A Method for Ionospheric Scintillation Map Reconstruction Based on Neural Network Error Compensation

Abstract

This invention relates to the field of ionospheric technology, specifically to a method for reconstructing ionospheric scintillation maps based on neural network error compensation. First, ionospheric scintillation observation data from discrete GNSS monitoring stations and relevant background environmental parameters are acquired. After preprocessing, ordinary Kriging interpolation is used to generate an initial ionospheric scintillation map. The difference between the interpolated estimated values ​​and the actual values ​​at each station is extracted as the interpolation residual. Combined with the background environmental parameters, the original dataset is obtained. Samples are constructed using a sliding window mechanism and input into a Long Short-Term Memory (LSTM) network model for training, resulting in an LSTM residual prediction model. The environmental parameters of the area to be reconstructed are input into the trained model to output the prediction residual. Based on spatial distance, a Gaussian decay function is used to adaptively allocate weights, and the residual is dynamically fused with the initial interpolated map to obtain a high-fidelity reconstructed map. This invention effectively solves the smoothing degradation problem of traditional interpolation in blind areas without stations, while also considering robustness in densely populated areas, thus improving the accuracy of global ionospheric scintillation reconstruction.

Description

Technical Field

[0001] This invention relates to the field of ionospheric technology, and more specifically to a method for reconstructing ionospheric scintillation maps based on neural network error compensation. Background Technology

[0002] The ionized region of the atmosphere, approximately 60-1000 km above the Earth's surface, contains a large number of free electrons. Under the influence of solar ultraviolet radiation and X-rays, this forms a neutral ionized region composed of charged particles, known as the ionosphere. When small-scale plasma inhomogeneities or traveling wave disturbances occur in the ionosphere, they cause refraction, diffraction, and scattering effects on radio signals penetrating this region. This results in violent and random fluctuations in the amplitude and phase of GNSS signals, a phenomenon known as ionospheric scintillation. High-intensity ionospheric scintillation can cause cycle slips or even signal loss in satellite navigation receivers, seriously threatening the integrity, continuity, and availability of high-precision positioning, timing, and communication systems. Therefore, large-scale, high-precision space monitoring and situation reconstruction of ionospheric scintillation phenomena are urgent needs in the fields of space weather and navigation.

[0003] Mapping ionospheric scintillation is a core method for intuitively representing the spatial distribution and evolution of scintillation. Currently, engineering practices mainly rely on ground-based professional scintillation monitoring instruments or conventional GNSS receiver networks to acquire discrete observation data, and use traditional spatial interpolation algorithms such as ordinary kriging interpolation and inverse distance weighted interpolation to perform two-dimensional or three-dimensional gridding of discrete points. However, these traditional pure mathematical interpolation methods are highly dependent on the geographical distribution density of ground-based observation stations. In data-blind areas such as low latitudes and equatorial anomalies in my country, vast ocean areas, and remote western regions, due to the lack of sufficient station support, traditional interpolation algorithms are prone to severe smoothing degradation effects, failing to accurately reproduce the subtle distortion structures caused by inhomogeneities, resulting in huge reconstruction errors in scintillation maps in these blind areas. Because the physical processes that trigger ionospheric scintillation are extremely complex, the generation and evolution of inhomogeneities are driven not only by various nonlinear physical factors such as background electric and magnetic fields, but also by highly complex spatiotemporal dynamic characteristics. Traditional static empirical models and simple spatial geometric interpolation are no longer sufficient to overcome the accuracy bottleneck in areas without stations. With the rapid development of deep learning technology, neural networks, with their powerful ability to extract high-dimensional nonlinear features and learn temporal patterns, have begun to be introduced into the field of ionospheric research. However, existing deep learning-based prediction and reconstruction models are mostly purely data-driven "black box" models, often neglecting the fundamental robustness of traditional physical interpolation in densely populated areas. Summary of the Invention

[0004] The purpose of this invention is to provide an ionospheric scintillation map reconstruction method based on neural network error compensation. It utilizes a long short-term memory network to extract the nonlinear evolution characteristics of ionospheric scintillation interpolation error in the time dimension, solving the problem that traditional spatial interpolation algorithms are prone to severe smoothing degradation and data distortion in blind areas without stations. At the same time, through a spatial adaptive weight fusion mechanism, it preserves the robustness of physical interpolation in densely populated areas, thereby improving the reconstruction accuracy of large-scale ionospheric scintillation maps.

[0005] To achieve the above objectives, this invention provides a method for reconstructing ionospheric scintillation maps based on neural network error compensation, comprising the following steps:

[0006] Step 1: Obtain multi-source observation data and background environmental parameters related to ionospheric scintillation, including the ionospheric amplitude scintillation index S4 value, solar radio radiation flux F10.7, geomagnetic indices Kp and Dst, and the background total electron content gradient value at the observation station. After preprocessing, these are used as the characteristic parameters required for prediction.

[0007] Step 2: Using the ordinary Kriging spatial interpolation algorithm, the discrete S4 values ​​observed by the ionospheric monitoring receiver are mapped in two dimensions to generate an initial ionospheric scintillation interpolation map.

[0008] Step 3: Extract the initial interpolation grid values ​​at the known observation station locations, and subtract them from the actual S4 observation values ​​of the station to calculate the interpolation error of each observation station at each historical time. This error is defined as the interpolation residual and, together with the background environment parameters from Step 1, constitutes the original dataset.

[0009] Step 4: Divide the original dataset into training set, validation set and test set according to a certain ratio, and use a sliding window mechanism to convert the feature parameters and interpolation residuals of the historical continuous time steps into time series sample pairs;

[0010] Step 5: Select a Long Short-Term Memory (LSTM) network model, train the input model with time series samples from the training set, fit the nonlinear evolution of the spatial interpolation residuals in the time dimension, and construct an LSTM residual prediction model.

[0011] Step 6: Input the environmental parameters of the region to be reconstructed into the trained LSTM residual prediction model and output the predicted residual value at the corresponding time of the grid point; based on the spatial distance weight matrix, dynamically fuse the predicted residual value with the initial ionospheric scintillation interpolation map to obtain the final high-fidelity ionospheric scintillation reconstruction map.

[0012] Optionally, step 4, which uses a sliding window mechanism, involves setting the time window size to t, using the background environment parameters and interpolation residuals from the past t+1 consecutive time steps as the input feature matrix, and using the true interpolation residual at time t+1 as the target label. This process is repeated across the entire dataset to construct a time-series sample suitable for supervised learning.

[0013] Optionally, step 5, the training process of the Long Short-Term Memory network model, includes the following steps:

[0014] Step 5.1: Read the hidden state from the previous time step and the input features from the current time step through the forget gate of the LSTM unit, calculate the discard probability using the Sigmoid function, and determine the historical residual information that needs to be forgotten from the cell state;

[0015] Step 5.2: The Sigmoid layer of the input gate determines the new residual information that needs to be updated, and the tanh layer generates the candidate cell state vector at the current time step;

[0016] Step 5.3: Combine the output of the forget gate in Step 5.1 with the candidate vector of the input gate in Step 5.2, perform dot multiplication and addition operations to update the cell state at the current time.

[0017] Step 5.4: Calculate the hidden state at the current time step based on the updated cell state through the output gate, and map it to the prediction residual output through the fully connected network layer; use the mean squared error as the loss function, and continuously update the network weight matrix through the backpropagation algorithm over time.

[0018] Optionally, the dynamic fusion process in step 6 involves calculating the spatial Euclidean distance d from the grid point to be reconstructed to the nearest known real observation station. When d is less than the set distance threshold, the final reconstruction result mainly depends on the initial ionospheric scintillation interpolation map. When d increases or is in a blind zone without observation stations, the weight of the predicted residual value output by the LSTM residual prediction model in the fusion calculation is increased.

[0019] Optionally, the reconstructed region in step 6 includes the blank region without observation stations. The dynamic allocation of weights is specifically calculated using a Gaussian decay function, and the reconstruction formula is expressed as follows:

[0020] Final reconstructed value = initial interpolation baseline value + weight term * predicted residual value.

[0021] This invention provides a method for reconstructing ionospheric scintillation maps based on neural network error compensation. The method involves acquiring ionospheric scintillation observation data and related background environmental parameters from discrete GNSS monitoring stations, preprocessing these parameters, and using them as feature values ​​for the original dataset. A spatial interpolation algorithm is used to perform two-dimensional gridding mapping on the discrete observation data, generating an initial ionospheric scintillation interpolation map. The difference between the initial interpolation estimate and the actual observation value at the observation station is extracted as the interpolation residual, which, along with the background environmental parameters, constitutes the original dataset. The original dataset is divided into training, validation, and test sets, and a sliding window mechanism is used to construct time-series sample pairs. The time-series samples from the training set are input into a long short-term memory network for training, constructing a residual prediction model. Finally, the environmental parameters of the area to be reconstructed are input into the trained residual prediction model to output the predicted residual value. Adaptive weights are calculated based on spatial distance, and the predicted residual is dynamically fused with the initial interpolation map to obtain a high-fidelity ionospheric scintillation reconstruction map. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a block diagram illustrating the principle of an ionospheric scintillation map reconstruction method based on neural network error compensation according to the present invention.

[0024] Figure 2 This is a schematic diagram of the training process for interpolation residual prediction using a Long Short-Term Memory (LSTM) network, as described in this invention.

[0025] Figure 3 This is a schematic diagram of the adaptive dynamic fusion process of the present invention. Detailed Implementation

[0026] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0027] This invention provides a method for reconstructing ionospheric scintillation maps based on neural network error compensation, comprising the following steps:

[0028] Step 1: Obtain multi-source observation data and background environmental parameters related to ionospheric scintillation, including the ionospheric amplitude scintillation index S4 value, solar radio radiation flux F10.7, geomagnetic indices Kp and Dst, and the background total electron content gradient value at the observation station. After preprocessing, these are used as the characteristic parameters required for prediction.

[0029] Step 2: Using the ordinary Kriging spatial interpolation algorithm, the discrete S4 values ​​observed by the ionospheric monitoring receiver are mapped in two dimensions to generate an initial ionospheric scintillation interpolation map.

[0030] Step 3: Extract the initial interpolation grid values ​​at the known observation station locations, and subtract them from the actual S4 observation values ​​of the station to calculate the interpolation error of each observation station at each historical time. This error is defined as the interpolation residual and, together with the background environment parameters from Step 1, constitutes the original dataset.

[0031] Step 4: Divide the original dataset into training set, validation set and test set according to a certain ratio, and use a sliding window mechanism to convert the feature parameters and interpolation residuals of the historical continuous time steps into time series sample pairs;

[0032] Step 5: Select a Long Short-Term Memory (LSTM) network model, train the input model with time series samples from the training set, fit the nonlinear evolution of the spatial interpolation residuals in the time dimension, and construct an LSTM residual prediction model.

[0033] Step 6: Input the environmental parameters of the region to be reconstructed into the trained LSTM residual prediction model and output the predicted residual value at the corresponding time of the grid point; based on the spatial distance weight matrix, dynamically fuse the predicted residual value with the initial ionospheric scintillation interpolation map to obtain the final high-fidelity ionospheric scintillation reconstruction map.

[0034] The specific process is as follows: Figure 1 As shown, this invention focuses on signal nonlinear distortion environments caused by ionospheric scintillation, small-scale inhomogeneities, and traveling wave disturbances. The following description, in conjunction with specific implementation steps and embodiments, provides further details:

[0035] Step 1: Obtain multi-source observation data and background environmental parameters related to ionospheric scintillation.

[0036] Specifically, the ionospheric amplitude scintillation index S4 value of discrete Global Navigation Satellite System (GNSS) monitoring stations within the target area is obtained, along with the corresponding solar radio flux F10.7, geomagnetic indices Kp and Dst, and the background total electron content (TEC) gradient value at the observation station. Due to the significant differences in the dimensions and orders of magnitude of the various background environmental parameters, to accelerate model convergence and improve prediction accuracy, the Min-Max Normalization method is used to map all feature parameters to the [0,1] interval. Let the original sequence be... The normalized sequence is The calculation formula is as follows:

[0037]

[0038] in, and These are the maximum and minimum values ​​of the feature in the sample set, respectively. After preprocessing, they serve as the original dataset feature values ​​required by the prediction model.

[0039] Step 2: For the obtained discrete S4 observations, perform two-dimensional gridding mapping using the Ordinary Kriging spatial interpolation algorithm.

[0040] In practice, the experimental semivariance between each known observation point is first calculated. To characterize the spatial autocorrelation of scintillation intensity:

[0041]

[0042] in, The spatial lag distance between two points. The distance is Number of point pairs for The observed value at that location.

[0043] After fitting the theoretical semivariance function using a spherical or exponential model, the Kriging weight coefficients are solved. Generate an initial ionospheric scintillation interpolation map of the target area. For unknown points of the target... Its initial interpolation estimate Obtained by linear combination of known observation points:

[0044]

[0045] Among them, the weighting coefficient This is obtained by solving the following system of unbiased optimal condition equations. For Lagrange multipliers:

[0046]

[0047]

[0048] Step 3: Error extraction and dataset construction.

[0049] Extract the known observation station locations from step 2 Initial interpolation grid estimate at [location] Compare it with the actual S4 observations at the site. The difference is defined as the interpolation residual. :

[0050]

[0051] Align the interpolation residual with the normalized background environment parameters from step 1 in the time dimension to form the original time-series dataset.

[0052] Step 4: Data partitioning and time series sample construction.

[0053] The original dataset was divided into training, validation, and test sets in a 7:2:1 ratio. A sliding window mechanism was used to construct time-series sample pairs: Let N be the total number of observation epochs in the original dataset, and F... k This represents the multidimensional feature column vector of the k-th observation epoch, containing background environmental parameters such as solar radio flux, geomagnetic index, and TEC gradient, as well as the initial interpolation residuals. The actual interpolation residual at the corresponding time point is denoted as Set the time window size to t, for example, t=12, representing the past 12 observation epochs. Concatenate the feature vectors of the past t consecutive time points to construct the input feature matrix. Its mathematical expression is:

[0054]

[0055] The true interpolation residual at the next time point immediately following the current time window (i.e., the (t+1)th time point) is used as the target label for model fitting. ,Right now:

[0056]

[0057] Set the step size to 1 in this window, and adjust it according to the time sequence number. ( The algorithm iterates through the entire dataset, continuously extracting feature matrices and label pairs, ultimately constructing a dataset in the form of (...). This dataset collection. Through this sliding mechanism, static discrete datasets are successfully transformed into high-dimensional temporal samples suitable for supervised learning of Long Short-Term Memory (LSTM) networks.

[0058] Step 5: As Figure 2 As shown, a Long Short-Term Memory (LSTM) network residual prediction model is constructed and trained. The time-series sample pairs from the training set in step 4 are input into the LSTM residual prediction model. The specific training process includes:

[0059] Step 5.1: First, read the hidden state h from the previous time step through the forget gate of the LSTM unit. t-1 and the input feature matrix at the current time The probability of dropping the item is calculated using the Sigmoid function. The decision requires starting from the previous cell state. Forgotten historical residual information, calculation formula:

[0060]

[0061] Step 5.2: Calculate the input gate vector through the Sigmoid layer of the input gate. The new residual information that needs to be updated is determined by the tanh layer, which then generates the candidate cell state vector for the current time step. :

[0062]

[0063]

[0064] Step 5.3: Combine the output of the forget gate in Step 5.1 The candidate vectors for the input gate in step 5.2 Perform Hadamard product and addition operations to update the cell state at the current time step. :

[0065]

[0066] Step 5.4: Finally, calculate the output control vector through the output gate. Based on the updated cell state Calculate the hidden state at the current time step. :

[0067]

[0068]

[0069] The high-dimensional hidden state mapping extracted through the fully connected network layer (Dense Layer) outputs the final prediction residual. :

[0070]

[0071] In the above formula, These represent the weight matrices of the corresponding network layers. This indicates the corresponding bias term.

[0072] In this process, mean squared error (MSE) is used as the target loss function, and the Adam optimizer iteratively updates the network weight matrix using the backpropagation over time (BPTT) algorithm. The model's loss value is monitored on the validation set; if the loss stops decreasing after several consecutive epochs, an early stopping mechanism is triggered to save the optimal model parameters.

[0073] Step 6: Blind Spot Reconstruction and Dynamic Fusion. Please refer to [link / reference]. Figure 3 The current environmental parameters of the area to be reconstructed (including vast oceans or remote inland blank areas without observation stations) are input into the trained LSTM residual prediction model, and the predicted residual value of the grid point at the corresponding time is output, denoted as . Then, spatially adaptive dynamic fusion is performed:

[0074] Calculate the spatial Euclidean distance *d* from the grid point to be reconstructed to the nearest known real observation station; then, assign spatial compensation weights *W(d)* using a Gaussian decay function. Let the initial interpolation reference value for this grid point be obtained in step 2. The final reconstructed value The calculation formula is:

[0075]

[0076]

[0077] That is, the final reconstruction is as follows:

[0078]

[0079] Where σ is the distance scale parameter controlling the weight decay rate. From the above formula mechanism, it can be seen that when the grid points are in a densely populated area (d approaches 0), the weight term... Approaching 0, the compensation weight of the prediction residual is extremely small, and the reconstruction result mainly relies on the robust output of physical Kriging interpolation; when the grid points are in the stationless blind zone (d gradually increases), traditional interpolation fails, and the Gaussian function makes the weight of the prediction residual increase rapidly and approach 1. The model smoothly transitions to being dominated by the dynamic residual predicted by LSTM, thereby filling the data gaps and finally obtaining a high-fidelity ionospheric scintillation reconstruction map of the entire domain.

[0080] In summary, compared with existing technical solutions, the present invention has the following beneficial effects:

[0081] This invention employs a reconstruction framework combining physical interpolation benchmarks and deep network compensation. It ensures the fundamental physical robustness of densely populated areas through ordinary Kriging interpolation and utilizes LSTM to accurately uncover the nonlinear evolution of interpolation residuals over time. This effectively overcomes the limitations of single spatial interpolation algorithms, which are prone to smoothing degradation and data distortion in blind areas without stations (vast oceans or remote inland regions). Furthermore, this invention constructs a spatially adaptive dynamic fusion mechanism, employing a dynamic weight allocation strategy based on a Gaussian decay function. This ensures that the reconstruction results smoothly rely on traditional physical interpolation in densely populated areas, while in blind areas without observation data, the Gaussian decay mechanism allows the model to smoothly transition to dynamic residual dominance based on LSTM predictions. This achieves a degree of complementary advantages between sparse and dense areas. Furthermore, when constructing the residual time series prediction dataset, this invention deeply couples multi-source space environment parameters such as solar radio radiation flux, geomagnetic index, and total electron content. This enables the model to accurately perceive the driving modulation effect of the external macro environment when facing complex ionospheric inhomogeneities and nonlinear random scintillation caused by traveling wave disturbances, thereby improving the reliability and generalization ability of the scintillation reconstruction map under severe space weather events.

[0082] The above-disclosed embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of the invention. Those skilled in the art will understand that implementing all or part of the above-described embodiments and making equivalent changes in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A method for reconstructing an ionospheric scintillation map based on neural network error compensation, characterized in that, Includes the following steps: Step 1: Obtain multi-source observation data and background environmental parameters related to ionospheric scintillation, including the ionospheric amplitude scintillation index S4 value, solar radio radiation flux F10.7, geomagnetic indices Kp and Dst, and the background total electron content gradient value at the observation station. After preprocessing, these are used as the characteristic parameters required for prediction. Step 2: Using the ordinary Kriging spatial interpolation algorithm, the discrete S4 values ​​observed by the ionospheric monitoring receiver are mapped in two dimensions to generate an initial ionospheric scintillation interpolation map. Step 3: Extract the initial interpolation grid values ​​at the known observation station locations, and subtract them from the actual S4 observation values ​​of the station to calculate the interpolation error of each observation station at each historical time. This error is defined as the interpolation residual and, together with the background environment parameters from Step 1, constitutes the original dataset. Step 4: Divide the original dataset into training set, validation set and test set according to a certain ratio, and use a sliding window mechanism to convert the feature parameters and interpolation residuals of the historical continuous time steps into time series sample pairs; Step 5: Select a Long Short-Term Memory (LSTM) network model, train the input model with time series samples from the training set, fit the nonlinear evolution of the spatial interpolation residuals in the time dimension, and construct an LSTM residual prediction model. Step 6: Input the environmental parameters of the region to be reconstructed into the trained LSTM residual prediction model and output the predicted residual value at the corresponding time of the grid point; based on the spatial distance weight matrix, dynamically fuse the predicted residual value with the initial ionospheric scintillation interpolation map to obtain the final high-fidelity ionospheric scintillation reconstruction map.

2. The ionospheric scintillation map reconstruction method based on neural network error compensation as described in claim 1, characterized in that, Step 4, using the sliding window mechanism, involves setting the time window size to t, using the background environment parameters and interpolation residuals from the past t+1 consecutive time steps as the input feature matrix, and using the true interpolation residual at time t+1 as the target label. This process is repeated across the entire dataset to construct a time series sample suitable for supervised learning.

3. The ionospheric scintillation map reconstruction method based on neural network error compensation as described in claim 2, characterized in that, Step 5, the training process of the Long Short-Term Memory network model, includes the following steps: Step 5.1: Read the hidden state from the previous time step and the input features from the current time step through the forget gate of the LSTM unit, calculate the discard probability using the Sigmoid function, and determine the historical residual information that needs to be forgotten from the cell state; Step 5.2: The Sigmoid layer of the input gate determines the new residual information that needs to be updated, and the tanh layer generates the candidate cell state vector at the current time step; Step 5.3: Combine the output of the forget gate in Step 5.1 with the candidate vector of the input gate in Step 5.2, perform dot multiplication and addition operations to update the cell state at the current time. Step 5.4: Calculate the hidden state at the current time step based on the updated cell state through the output gate, and map it to the prediction residual output through the fully connected network layer; use the mean squared error as the loss function, and continuously update the network weight matrix through the backpropagation algorithm over time.

4. The ionospheric scintillation map reconstruction method based on neural network error compensation as described in claim 3, characterized in that, The dynamic fusion process in step 6 involves calculating the spatial Euclidean distance d from the grid point to be reconstructed to the nearest known real observation station. When d is less than the set distance threshold, the final reconstruction result mainly depends on the initial ionospheric scintillation interpolation map. When d increases or is in a blind zone without observation stations, the weight of the predicted residual value output by the LSTM residual prediction model in the fusion calculation is increased.

5. The ionospheric scintillation map reconstruction method based on neural network error compensation as described in claim 4, characterized in that, Step 6 reconstructs the region including blank areas without observation stations. The dynamic allocation of weights utilizes a Gaussian decay function for fusion calculation. The specific reconstruction formula is as follows: Final reconstructed value = initial interpolation baseline value + weight term * predicted residual value.

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