters such as temperature, salinity, ocean current, relative humidity, air pressure, and wind speed at different heights of the target sea area. During data processing, outliers in the data are first removed and missing data are filled in. Then, all data are unified to the same geographic coordinate system and time reference to complete spatiotemporal alignment. Based on the collected basic meteorological parameters, the Richardson number, which characterizes the turbulent stability of the air-sea coupling process, is obtained. Finally, the normalization of all parameters is completed to form a grid-aligned multi-source meteorological standardized dataset.

[0013] Furthermore, during the training process of the physical constraint deep neural network, a total loss function integrating regularization constraints based on atmospheric waveguide physical laws is constructed. The network weights are iteratively optimized through backpropagation of the total loss function, as shown in the formula:

[0014]

[0015] in, This represents the total loss value of the physically constrained deep neural network, used to measure the overall bias of the network's prediction results; The mean square error loss is specifically the mean square error between the predicted values ​​of atmospheric waveguide characteristic parameters obtained by mapping the vertical eddy diffusion coefficient and vertical eddy diffusion viscosity of the ocean model output by the network and the true values ​​of atmospheric waveguide characteristic parameters extracted from the sounding meteorological data in S100. This is the physical constraint weight coefficient, with a value ranging from 0.1 to 10, used to balance the weight between the accuracy of data fitting and the conformity to physical laws; The residual loss is the atmospheric waveguide physics prediction equation. Specifically, it is the calculated deviation value of both sides of the equation after the waveguide characteristic parameters predicted by the network are substituted into the hydrodynamic and thermodynamic physics prediction equation for atmospheric waveguide formation. It is used to constrain the network output results to conform to the objective physical laws of atmospheric waveguide formation.

[0016] Furthermore, the physically constrained deep neural network adopts a fully connected network structure, with an input layer, hidden layer, and output layer set sequentially: the number of neurons in the hidden layer is 128, 256, 256, 128, 64, and 32 respectively; the input vector of the input layer is the four-dimensional feature vector of temperature, salinity, ocean current, and Richardson number at different altitudes in the target sea area from the multi-source meteorological normalized dataset obtained by S100, where the Richardson number is used to characterize the turbulent stability in the air-sea coupling process; the output parameters of the output layer are the vertical eddy diffusion coefficient and vertical eddy diffusion viscosity of the ocean model; by constructing a mapping relationship between the vertical eddy diffusion coefficient and atmospheric waveguide characteristic parameters, the network output parameters are converted into a mesoscale atmospheric waveguide characteristic parameter field, which includes waveguide height, waveguide thickness, waveguide intensity, and atmospheric refractive index vertical gradient.

[0017] Furthermore, the interface tilt angle correction factor performs a weighted correction on the lateral transition probability matrix of the two-dimensional coupled Markov chain, as shown in the formula:

[0018]

[0019] in, This is the interface tilt angle correction factor, used to weight and adjust the element values ​​of the lateral transition probability matrix to adapt to the simulation requirements of waveguide interfaces with different tilt directions. The actual tilt angle of the waveguide interface within the target interpolation region is calculated using the waveguide height difference between adjacent grids in the mesoscale atmospheric waveguide characteristic parameter field output by S200. This is the default horizontal interface reference angle for a two-dimensional coupled Markov chain, with a value of 0. The adaptive adjustment coefficient ranges from 0.5 to 2 and is adaptively adjusted according to the tilt variation of the waveguide interface in the target sea area.

[0020] By using the modified lateral transfer probability matrix, the limitation of the waveguide interface tilt direction on the simulation results of non-uniform waveguide profiles is eliminated.

[0021] Furthermore, the specific process of small-scale waveguide modeling is as follows: A multi-directional one-dimensional Markov chain is coupled to construct a two-dimensional coupled Markov chain model; using the 25km×25km grid node values ​​of the mesoscale atmospheric waveguide characteristic parameter field as boundary reference values, the mesoscale grid is divided into a 9km×9km fine-grained interpolation grid; the state transition probabilities of atmospheric waveguide parameters at adjacent grid nodes are statistically analyzed, and a longitudinal transition probability matrix and an initial transverse transition probability matrix are constructed respectively; the element values ​​of the initial transverse transition probability matrix are weighted and corrected using an interface tilt angle correction factor to obtain a corrected transverse transition probability matrix that adapts to the tilt direction of the waveguide interface; based on the longitudinal transition probability matrix and the corrected transverse transition probability matrix, spatial interpolation prediction is performed on the state of unknown waveguide parameters within the fine-grained grid to generate a small-scale atmospheric waveguide profile model of the target sea area.

[0022] Furthermore, the multi-scale Transformer fusion model with a hierarchical attention mechanism sets up an encoder and decoder structure. The encoder has three parallel attention branches: the first branch corresponds to mesoscale global feature extraction, with the input being the mesoscale atmospheric waveguide feature parameter field obtained by S200; the second branch corresponds to small-scale local feature extraction, with the input being the small-scale atmospheric waveguide profile model obtained by S300; and the third branch corresponds to accurate feature extraction from radiosonde measurements, with the input being the radiosonde meteorological data from the multi-source meteorological standardized dataset obtained by S100. The hierarchical attention mechanism assigns adaptive weights to features at different scales, completing the adaptive fusion of cross-scale spatiotemporal features. Based on the fused cross-scale features, the decoder outputs the continuous spatiotemporal forecast results of low-altitude atmospheric waveguides for the target sea area for the next 24 to 72 hours, with a temporal resolution of 1 hour and a spatial resolution of 9 km × 9 km.

[0023] Furthermore, during the training process of the multi-scale Transformer fusion model with hierarchical attention mechanism, the spatiotemporal dimension of the input multi-scale dataset is expanded by using a sliding window method. The waveguide feature parameters extracted from the radiosonde meteorological data obtained by S100 are used as ground truth labels to iteratively train the model, and the model is generalized and adapted to different sea areas through transfer learning.

[0024] Furthermore, the specific process of simulating and calculating the electromagnetic propagation characteristics is as follows:

[0025] The first step is to extract the waveguide height, waveguide thickness, waveguide intensity, and atmospheric refractive index vertical gradient parameters corresponding to the spatiotemporal location based on the spatiotemporal continuous forecast results of the low-altitude atmospheric waveguide obtained by S400, and construct a continuously changing atmospheric refractive index profile.

[0026] The second step is to solve the narrow-angle parabolic equation for electromagnetic wave propagation using the step-by-step Fourier parabolic equation method:

[0027]

[0028] in, The amplitude of the electromagnetic wave scalar field; For the distance of propagation; For height; For free space wavenumber; The highly correlated atmospheric refractive index is constructed based on the forecast results;

[0029] Step 3: Calculate the propagation loss based on the solved field amplitude:

[0030]

[0031] in, For propagation loss; The amplitude of the reference field at the free-space launch end; The amplitude of the electromagnetic wave scalar field;

[0032] The fourth step is to define the beyond-line-of-sight coverage range as the farthest propagation distance where the propagation loss is less than the maximum allowable loss of the target system, and the radar blind zone as the spatial region where the field strength is lower than the system's receiving sensitivity; and to output an electromagnetic propagation optimization scheme adapted to the communication and detection scenarios by combining the operating parameters of the target's marine electromagnetic system.

[0033] On the other hand, a low-altitude atmospheric waveguide analysis system for electromagnetic propagation optimization includes:

[0034] Data processing module: used to collect three types of marine meteorological data from the target sea area, and after cleaning, spatiotemporal alignment, Richardson number calculation and normalization, construct a multi-source meteorological standardized dataset;

[0035] Parameter optimization module: It has a built-in physical constraint deep neural network with embedded atmospheric waveguide physical prediction equations. It takes a standardized dataset as input, replaces the traditional air-sea coupling parameterization scheme, and generates a mesoscale atmospheric waveguide characteristic parameter field.

[0036] Small-scale waveguide modeling module: Using mesoscale parameter fields as boundary constraints, a two-dimensional coupled Markov chain model with interface tilt angle correction mechanism is used to complete fine-grained spatial interpolation and non-uniform waveguide profile simulation, generating a small-scale atmospheric waveguide profile model.

[0037] Waveguide spatiotemporal forecasting module: It has a built-in multi-scale Transformer fusion model with a hierarchical attention mechanism, which simultaneously inputs multi-scale waveguide data and radiosonde measurement data, completes cross-scale feature fusion, and outputs continuous spatiotemporal forecasting results of low-altitude atmospheric waveguides;

[0038] Characteristic analysis and closed-loop optimization module: Based on the forecast results, an atmospheric refractive index profile is constructed and electromagnetic propagation characteristics are simulated. Combined with the working parameters of the marine electromagnetic system, an electromagnetic propagation optimization strategy is output. At the same time, the deviation between the measured and predicted electromagnetic propagation is fed back to the preceding module to complete the full-process iterative optimization.

[0039] Compared with existing technologies, this low-altitude atmospheric waveguide analysis method and system for electromagnetic propagation optimization has the following advantages:

[0040] I. This invention utilizes standardized processing of multi-source marine meteorological data and integrates atmospheric waveguide physical laws to construct a physically constrained deep neural network, replacing the traditional air-sea coupling parameterization scheme. This allows the generation of atmospheric waveguide characteristic parameter fields to better reflect the actual physical processes of air-sea coupling. Simultaneously, an interface tilt angle correction mechanism is introduced in small-scale waveguide modeling to optimize the spatial interpolation effect of the two-dimensional coupled Markov chain model. This effectively solves the problem of traditional modeling's inability to adapt to non-uniform waveguide profile features, achieving refined waveguide modeling from mesoscale to small scale. It significantly improves the accuracy of atmospheric waveguide characteristic representation at different scales, enabling the waveguide model to accurately reflect the actual waveguide distribution in the target sea area, providing high-quality basic data support for subsequent spatiotemporal forecasting.

[0041] Second, this invention constructs a multi-scale Transformer fusion model with a hierarchical attention mechanism, achieving cross-scale adaptive fusion of mesoscale and small-scale waveguide features with radiosonde data, thus improving the continuity and accuracy of low-altitude atmospheric waveguide spatiotemporal forecasts. Simultaneously, based on the forecast results, it constructs atmospheric refractive index profiles and simulates electromagnetic propagation characteristics. Combined with targeted optimization strategies outputting the operating parameters of the marine electromagnetic system, it establishes a reverse feedback mechanism for the deviation between measured and predicted electromagnetic propagation, driving iterative optimization of the entire process of each preceding model and achieving coordinated adjustment of waveguide analysis and electromagnetic propagation optimization. This continuously improves the overall analysis and optimization effect, better adapting to the actual application needs of marine electromagnetic systems and significantly enhancing the practicality and adaptability of electromagnetic propagation optimization strategies.

[0042] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0044] Figure 1 This is a step-by-step framework diagram of a low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization.

[0045] Figure 2 This is a data processing flowchart for a low-altitude atmospheric waveguide analysis method used for electromagnetic propagation optimization.

[0046] Figure 3 This is an overall flowchart of a low-altitude atmospheric waveguide analysis system for electromagnetic propagation optimization. Detailed Implementation

[0047] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0048] Example 1:

[0049] Data Processing: Simultaneous acquisition of three types of marine meteorological data was conducted for the target sea area. These included mesoscale numerical model meteorological data covering multiple altitudes of the target sea area, radiosonde observation meteorological data covering the entire low-altitude region, and sea surface observation meteorological data collected from fixed sea stations and buoys. All three types of data comprehensively cover basic meteorological parameters such as temperature, salinity, ocean current, relative humidity, air pressure, and wind speed at different altitudes in the target sea area. The simultaneous acquisition of multiple types of data can comprehensively cover the meteorological information dimensions of the target sea area from the upper atmosphere to the sea surface, and from model simulation to actual observation, allowing subsequent analysis to fully rely on multi-source heterogeneous meteorological data. The three types of collected data underwent comprehensive preprocessing. First, outliers were removed and missing data were filled in, ensuring both data integrity and accuracy. Then, all data were unified to the same geographic coordinate system and time base to achieve spatiotemporal alignment, eliminating differences in the spatiotemporal dimensions of multi-source data and providing a unified analytical basis for meteorological data from different sources. Subsequently, Richardson's number, which characterizes the turbulent stability of the ocean-atmosphere coupling process, was calculated based on the collected basic meteorological parameters, enriching the feature dimensions of the meteorological data and accurately depicting the key turbulent features in the ocean-atmosphere coupling process. Finally, all parameters were normalized to eliminate dimensional differences between different parameters, ensuring that all parameters are within a uniform and comparable range. This resulted in a grid-aligned multi-source meteorological standardized dataset. This dataset provides a reliable and unified data source for all subsequent waveguide analysis-related model training, parameter calculation, and feature extraction, ensuring the consistency and accuracy of subsequent analytical steps.

[0050] Parameter optimization: Using the completed multi-source meteorological standardized dataset as the core input data, a physically constrained deep neural network embedded with atmospheric waveguide physical prediction equations was constructed. This network adopts a fully connected network structure, with an input layer, hidden layers, and an output layer set sequentially. The number of neurons in the hidden layer is 128, 256, 256, 128, 64, and 32 respectively. This gradient setting of the number of neurons can adapt to the feature extraction, transformation, and depth mapping requirements of the multi-source meteorological standardized data, allowing the network to efficiently process four-dimensional feature vectors and output accurate ocean model-related parameters. The input vector of the input layer is the four-dimensional feature vector of temperature, salinity, ocean current, and Richardson number at different altitudes in the target sea area from the multi-source meteorological standardized dataset. The input of the four-dimensional feature vector can comprehensively capture the key influencing factors in the air-sea coupling process, allowing the network to fully learn the intrinsic relationship between air-sea coupling and atmospheric waveguide characteristics. The output parameters of the output layer are the vertical eddy diffusion coefficient and vertical eddy diffusion viscosity of the ocean model, providing the core transformation basis for the subsequent generation of atmospheric waveguide feature parameter fields. During the training process of this network, a total loss function incorporating regularization constraints based on atmospheric waveguide physical laws is constructed. The network weights are iteratively optimized through backpropagation of the total loss function, as shown in the formula: ,in, This represents the total loss value of the physically constrained deep neural network. This is the mean square error loss; These are the physical constraint weighting coefficients; The residual loss of the atmospheric waveguide physics prediction equation is used. The construction of the total loss function ensures both the accuracy of data fitting during network training and that the network output strictly conforms to the objective physical laws of atmospheric waveguide formation, avoiding overfitting and deviation from actual physical laws. After network training is completed, this physically constrained deep neural network replaces the traditional air-sea coupling parameterization scheme of mesoscale numerical models, making up for the insufficient accuracy and poor adaptability of traditional models in air-sea coupling simulation, and significantly improving the accuracy of air-sea coupling simulation in the mesoscale range. Then, by constructing the mapping relationship between the vertical eddy diffusion coefficient and atmospheric waveguide characteristic parameters, the network output parameters are converted into a mesoscale atmospheric waveguide characteristic parameter field of the target sea area. This characteristic parameter field includes core atmospheric waveguide characteristic parameters such as waveguide height, waveguide thickness, waveguide intensity, and vertical gradient of atmospheric refractive index, so that the waveguide characteristics in the mesoscale range present a continuous state that conforms to the actual sea area distribution, providing accurate and comprehensive boundary reference for subsequent small-scale waveguide modeling, and enabling the small-scale modeling to have reliable mesoscale global characteristic support.

[0051] Small-scale waveguide modeling: Using the mesoscale atmospheric waveguide characteristic parameter field obtained in the parameter optimization stage as the core boundary constraint, a multi-directional one-dimensional Markov chain is first coupled to build a two-dimensional coupled Markov chain model. The coupling of the multi-directional one-dimensional Markov chain can adapt to the waveguide parameter interpolation requirements in two-dimensional space, allowing the model to accurately simulate small-scale waveguide parameters in the two-dimensional space of the target sea area. Then, using the 25km×25km grid node value of the mesoscale atmospheric waveguide characteristic parameter field as the boundary reference value, the mesoscale grid is finely divided into a 9km×9km fine-grained interpolation grid. The fine division of the grid can significantly improve the spatial resolution of the waveguide profile, allowing the waveguide characteristics in the small-scale range to be characterized more meticulously and more closely match the actual waveguide distribution in the target sea area. Subsequently, the state transition probabilities of atmospheric waveguide parameters at adjacent grid nodes are statistically analyzed, and longitudinal transition probability matrices and initial transverse transition probability matrices are constructed. The statistical analysis and matrix construction of state transition probabilities provide a probabilistic basis for spatial interpolation that conforms to the natural variation law of waveguide parameters, ensuring that the interpolation results do not deviate from the actual variation trend of waveguide parameters. Then, the element values ​​of the initial transverse transition probability matrix are weighted and corrected using an interface tilt angle correction factor, as shown in the formula: ,in, This is a correction factor for the interface tilt angle; The actual tilt angle of the waveguide interface within the target interpolation region; The default horizontal interface reference angle for a two-dimensional coupled Markov chain; To adaptively adjust the coefficients, a corrected lateral transfer probability matrix is ​​obtained to adapt to the tilt direction of the waveguide interface. The weighted correction of the interface tilt angle correction factor can accurately adapt to the simulation requirements of waveguide interfaces with different tilt directions, eliminating the limitation of the waveguide interface tilt direction on the simulation results of non-uniform waveguide profiles. This allows the simulation results to closely match the actual tilt state of the waveguide interface in the actual sea area. Finally, based on the longitudinal transfer probability matrix and the corrected lateral transfer probability matrix, spatial interpolation prediction is performed on the state of unknown waveguide parameters within the fine-grained grid. This completes the fine-grained spatial interpolation and non-uniform waveguide profile simulation, ultimately generating a small-scale atmospheric waveguide profile model of the target sea area. This model can accurately reproduce the detailed changes of the waveguide profile within a small scale range of the target sea area, extending the characterization of waveguide features from the macroscopic mesoscale to the microscopic small scale. This provides fine-grained local feature support for subsequent cross-scale feature fusion and waveguide spatiotemporal forecasting, allowing cross-scale analysis to take into account both global and local features.

[0052] Waveguide Spatiotemporal Forecasting: A multi-scale Transformer fusion model with a hierarchical attention mechanism is constructed by simultaneously inputting mesoscale atmospheric waveguide characteristic parameter fields, small-scale atmospheric waveguide profile models, and radiosonde data from a multi-source meteorological standardized dataset. The simultaneous input of multi-type, multi-scale data allows the model to fully acquire waveguide-related features from different scales and sources in the target sea area, ensuring comprehensive feature extraction and enabling the model to learn the spatiotemporal variation patterns of waveguide features from global, local, and experimental dimensions. The model employs an encoder and decoder structure. The encoder incorporates three parallel attention branches: the first branch corresponds to mesoscale global feature extraction, with input being the mesoscale atmospheric waveguide characteristic parameter field; the second branch corresponds to small-scale local feature extraction, with input being the small-scale atmospheric waveguide profile model; and the third branch corresponds to precise feature extraction from radiosonde measurements, with input being actual radiosonde meteorological data. These three parallel attention branches can selectively extract features of different scales and types, improving the accuracy of feature extraction and ensuring that core features at each scale are fully captured. During model training, a sliding window approach is used to expand the spatiotemporal dimensions of the input multi-scale dataset, enriching the model's training sample library and improving its adaptability to different spatiotemporal scenarios. This allows the model to cope with the complex spatiotemporal changes in waveguide characteristics of the target sea area. Simultaneously, waveguide feature parameters extracted from radiosonde meteorological data are used as ground truth labels for iterative training of the model, ensuring that the model's forecast results always closely match the actual measured conditions and guaranteeing the accuracy of the forecast results. Furthermore, transfer learning is used to achieve generalization adaptation of the model in different sea areas, enabling the model to maintain stable and accurate performance in waveguide forecasts in different sea areas, breaking the limitations of the model's sea area application. After training, an adaptive weight is assigned to features of different scales through a hierarchical attention mechanism. This allows the model to focus on the core features that are more valuable for waveguide spatiotemporal forecasting, while weakening the interference of secondary features. This achieves efficient and accurate adaptive fusion of cross-scale spatiotemporal features. The decoder then outputs continuous spatiotemporal forecasts of low-altitude atmospheric waveguides for the target sea area for the next 24 to 72 hours, with a temporal resolution of 1 hour and a spatial resolution of 9 km × 9 km. These forecasts have clear and detailed temporal and spatial resolutions, providing continuous, accurate, and detailed waveguide data support for subsequent electromagnetic propagation characteristic simulations. This allows electromagnetic propagation analysis to be conducted based on spatiotemporally continuous waveguide data, improving the scientific rigor and practicality of the analysis results.

[0053] Characteristic Analysis and Closed-Loop Optimization: Based on the continuous spatiotemporal forecast results of low-altitude atmospheric waveguides, waveguide height, waveguide thickness, waveguide intensity, and atmospheric refractive index vertical gradient parameters at corresponding spatiotemporal locations are extracted to construct a continuously varying atmospheric refractive index profile. This profile ensures that the spatiotemporal variation of atmospheric refractive index is highly consistent with the actual spatiotemporal distribution of waveguides in the target sea area, laying an accurate atmospheric medium foundation for electromagnetic wave propagation characteristic simulation and allowing the simulation process to be conducted based on a realistic medium environment. Subsequently, the step-by-step Fourier parabolic equation method is used to solve the narrow-angle parabolic equation for electromagnetic wave propagation. This method can accurately calculate the scalar field amplitude of electromagnetic waves in the low-altitude atmospheric waveguide environment. The formula is: ,in, The amplitude of the electromagnetic wave scalar field; For the distance of propagation; For height; For free space wavenumber; The highly correlated atmospheric refractive index is constructed based on the forecast results; the propagation state of electromagnetic waves in the waveguide environment is realistically reproduced; and the propagation loss is calculated based on the obtained electromagnetic wave scalar field amplitude using the propagation loss calculation formula, which is: ,in, For propagation loss; The amplitude of the reference field at the free-space launch end; The electromagnetic wave scalar field amplitude is used to transform abstract field amplitude data into intuitive propagation loss data that can be used for engineering applications. Then, the farthest propagation distance where the propagation loss is less than the maximum allowable loss of the target system is defined as the over-the-horizon coverage range, and the spatial region where the field strength is lower than the system's receiving sensitivity is defined as the radar blind zone. This definition method ensures that the analysis results of the over-the-horizon coverage range and radar blind zone are completely consistent with the actual operating threshold of the target marine electromagnetic system, giving the analysis results direct engineering application value. Combined with the operating parameters of the target marine electromagnetic system, an electromagnetic propagation optimization strategy adapted to the scenario of marine electromagnetic detection and communication collaboration is output. This strategy can specifically solve problems such as excessive propagation loss, too many radar blind zones, and insufficient over-the-horizon coverage in the process of marine electromagnetic detection and communication, providing a scientific and practical basis for parameter adjustment, working area planning, and detection and communication link design of the target marine electromagnetic system. Simultaneously, measured data of electromagnetic propagation in the target sea area are collected using marine measuring equipment. Specialized algorithms are employed to calculate the deviation between the measured and predicted electromagnetic propagation results. This deviation is then fed back to preceding models, including physically constrained deep neural networks, two-dimensional coupled Markov chain models, and multi-scale Transformer fusion models with hierarchical attention mechanisms. Each model adjusts and optimizes its network weights, matrix parameters, and model structure based on the feedback deviation data, completing the iterative optimization of the entire low-altitude atmospheric waveguide analysis process. Figure 1As shown, this allows the entire method to be continuously corrected based on actual measurements, thereby constantly improving the accuracy of waveguide forecasting and the adaptability of electromagnetic propagation optimization strategies, ensuring that the method remains highly consistent with actual sea conditions in long-term applications.

[0054] Example 2:

[0055] Data Processing Module: This module conducts precise acquisition of three types of marine meteorological data for the target sea area of ​​over-the-horizon electromagnetic communication. These include mesoscale numerical model meteorological data covering multiple altitudes of the target sea area, radiosonde observations covering the entire low-altitude region, and sea surface observations from fixed stations and buoys. All three types of data comprehensively include basic meteorological parameters such as temperature, salinity, ocean currents, relative humidity, air pressure, and wind speed at different altitudes within the target sea area. This comprehensive acquisition of multiple meteorological data types allows the module to obtain complete meteorological information for the target sea area, from high altitudes to the sea surface, and from model simulations to actual measurements, laying a comprehensive meteorological data foundation for the subsequent operation of the entire system. After data acquisition, this module performs comprehensive cleaning of all collected data, removing outliers and filling in missing data to ensure the integrity and accuracy of meteorological data and prevent interference from incomplete or abnormal data in subsequent analysis. Then, all data is unified to the same geographic coordinate system and time base for spatiotemporal alignment, eliminating differences in the spatiotemporal dimensions of multi-source heterogeneous data and achieving effective fusion of meteorological data from different sources. This allows subsequent modules to conduct analysis based on a unified spatiotemporal benchmark dataset. Next, Richardson's number, which characterizes the turbulent stability of the ocean-atmosphere coupling process, is accurately calculated based on basic meteorological parameters, enriching the feature dimensions of the meteorological data and enabling the dataset to accurately depict key turbulent features in the ocean-atmosphere coupling process, thus improving the feature information related to ocean-atmosphere coupling. Finally, normalization is performed on all parameters to eliminate dimensional differences between different meteorological parameters, ensuring all parameters are within a unified numerical range and eliminating analytical biases caused by dimensional differences. Ultimately, a grid-aligned, multi-source meteorological standardized dataset is constructed, such as... Figure 2 As shown, this module synchronously transmits the completed multi-source meteorological standardized dataset to the parameter optimization module and the waveguide spatiotemporal forecasting module, ensuring the continuity and data consistency of subsequent module work. This allows both modules to rely on the same standardized and accurate dataset for model training and feature extraction, ensuring the accuracy of the entire system's analysis results from the data source.

[0056] Parameter Optimization Module: The parameter optimization module receives multi-source meteorological standardized datasets transmitted from the data processing module in real time, using them as core input data. It directly calls the physical constraint deep neural network embedded in the module, which incorporates atmospheric waveguide physical prediction equations. This network is a fully connected network structure. Its input layer can accurately receive four-dimensional feature vectors of temperature, salinity, ocean current, and Richardson number at different altitudes in the target sea area. The input of the four-dimensional feature vectors allows the network to comprehensively capture the key influencing factors of the ocean-atmosphere coupling process and fully learn the intrinsic relationship between ocean-atmosphere coupling and atmospheric waveguide characteristics. The number of neurons in the hidden layer is 128, 256, 256, 128, 64, and 32 respectively. This gradient setting of the number of neurons can efficiently complete the extraction, transformation, and deep mapping of multi-source meteorological features, allowing the network to accurately process the four-dimensional feature vectors and output ocean model-related parameters that conform to reality. The output layer stably outputs the vertical eddy diffusion coefficient and vertical eddy diffusion viscosity of the ocean model, providing the core transformation basis for the generation of mesoscale atmospheric waveguide characteristic parameter fields. During network training, this module autonomously constructs a total loss function that incorporates regularization constraints based on atmospheric waveguide physical laws. Through backpropagation of this total loss function, the network weights are iteratively optimized. This construction ensures both accurate data fitting and that the network output strictly adheres to the objective physical laws governing atmospheric waveguide formation, preventing overfitting and deviation from actual physical realities. This results in ocean model parameters that more closely match the actual conditions of the target sea area. After training, the module replaces the traditional air-sea coupling parameterization scheme of mesoscale numerical models with this physically constrained deep neural network. This overcomes the limitations of traditional models in terms of insufficient accuracy and poor adaptability in air-sea coupling simulations, significantly improving the accuracy of air-sea coupling simulations at the mesoscale. Furthermore, by constructing a mapping relationship between the vertical eddy diffusion coefficient and atmospheric waveguide characteristic parameters, the module accurately converts the network-output ocean model parameters into a mesoscale atmospheric waveguide characteristic parameter field for the target sea area. This parameter field includes core parameters such as waveguide height, waveguide thickness, waveguide intensity, and the vertical gradient of atmospheric refractive index, allowing the mesoscale waveguide characteristics to exhibit a continuous spatial distribution, accurately reflecting the overall waveguide characteristics within the mesoscale range of the target sea area. The module synchronously transmits the generated mesoscale atmospheric waveguide characteristic parameter field to the small-scale waveguide modeling module and the waveguide spatiotemporal prediction module, providing accurate boundary references for small-scale waveguide modeling and core data for mesoscale global feature extraction in waveguide spatiotemporal prediction, thus ensuring reliable mesoscale feature support for the work of both modules.

[0057] Small-scale waveguide modeling module: This module receives the mesoscale atmospheric waveguide characteristic parameter field transmitted by the parameter optimization module in real time and uses it as the core boundary constraint. The module first autonomously constructs a two-dimensional coupled Markov chain model formed by multi-directional one-dimensional Markov chain coupling. The coupling of the multi-directional one-dimensional Markov chain can adapt to the waveguide parameter interpolation requirements in two-dimensional space, allowing the model to efficiently and accurately simulate small-scale waveguide parameters within the target sea area in two-dimensional space. Subsequently, the module uses the 25km×25km grid node values ​​of the mesoscale atmospheric waveguide characteristic parameter field as boundary reference values, and finely divides the mesoscale grid into a 9km×9km fine-grained interpolation grid. This finer grid division significantly improves the spatial resolution of the waveguide profile, allowing for a more detailed characterization of waveguide features within a small scale range, better reflecting the actual waveguide distribution in the target sea area, and extending the analysis of waveguide features from the macroscopic mesoscale to the microscopic small scale. The module then calculates the state transition probabilities of atmospheric waveguide parameters at adjacent grid nodes, constructing a longitudinal transition probability matrix and an initial transverse transition probability matrix. The accurate statistics and matrix construction of the state transition probabilities provide a probabilistic basis for spatial interpolation that conforms to the natural variation law of waveguide parameters, ensuring that the interpolation results do not deviate from the actual variation trend of waveguide parameters and guaranteeing the scientific nature of the interpolation. Then, the element values ​​of the initial transverse transition probability matrix are weighted and corrected by the interface tilt angle correction factor to obtain a corrected transverse transition probability matrix that adapts to the tilt direction of the waveguide interface. The weighted correction by the interface tilt angle correction factor can accurately adapt to the actual tilt state of the waveguide interface in the target sea area, eliminating the limitation of the waveguide interface tilt direction on the simulation results of non-uniform waveguide profiles, and allowing the simulation results to truly restore the tilt characteristics of the waveguide interface in the actual sea area. Finally, based on the longitudinal transition probability matrix and the corrected lateral transition probability matrix, the module performs spatial interpolation prediction of the unknown waveguide parameter states within the fine-grained grid, completing fine-grained spatial interpolation and non-uniform waveguide profile simulation. This accurately generates a small-scale atmospheric waveguide profile model for the target sea area. This model can accurately reproduce the detailed changes in the waveguide profile within a small scale range of the target sea area. The module transmits this model to the waveguide spatiotemporal prediction module in real time, providing core fine-grained data support for the small-scale local feature extraction of waveguide spatiotemporal prediction. This allows cross-scale feature fusion to take into account both global and local features, improving the accuracy of waveguide spatiotemporal prediction.

[0058] Waveguide Spatiotemporal Prediction Module: The waveguide spatiotemporal prediction module synchronously receives radiosonde-based meteorological data transmitted by the data processing module, mesoscale atmospheric waveguide characteristic parameter fields transmitted by the parameter optimization module, and small-scale atmospheric waveguide profile models transmitted by the small-scale waveguide modeling module. The synchronous reception of these three types of data allows the module to fully acquire waveguide-related features from different scales and sources in the target sea area, ensuring the comprehensiveness of feature extraction and enabling subsequent models to learn the spatiotemporal variation patterns of waveguide features from three dimensions: global, local, and measured. The module takes three types of data as core inputs and directly calls the built-in multi-scale Transformer fusion model with a hierarchical attention mechanism. The encoder of this model completes the targeted extraction of mesoscale global features, small-scale local features, and accurate features from radiosonde measurements through three layers of parallel attention branches. The three-layer parallel attention branches enable features of different scales and types to be fully and accurately captured, improving the efficiency and accuracy of feature extraction. Then, through the hierarchical attention mechanism, adaptive weights are assigned to features of different scales, allowing the model to automatically focus on the feature information that is more valuable for waveguide spatiotemporal prediction, weaken the interference of secondary features, and achieve efficient and accurate adaptive fusion of cross-scale spatiotemporal features. When training the model, this module uses a sliding window approach to expand the spatiotemporal dimensions of the input multi-scale dataset, enriching the model's training sample library and improving its adaptability to different spatiotemporal scenarios. This allows the model to cope with the complex spatiotemporal changes in waveguide characteristics of the target sea area. At the same time, waveguide feature parameters extracted from radiosonde meteorological data are used as ground truth labels to iteratively train the model, ensuring that the model's forecast results always closely match the actual measured conditions and guaranteeing the accuracy of the forecast results. Furthermore, transfer learning is used to achieve generalization and adaptation of the model in different sea areas, enabling the model to maintain stable and accurate results in waveguide forecasts in different sea areas, breaking the limitations of the model's sea area application. Based on the fused cross-scale core features, the model's decoder accurately outputs continuous spatiotemporal forecasts of low-altitude atmospheric waveguides for the target sea area over the next 24 to 72 hours, with a temporal resolution of 1 hour and a spatial resolution of 9 km × 9 km. These forecasts possess clear and refined temporal and spatial resolutions, fully presenting the continuous spatiotemporal changes in waveguide characteristics of the target sea area. The module transmits these forecasts in real time to the characteristic analysis and closed-loop optimization module, providing continuous, accurate, and detailed waveguide data support for subsequent electromagnetic propagation characteristic simulation and optimization strategy formulation, ensuring the scientific rigor and practicality of electromagnetic propagation analysis.

[0059] The Characteristic Analysis and Closed-Loop Optimization Module receives real-time spatiotemporal forecast results of low-altitude atmospheric waveguides from the waveguide spatiotemporal forecast module. Based on these results, it accurately extracts core parameters such as waveguide height, waveguide thickness, waveguide intensity, and vertical gradient of atmospheric refractive index at the corresponding spatiotemporal location, constructing a continuously varying atmospheric refractive index profile. This profile ensures that the spatiotemporal variation of atmospheric refractive index is highly consistent with the actual spatiotemporal distribution of waveguides in the target sea area, laying a precise atmospheric medium foundation for electromagnetic wave propagation characteristic simulation and allowing the simulation process to be conducted based on a realistic medium environment. The module then uses the step-by-step Fourier parabolic equation method to solve the narrow-angle parabolic equation for electromagnetic wave propagation. This method accurately calculates the scalar field amplitude of electromagnetic waves in the low-altitude atmospheric waveguide environment, realistically reproducing the actual propagation state of electromagnetic waves in over-the-horizon electromagnetic communication scenarios at sea. Finally, the module converts the solved scalar field amplitude into intuitive propagation loss data using the propagation loss calculation formula, allowing abstract electromagnetic propagation state data to be directly applied to engineering analysis. The module combines the operating parameters of the maritime over-the-horizon electromagnetic communication system, defining the over-the-horizon coverage area as the farthest propagation distance where the propagation loss is less than the system's maximum allowable loss, and the communication blind zone as the spatial area where the field strength is lower than the system's receiving sensitivity. This definition method ensures that the analysis results of the over-the-horizon coverage area and the communication blind zone are perfectly aligned with the actual operating thresholds of the maritime over-the-horizon electromagnetic communication system, giving the analysis results direct engineering application value. Subsequently, based on the analysis results, an electromagnetic propagation optimization strategy adapted to the maritime over-the-horizon electromagnetic communication scenario is output. This strategy can specifically solve practical problems such as excessive propagation loss, too many communication blind zones, and insufficient over-the-horizon coverage in the maritime over-the-horizon electromagnetic communication process, providing a scientific and practical basis for parameter adjustment, communication link planning, and base station site selection of the maritime over-the-horizon electromagnetic communication system. Simultaneously, this module continuously collects measured data on electromagnetic propagation in the target sea area using marine measurement equipment. It employs specialized algorithms to accurately calculate the deviation between the measured and predicted electromagnetic propagation results. This deviation is then fed back to all preceding modules, including the data processing module, parameter optimization module, small-scale waveguide modeling module, and waveguide spatiotemporal prediction module. Each module iteratively adjusts its processing flow, model parameters, and network weights based on the feedback deviation data, achieving closed-loop optimization of the entire system. Figure 3 As shown, this allows the entire system to continuously correct itself based on actual measurements, thereby improving the accuracy of waveguide forecasting and the adaptability of electromagnetic propagation optimization strategies. This ensures that the system remains highly compatible with actual sea conditions in long-term applications of over-the-horizon electromagnetic communication at sea, providing reliable technical support for such communication.

[0060] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization, characterized in that, The method includes: S100. Data Processing: Synchronously collect various types of marine meteorological data from the target sea area, complete data cleaning, spatiotemporal alignment and normalization processing, and construct a unified spatiotemporal dimension multi-source meteorological standardized dataset. S200, Parameter Optimization: Using a multi-source meteorological standardized dataset as input, a physically constrained deep neural network embedded with atmospheric waveguide physical prediction equations is constructed to replace the traditional ocean-atmosphere coupling parameterization scheme of mesoscale numerical models and generate a mesoscale atmospheric waveguide characteristic parameter field for the target sea area. S300, Small-scale waveguide modeling: Using the characteristic parameter field of the mesoscale atmospheric waveguide as the boundary constraint, a two-dimensional coupled Markov chain model with an interface tilt angle correction mechanism is constructed to complete fine-grained spatial interpolation and non-uniform waveguide profile simulation, and generate a small-scale atmospheric waveguide profile model of the target sea area. S400, waveguide spatiotemporal forecast: Simultaneously input mesoscale atmospheric waveguide characteristic parameter field, small-scale atmospheric waveguide profile model and radiosonde data in multi-source meteorological standardized dataset, construct multi-scale Transformer fusion model with hierarchical attention mechanism, complete cross-scale feature extraction and adaptive fusion, and output spatiotemporal continuous forecast results of low-altitude atmospheric waveguide in target sea area; S500, Characteristic Analysis and Closed-Loop Optimization: Based on the spatiotemporal continuous forecast results of low-altitude atmospheric waveguides, an atmospheric refractive index profile is constructed and electromagnetic wave propagation characteristics are simulated. Combined with the working parameters of the target marine electromagnetic system, an electromagnetic propagation optimization strategy is output. At the same time, the deviation between the measured and predicted electromagnetic propagation is fed back to the preceding models to complete the full-process iterative optimization.

2. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S100, the specific process of data processing is as follows: three types of marine meteorological data are collected synchronously, namely, mesoscale numerical model meteorological data covering multiple heights of the target sea area, radiosonde observation meteorological data covering the entire low-altitude region, and sea surface observation meteorological data collected by fixed sea surface stations and buoys; all three types of data include basic meteorological parameters such as temperature, salinity, ocean current, relative humidity, air pressure, and wind speed at different heights of the target sea area; during the data processing, outliers in the data are first removed and missing data are filled in, then all data are unified to the same geographic coordinate system and time reference to complete spatiotemporal alignment, Richardson number, which characterizes the turbulent stability of the air-sea coupling process, is obtained based on the collected basic meteorological parameters, and finally, the normalization of all parameters is completed to form a grid-aligned multi-source meteorological standardized dataset.

3. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S200, during the training process of the physically constrained deep neural network, a total loss function incorporating regularization constraints based on atmospheric waveguide physical laws is constructed. The network weights are iteratively optimized through backpropagation of the total loss function, as shown in the formula: in, This represents the total loss value of the physically constrained deep neural network. This is the mean square error loss; These are the physical constraint weighting coefficients; This represents the residual loss in the atmospheric waveguide physics prediction equation.

4. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S200, the physically constrained deep neural network adopts a fully connected network structure, with an input layer, a hidden layer, and an output layer set sequentially: the number of neurons in the hidden layer is 128, 256, 256, 128, 64, and 32 respectively; the input vector of the input layer is the four-dimensional feature vector of temperature, salinity, ocean current, and Richardson number at different altitudes in the target sea area from the multi-source meteorological normalized dataset obtained in S100; the output parameters of the output layer are the vertical eddy diffusion coefficient and vertical eddy diffusion viscosity of the ocean model; by constructing a mapping relationship between the vertical eddy diffusion coefficient and atmospheric waveguide feature parameters, the network output parameters are converted into a mesoscale atmospheric waveguide feature parameter field, wherein the atmospheric waveguide feature parameters include waveguide height, waveguide thickness, waveguide intensity, and atmospheric refractive index vertical gradient.

5. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S300, the interface tilt angle correction factor performs a weighted correction on the lateral transition probability matrix of the two-dimensional coupled Markov chain, as shown in the formula: in, This is a correction factor for the interface tilt angle; The actual tilt angle of the waveguide interface within the target interpolation region; The default horizontal interface reference angle for a two-dimensional coupled Markov chain; For adaptive adjustment coefficients; By using the modified lateral transfer probability matrix, the limitation of the waveguide interface tilt direction on the simulation results of non-uniform waveguide profiles is eliminated.

6. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S300, the specific process of small-scale waveguide modeling is as follows: A multi-directional one-dimensional Markov chain is coupled to construct a two-dimensional coupled Markov chain model; the mesoscale grid is divided into a 9km×9km fine-grained interpolation grid, using the 25km×25km grid node values ​​of the mesoscale atmospheric waveguide characteristic parameter field as boundary reference values; the state transition probabilities of atmospheric waveguide parameters at adjacent grid nodes are statistically analyzed, and a longitudinal transition probability matrix and an initial transverse transition probability matrix are constructed respectively; the element values ​​of the initial transverse transition probability matrix are weighted and corrected using an interface tilt angle correction factor to obtain a corrected transverse transition probability matrix that adapts to the tilt direction of the waveguide interface; based on the longitudinal transition probability matrix and the corrected transverse transition probability matrix, spatial interpolation prediction is performed on the state of unknown waveguide parameters within the fine-grained grid to generate a small-scale atmospheric waveguide profile model of the target sea area.

7. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S400, the multi-scale Transformer fusion model with hierarchical attention mechanism sets up encoder and decoder structures. The encoder has three parallel attention branches: the first branch corresponds to mesoscale global feature extraction, and the input is the mesoscale atmospheric waveguide feature parameter field obtained in S200. The second branch corresponds to small-scale local feature extraction, with the input being the small-scale atmospheric waveguide profile model obtained from S300; the third branch corresponds to accurate feature extraction from radiosonde measurements, with the input being the radiosonde meteorological data from the multi-source meteorological standardized dataset obtained from S100; an adaptive weight is assigned to features of different scales through a hierarchical attention mechanism to complete the adaptive fusion of cross-scale spatiotemporal features; based on the fused cross-scale features, the decoder outputs the continuous spatiotemporal forecast results of the low-altitude atmospheric waveguide for the target sea area for the next 24 to 72 hours, with a temporal resolution of 1 hour and a spatial resolution of 9 km × 9 km.

8. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S400, during the training of the multi-scale Transformer fusion model with hierarchical attention mechanism, the spatiotemporal dimension of the input multi-scale dataset is expanded using a sliding window method. The waveguide feature parameters extracted from the radiosonde meteorological data obtained in S100 are used as ground truth labels to iteratively train the model, and the model is generalized and adapted to different sea areas through transfer learning.

9. The low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization according to claim 1, characterized in that, In step S500, the specific process of the electromagnetic propagation characteristic simulation calculation is as follows: The first step is to extract the waveguide height, waveguide thickness, waveguide intensity, and atmospheric refractive index vertical gradient parameters corresponding to the spatiotemporal location based on the spatiotemporal continuous forecast results of the low-altitude atmospheric waveguide obtained by S400, and construct a continuously changing atmospheric refractive index profile. The second step is to solve the narrow-angle parabolic equation for electromagnetic wave propagation using the step-by-step Fourier parabolic equation method: in, The amplitude of the electromagnetic wave scalar field; For the distance of propagation; For height; For free space wavenumber; The highly correlated atmospheric refractive index is constructed based on the forecast results; Step 3: Calculate the propagation loss based on the solved field amplitude: in, For propagation loss; The amplitude of the reference field at the free-space launch end; The amplitude of the electromagnetic wave scalar field; The fourth step is to define the beyond-line-of-sight coverage range as the farthest propagation distance where the propagation loss is less than the maximum allowable loss of the target system, and the radar blind zone as the spatial region where the field strength is lower than the system's receiving sensitivity; and to output an electromagnetic propagation optimization scheme adapted to the communication and detection scenarios by combining the operating parameters of the target's marine electromagnetic system.

10. A low-altitude atmospheric waveguide analysis system for electromagnetic propagation optimization, the system being applicable to the low-altitude atmospheric waveguide analysis method for electromagnetic propagation optimization as described in any one of claims 1-9, characterized in that, The system includes: Data processing module: used to collect three types of marine meteorological data from the target sea area, and after cleaning, spatiotemporal alignment, Richardson number calculation and normalization, construct a multi-source meteorological standardized dataset; Parameter optimization module: It has a built-in physical constraint deep neural network with embedded atmospheric waveguide physical prediction equations. It takes a standardized dataset as input, replaces the traditional air-sea coupling parameterization scheme, and generates a mesoscale atmospheric waveguide characteristic parameter field. Small-scale waveguide modeling module: Using mesoscale parameter fields as boundary constraints, a two-dimensional coupled Markov chain model with interface tilt angle correction mechanism is used to complete fine-grained spatial interpolation and non-uniform waveguide profile simulation, generating a small-scale atmospheric waveguide profile model. Waveguide spatiotemporal forecasting module: It has a built-in multi-scale Transformer fusion model with a hierarchical attention mechanism, which simultaneously inputs multi-scale waveguide data and radiosonde measurement data, completes cross-scale feature fusion, and outputs continuous spatiotemporal forecasting results of low-altitude atmospheric waveguides; Characteristic analysis and closed-loop optimization module: Based on the forecast results, an atmospheric refractive index profile is constructed and electromagnetic propagation characteristics are simulated. Combined with the working parameters of the marine electromagnetic system, an electromagnetic propagation optimization strategy is output. At the same time, the deviation between the measured and predicted electromagnetic propagation is fed back to the preceding module to complete the full-process iterative optimization.

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