A method for improving accuracy of a BDGIM ionospheric model based on reverse correction
By dividing the BDGIM model into grid points and using machine learning to predict the deviation, combined with space physical parameters, a high-precision ionospheric parameter field generation was achieved, solving the problem of improving the accuracy of the BDGIM model under limited regional observation conditions and improving the positioning accuracy of single-frequency users.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI ASTRONOMICAL OBSERVATORY CHINESE ACAD OF SCI
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-19
AI Technical Summary
Existing BDGIM models cannot meet the requirements for high-precision positioning under limited regional observation conditions, especially in peak ionospheric years or in the mid-to-low latitude regions of the Southern Hemisphere where positioning errors are significant. Traditional methods also suffer from decreased accuracy and high computational resource consumption in sparsely observed regions.
By dividing the global area into regular grid points, the deviation between the model output value and the reference value is calculated. A deviation prediction model is established using machine learning methods and embedded into the user terminal for real-time correction. Models such as LSTM and CNN are used in combination with spatial physical parameters to achieve high-precision prediction.
It achieves high spatiotemporal resolution generation of ionospheric parameter fields, improves the accuracy of BDGIM model and single-frequency user positioning and timing accuracy, and overcomes the shortcomings of traditional models in terms of representation ability and generalization.
Smart Images
Figure CN122239084A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ionospheric modeling technology in the BeiDou system, and in particular to a method for improving the accuracy of BDGIM ionospheric models based on reverse correction. Background Technology
[0002] Ionospheric delay error is a key factor limiting the positioning accuracy of single-frequency users in the BeiDou Navigation Satellite System. To improve the service performance of single-frequency users, BeiDou satellites broadcast BeiDou Global Ionospheric Delay Correction Model (BDGIM) parameters on the B1C and B2a frequencies to correct ionospheric delay in user positioning processing in real time. However, due to the uneven distribution of global ground monitoring stations and the strict limitations on downlink navigation signal message compilation capacity, the BDGIM model parameters can only correct a certain degree of ionospheric delay. The residual ionospheric delay error becomes a bottleneck factor affecting the positioning accuracy of single-frequency users. Especially in years with peak ionospheric activity or in the mid-to-low latitude regions of the Southern Hemisphere, the positioning error of single-frequency users can even exceed 10 meters, making it difficult to meet the application requirements of high-precision positioning, navigation, and timing services.
[0003] Currently, research on improving the accuracy of the BDGIM model is insufficient. How to overcome the bottleneck of correcting residual errors in the model while maintaining the compatibility of the existing BeiDou system architecture has become an urgent technical problem to be solved in the field of satellite navigation.
[0004] Among existing technical approaches, fitting spherical harmonic coefficients to global GNSS network data can effectively characterize large-scale ionospheric variations. However, this method is highly dependent on the density and uniformity of the global reference station network, and its accuracy drops significantly in sparsely observed areas such as the ocean. Furthermore, in the absence of dense global observations, this method struggles to obtain a high-precision global ionospheric delay correction model. Methods for fine-grained ionospheric modeling based on multi-source data assimilation effectively correct systematic biases in the background model by fusing multi-source observations using techniques such as ensemble Kalman filtering. However, the performance of this method is highly dependent on the complexity of the data assimilation system itself, including the accurate setting of background model errors, the construction of observation operators, and the enormous consumption of computational resources. In practical operational use, real-time acquisition, quality control, and efficient assimilation of multi-source data present significant challenges, limiting its application in high-time-sensitivity scenarios. Collaborative solution methods for regional high-precision ionospheric delay correction employ a distributed architecture to alleviate data transmission and computational pressure. However, the core accuracy of this method is limited by the distribution density of regional reference stations, and its accuracy rapidly decays in sparsely populated peripheral areas. Furthermore, this method essentially relies on empirical or semi-empirical function models (such as spherical harmonics, polynomials, etc.) for interpolation, which is insufficient in capturing the nonlinear and non-stationary characteristics that are prevalent in the ionosphere. As a result, the accuracy and robustness of the model are difficult to guarantee during strong gradients or sudden disturbances.
[0005] In summary, existing ionospheric modeling methods cannot meet the accuracy improvement requirements of BDGIM models with limited regional observations. This highlights the urgent need to explore new methods. Artificial intelligence technology, especially its powerful nonlinear mapping, pattern recognition, and end-to-end learning capabilities, provides a revolutionary solution for modeling, processing, and real-time correction of ionospheric model errors. By directly learning the intrinsic laws and driving patterns of ionospheric changes from ionospheric delay error sequence data and establishing the correlation between ionospheric delay error sequences and space physics parameters, it is expected to overcome the limitations of traditional physical or empirical models and significantly improve ionospheric modeling, especially the accuracy and efficiency of forecasting and current reporting during disturbances. Summary of the Invention
[0006] Based on the above analysis, this invention aims to disclose a method for improving the accuracy of BDGIM ionospheric models based on reverse correction; and to solve the problem that existing methods cannot meet the accuracy improvement requirements of BDGIM models with only limited regional observations.
[0007] This invention discloses a method for improving the accuracy of the BDGIM ionospheric model based on inverse correction, comprising:
[0008] S1. Divide the global area into regular grid points, determine the model output value of the global ionospheric delay correction model at each grid point, calculate the deviation between the model output value and the corresponding global ionospheric reference value, and establish a dataset characterizing the spatiotemporal distribution characteristics of the deviation. S2. Using time information, spatial location information, and spatial physical parameters as input variables, and the deviation as the output variable, a prediction model for the deviation is established using machine learning methods. S3. The prediction model is embedded into the user terminal. The user terminal calls the prediction model to calculate the current deviation based on the current time, current location and corresponding spatial physical parameters, and corrects the current deviation to the real-time output of the global ionospheric delay correction model to obtain the corrected ionospheric delay.
[0009] Further, S1 includes: S1-1. Using the epoch time and grid point coordinates of the global ionospheric reference value as input, calculate the zenith ionospheric delay of the corresponding puncture point at the reference frequency, and convert the zenith ionospheric delay into the total electron content of the ionosphere to obtain the model output value. S1-2. The total electron content of the ionosphere of the global ionospheric reference value is interpolated in the time dimension to obtain a reference value sequence that matches the time resolution of the model calculation value; S1-3. Calculate the difference between the model-calculated value and the reference value sequence to obtain the deviation.
[0010] Furthermore, the global ionospheric reference value is the post-hoc global ionospheric map (GIM) product published by the International GNSS Service Organization (IGS). The regular grid points are determined by dividing the global area into equal latitude and longitude grids, with a resolution of 5°×5°. The epoch time of the GIM product is used as the calculation time of the global ionospheric delay correction model, and the latitude and longitude coordinates of the regular grid points are used as the coordinates of the puncture point to calculate the zenith ionospheric delay at the reference frequency corresponding to the puncture point.
[0011] Further, S2 includes: S2-1. Collect the deviation as the dependent variable, and use time information, spatial location information and spatial physical parameters as candidate input features to perform feature screening and data preprocessing to construct a model training sample set. S2-2. Using the input features in the training sample set of the model as independent variables and the deviation as the dependent variable, a prediction model for the deviation is established using machine learning methods. S2-3. Use the model training sample set to iteratively train the prediction model, optimize the model parameters, and obtain the trained prediction model.
[0012] Furthermore, in S2-1, the space physics parameters include the solar activity index F10.7, the geomagnetic activity index Kp, and Ap.
[0013] Furthermore, in S2-2, the machine learning method includes at least one of Long Short-Term Memory Neural Network (LSTM), Recurrent Neural Network (RNN), Convolutional Neural Network (CNN), Transformer model, Support Vector Machine (SVM), and Random Forest (RF).
[0014] Furthermore, when the machine learning method is a Long Short-Term Memory Neural Network (LSTM), a two-layer LSTM structure is adopted, and a batch normalization layer and a random deactivation Dropout layer are introduced after the LSTM layer. The output layer is a fully connected layer, and the activation function is a linear function or a ReLU function. Early stopping is used to monitor the validation set loss to prevent overfitting.
[0015] Furthermore, in S2-3, the iterative training uses the Adam optimizer, and the loss function is selected as mean squared error (MSE) or mean absolute error (MAE); or the loss function is a joint loss function of physical constraints and data fitting.
[0016] Furthermore, the loss function is a joint loss function of physical constraints and data fitting, and its formula is as follows: ; in, The data fitting term is constructed based on the deviation between the predicted value and the true value of the deviation. The physical constraints are constructed based on prior knowledge of the physical behavior of the ionosphere. This is a balancing coefficient used to adjust the weighting ratio between data fitting and physical constraints.
[0017] Furthermore, S3 includes: S3-1. The prediction model is embedded in the user terminal, and the user terminal calls the prediction model to calculate the current deviation based on the current time, current location and corresponding spatiotemporal environment parameters. S3-2 The current deviation is superimposed on the real-time output of the global ionospheric delay correction model to obtain the corrected ionospheric delay. The corrected ionospheric delay is used for the positioning calculation of the user terminal to improve positioning accuracy.
[0018] This invention can achieve one of the following beneficial effects: This invention proposes a method for improving the accuracy of the BDGIM ionospheric model based on inverse correction. This method directly learns the complex nonlinear mapping relationship between the spatiotemporal variation characteristics of the total electron content (TEC) error in the ionosphere and various space environment parameters (such as the solar activity index and geomagnetic index) from the global high-spatial-temporal ionospheric delay variation characteristics. The trained machine learning model can directly and end-to-end generate high-precision, high-spatial-temporal resolution ionospheric parameter fields, effectively overcoming the shortcomings of traditional models in terms of representation ability and generalization.
[0019] Furthermore, a statistical model of how the error of the gridded BDGIM ionospheric delay correction model varies with spatial physical parameters, established through machine learning, is embedded into the user receiving terminal. Using this model and real-time acquired spatial physical parameters, the user terminal can know the BDGIM ionospheric delay correction model error in its area in real time and make real-time corrections, thereby improving the accuracy of the BDGIM ionospheric delay correction model and the accuracy of single-frequency user positioning and timing. Attached Figure Description
[0020] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart of the method for improving the accuracy of the BDGIM ionosphere model based on reverse correction in an embodiment of the present invention. Detailed Implementation
[0021] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and, together with the embodiments of the present invention, serve to illustrate the principles of the present invention.
[0022] One embodiment of the present invention discloses a method for improving the accuracy of the BDGIM ionospheric model based on inverse correction, such as... Figure 1 As shown, it includes the following steps: S1. Divide the global area into regular grid points, determine the model output value of the global ionospheric delay correction model at each grid point, calculate the deviation between the model output value and the corresponding global ionospheric reference value, and establish a dataset characterizing the spatiotemporal distribution characteristics of the deviation. S2. Using time information, spatial location information, and spatial physical parameters as input variables, and the deviation as the output variable, a prediction model for the deviation is established using machine learning methods. S3. The prediction model is embedded into the user terminal. The user terminal calls the prediction model to calculate the current deviation based on the current time, current location and corresponding spatial physical parameters, and corrects the current deviation to the real-time output of the global ionospheric delay correction model to obtain the corrected ionospheric delay.
[0023] Specifically, S1 includes: S1-1. Using the epoch time and grid point coordinates of the global ionospheric reference value as input, calculate the zenith ionospheric delay of the corresponding puncture point at the reference frequency, and convert the zenith ionospheric delay into the total electron content of the ionosphere to obtain the model output value. The global ionospheric reference value is the post-hoc global ionospheric map (GIM) product published by the International GNSS Service Organization (IGS). The regular grid points are determined by dividing the global area into equal latitude and longitude grids, with a resolution of 5°×5°. The epoch time of the GIM product is used as the calculation time of the global ionospheric delay correction model, and the latitude and longitude coordinates of the regular grid points are used as the coordinates of the puncture point to calculate the zenith ionospheric delay at the reference frequency corresponding to the puncture point. Preferably, the calculation of the zenith ionospheric delay introduces a puncture point elevation angle weighting strategy: when the elevation angle of the puncture point is lower than a preset threshold, the weight of the puncture point in the calculation of the electron content of the grid points is reduced, or the search radius is expanded to include more high elevation angle puncture points for weighted averaging, so as to weaken the multipath effect and mapping function error of low elevation angle observations; Furthermore, multi-source GIM products were used as a reference benchmark, and GIM products published by CODE, JPL, and ESA analysis centers were also obtained. The consistency of the electron content values of each center was verified, and the median or weighted average of the multiple centers was used as the global ionospheric reference value to reduce the impact of systematic errors from a single analysis center.
[0024] S1-2. The total electron content of the ionosphere of the global ionospheric reference value is interpolated in the time dimension to obtain a reference value sequence that matches the time resolution of the model calculation value; The interpolation process in the time dimension is linear interpolation between epochs, and the time resolution is 10 minutes. Preferably, before interpolation, the GIM product is subjected to integrity checks and outlier marking: missing epochs or grid points are filled by spatial-temporal joint interpolation of adjacent times or adjacent grid points; changes in electron content gradients exceeding a preset threshold are marked as outliers, and the deviation calculation results at the corresponding times are removed.
[0025] S1-3. Calculate the difference between the model-calculated value and the reference value sequence to obtain the deviation amount; The deviation is calculated using the following formula: ; in, express Time Latitude ,longitude BDGIM ionospheric delay correction model error at the location; This represents the calculated value from the model. This represents the global ionospheric reference value; Furthermore, after establishing the spatiotemporal distribution dataset of the deviation, the dataset is downsampled or compressed to reduce the input dimension and computational load for subsequent machine learning training; or hierarchical statistics are performed according to latitude zones to identify the seasonal variation characteristics and solar activity cycle variation characteristics of the deviation in different latitude regions, which serve as prior knowledge for subsequent feature engineering.
[0026] Specifically, S2 includes: S2-1. Collect the deviation as the dependent variable, and use time information, spatial location information and spatial physical parameters as candidate input features to perform feature screening and data preprocessing to construct a model training sample set. The space physics parameters include the solar activity index F10.7, the geomagnetic activity index Kp, and Ap; The feature selection includes calculating the correlation coefficient between the candidate input features and the deviation, and selecting significantly correlated features as model input features; The data preprocessing includes standardizing or normalizing the filtered features and constructing multivariate time series samples using a sliding window approach. Preferably, the spatial location information uses geomagnetic latitude rather than geographic latitude to better characterize the latitudinal distribution characteristics of physical structures such as the ionospheric equatorial anomaly.
[0027] S2-2. Using the input features in the training sample set of the model as independent variables and the deviation as the dependent variable, a prediction model for the deviation is established using machine learning methods. The machine learning methods include at least one of the following: Long Short-Term Memory Neural Network (LSTM), Recurrent Neural Network (RNN), Convolutional Neural Network (CNN), Transformer model, Support Vector Machine (SVM), and Random Forest (RF). When the machine learning method is a Long Short-Term Memory (LSTM) neural network, a two-layer LSTM structure is adopted. A batch normalization layer and a random deactivation Dropout layer are introduced after the LSTM layer. The output layer is a fully connected layer. The activation function is a linear function or a ReLU function. Early stopping is used to monitor the validation set loss to prevent overfitting.
[0028] Preferably, a self-attention mechanism is introduced, which visualizes the attention weights of each input feature in the time step or spatial dimension, identifies historical moments or spatial regions that significantly contribute to the prediction of the current deviation, and provides data-driven evidence for the analysis of ionospheric physical mechanisms. Furthermore, a regional model strategy is adopted: the globe is divided into low-latitude regions (|geomagnetic latitude| < 30°), mid-latitude regions (30° ≤ |geomagnetic latitude| < 60°), and high-latitude regions (|geomagnetic latitude| ≥ 60°), or the globe is divided into 18 dimensional regions at 10° intervals, and the prediction model for each region is established separately; or the model is separated according to the Northern and Southern Hemispheres and the day and night sides, in order to adapt to the significant differences in the ionospheric driving mechanisms in different regions; Alternatively, an ensemble learning architecture can be adopted: establish multiple base models based on LSTM time series modeling, Transformer global attention mechanism, and random forest feature engineering, respectively, and integrate them using stacking or Bayesian model averaging (BMA). The performance of each base model on the validation set is used as the weight, and the final bias prediction value and its uncertainty range are fused and output.
[0029] S2-3. Use the model training sample set to iteratively train the prediction model, optimize the model parameters, and obtain the trained prediction model. The iterative training employs the Adam optimizer, and the loss function is either mean squared error (MSE) or mean absolute error (MAE); or the loss function is a joint loss function of physical constraints and data fitting. ; in, The data fitting term is constructed based on the deviation between the predicted value and the true value of the deviation. The physical constraints are constructed based on prior knowledge of the physical behavior of the ionosphere. This is a balancing coefficient used to adjust the weight ratio between data fitting and physical constraints; The data fitting term Including at least one of the following: mean squared error (MSE), mean absolute error (MAE), Huber loss, and log-cosh loss; The physical constraints Constructed based on at least one of the following ionospheric physical priors: Spatiotemporal continuity constraint: penalty for the rate of change between the error prediction values of adjacent grid points or adjacent time points; Latitudinal symmetry constraint: similarity penalty for error distribution of symmetrical latitudinal zones in the Northern and Southern Hemispheres; Diurnal variation periodicity constraint: a periodic penalty associated with local time and error prediction; Solar activity correlation constraint: fidelity penalty for the correlation between the solar activity index and the error prediction value.
[0030] Preferably, the balance coefficient These are dynamic adaptive coefficients that are dynamically adjusted according to the training epoch or the model's convergence state. Initially, the focus is on data fitting, and later the weights of physical constraints are gradually increased. Furthermore, the prediction model supports online learning and incremental updates; by periodically receiving newly generated GIM product data, the prediction model is incrementally trained or transfer-learned to adapt the model parameters to changes in the solar activity cycle or long-term trend evolution; or an online learning framework is used to fine-tune the model based on sparse observation data returned by the user terminal. The trained prediction model is subjected to knowledge distillation or quantization pruning to compress the number of model parameters to less than 10% of the original size, thus adapting to the storage and computation constraints of embedded navigation chips.
[0031] Specifically, S3 includes: S3-1. The prediction model is embedded in the user terminal, and the user terminal calls the prediction model to calculate the current deviation based on the current time, current location and corresponding spatiotemporal environment parameters. The user terminal is a single-frequency user terminal of the BeiDou satellite navigation system. The current location is determined by the positioning module of the user terminal, and the current time is determined by the clock module of the user terminal; Preferably, the current deviation is obtained by spatial interpolation of the prediction results of the grid point to which the current location of the user terminal belongs; when the regular grid point to which the current location belongs is determined, or when the current location is located between grid points, the prediction results of adjacent grid points are bilinearly interpolated.
[0032] Furthermore, a federated learning architecture is adopted: each user terminal uses private data locally to fine-tune the model, and only uploads gradient updates to the server for aggregation, thus protecting user location privacy.
[0033] S3-2 The current deviation is superimposed on the real-time output of the global ionospheric delay correction model to obtain the corrected ionospheric delay. The superposition is an algebraic superposition. When the current deviation is positive, a subtraction operation is performed; when the current deviation is negative, a compensation operation is performed. Preferably, the correction strategy is adaptively adjusted according to the intensity of space weather activity; when the geomagnetic index Kp in the space physical parameters exceeds the activity threshold, the weight of the current deviation in the final ionospheric delay is increased, or a high temporal resolution mode is triggered to shorten the calling interval of the prediction model; when in a period of ionospheric calm, the calling frequency is reduced to save terminal computing resources. Furthermore, when the user terminal has dual-frequency observation capability, the dual-frequency non-ionospheric combined solution result is used as the true value to calibrate the predicted value of the deviation at the current moment in real time, and the calibrated residual is used to update the local parameters of the prediction model, thereby achieving a collaborative accuracy improvement for single and dual-frequency users.
[0034] To eliminate the prediction uncertainty of the current deviation amount output by the prediction model, this embodiment also provides the following solution: calculate the protection level of the corrected ionospheric delay amount by combining the inherent error of the global ionospheric delay correction model; when the protection level exceeds the integrity risk threshold required by the navigation application, issue an alarm to the user or switch to a conservative error boundary model.
[0035] The corrected ionospheric delay is used for positioning calculation of the single-frequency user terminal to improve positioning accuracy. Furthermore, the globally distributed IGS reference stations can be used as checkpoints to compare the corrected ionospheric delay with the ionospheric delay calculated by the dual-frequency reference stations, statistically analyze the corrected residuals of each grid point, periodically generate accuracy evaluation reports, and use them to guide the retraining or structural optimization of the prediction model, forming an end-to-end closed-loop verification.
[0036] In summary, the BDGIM ionospheric model accuracy improvement method based on inverse correction disclosed in this embodiment directly learns the complex nonlinear mapping relationship between the spatiotemporal variation characteristics of the total electron content (TEC) error in the ionosphere and various space environment parameters (such as the solar activity index and geomagnetic index) from the global high-spatial-temporal ionospheric delay variation characteristics. The trained machine learning model can directly and end-to-end generate high-precision, high-spatial-temporal resolution ionospheric parameter fields, effectively overcoming the shortcomings of traditional models in terms of representation ability and generalization.
[0037] Furthermore, a statistical model of how the error of the gridded BDGIM ionospheric delay correction model varies with spatial physical parameters, established through machine learning, is embedded into the user receiving terminal. Using this model and real-time acquired spatial physical parameters, the user terminal can know the BDGIM ionospheric delay correction model error in its area in real time and make real-time corrections, thereby improving the accuracy of the BDGIM ionospheric delay correction model and the accuracy of single-frequency user positioning and timing.
[0038] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for improving the accuracy of BDGIM ionospheric models based on inverse correction, characterized in that, include: S1. Divide the global area into regular grid points, determine the model output value of the global ionospheric delay correction model at each grid point, calculate the deviation between the model output value and the corresponding global ionospheric reference value, and establish a dataset characterizing the spatiotemporal distribution characteristics of the deviation. S2. Using time information, spatial location information, and spatial physical parameters as input variables, and the deviation as the output variable, a prediction model for the deviation is established using machine learning methods. S3. The prediction model is embedded into the user terminal. The user terminal calls the prediction model to calculate the current deviation based on the current time, current location and corresponding spatial physical parameters, and corrects the current deviation to the real-time output of the global ionospheric delay correction model to obtain the corrected ionospheric delay.
2. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 1, characterized in that, S1 includes: S1-1. Using the epoch time and grid point coordinates of the global ionospheric reference value as input, calculate the zenith ionospheric delay of the corresponding puncture point at the reference frequency, and convert the zenith ionospheric delay into the total electron content of the ionosphere to obtain the model output value. S1-2. The total electron content of the ionosphere of the global ionospheric reference value is interpolated in the time dimension to obtain a reference value sequence that matches the time resolution of the model calculation value; S1-3. Calculate the difference between the model-calculated value and the reference value sequence to obtain the deviation.
3. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 2, characterized in that, The global ionospheric reference value is the post-hoc global ionospheric map (GIM) product published by the International GNSS Service Organization (IGS). The regular grid points are determined by dividing the global area into equal latitude and longitude grids, with a resolution of 5°×5°. The epoch time of the GIM product is used as the calculation time of the global ionospheric delay correction model, and the latitude and longitude coordinates of the regular grid points are used as the coordinates of the puncture point to calculate the zenith ionospheric delay at the reference frequency corresponding to the puncture point.
4. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 1, characterized in that, S2 includes: S2-1. Collect the deviation as the dependent variable, and use time information, spatial location information and spatial physical parameters as candidate input features to perform feature screening and data preprocessing to construct a model training sample set. S2-2. Using the input features in the training sample set of the model as independent variables and the deviation as the dependent variable, a prediction model for the deviation is established using machine learning methods. S2-3. Use the model training sample set to iteratively train the prediction model, optimize the model parameters, and obtain the trained prediction model.
5. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 4, characterized in that, In S2-1, the space physics parameters include the solar activity index F10.7, the geomagnetic activity index Kp, and Ap.
6. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 4, characterized in that, In S2-2, the machine learning method includes at least one of Long Short-Term Memory Neural Network (LSTM), Recurrent Neural Network (RNN), Convolutional Neural Network (CNN), Transformer model, Support Vector Machine (SVM), and Random Forest (RF).
7. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 5, characterized in that, When the machine learning method is a Long Short-Term Memory (LSTM) neural network, a two-layer LSTM structure is adopted. A batch normalization layer and a random deactivation Dropout layer are introduced after the LSTM layer. The output layer is a fully connected layer. The activation function is a linear function or a ReLU function. Early stopping is used to monitor the validation set loss to prevent overfitting.
8. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 5, characterized in that, In S2-3, the iterative training uses the Adam optimizer, and the loss function is either mean squared error (MSE) or mean absolute error (MAE); or the loss function is a joint loss function of physical constraints and data fitting.
9. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 8, characterized in that, The loss function is a joint loss function of physical constraints and data fitting, and its formula is as follows: ； in, The data fitting term is constructed based on the deviation between the predicted value and the true value of the deviation. The physical constraints are constructed based on prior knowledge of the physical behavior of the ionosphere. This is a balancing coefficient used to adjust the weighting ratio between data fitting and physical constraints.
10. The method for improving the accuracy of the BDGIM ionospheric model based on reverse correction according to claim 1, characterized in that, S3 includes: S3-1. The prediction model is embedded in the user terminal, and the user terminal calls the prediction model to calculate the current deviation based on the current time, current location and corresponding spatiotemporal environment parameters. S3-2 The current deviation is superimposed on the real-time output of the global ionospheric delay correction model to obtain the corrected ionospheric delay. The corrected ionospheric delay is used for the positioning calculation of the user terminal to improve positioning accuracy.