Establishment of self-correlation model of random errors of beidou ionosphere and correction method and device

Abstract

The application provides a Beidou ionosphere random error autocorrelation model establishing and correcting method and device, a deep learning neural network model for predicting Beidou ionosphere random error is established by combining a convolutional neural network, a long short-term memory neural network and an attention mechanism, based on the predicted Beidou ionosphere random error, a time autocorrelation function of the Beidou ionosphere random error and a space autocorrelation function of the Beidou ionosphere random error are fitted respectively, and a Beidou ionosphere random error autocorrelation model is established. The application can predict the Beidou ionosphere random error without knowing an accurate physical model, and provides technical support for high-precision prediction of a Beidou ionosphere model and analysis of Beidou ionosphere random error.

Description

Technical Field

[0001] This invention belongs to the field of ionospheric technology and relates to a technical solution for establishing an autocorrelation model of random errors in the BeiDou ionosphere and for error correction. Background Technology

[0002] Ionospheric delay error is one of the main sources of error affecting GNSS satellite navigation and positioning. This error can reach several meters or even tens of meters, requiring correction through ionospheric delay algorithms or models. For dual-frequency or multi-frequency GNSS receiver users, the impact of ionospheric error can be eliminated by combining observations from different frequencies. However, for most real-time single-frequency receiver users, the most common and effective method to reduce ionospheric delay error is to utilize broadcast ionospheric models.

[0003] On July 31, 2020, the BeiDou-3 Navigation Satellite System was officially launched and began providing positioning and navigation services globally. The BeiDou-3 system broadcasts BDGIM broadcast ionospheric model parameters on new signal systems such as B1C and B2a for correcting ionospheric delay errors for BeiDou single-frequency users. Research shows that the BDGIM model has an average ionospheric delay correction rate of approximately 75% globally. The BDGIM model is simplified from a spherical harmonic function model, and its model structure and calculation process are relatively complex. The broadcast parameters of the BDGIM model are fitted based on observation data from BeiDou monitoring stations distributed throughout China, and are updated every two hours. Due to limitations in ionospheric modeling input data, model structure, and processing strategies, the BDGIM model suffers from negative ionospheric TEC values ​​in high-latitude regions and low model accuracy in vast ocean areas, severely restricting the global high-precision application of the BeiDou-3 Navigation Satellite System. Currently, we are in the peak solar activity year of the 25th solar cycle. Frequent geomagnetic storms and ionospheric anomalous disturbances have exacerbated the random variation of ionospheric electron content, resulting in a significant decrease in the accuracy of the BDGIM model and posing a great challenge to satellite navigation and positioning services.

[0004] Previous studies have typically focused on the accuracy of time delay error correction in the BeiDou broadcast ionospheric model, neglecting the random error characteristics of this model. Some research indicates that in high-precision positioning and BeiDou integrated navigation systems using the BeiDou ionospheric model as constraint information, the random model of the BeiDou ionosphere plays a crucial role, directly impacting the reliability and stability of high-precision positioning and navigation. In particular, ionospheric anomalies that may occur during periods of solar activity can lead to performance degradation and increased integrity risks for the BeiDou integrated navigation system. Therefore, combining statistical characteristics from different satellite orbits and spatial and temporal domain data analysis of the BeiDou system, mining the spatiotemporal correlation information of BeiDou ionospheric random errors, and constructing an autocorrelation model of BeiDou ionospheric random errors has significant scientific and engineering value.

[0005] Related terms:

[0006] GNSS stands for Global Navigation Satellite System

[0007] BDGIM represents the BeiDou global ionospheric delay correction model.

[0008] IGS stands for International Geodynamics Service

[0009] TEC represents the total electron content in the ionosphere.

[0010] VTEC indicates the total vertical electron content of the ionosphere. Summary of the Invention

[0011] This invention is mainly aimed at the BeiDou ionospheric random error model. It provides a method for establishing the BeiDou ionospheric random error autocorrelation model based on a deep learning neural network model.

[0012] The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions:

[0013] A method for establishing an autocorrelation model of random errors in the BeiDou ionosphere is proposed. This method combines convolutional neural networks, long short-term memory neural networks, and attention mechanisms to establish a deep learning neural network model for predicting random errors in the BeiDou ionosphere. Based on the predicted random errors in the BeiDou ionosphere, the time autocorrelation function and the spatial autocorrelation function of the random errors in the BeiDou ionosphere are fitted respectively to establish the autocorrelation model of random errors in the BeiDou ionosphere.

[0014] Furthermore, the random error of the BeiDou ionosphere is calculated using the BeiDou ionosphere model and the global ionosphere model, and combined with the space weather index to form the input dataset.

[0015] Moreover, the deep learning neural network model for predicting random errors in the BeiDou ionosphere includes an input layer, a convolutional layer, a long short-term memory neural network layer, an attention mechanism layer, and a fully connected layer arranged sequentially. The input dataset enters the input layer of the deep learning neural network model, and the fully connected layer outputs the predicted value of random errors in the BeiDou ionosphere.

[0016] Moreover, the convolutional layer consists of two one-dimensional convolutional layers and a max pooling layer.

[0017] Furthermore, a second-order Gaussian-Markov process is used to fit the time autocorrelation function of the random error, while a multinomial regression method is used to find the optimal fitting curve to fit the spatial autocorrelation function of the random error.

[0018] Furthermore, the implementation method for establishing the BeiDou ionospheric random error autocorrelation model is as follows:

[0019] A time autocorrelation model is established based on the time autocorrelation function of the BeiDou ionospheric random error, and a spatial autocorrelation model is established based on the spatial autocorrelation function of the BeiDou ionospheric random error.

[0020] By fusing the BeiDou time autocorrelation model and the spatial autocorrelation model, a spatiotemporal autocorrelation model of BeiDou ionospheric random error is established.

[0021] Historical data was used to estimate the parameters of the spatiotemporal autocorrelation model of BeiDou ionospheric random error. Based on the prediction results and actual observation data, the model parameters were adjusted and optimized.

[0022] On the other hand, the present invention also provides a method for correcting random errors in the ionosphere based on the above-mentioned method for establishing a random error autocorrelation model of the ionosphere. The random error of the ionosphere at a specific time and location is calculated according to the established random error autocorrelation model of the ionosphere, which supports the calculation of position parameters in high-precision positioning or integrated navigation.

[0023] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the BeiDou ionospheric random error autocorrelation model establishment method or the BeiDou ionospheric random error correction method as described above.

[0024] On the other hand, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the method for establishing the autocorrelation model of BeiDou ionospheric random error or the method for correcting BeiDou ionospheric random error as described above.

[0025] On the other hand, the present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the method for establishing a BeiDou ionospheric random error autocorrelation model or the method for correcting BeiDou ionospheric random errors as described above.

[0026] In the aforementioned technical solution for establishing an autocorrelation model of BeiDou ionospheric random errors, the main approach is to use historical data on BeiDou ionospheric random errors, combined with space weather indices such as solar activity and geomagnetic activity, to form an input dataset. Based on this dataset, a deep learning neural network model is introduced to predict BeiDou ionospheric random errors and establish an autocorrelation model of these errors. This invention enables the prediction of BeiDou ionospheric random errors even without knowing the exact physical model, providing technical support for high-precision forecasting and analysis of BeiDou ionospheric random errors.

[0027] Therefore, the present invention has the following advantages:

[0028] 1. Using a deep learning neural network model to predict random errors in the BeiDou ionosphere does not require a deterministic physical model and has stronger generalization ability;

[0029] 2. Using a second-order Gaussian-Markov process to fit the time autocorrelation function of random errors can more accurately describe the trend of random errors in the time domain;

[0030] 3. Using the multinomial regression method to find the spatial autocorrelation function of the random error fitting the optimal fitting curve can more conveniently calculate the spatial correlation of random errors between any distances.

[0031] The present invention is simple and convenient to implement, highly practical, and solves the problems of low practicality and inconvenience in actual application of related technologies. It can improve user experience and has significant market value. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the data processing flow in an embodiment of the present invention.

[0033] Figure 2 This is a structural diagram of a convolutional neural network-long short-term memory neural network-attention mechanism neural network model according to an embodiment of the present invention.

[0034] Figure 3 This is a schematic diagram illustrating the results of finding the optimal fitting curve using the polynomial regression method in this embodiment of the invention. Detailed Implementation

[0035] This invention proposes a method for predicting BeiDou ionospheric random errors based on a BeiDou ionospheric random error dataset and a deep learning neural network model. On this basis, it establishes the time autocorrelation function and spatial autocorrelation function of BeiDou ionospheric random errors. Finally, it establishes an autocorrelation model of BeiDou ionospheric random errors and an error correction method.

[0036] The following will further explain the concept, specific structure and technical effects of the present invention in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, features and effects of the present invention.

[0037] Example 1:

[0038] A method for establishing a BeiDou ionospheric random error autocorrelation model is proposed. The method uses a convolutional neural network-long short-term memory neural network-attention mechanism model to predict BeiDou ionospheric random errors, a second-order Gaussian-Markov process to fit the temporal autocorrelation function of the random errors, and a multinomial regression method to find the optimal fitting curve to fit the spatial autocorrelation function of the random errors. Finally, the BeiDou ionospheric random error autocorrelation model and error correction method are established.

[0039] See Figure 1The present invention provides a method for establishing a BeiDou ionospheric random error autocorrelation model, comprising the following steps:

[0040] Step 1: Calculate the BeiDou ionospheric random error using the BeiDou ionospheric model and the global ionospheric model, and combine it with the space weather index to form the input dataset.

[0041] Preferably, using the global ionospheric model published by IGS as a reference, the difference between the BeiDou ionospheric TEC and the IGS global ionospheric model TEC at each grid point is calculated and defined as the BeiDou ionospheric random error. The grid points are selected according to the IONEX standard format, i.e., a spatial resolution of 2.5° × 5.0° and a temporal resolution of 1 hour. There are 5183 ionospheric VTEC grid points at each epoch. Due to the large amount of ionospheric model data from 2020 to 2024, parallel computing is used to calculate the BeiDou ionospheric random error, and the resulting data format is IONEX.

[0042] The formula for calculating the random error TECres of the BeiDou ionosphere is as follows:

[0043] TECres = VTEC bdgim -VTEC igsg

[0044] Among them, VTEC bdgim VTEC represents the total electron content of the vertical ionosphere calculated based on the BeiDou ionospheric model. igsg This represents the total electron content of the vertical ionosphere calculated based on the IGS global grid ionospheric model.

[0045] The variation of BeiDou ionospheric random error is related to solar activity and geomagnetic activity. The solar activity index F10.7 is used to characterize the intensity of solar activity, and the geomagnetic index Kp and the disturbance storm time index Dst are used to characterize geomagnetic activity. In the preferred embodiment, a seven-dimensional vector including ionospheric random error VTEC residual, F10.7, Kp, Dst, latitude, longitude, and intra-second is constructed as the input dataset.

[0046] Step 2: Based on the characteristics of the input data and the features of different neural networks, construct the optimal neural network model to predict the random error of the BeiDou ionosphere.

[0047] Currently, the most commonly used network models in deep learning are Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). The former excels at extracting spatial structure information, while the latter is more suitable for processing time-series data. Long Short-Term Memory (LSTM) neural networks are an improvement on RNNs, introducing state values ​​and "gate" control structures. To selectively filter information, data transmission between different units in the hidden layer is controlled by three gates: the input gate, the forget gate, and the output gate. This invention proposes to construct an optimal neural network by combining the characteristics of different neural networks.

[0048] Step 3: Based on the predicted BeiDou ionospheric random errors, a random error time series is generated, and a time autocorrelation function of the BeiDou ionospheric random errors is established.

[0049] Random error prediction values ​​at different times were selected from typical grid points, the random error file was read, and the random error time series file was output. For different grid points, a second-order Gaussian-Markov process was used to fit the time autocorrelation function to establish a time correlation model for BeiDou ionospheric random errors.

[0050] Step 4: Based on the predicted BeiDou ionospheric random error, calculate the distance and variance between grid points and establish the spatial autocorrelation function of the BeiDou ionospheric random error.

[0051] The random error file is read, and the distance and variance between grid points are calculated based on the latitude and longitude information and random error information of the standard grid points. A multinomial regression method is used to find the optimal fitting curve to fit the relationship between distance and variance, establishing a spatial correlation model for the random errors of the BeiDou ionosphere.

[0052] Step 5: Based on the results obtained in Steps 3 and 4, establish the BeiDou ionospheric random error autocorrelation model and error correction method.

[0053] Example 2:

[0054] Based on the process of Example 1, in step 2, an optimal neural network model is established using a convolutional neural network-long short-term memory neural network-attention mechanism model.

[0055] Simple LSTM networks have limitations when dealing with ionospheric random error data that exhibits both temporal and spatial characteristics. This embodiment establishes a convolutional neural network-long short-term memory neural network-attention mechanism neural network model, with the following structural framework: Figure 2As shown. Based on the input dataset obtained in step 1, the data first enters the convolutional layer through the input layer. This convolutional layer is mainly responsible for feature extraction and consists of two one-dimensional convolutional layers and a max pooling layer. In specific implementations, more one-dimensional convolutional layers can be set as needed. The first convolutional layer reads the input sequence and projects the result onto the feature map, which is then input into the second convolutional layer. The second convolutional layer performs the same operation on the feature map created by the first layer, attempting to amplify its salient features. The output of the second convolutional layer enters the max pooling layer. Max pooling means taking the maximum value in the sample as the sample value after sampling. The max pooling layer simplifies the feature map and then flattens the extracted feature map into a long vector, which is used as the input for the next step. Then, the data output from the max pooling layer flows into the Long Short-Term Memory (LSTM) neural network layer. The LSTM model is mainly responsible for the long-term and short-term dependencies of the time series clock, capturing temporal features through its internal gating mechanism (input gate, forget gate, and output gate). Next, the data output from the Long Short-Term Memory (LSTM) neural network layer flows into the Attention Layer. The Attention model is mainly responsible for calculating the importance of each feature, i.e., performing a weighted average of the LSTM model's output vector. Then, the data flows into the Fully-Connected Layer. The Fully-Connected model converts the output of the Attention model into the required dimensions, ultimately obtaining the predicted value of the BeiDou ionospheric random error (VTEC residual).

[0056] Example 3:

[0057] Based on the process of Example 1, in step 3, a second-order Gauss-Markov process is used to fit the time autocorrelation function of the random error.

[0058] The transfer function of a second-order Gaussian-Markov process is expressed as:

[0059]

[0060] ω0≡2πf0=2π / (24h), τ c ≡35h,

[0061] In the formula, G(s) represents the transfer function, s represents the Laplace variable, σ represents the noise parameter, ω0 represents the angular frequency, f0 represents the frequency, 24h represents a natural period of 24 hours, and τ c The time constant is 35 hours, and ζ represents the damping ratio.

[0062] In this embodiment, the time autocorrelation function is expressed as:

[0063]

[0064] In the formula, R(t) lag ) represents the autocorrelation function, which describes the oscillation process that decays over time, t lag σ represents the lag time. 2 Let ω represent the variance, e represent the base of the natural logarithm, and ω represent the variability. d ω represents the angular frequency of the damped oscillation, and k represents a function of the damping ratio used to adjust the amplitude of the sine term.

[0065] Example 4:

[0066] Based on the process of Example 1, in step 4, a multinomial regression method is used to find the spatial autocorrelation function of the random error fitting the optimal fitting curve.

[0067] First, calculate the great circle distance D between two grid points, expressed by the formula:

[0068]

[0069] In the formula, R represents the Earth's radius. This represents the latitude and longitude of the first grid point p1. This represents the latitude and longitude of the second grid point p2.

[0070] Then calculate the variance of the two grid points. The formula is expressed as:

[0071]

[0072] In the formula, res1 represents the random error of the BeiDou ionosphere at the first grid point p1, res2 represents the random error of the BeiDou ionosphere at the second grid point p2, and E[] represents the expected value.

[0073] Finally, based on all great circle distances and variances, a multinomial regression method is used to find the optimal fitting curve. The process involves: first, selecting an appropriate polynomial order based on the data distribution and trend, typically starting with low-order polynomials and gradually increasing the order until a satisfactory fit is achieved; second, estimating the coefficients of the multinomial regression model using the least squares method; then, evaluating the multinomial model through goodness-of-fit calculations, residual analysis, and cross-validation, selecting the polynomial order that maximizes the goodness of fit and whose residual distribution most closely approximates a random distribution; and finally, calculating the variance inflation factor to check for multicollinearity among the polynomial terms, using the Breusch-Pagan test to check for heteroscedasticity of the residuals, thus determining the optimal multinomial regression model.

[0074] Example 5:

[0075] Based on the process in Example 1, after completing the time autocorrelation function and spatial autocorrelation function of the BeiDou ionospheric random error, the BeiDou ionospheric random error autocorrelation model is established to support error correction.

[0076] First, a time autocorrelation model is established based on the time autocorrelation function of the BeiDou ionospheric random error, such as the autoregressive moving average model (ARMA). Then, a spatial autocorrelation model is established based on the spatial autocorrelation function of the BeiDou ionospheric random error, such as Kriging interpolation.

[0077] Secondly, the BeiDou temporal autocorrelation model and spatial autocorrelation model are integrated to establish a BeiDou random error spatiotemporal autocorrelation model, such as the spatiotemporal autoregressive model (STARMA). For BeiDou random errors, since each error value has both temporal and spatial information (coordinates), the random error at each grid point at a specific future time is first calculated based on the temporal autocorrelation model of each grid point, and then the random error at any spatial point is calculated based on the spatial autocorrelation model.

[0078] Then, historical data was used to estimate the parameters of the BeiDou ionospheric random error spatiotemporal autocorrelation model, and the model's fitting effect and predictive ability were evaluated using cross-validation. Based on the prediction results and actual observation data, the model parameters were adjusted to optimize model performance.

[0079] Example 6:

[0080] Based on the process of Example 1, the BeiDou ionospheric random error correction is realized based on the established BeiDou ionospheric random error autocorrelation model.

[0081] First, based on the positions of BeiDou satellites and ground observation stations, the location of the ionospheric puncture point at a specific moment is calculated using the distance intersection method. Then, based on the established BeiDou ionospheric random error autocorrelation model (e.g., STARMA), the BeiDou ionospheric random error at a specific location at a specific moment is calculated. Finally, in high-precision positioning or integrated navigation, the ionospheric time delay error information calculated based on the BeiDou ionospheric model is introduced as the observation model, and the random error information calculated based on the BeiDou ionospheric random error autocorrelation model is introduced as the random model to perform high-precision position calculation.

[0082] Example 7:

[0083] The present invention provides another embodiment, further in embodiment 1, in addition to the data from 2020 to 2024, data from 1998 to 2023 can be added to improve the accuracy of the time autocorrelation function and spatial autocorrelation function of the BeiDou ionospheric random error.

[0084] To facilitate understanding of the technical effects of this invention, the following experimental data is provided:

[0085] In using the method of this invention to find the optimal fitting curve in multinomial regression, the main factors are the great circle distance D and variance σ between any two grid points. 2 Find the optimal fitting curve. Assume 10 sets of observation data are given, and the great circle distances and variances are shown in the table below:

[0086] Table 1 Great circle distance and variance

[0087] 1 50.26 1.22 2 98.45 2.38 3 146.67 3.39 4 253.12 6.96 5 564.21 7.18 6 1336.01 5.87 7 863.49 6.87 8 532.11 7.09 9 787.23 5.49 10 123.95 3.04

[0088] Based on the above 10 sets of data, the optimal curve found is a fifth-order polynomial, as shown in the graph below. Figure 3 As shown. Its mean square error is 0.04, and its coefficient of determination is 0.99. The spatial autocorrelation function given based on the above data is as follows:

[0089] V = 1.7264 - 0.0263d + 4.2522 × 10 -4 d 2 -1.2704×10 -6 d 3 +1.4180×10 -9 d 4 -5.4119×10 -13 d 5

[0090] In the formula, V represents the variance and d represents the great circle distance.

[0091] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0092] The electronic device for establishing the BeiDou ionospheric random error autocorrelation model provided by the present invention is described below. The electronic device for establishing the BeiDou ionospheric random error autocorrelation model described below and the BeiDou ionospheric random error autocorrelation model establishment method described above can be referred to in correspondence with each other.

[0093] The electronic device may include a processor, a communications interface, a memory, and a communication bus. The processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute the BeiDou ionospheric random error autocorrelation model establishment method, which mainly includes the software processing part mentioned above.

[0094] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0095] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the software processing part of the BeiDou ionospheric random error autocorrelation model establishment method provided by the above methods.

[0096] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is implemented to perform the software processing portion of the BeiDou ionospheric random error autocorrelation model establishment method provided by the above methods.

[0097] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0098] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for establishing a BeiDou ionospheric random error autocorrelation model, characterized in that: A deep learning neural network model for predicting BeiDou ionospheric random errors was established by combining convolutional neural networks, long short-term memory neural networks, and attention mechanisms. Based on the predicted BeiDou ionospheric random errors, the time autocorrelation function and the spatial autocorrelation function of the BeiDou ionospheric random errors were fitted respectively to establish an autocorrelation model of BeiDou ionospheric random errors. Among them, a second-order Gaussian-Markov process is used to fit the time autocorrelation function of the random error, which is expressed as: ， In the formula, This represents the autocorrelation function, which describes the oscillation process that decays over time. Indicates the lag time. Represents variance. The base of the natural logarithm. This represents the angular frequency of the damped oscillation. A function representing the damping ratio, used to adjust the amplitude of the sine term; The spatial autocorrelation function of the random error fitting the optimal fitting curve is obtained by using the polynomial regression method. This includes calculating the great circle distance and variance between grid points, and using the polynomial regression method to optimally fit the relationship between the great circle distance and the variance to obtain the spatial autocorrelation function. The implementation method for establishing the BeiDou ionospheric random error autocorrelation model is as follows: A time autocorrelation model is established based on the time autocorrelation function of the BeiDou ionospheric random error, and a spatial autocorrelation model is established based on the spatial autocorrelation function of the BeiDou ionospheric random error. By fusing the BeiDou time autocorrelation model and the spatial autocorrelation model, a spatiotemporal autocorrelation model of BeiDou ionospheric random error is established. Historical data was used to estimate the parameters of the spatiotemporal autocorrelation model of BeiDou ionospheric random error. Based on the prediction results and actual observation data, the model parameters were adjusted and optimized.

2. The method for establishing a BeiDou ionospheric random error autocorrelation model according to claim 1, characterized in that: The random error of the BeiDou ionosphere is calculated using the BeiDou ionosphere model and the global ionosphere model, and combined with the space weather index to form the input dataset.

3. The method for establishing a BeiDou ionospheric random error autocorrelation model according to claim 2, characterized in that: The deep learning neural network model for predicting random errors in the BeiDou ionosphere includes an input layer, a convolutional layer, a long short-term memory neural network layer, an attention mechanism layer, and a fully connected layer arranged sequentially. The input dataset enters the input layer of the deep learning neural network model, and the fully connected layer outputs the predicted value of random errors in the BeiDou ionosphere.

4. The method for establishing a BeiDou ionospheric random error autocorrelation model according to claim 3, characterized in that: The convolutional layer consists of two one-dimensional convolutional layers and a max pooling layer.

5. A method for correcting random errors in the BeiDou ionosphere based on the method for establishing a BeiDou ionospheric random error autocorrelation model according to any one of claims 1 to 4, characterized in that: The BeiDou ionospheric random error at a specific time and location is calculated based on the established BeiDou ionospheric random error autocorrelation model, supporting the solution of position parameters in high-precision positioning or integrated navigation.

6. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the BeiDou ionospheric random error autocorrelation model establishment method as described in any one of claims 1 to 4 or the BeiDou ionospheric random error correction method as described in claim 5.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the BeiDou ionospheric random error autocorrelation model establishment method as described in any one of claims 1 to 4 or the BeiDou ionospheric random error correction method as described in claim 5.

8. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the BeiDou ionospheric random error autocorrelation model establishment method as described in any one of claims 1 to 4 or the BeiDou ionospheric random error correction method as described in claim 5.

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