Short wave positioning method based on ionized layer model

Abstract

The invention relates to the technical field of short-wave communication, and discloses an ionosphere model-based short-wave positioning method, which comprises the following steps of: acquiring multi-site ionosphere observation data, and generating a spatial-temporal characteristic tensor and a noise covariance matrix; calculating a long-range dependency relationship of the spatial-temporal feature sequence by using a Transform encoder, and generating a global feature vector; and inputting the global feature vector into a neural stochastic differential equation network to generate a state-dependent diffusion coefficient function. According to the invention, the long-range dependence modeling capability of the time sequence Transform, the randomness description capability of the neural stochastic differential equation and the probability trajectory optimization capability of the flow matching algorithm are fused, so that the defect that the deterministic propagation rule and the random fluctuation characteristic of the ionospheric disturbance cannot be processed at the same time in the traditional method is overcome; the technical problem that short-wave positioning lacks reliability evaluation under the disturbance condition is solved.

Description

Technical Field

[0001] This invention relates to the field of shortwave communication, and more specifically, to a shortwave positioning method based on an ionospheric model. Background Technology

[0002] In the field of shortwave communication positioning technology, ionospheric disturbances are a key factor affecting positioning accuracy. Two types of disturbances exist in the ionosphere: traveling disturbances (TID) and random fluctuations. TIDs exhibit deterministic propagation patterns, while random fluctuations are unpredictable. Traditional deterministic prediction models ignore the inherent randomness of the ionosphere, resulting in a lack of reliability assessment for positioning results under disturbed conditions; while purely stochastic models cannot capture the physical propagation laws of TIDs, leading to poor physical consistency in prediction results.

[0003] Therefore, how can we provide shortwave localization results with uncertainty quantification while considering the deterministic propagation law and random fluctuation characteristics of ionospheric disturbances? Summary of the Invention

[0004] This invention provides a shortwave localization method based on an ionospheric model, which solves the technical problem in related technologies of how to provide shortwave localization results with uncertainty quantification while considering the deterministic propagation law and random fluctuation characteristics of ionospheric disturbances.

[0005] This invention provides a shortwave localization method based on an ionospheric model, comprising the following steps: S100: Acquire multi-site ionospheric observation data and generate spatiotemporal feature tensors and noise covariance matrices; S200: Utilizes the Transformer encoder to calculate the long-range dependencies of spatiotemporal feature sequences and generate a global feature vector; S300: Input the global feature vector into the neural stochastic differential equation network to generate a state-dependent diffusion coefficient function; The neural stochastic differential equation network consists of the following components: an input layer, a drift network, a diffusion network, a stochastic differential equation solver, and an output layer. The input layer takes the residual sequence as input, and then the drift term and diffusion coefficient are calculated in parallel by the drift network and the diffusion network. These are then input into the stochastic differential equation solver for numerical integration, and finally the output layer outputs the state evolution trajectory. S400: Generates a set of perturbation evolution trajectory samples through a neural stochastic differential equation network; S500: Based on the flow matching algorithm, optimizes the trajectory generation process and outputs the probability distribution of disturbance intensity; The specific implementation of the flow matching algorithm uses a neural ordinary differential equation as the generator and a continuous normalized flow framework. S600: Updates shortwave propagation path parameters based on perturbation probability distribution and outputs positioning results with confidence.

[0006] Furthermore, in S100, ionospheric TID observation sequence data, including electron density, TID intensity and propagation velocity, are acquired from multiple ground observation stations, while perturbation statistical characteristic data are also acquired.

[0007] Furthermore, in the S200, the Transformer encoder includes: Input layer: Receives spatiotemporal feature sequences; Location coding layer: Encodes spatiotemporal location using sine and cosine functions; Multi-head self-attention layer: includes Each attention head computes a query matrix, a key matrix, and a value matrix. Feedforward network layer: consists of two linear transformations and a ReLU activation function; Output layer: Outputs the global feature vector.

[0008] Furthermore, based on the residual between the global feature vector obtained from S200 and the actual observed values, the random perturbation component sequence is calculated. The residual sequence and perturbation statistical characteristics are input into the neural stochastic differential equation network to learn the nonlinear mapping relationship between the state and the noise intensity, and output the diffusion coefficient function that characterizes the noise intensity under different states. Before calculating the residuals, the same standardization process is applied to the global eigenvectors and the actual observations.

[0009] Furthermore, the drift network consists of three fully connected neural networks, the diffusion network consists of two fully connected neural networks, and the stochastic differential equation solver adopts the Euler-Maruyama numerical integration method.

[0010] Furthermore, the trajectory sampling process is as follows: the number of samplings is set, and in each sampling, a noise sequence is sampled from the standard normal distribution. The trajectory is generated by the solver of the neural stochastic differential equation network, and finally the perturbation evolution trajectory sample set is obtained. During the sampling process, the sampling process is terminated early when the trajectory convergence criterion is met; The trajectory convergence criterion is defined as the state change amplitude of three consecutive time steps being less than a preset threshold.

[0011] Furthermore, the flow matching algorithm is used to learn the probability measure mapping from the initial distribution to the target distribution. The generator parameters are optimized by minimizing the transmission cost of the trajectory. Based on the optimized trajectory generator, a large number of possible perturbation evolution paths are sampled, and the statistical characteristics of the trajectory set, including mean, variance and quantiles, are calculated. The probability distribution parameters of the perturbation intensity at the predicted time are then output.

[0012] Furthermore, the flow matching algorithm is implemented through the following steps: A velocity field network was constructed, consisting of four fully connected layers with 128 neurons per layer, using the Swish activation function. Define the transmission cost function; Minimize the cost function using the Adam optimizer, with the learning rate set to... The batch size is 256, and the number of training iterations is 10,000. For each sample, the solution is obtained by solving the constant differential equation from... arrive The obtained probability stream mapping.

[0013] Furthermore, in S600, the probability distribution of perturbation intensity obtained in S500 is converted into the uncertainty range of ionospheric electron density, and electron density distribution parameters are generated for each height layer. The refractive index of the parabolic path is updated based on the density distribution parameters. Multiple possible values ​​are sampled from the time delay distribution using the Monte Carlo method. Positioning calculations are performed on each sampled value to obtain the probability distribution of the positioning results. The final positioning coordinates are calculated by weighted averaging, and a confidence ellipse is generated based on the covariance matrix of the positioning results. The neural stochastic differential equation network generates a set of perturbation evolution trajectory samples, which are then converted into actual time delay parameters through a dedicated decoding layer.

[0014] Furthermore, the major and minor axes of the confidence ellipse correspond to the square roots of the eigenvalues ​​of the covariance matrix, respectively, and the direction of the ellipse is determined by the eigenvectors.

[0015] The beneficial effects of this invention are as follows: This implementation overcomes the shortcomings of traditional methods that cannot simultaneously handle the deterministic propagation law and random fluctuation characteristics of ionospheric disturbances by integrating the long-range dependency modeling capability of temporal Transformer, the stochastic characterization capability of neural stochastic differential equations, and the probabilistic trajectory optimization capability of flow matching algorithm. It solves the technical problem of lack of reliability assessment for shortwave positioning under disturbance conditions.

[0016] Specifically, Transformer's self-attention mechanism can directly model the dependency relationship of arbitrary spatiotemporal distance, accurately capturing the long-distance propagation effect of TID; Neural SDE unifies deterministic dynamics and random perturbations within a framework, and the diffusion term adaptively characterizes the noise intensity under different states; The flow matching algorithm avoids the cumulative error of traditional numerical integration by learning the optimal transport mapping between probability measures.

[0017] Therefore, this implementation can provide shortwave positioning results with uncertainty quantification, providing users with positioning reliability assessment. Attached Figure Description

[0018] Figure 1 This is a flowchart of a shortwave localization method based on an ionospheric model proposed in this invention; Figure 2 This is a schematic diagram of the Transformer encoder proposed in this invention; Figure 3 This is a flowchart of the flow matching algorithm proposed in this invention. Detailed Implementation

[0019] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0020] like Figure 1 - Figure 3 As shown, a shortwave localization method based on an ionospheric model includes the following steps: S100: Acquire multi-site ionospheric observation data and generate spatiotemporal feature tensors and noise covariance matrices; Specifically, ionospheric TID observation sequence data, including parameters such as electron density, TID intensity and propagation velocity, were obtained from multiple ground observation stations. At the same time, disturbance statistical characteristic data were obtained. The observation data were organized into a three-dimensional tensor form according to the time and spatial dimensions, and the noise covariance matrix was calculated based on historical disturbance data.

[0021] The raw observation data is preprocessed, including the maximum-minimum normalization of physical quantities such as electron density, TID intensity and propagation speed, so that parameters of different dimensions are uniformly mapped to the [0,1] interval, thus eliminating the influence of dimensional differences on model training.

[0022] It should be noted that the dimension of the spatiotemporal feature tensor is . ,in Indicates the number of time steps. Indicates the number of observation stations. The feature dimension is represented; the noise covariance matrix is ​​obtained by calculating the second-order statistics of historical perturbation data.

[0023] To ensure the accuracy of the covariance matrix calculation, the time data was linearly transformed, converting absolute time into relative time intervals, with the unit uniformly set to hours.

[0024] S200: Utilizes the Transformer encoder to calculate the long-range dependencies of spatiotemporal feature sequences and generate a global feature vector; Specifically, the preprocessed spatiotemporal feature tensor is input into the Transformer encoder, and the attention weights between different spatiotemporal locations are calculated through a multi-head self-attention layer to capture the long-distance propagation pattern of TID in time and space, and output a feature vector containing global dependency information.

[0025] Before inputting into the Transformer, the feature dimensions were standardized (mean 0, standard deviation 1) to ensure that different features contribute equally to the model.

[0026] It should be noted that the Transformer encoder includes: Input layer: receiving dimension is The spatiotemporal feature sequence, where For time steps, For the number of observation stations, For feature dimensions; Location coding layer: Spatiotemporal location is encoded using sine and cosine functions. The coding formula is as follows: ; ; Where pos is the position index in the sequence (starting from 0), and i is the dimension index (starting from 0 to 1). ), 10000 represents the dimension of the hidden layer in the model, and 10000 is a scaling factor used to control the encoding frequency at different locations. and Representing positions respectively In the and The encoded value of the dimension; Multi-head self-attention layer: includes Each attention head computes a query matrix. Key matrix Sum matrix : ; ; ; Attention weights are calculated as follows The output is ;in For the input matrix, , , The learnable weight matrix (all dimensions are 1) ), The dimension of the key vector (equal to) ),in It is a normalized exponential function that transforms a vector into a probability distribution. The attention weight matrix (dimension 1) ), For the first The output features of each head (dimension: ); Feedforward network layer: Consists of two linear transformations and a ReLU activation function, calculated as follows: ; in, The first layer weight matrix (dimension 1) ), The second layer weight matrix (dimension: ), and These are the corresponding bias vectors. For the hidden layer dimension of the feedforward network, It is the ReLU activation function. Indicates a feedforward network; Output layer: Output dimension is The global feature vector, where To output feature dimensions, For time steps, This represents the number of observation stations.

[0027] Training methods for Transformer encoders include: Training mode: Supervised learning mode is adopted, using historical ionospheric perturbation data as labels; Optimization strategy: Use the Adam optimizer, with the learning rate set to... Cosine annealing learning rate scheduling is used; Loss function: Mean squared error loss function using spatiotemporal dimensions: ; in, This represents the mean squared error loss value. For the first Each sample in time The actual perturbation value, For the corresponding predicted disturbance value, For batch size, Given the time series length, the true and predicted values ​​were normalized in the same way before calculating the loss to ensure consistency of units.

[0028] Furthermore, the length of the time series Based on the TID propagation characteristics, a 24-time-step interval (corresponding to a 24-hour observation cycle) is set to ensure the capture of the complete diurnal variation cycle. Batch size The available GPU memory is set between 32 and 128, with a default value of 64. The loss function contributes equally to the loss at each time step, without time weighting, to ensure consistent prediction accuracy across all time points.

[0029] Furthermore, the specific parameters for cosine annealing learning rate scheduling are set as follows: initial learning rate. Minimum learning rate ,cycle For each epoch, the learning rate changes according to the following formula: ; in, For the current epoch (from 0 to ...) ), It is pi (approximately 3.14159). For the first The learning rate for each epoch.

[0030] The early stopping strategy during training involves stopping training if the validation loss does not improve for five consecutive epochs and restoring the model parameters with the lowest validation loss. The maximum number of training epochs is set to 100.

[0031] S300: Input the global feature vector into the neural stochastic differential equation network to generate a state-dependent diffusion coefficient function; Specifically, based on the residual between the global feature vector obtained from S200 and the actual observed values, a random perturbation component sequence is calculated. The residual sequence and perturbation statistical characteristics are input into a neural stochastic differential equation network to learn the nonlinear mapping relationship between the state and the noise intensity, and output the diffusion coefficient function that characterizes the noise intensity under different states.

[0032] Before calculating the residuals, the same standardization process is applied to the global eigenvectors and the actual observations to ensure the consistency of the dimensions in the residual calculation.

[0033] It should be noted that neural stochastic differential equation networks consist of the following components: Input layer: receiving dimension is The residual sequence, where For batch size, For time steps, Input feature dimension; Drift Network It consists of a three-layer fully connected neural network, with the number of neurons in each layer being as follows: The activation function is Tanh. The drift term is calculated as follows: ; in, This indicates the concatenation of state and time. Let be the state vector at time t. The time variable is linearly scaled to match the state. Dimensions The weight matrix (dimensions are respectively) , , ), The corresponding bias vectors (dimensions are respectively) , , ), For drift network functions, These are the learnable parameters of the drift network; diffusion network It consists of two fully connected neural networks, with the number of neurons in each layer being as follows: The activation function is Softplus. The diffusion coefficient is calculated as follows: ; in, The weight matrix (dimensions are respectively) , ), The corresponding bias vectors (dimensions are respectively) , ); The Softplus function includes: ; Ensure the diffusion coefficient is positive; Stochastic differential equation solver: Employs the Euler-Maruyama numerical integration method; the discretization formula is as follows: ; in, Let be a standard normally distributed random variable. For physical time variables, Maximum forecast duration (set to 24 hours). Set the time step (to 0.1 hours). and The output has been ensured to be consistent with the state through network architecture design. Having the same dimensions ensures the consistency of dimensions among all terms in the equation; Furthermore, the state vector Dimensions Set to twice the dimension of the ionospheric parameters (corresponding to position and velocity), with the value range determined through statistical analysis of the training data. ,in The standard deviation for each dimension. Time variable. Normalization was performed in the numerical computation, and mapped to... To improve numerical stability, the original physical time is mapped to an interval using a linear mapping. recover.

[0034] Output layer: Output dimension is The state trajectory sequence.

[0035] The data transfer relationship is as follows: the input residual sequence is first processed by a drift network and a diffusion network in parallel to obtain the drift term and diffusion coefficient. Then, it is input into a stochastic differential equation solver for numerical integration, and finally, the state evolution trajectory is output. The outputs of the drift network and the diffusion network are designed with appropriate activation functions and layer structures to ensure that the outputs have physically appropriate dimensions and value ranges.

[0036] Training methods for neural stochastic differential equation networks include: Training mode: The variational inference training mode is adopted, and the network parameters are optimized by maximizing the lower bound of evidence (ELBO); Optimization strategy: Use the Adam optimizer, with the learning rate set to... Gradient clipping is used to prevent gradient explosion, and the clipping threshold is set to... ; Furthermore, for the gradient clipping operation, the gradient norm is defined. ,in Let be the gradient of each parameter. When Exceeding the threshold When the gradient is scaled to This is to ensure training stability.

[0037] Loss function: A variational loss function is used, which includes reconstruction loss and KL divergence regularization term. ; in, The total loss of the variational autoencoder, For coding distribution, For decoding distribution, As latent variables, For input data, and These are the parameters for the generator network and the inference network, respectively. This is the balance coefficient; The KL divergence is as follows: ; Among them, the two probability distributions are used to measure the probability distributions. and The differences between them and Let x and y represent the probability density values ​​of distributions P and Q at point x, respectively.

[0038] Furthermore, reconstruction loss Specifically, it is calculated using the negative log-likelihood loss: ; in, For the first Each sample in time The true value, For the corresponding reconstructed value, For batch size, The time series length is represented by this loss term. This term ensures that the neural SDE model can accurately reconstruct the input sequence.

[0039] Furthermore, the balance coefficient The value was set between 0.1 and 1.0, and the optimal value was determined to be 0.5 through verification experiments. This parameter controls the balance between reconstruction accuracy and the degree of regularization in the tidal space. Too small a value will lead to insufficient tidal space, while too large a value will inhibit reconstruction quality.

[0040] The validation experiments employed a grid search method, testing the model's performance on the validation set among candidate values ​​{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0}. The weighted sum of reconstruction error and KL divergence on the validation set was used as the evaluation metric, with weights of 1.0 and 0.3, respectively. Each parameter configuration was tested three times, and the model with the best average performance was selected. value.

[0041] S400: Generates a set of perturbation evolution trajectory samples through a neural stochastic differential equation network; Specifically, a neural stochastic differential equation network constructed using S300 is used to generate multiple possible perturbation evolution trajectories through multiple samplings. Each sampling uses a different random seed to generate an independent noise sequence, forming a trajectory sample set that characterizes the uncertainty of ionospheric perturbation.

[0042] It should be noted that the trajectory sampling process includes: setting the number of samples. For each sampling From the standard normal distribution Medium-sampled noise sequence (indicating the first) Trajectory in time The noise value is used to generate trajectories through the solver of a neural stochastic differential equation network. (indicating the first) Trajectory in time (state values), ultimately yielding a sample set of perturbation evolution trajectories. (representing all) A set of trajectories.

[0043] Furthermore, the initial state of trajectory sampling (express The state vector at time t is determined in the following three ways: (1) The feature vector output by the Transformer encoder in S200 is transformed through a linear mapping layer to obtain the initial state, ensuring that the initial state is consistent with the encoded feature space; (2) For scenarios with known historical data, the observation value at the most recent time point is directly used as the initial state, and mapped to the state space through a linear transformation; (3) For new observation scenarios, a multivariate normal distribution is constructed using the statistical properties (mean and covariance) of the training data, and the initial state is sampled from this distribution. The selection of the initial state is dynamically switched according to the actual application scenario.

[0044] Furthermore, the number of samples The value is selected between 500 and 10000, and dynamically adjusted according to computing resources and accuracy requirements to ensure sufficient scanning trajectory space.

[0045] During the sampling process, when the trajectory convergence criterion (defined as the amplitude of state change over three consecutive time steps being less than a preset threshold) is reached... If the conditions are met, the sampling process will be terminated early.

[0046] S500: Based on the flow matching algorithm, optimizes the trajectory generation process and outputs the probability distribution of disturbance intensity; Specifically, the flow matching algorithm is used to learn the probability measure mapping from the initial distribution to the target distribution. The generator parameters are optimized by minimizing the transmission cost of the trajectory. Based on the optimized trajectory generator, a large number of possible perturbation evolution paths are sampled, and the statistical characteristics of the trajectory set, including mean, variance and quantiles, are calculated. The probability distribution parameters of the perturbation intensity at the predicted time are then output.

[0047] The probability distribution parameters output by the model are denormalized and converted back to the scale of the original physical quantities to preserve their physical meaning.

[0048] Furthermore, the specific implementation of the flow matching algorithm uses Neural ODEs as the generator and employs the Continuous Normalizing Flow framework. The algorithm is implemented through the following steps: (1) Constructing the velocity field network (in For network parameters, For state vectors, (The time variable) consists of 4 fully connected layers, each with 128 neurons, and uses the Swish activation function; (2) Define the transmission cost function: ; in, For the initial distribution, For the target distribution, It is an intermediate distribution. For time state, A uniform distribution ranging from 0 to 1. For the transmission cost function, Let represent the gradient term, where and Approximated by forward and backward KL divergence estimators, respectively; (3) Minimize the cost function using the Adam optimizer, with the learning rate set to The batch size is 256, and the number of training iterations is 10,000. (4) For each sample, solve the ODE from arrive Obtain the probability flow map.

[0049] Generator parameters The optimization adopts the gradient descent method. The negative log-likelihood loss on the validation set is calculated every 10 iterations. When the validation loss does not improve after 5 consecutive validations, a learning rate decay strategy is adopted with a decay factor of 0.5.

[0050] Furthermore, the transmission cost function time variables in The normalized time of the probability flow evolution is independent of physical time, where Corresponding initial distribution , Corresponding target distribution .

[0051] distributed Indicates time The intermediate distribution satisfies The linear interpolation relationship.

[0052] gradient term Calculated through backpropagation, where and It is approximated by the forward and backward KL divergence estimators, respectively.

[0053] The convergence criterion for the algorithm is set to the negative log-likelihood on the validation set changing less than 10 times over 10 consecutive iterations. Or it can reach the maximum number of iterations of 10,000.

[0054] In this embodiment of the application, in order to improve the accuracy of probability distribution estimation, the kernel density estimation method is used to perform nonparametric probability density estimation on the trajectory sample to obtain a continuous probability density function.

[0055] Furthermore, the kernel density estimation uses a Gaussian kernel function: ; Among them, Points to be estimated. For sample points, For bandwidth parameters, Represents Euclidean distance, bandwidth parameter Determined adaptively using Silverman rules: ,in The standard deviation of the sample is 1. Interquartile range, This represents the number of samples.

[0056] In practical applications, when the sample exhaustion is insufficient (i.e., the number of trajectories is less than 50), a cross-validation-based method is used to dynamically adjust the bandwidth parameters.

[0057] S600: Updates shortwave propagation path parameters based on perturbation probability distribution and outputs positioning results with confidence. Specifically, the probability distribution of perturbation intensity obtained from S500 is converted into the uncertainty range of ionospheric electron density, electron density distribution parameters are generated for each height layer, and the refractive index of the parabolic path is updated based on the density distribution parameters. The calculation formula is as follows: ; in, For refractive index, For plasma frequency, The operating frequency is the plasma frequency. With electron density The relationship is MHz.

[0058] The Monte Carlo method is used to sample multiple possible values ​​from the time delay distribution. Positioning calculations are performed on each sampled value to obtain the probability distribution of the positioning result. The final positioning coordinates are calculated by weighted averaging, and a confidence ellipse is generated based on the covariance matrix of the positioning result.

[0059] The neural stochastic differential equation network generates a sample set of perturbation evolution trajectories, which is then converted into actual time delay parameters through a dedicated decoding layer, ensuring that the output results have clear physical meaning and are executable.

[0060] Furthermore, the number of sampling points in the Monte Carlo method is adaptively determined according to the required confidence level. The default is to use 1000 sampling points. When the rate of change of the width of the 95% confidence interval is less than 1% for three consecutive times, the sampling is considered sufficient and sampling is stopped.

[0061] The specific sampling process is as follows: (1) N electron density samples are obtained from the electron density distribution. ; (2) Calculate the corresponding refractive index for each sample. and delay parameters ; (3) Using a ray tracing algorithm, based on the time delay parameter Calculate the corresponding launch point location .

[0062] The ray tracing algorithm uses the Runge-Kutta method with a variable step size to solve the ray path equation. The step size is adaptively adjusted according to the gradient change, ranging from 0.1km to 10km.

[0063] It should be noted that the major and minor axes of the confidence ellipse correspond to the square roots of the eigenvalues ​​of the covariance matrix, and the direction of the ellipse is determined by the eigenvectors.

[0064] Furthermore, the confidence ellipse is constructed based on the confidence level. For a 95% confidence level, the ellipse equation is defined as: ; in, To locate the center point, and These are the lengths of the major and minor semi-axles, with values ​​of [value missing]. and ,in and Let be the eigenvalues ​​of the covariance matrix, satisfying The constraints are as follows. For other confidence levels, such as 90% and 99%, the constant 5.991 is replaced with 4.605 and 9.210, respectively.

[0065] Furthermore, the covariance matrix The calculation uses a weighted estimation method: ; in, For the first The weight of each sampling point For the first The coordinates of each sampling point The coordinates of the center point are used to locate the coordinates, and the denominator is the Bessel correction factor.

[0066] To ensure the positive definiteness of the covariance matrix, when the eigenvalues ​​are less than a preset threshold... When, replace it with And reconstruct the covariance matrix. Confidence ellipse direction angle. Determined by the principal eigenvectors of the covariance matrix, the calculation formula is as follows: ,in For corresponding eigenvalues eigenvectors.

[0067] In this embodiment of the application, in order to improve positioning accuracy, S600 also includes adaptive weight adjustment based on historical positioning error, which dynamically adjusts the weight coefficient of each sampling path according to the historical performance under different disturbance conditions.

[0068] Furthermore, the adaptive weight adjustment uses an exponentially weighted moving average method to calculate the historical positioning error under various disturbance conditions. The formula for calculating the weight coefficient is as follows: ; in, For the first Historical positioning error of each sampling path The hyperparameter used to control the rate of weight decay is set to a default value of 0.5. The total number of sampling points. This hyperparameter is determined by minimizing the weighted localization error on the training set, specifically by selecting the optimal value from the candidate values ​​{0.1, 0.3, 0.5, 0.7, 1.0}. To ensure the stability of the weight adjustment, a weight pruning technique is applied, limiting the weight of a single sampling path to no more than 0.3, while ensuring that the total weight sum is 1.

[0069] Based on the steps of the shortwave localization method based on the ionospheric model described above, the following is an example background: In a shortwave communication positioning mission, it was necessary to accurately locate a transmitter in an unknown location. This transmitter was situated in a sea area and communicated with multiple ground receiving stations via shortwave signals. Due to ionospheric disturbances, the accuracy of traditional positioning methods was limited.

[0070] Therefore, the shortwave localization method based on the ionospheric model of this invention is used for localization. The following example is given, and the specific steps are as follows: S100: Acquire multi-site ionospheric observation data A 24-hour continuous ionospheric TID (Transient Intensity Disturbances) observation sequence was obtained from five ground-based observation stations distributed along the eastern coast of my country, including parameters such as electron density, TID intensity, and propagation velocity. The observation data showed that a moderate-intensity perturbation existed in the ionosphere on that day, mainly manifested as periodic fluctuations in electron density. This observation data was organized into a three-dimensional tensor, with a 24-hour time dimension and the five observation stations as spatial dimensions. The characteristic dimensions included physical quantities such as electron density, TID intensity, and propagation velocity. Simultaneously, a noise covariance matrix was calculated based on historical perturbation data from the past month to characterize the statistical properties of the perturbation.

[0071] The original observation data was preprocessed, and different physical quantities were uniformly mapped to the [0,1] interval through maximum-minimum normalization, thus eliminating the influence of dimensional differences on model training.

[0072] S200: Calculating spatiotemporal features using a Transformer encoder The preprocessed spatiotemporal feature tensors are input into a pre-trained Transformer encoder. This encoder contains eight attention heads, with a hidden layer dimension of 256 for the model and a hidden layer dimension of 1024 for the feedforward network. Through a multi-head self-attention mechanism, the model successfully captures the long-distance propagation pattern of TID in time and space, particularly identifying the propagation delay relationship of perturbations between different observation stations.

[0073] The location encoding layer encodes spatiotemporal location using sine and cosine functions, enabling the model to perceive the spatiotemporal structure of the data. The multi-head self-attention layer calculates attention weights between different spatiotemporal locations, discovering that perturbations are stronger in the afternoon (12:00-16:00) and exhibit a trend of propagation from lower to higher dimensions. The feedforward network layer and output layer further process these features, ultimately outputting a feature vector containing global dependency information.

[0074] S300: Inputting global feature vectors into a neural stochastic differential equation network Based on the residuals between the global feature vector output by the Transformer encoder and the actual observations, a sequence of random perturbation components was calculated. These residual sequences show that the model performs well in capturing large-scale perturbation trends, but has some error in predicting small-scale, rapidly changing perturbations.

[0075] The residual sequence and perturbation statistics are input into a neural stochastic differential equation network, which consists of two main components: a drift network and a diffusion network. The drift network, composed of three fully connected neural networks using the Tanh activation function, is responsible for learning the deterministic evolutionary trend of the system; the diffusion network, composed of two fully connected neural networks using the Softplus activation function, is responsible for learning the stochastic intensity of state dependencies.

[0076] Using the Euler-Maruyama numerical integration method, the network learned the nonlinear mapping relationship between the state and the noise intensity, and output a diffusion coefficient function characterizing the noise intensity under different states. The results show that the perturbation intensity is positively correlated with the electron density, and the randomness of the perturbation is correspondingly enhanced in regions of higher electron density.

[0077] S400: Generating a sample set of perturbation evolution trajectories using a neural stochastic differential equation network. By constructing a neural stochastic differential equation network and setting the sampling number to 1000, multiple possible perturbation evolution trajectories were generated. Each sampling used a different random seed to generate an independent noise sequence, forming a trajectory sample set characterizing the uncertainty of ionospheric perturbations.

[0078] The initial state of trajectory sampling was obtained by transforming the feature vector output by the Transformer encoder through a linear mapping layer. During the sampling process, it was observed that most trajectories exhibited similar evolutionary trends in the first 6 hours, and then gradually dispersed, reflecting the characteristic that prediction uncertainty increases with time. Some trajectories reached the convergence criteria after 16 hours, thus terminating sampling prematurely.

[0079] S500: Based on the flow matching algorithm, optimizes the trajectory generation process and outputs the probability distribution of disturbance intensity; A flow matching algorithm was used to learn a probability measure mapping from an initial distribution to a target distribution. This algorithm uses a neural frequent differential equation as the generator and is implemented through a continuous normalized flow framework. The velocity field network consists of four fully connected layers, each with 128 neurons, and uses the Swish activation function.

[0080] The generator parameters were optimized by minimizing the transmission cost of the trajectory, and a large number of possible perturbation evolution paths were sampled based on the optimized trajectory generator. The statistical properties of the trajectory set, including mean, variance, and quantiles, were calculated, and the probability distribution parameters of the perturbation intensity at the predicted time were output.

[0081] To improve the accuracy of probability distribution estimation, a kernel density estimation method was used to perform nonparametric probability density estimation on the trajectory samples, resulting in a continuous probability density function. The results show that the disturbance intensity exhibits different distribution characteristics at different spatiotemporal locations, with some regions showing a bimodal distribution, reflecting that the disturbance may have two main modes.

[0082] S600: Updating shortwave propagation path parameters based on perturbation probability distribution The probability distribution of perturbation intensity was converted into the uncertainty range of ionospheric electron density, and electron density distribution parameters were generated for each height layer. Based on these distribution parameters, the refractive index calculation formula for the parabolic path was updated, and multiple possible propagation paths were generated using the Monte Carlo method.

[0083] For the received shortwave signal, the probability distributions of observed parameters such as angle of arrival, time delay, and Doppler shift were calculated and compared with the actual observed values. Using Bayesian inference, the posterior probability distribution of the transmitter location was updated, yielding a localization result with confidence intervals.

[0084] Finally, the system outputs the most probable location of the emission source and its 95% confidence interval. Compared with traditional positioning methods, this method considers the randomness of ionospheric disturbances, provides more reliable positioning results and uncertainty quantification, and the confidence interval of the positioning results can better cover the true location of the emission source.

[0085] The embodiments of the present invention have been described above, but the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention, all of which are within the protection scope of the present invention.

Claims

1. A shortwave localization method based on an ionospheric model, characterized in that, Includes the following steps: S100: Acquire multi-site ionospheric observation data and generate spatiotemporal feature tensors and noise covariance matrices; S200: Utilizes the Transformer encoder to calculate the long-range dependencies of spatiotemporal feature sequences and generate a global feature vector; S300: Input the global feature vector into the neural stochastic differential equation network to generate a state-dependent diffusion coefficient function; The neural stochastic differential equation network consists of the following components: an input layer, a drift network, a diffusion network, a stochastic differential equation solver, and an output layer. The input layer takes the residual sequence as input, and then the drift term and diffusion coefficient are calculated in parallel by the drift network and the diffusion network. These are then input into the stochastic differential equation solver for numerical integration, and finally the output layer outputs the state evolution trajectory. S400: Generates a set of perturbation evolution trajectory samples through a neural stochastic differential equation network; S500: Based on the flow matching algorithm, optimizes the trajectory generation process and outputs the probability distribution of disturbance intensity; The specific implementation of the flow matching algorithm uses a neural ordinary differential equation as the generator and a continuous normalized flow framework. S600: Updates shortwave propagation path parameters based on perturbation probability distribution and outputs positioning results with confidence.

2. The shortwave localization method based on an ionospheric model according to claim 1, characterized in that, In S100, ionospheric TID observation sequence data, including electron density, TID intensity and propagation velocity, are acquired from multiple ground observation stations, while perturbation statistical characteristic data are also acquired.

3. The shortwave localization method based on an ionospheric model according to claim 1, characterized in that, In the S200, the Transformer encoder includes: Input layer: Receives spatiotemporal feature sequences; Location coding layer: Encodes spatiotemporal location using sine and cosine functions; Multi-head self-attention layer: includes Each attention head computes a query matrix, a key matrix, and a value matrix. Feedforward network layer: consists of two linear transformations and a ReLU activation function; Output layer: Outputs the global feature vector.

4. The shortwave localization method based on an ionospheric model according to claim 1, characterized in that, Based on the residual between the global feature vector obtained from S200 and the actual observed values, the random perturbation component sequence is calculated. The residual sequence and perturbation statistical characteristics are input into the neural stochastic differential equation network to learn the nonlinear mapping relationship between the state and the noise intensity, and output the diffusion coefficient function that characterizes the noise intensity under different states. Before calculating the residuals, the same standardization process is applied to the global eigenvectors and the actual observations.

5. The shortwave localization method based on an ionospheric model according to claim 1, characterized in that, The drift network consists of three fully connected neural networks, the diffusion network consists of two fully connected neural networks, and the stochastic differential equation solver adopts the Euler-Maruyama numerical integration method.

6. The shortwave localization method based on an ionospheric model according to claim 1, characterized in that, The trajectory sampling process is as follows: the number of samplings is set, and in each sampling, a noise sequence is sampled from the standard normal distribution. The trajectory is generated by the solver of the neural stochastic differential equation network, and finally the perturbation evolution trajectory sample set is obtained. During the sampling process, the sampling process is terminated early when the trajectory convergence criterion is met; The trajectory convergence criterion is defined as the state change amplitude of three consecutive time steps being less than a preset threshold.

7. The shortwave localization method based on an ionospheric model according to claim 1, characterized in that, In S500, the flow matching algorithm is used to learn the probability measure mapping from the initial distribution to the target distribution. The generator parameters are optimized by minimizing the transmission cost of the trajectory. Based on the optimized trajectory generator, a large number of possible perturbation evolution paths are sampled, and the statistical characteristics of the trajectory set, including mean, variance and quantiles, are calculated. The probability distribution parameters of the perturbation intensity at the predicted time are output.

8. A shortwave localization method based on an ionospheric model according to claim 7, characterized in that, The flow matching algorithm is implemented through the following steps: A velocity field network was constructed, consisting of four fully connected layers with 128 neurons per layer, using the Swish activation function. Define the transmission cost function; Minimize the transport cost function using the Adam optimizer; For each sample, the solution is obtained by solving the constant differential equation from... arrive The obtained probability stream mapping.

9. A shortwave localization method based on an ionospheric model according to claim 1, characterized in that, In S600, the probability distribution of perturbation intensity obtained in S500 is converted into the uncertainty range of ionospheric electron density. Electron density distribution parameters are generated for each height layer, and the refractive index of the parabolic path is updated based on the density distribution parameters. Multiple possible values ​​are sampled from the time delay distribution using the Monte Carlo method. Positioning calculations are performed on each sampled value to obtain the probability distribution of the positioning results. The final positioning coordinates are calculated by weighted averaging, and a confidence ellipse is generated based on the covariance matrix of the positioning results. The neural stochastic differential equation network generates a set of perturbation evolution trajectory samples, which are then converted into actual time delay parameters through a dedicated decoding layer.

10. A shortwave localization method based on an ionospheric model according to claim 9, characterized in that, The major and minor axes of the confidence ellipse correspond to the square roots of the eigenvalues ​​of the covariance matrix, respectively, and the direction of the ellipse is determined by the eigenvectors.

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