Beidou ionosphere random error autocorrelation model establishing and correcting method and device

Abstract

The invention provides a Beidou ionosphere random error autocorrelation model establishment and correction method and device, and the method comprises the steps: building a deep learning neural network model for predicting a Beidou ionosphere random error through combining a convolutional neural network, a long-short-term memory neural network and an attention mechanism, and carrying out the correction of the Beidou ionosphere random error based on the predicted Beidou ionosphere random error. And respectively fitting the time autocorrelation function of the Beidou ionosphere random error and the space autocorrelation function of the Beidou ionosphere random error, and establishing a Beidou ionosphere random error autocorrelation model. The Beidou ionosphere random error prediction method can predict the Beidou ionosphere random error under the condition of not knowing an accurate physical model, and provides technical support for high-precision prediction of the Beidou ionosphere model and analysis of the Beidou ionosphere random error.

Description

Technical Field

[0001] The present invention belongs to the technical field of ionosphere, and relates to a technical solution for establishing a Beidou ionosphere random error autocorrelation model and error correction. Background Art

[0002] Ionospheric delay error is one of the main error sources affecting GNSS satellite navigation and positioning. This error can reach several meters or even dozens of meters, and needs to be corrected through ionospheric delay algorithms or models. For users of dual-frequency or multi-frequency GNSS receivers, the influence of ionospheric error can be eliminated by combining observations of different frequencies. For most real-time single-frequency receiver users, the most common and effective method to reduce ionospheric delay error is to rely on the broadcast ionospheric model.

[0003] On July 31, 2020, the Beidou-3 satellite navigation system was officially launched and provided positioning and navigation services globally. The Beidou-3 system broadcasts BDGIM broadcast ionospheric model parameters on new system signals such as B1C and B2a for ionospheric delay error correction of Beidou single-frequency users. Research shows that the average ionospheric delay correction rate of the BDGIM model globally is about 75%. The BDGIM model is simplified from the 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 the observation data of Beidou monitoring stations distributed in China, and a new set is updated every two hours. Due to limitations such as ionospheric modeling input data, model structure, and processing strategies, the BDGIM model has problems of negative ionospheric TEC values in high-latitude regions and low model accuracy in vast ocean regions, severely restricting the global high-precision application of the Beidou-3 satellite navigation system. Currently, it is the solar maximum year of the 25th solar activity cycle, and frequent geomagnetic storm events and ionospheric anomalies have exacerbated the random variation characteristics of ionospheric electron content, resulting in a significant reduction in the accuracy of the BDGIM model and posing a great challenge to satellite navigation and positioning services.

[0004] Previous studies usually focused on the delay error correction accuracy of the Beidou broadcast ionospheric model, ignoring the random error characteristics of the Beidou broadcast ionospheric model. Some studies have shown that in high-precision positioning and Beidou integrated navigation systems with the Beidou ionospheric model as constraint information, the random model of the Beidou ionosphere plays a crucial role and will directly affect the reliability and stability of high-precision positioning and navigation. Especially during solar active periods, ionospheric anomalies may occur, leading to a decline in the performance of the Beidou integrated navigation system and an increase in integrity risk. Therefore, combining the statistical characteristics of different satellite orbits of the Beidou system and data analysis in the spatial and temporal domains, and mining the spatio-temporal correlation information of Beidou ionospheric random errors, constructing a Beidou ionospheric random error autocorrelation model has important scientific significance and engineering value.

[0005] Related terms:

[0006] GNSS represents the Global Navigation Satellite System

[0007] BDGIM represents the Beidou Global Ionospheric Delay Correction Model

[0008] IGS represents the International Geodynamics Service

[0009] TEC represents the Total Electron Content in the ionosphere

[0010] VTEC represents the Vertical Total Electron Content in the ionosphere Summary of the Invention

[0011] The present invention is mainly proposed for the Beidou ionospheric random error model, and provides a method for establishing a Beidou ionospheric random error autocorrelation model based on a deep learning neural network model.

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

[0013] A method for establishing a Beidou ionospheric random error autocorrelation model, which combines a convolutional neural network, a long short-term memory neural network and an attention mechanism to establish a deep learning neural network model for predicting Beidou ionospheric random errors. Based on the predicted Beidou ionospheric random errors, the time autocorrelation function of the Beidou ionospheric random errors and the spatial autocorrelation function of the Beidou ionospheric random errors are respectively fitted to establish a Beidou ionospheric random error autocorrelation model.

[0014] Moreover, the Beidou ionospheric random errors are calculated by using the Beidou ionospheric model and the global ionospheric model, and combined with the space weather index to form an input data set.

[0015] Moreover, the deep learning neural network model for predicting Beidou ionospheric random errors 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 in sequence. The input data set enters the input layer of the deep learning neural network model, and the fully connected layer outputs the predicted value of the Beidou ionospheric random errors.

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

[0017] Moreover, when fitting the time autocorrelation function of the random errors by using a second-order Gaussian-Markov process, a polynomial regression method is used to find the optimal fitting curve to fit the spatial autocorrelation function of the random errors.

[0018] Moreover, the implementation manner of establishing the Beidou ionospheric random error autocorrelation model is as follows

[0019] Establish a time autocorrelation model based on the time autocorrelation function of the Beidou ionospheric random error, and establish a space autocorrelation model based on the space autocorrelation function of the Beidou ionospheric random error;

[0020] Fuse the Beidou time autocorrelation model and the space autocorrelation model to establish a spatio-temporal autocorrelation model of the Beidou ionospheric random error;

[0021] Use historical data to estimate the parameters of the spatio-temporal autocorrelation model of the Beidou ionospheric random error. According to the prediction results and actual observation data, adjust the model parameters for optimization.

[0022] On the other hand, the present invention also provides a method for correcting the Beidou ionospheric random error implemented based on the above method for establishing the Beidou ionospheric random error autocorrelation model. Calculate the Beidou ionospheric random error at a specific time and specific location according to the established Beidou ionospheric random error autocorrelation model, and support the solution 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 on the memory and executable on the processor. When the processor executes the program, it implements the above method for establishing the Beidou ionospheric random error autocorrelation model or the method for correcting the Beidou ionospheric random error.

[0024] On the other hand, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the above method for establishing the Beidou ionospheric random error autocorrelation model or the method for correcting the Beidou ionospheric random error.

[0025] On the other hand, the present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the above method for establishing the Beidou ionospheric random error autocorrelation model or the method for correcting the Beidou ionospheric random error.

[0026] In the above technical solution for establishing the Beidou ionospheric random error autocorrelation model, mainly based on the historical data of the Beidou ionospheric random error, combined with space weather indices, such as solar activity index and geomagnetic activity index, etc., to form an input data set. On this basis, a deep learning neural network model is introduced to predict the Beidou ionospheric random error and establish a Beidou ionospheric random error autocorrelation model. The present invention can predict the Beidou ionospheric random error without knowing the accurate physical model, and provide technical support for the high-precision prediction of the Beidou ionospheric model and the analysis of the Beidou ionospheric random error.

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

[0028] 1. Predicting the random error of the Beidou ionosphere using a deep learning neural network model does not require a definite physical model and has stronger generalization ability;

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

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

[0031] The implementation of the solution of the present invention is simple and convenient, with strong practicability, solves the problems of low practicability and inconvenient actual application existing in the related technologies, can improve the user experience, and has important market value. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0034] Figure 3 It is a schematic diagram of the result of using the polynomial regression method to find the optimal fitting curve in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The present invention proposes to predict the random error of the Beidou ionosphere based on the Beidou ionosphere random error data set and the deep learning neural network model. On this basis, establish the time autocorrelation function and spatial autocorrelation function of the Beidou ionosphere random error, and finally establish the Beidou ionosphere random error autocorrelation model and error correction method.

[0036] The following will further illustrate the concept, specific structure and technical effects generated by the present invention in conjunction with the 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 the Beidou ionosphere random error autocorrelation model uses a convolutional neural network-long short-term memory neural network-attention mechanism model to predict the random error of the Beidou ionosphere, uses a second-order Gaussian-Markov process to fit the time autocorrelation function of the random error, uses the polynomial regression method to find the optimal fitting curve to fit the spatial autocorrelation function of the random error, and finally establishes the Beidou ionosphere random error autocorrelation model and error correction method.

[0039] See Figure 1, a method for establishing a Beidou ionospheric random error autocorrelation model provided by an embodiment of the present invention includes the following steps:

[0040] Step 1, calculate the Beidou ionospheric random error using the Beidou ionospheric model and the global ionospheric model, and combine with the space weather index to form an input data set.

[0041] Preferably, taking the global ionospheric model published by IGS as a reference, calculate the difference between the Beidou ionospheric TEC and the IGS global ionospheric model TEC at each grid point, which is defined as the Beidou ionospheric random error. The selection of grid points follows the IONEX standard format, that is, the spatial resolution is 2.5°×5.0°, and the time resolution is 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, the parallel computing method is used to calculate the Beidou ionospheric random error, and the result data format is in IONEX format.

[0042] The calculation formula for the Beidou ionospheric random error TECres is as follows:

[0043] TECres = VTEC bdgim -VTEC igsg

[0044] where, VTEC bdgim represents the vertical total electron content of the ionosphere calculated according to the Beidou ionospheric model, and VTEC igsg represents the vertical total electron content of the ionosphere calculated according to the IGS global grid ionospheric model.

[0045] The change of the Beidou ionospheric random error is related to solar activity and geomagnetic activity. The solar activity index F10.7 is used to characterize the solar activity intensity, and the geomagnetic indices Kp and the disturbance storm time index Dst are used to characterize the geomagnetic activity. Preferably, an embodiment constructs a seven-dimensional vector including the ionospheric random error VTEC residual, F10.7, Kp, Dst, latitude, longitude, and seconds within a day as the input data set.

[0046] Step 2, according to the characteristics of the input data, combined with the characteristics of different neural networks, construct an optimal neural network model to predict the Beidou ionospheric random error.

[0047] The commonly used network models in current deep learning are convolutional neural networks (CNNs) and recurrent neural networks (RNNs). The former is good at extracting spatial structure information, while the latter is more suitable for processing time series data. The long short-term memory (LSTM) neural network is improved on the basis of the recurrent neural network, and a state value and a "gate" control structure are introduced based on the recurrent neural network. In order to selectively filter information, the data transmission between different units in the hidden layer is controlled by three gates: the input gate, the forget gate, and the output gate. The present 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 error, form a random error time series, and establish a time autocorrelation function of the Beidou ionospheric random error.

[0049] Select the predicted values of random errors at different times at typical grid points, read the random error file, and output the random error time series file. For different grid points, use the second-order Gaussian-Markov process to fit the time autocorrelation function and establish a time correlation model of the Beidou ionospheric random error.

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

[0051] Read the random error file, calculate the distance and variance between grid points according to the longitude, latitude information and random error information of the standard grid points. Use the polynomial regression method to find the optimal fitting curve to fit the relationship between distance and variance, and establish a spatial correlation model of the Beidou ionospheric random error.

[0052] Step 5: Combine the results obtained in Step 3 and Step 4 to establish a Beidou ionospheric random error autocorrelation model and an error correction method.

[0053] Example 2:

[0054] On the basis of the process in Example 1, further in Step 2, use a convolutional neural network-long short-term memory neural network-attention mechanism model to establish an optimal neural network model.

[0055] A simple LSTM network has certain limitations for ionospheric random error data with both time and space characteristics. In this example, a convolutional neural network-long short-term memory neural network-attention mechanism neural network model is established, and the structural framework is as Figure 2As shown in the figure. Based on the input data set obtained in step 1, the data first enters the convolution layer through the input layer (InputLayer). The convolution layer is mainly responsible for feature extraction and consists of two one-dimensional convolution layers (1Dconvolution) and one max pooling layer (Max Pooling Layer). Specifically, more one-dimensional convolution layers can be set according to needs during implementation. The first convolution layer reads the input sequence and projects the result onto the feature map, and then inputs it to the second convolution layer. The second convolution layer performs the same operation on the feature map created by the first layer, attempting to amplify its significant features. The output of the second convolution layer enters the max pooling layer. Max pooling means taking the maximum value in the sample as the sampled sample value. 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 by the max pooling layer flows into the long short-term memory neural network layer (LSTM Layer). The LSTM model is mainly responsible for the long-term and short-term dependencies in the time series clock and captures time features through its internal gating mechanism (input gate, forget gate, and output gate). After that, the data output by the long short-term memory neural network layer flows into the attention mechanism layer (Attention Layer). The Attention model is mainly responsible for calculating the importance of each feature, that is, performing weighted average processing on the output vector of the LSTM model. Then, the data flows into the fully connected layer (Fully-Connected Layer). The Fully-Connected model converts the output of the Attention model into the required dimension, and finally obtains the prediction value of the Beidou ionospheric random error (the prediction value of VTEC residual).

[0056] Embodiment 3:

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

[0058] The transfer function of the 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 the natural period of 24 hours, τ c represents the time constant of 35 hours, and ζ represents the damping ratio.

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

[0063]

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

[0065] Example 4:

[0066] Based on the process of Example 1, further in Step 4, a polynomial regression method is adopted to find the optimal fitting curve to fit the spatial autocorrelation function of the random error.

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

[0068]

[0069] In the formula, R represents the radius of the earth, represents the longitude and latitude of the first grid point p1, represents the longitude and latitude 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 BeiDou ionospheric random error of the first grid point p1, res2 represents the BeiDou ionospheric random error of the second grid point p2, and E[] represents the expected value.

[0073] Finally, based on all the great circle distances and variances, a polynomial regression method is used to find the optimal fitting curve. The implementation method is as follows: First, according to the distribution and trend of the data, select an appropriate polynomial order. Usually, start with a low-order polynomial and gradually increase the order until the fitting effect is satisfactory. Second, use the least squares method to estimate the coefficients of the polynomial regression model. Then, evaluate the polynomial model through calculating the goodness of fit, residual analysis, and cross-validation methods, and select the polynomial order that maximizes the goodness of fit and whose residual distribution is closest to the random distribution. Finally, calculate the variance inflation factor to check the multicollinearity between polynomial terms, and use the Breusch-Pagan test to check the heteroscedasticity of the residuals to determine the optimal polynomial regression model.

[0074] Example 5:

[0075] On the basis of the process in Example 1, after further completing the time autocorrelation function and spatial autocorrelation function of the Beidou ionospheric random error, an autocorrelation model of the Beidou ionospheric random error is established to support error correction.

[0076] First, a time autocorrelation model is established according to the time autocorrelation function of the Beidou ionospheric random error, such as the autoregressive moving average model (ARMA), and a spatial autocorrelation model is established according to the spatial autocorrelation function of the Beidou ionospheric random error, such as Kriging interpolation.

[0077] Secondly, the Beidou time autocorrelation model and spatial autocorrelation model are fused to establish a spatio-temporal autocorrelation model of the Beidou random error, such as the spatio-temporal autoregressive model (STARMA). For the Beidou random error, since each error value has both time information and spatial information (coordinates) at the same time, first calculate the random error at each grid point at a specific future moment based on the time correlation model of each grid point, and then calculate the random error at any spatial point based on the spatial correlation model.

[0078] Then, use historical data to estimate the parameters of the spatio-temporal autocorrelation model of the Beidou ionospheric random error, and evaluate the fitting effect and prediction ability of the model through the method of cross-validation. According to the prediction results and actual observation data, adjust the model parameters to optimize the model performance.

[0079] Example 6:

[0080] On the basis of the process in Example 1, the correction of the Beidou ionospheric random error is realized based on the established autocorrelation model of the Beidou ionospheric random error.

[0081] First, according to the positions of the Beidou satellites and ground observation stations, the method of distance intersection is used to calculate the position of the ionospheric pierce point at a specific moment. Then, based on the established autocorrelation model of the Beidou ionospheric random error (such as STARMA) above, calculate the Beidou ionospheric random error at a specific position at a specific moment. Finally, in high-precision positioning or integrated navigation, introduce the ionospheric delay error information calculated according to the Beidou ionospheric model as the observation model, and introduce the random error information calculated according to the autocorrelation model of the Beidou ionospheric random error as the random model to perform high-precision position solution.

[0082] Example 7:

[0083] The present invention provides another example. Further in Example 1, in addition to the data from 2020 to 2024, the 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 the understanding of the technical effects of the present invention, the following provides corresponding experimental data:

[0085] In using the method of the present invention to find the optimal fitting curve through polynomial regression, it mainly depends on the great circle distance D and variance σ between any two grid points 2 to find the optimal fitting curve. Suppose 10 groups of observed data are given, and the great circle distance and variance values are shown in the following table:

[0086] Table 1 Great circle distance and variance values

[0087] Serial number Great circle distance (km) Variance 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] Through the above 10 groups of data, the optimal curve found is a fifth-order polynomial, and the curve graph is as Figure 3 shown. Its mean square error is 0.04 and the coefficient of determination is 0.99. The spatial autocorrelation function given according to the above data is expressed as:

[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 by the technical solution of the present invention can be automatically run by those skilled in the art using computer software technology. The system device for implementing the method, such as a computer-readable storage medium storing the corresponding computer program of the technical solution of the present invention and a computer device including running the corresponding computer program, should also be within the protection scope of the present invention.

[0092] Next, the electronic device for establishing the Beidou ionospheric random error autocorrelation model provided by the present invention will be described. The electronic device for establishing the Beidou ionospheric random error autocorrelation model described below can be correspondingly referred to the method for establishing the Beidou ionospheric random error autocorrelation model described above.

[0093] The electronic device may include: a processor, a communications interface, a memory, and a communication bus. Among them, the processor, the communications interface, and the memory complete their mutual communication through the communication bus. The processor can call the logical instructions in the memory to execute the method for establishing the Beidou ionospheric random error autocorrelation model, mainly including the software processing part in the above steps.

[0094] In addition, when the logical instructions in the above-mentioned memory are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, 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. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical discs that can store program codes.

[0095] On the other hand, the present invention also provides a computer program product. The computer program product 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 in the method for establishing the Beidou ionospheric random error autocorrelation model provided by the above-mentioned various methods.

[0096] On another aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is implemented to execute the software processing part in the method for establishing the Beidou ionospheric random error autocorrelation model provided by the above-mentioned various methods.

[0097] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without creative labor.

[0098] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the above technical solution, 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 enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment 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 are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for establishing a self - correlation model of Beidou ionospheric random errors, characterized in that: A deep learning neural network model for predicting the random error of the Beidou ionosphere is established by combining a convolutional neural network, a long short-term memory neural network, and an attention mechanism. Based on the predicted random error of the Beidou ionosphere, the temporal autocorrelation function and the spatial autocorrelation function of the random error of the Beidou ionosphere are respectively fitted to establish an autocorrelation model of the random error of the Beidou ionosphere.

2. A 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 space weather indices to form an input data set.

3. A 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 the random error of 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 in sequence. The input data set enters the input layer of the deep learning neural network model, and the fully connected layer outputs the predicted value of the random error of the Beidou ionosphere.

4. A 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 establishing a Beidou ionospheric random error autocorrelation model according to claim 1, characterized in that: When fitting the temporal autocorrelation function of the random error using a second-order Gaussian-Markov process, a polynomial regression method is used to find the optimal fitting curve to fit the spatial autocorrelation function of the random error.

6. The method for establishing a Beidou ionospheric random error autocorrelation model according to claim 1, characterized in that: The implementation method of establishing the autocorrelation model of the random error of the Beidou ionosphere is as follows. A temporal autocorrelation model is established based on the temporal autocorrelation function of the random error of the Beidou ionosphere, and a spatial autocorrelation model is established based on the spatial autocorrelation function of the random error of the Beidou ionosphere. The temporal autocorrelation model and the spatial autocorrelation model of Beidou are fused to establish a spatio-temporal autocorrelation model of the random error of the Beidou ionosphere. Historical data is used to estimate the parameters of the spatio-temporal autocorrelation model of the random error of the Beidou ionosphere. According to the prediction results and actual observation data, the model parameters are adjusted for optimization.

7. A Beidou ionospheric random error correction method implemented based on the Beidou ionospheric random error autocorrelation model establishment method according to any one of claims 1 to 6, characterized in that: The random error of the Beidou ionosphere at a specific time and specific location is calculated based on the established autocorrelation model of the random error of the Beidou ionosphere, supporting the solution of position parameters in high-precision positioning or integrated navigation.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the method for establishing the autocorrelation model of the random error of the Beidou ionosphere as described in any one of claims 1 to 6 or the method for correcting the random error of the Beidou ionosphere as described in claim 7.

9. 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 method for establishing the autocorrelation model of the random error of the Beidou ionosphere as described in any one of claims 1 to 6 or the method for correcting the random error of the Beidou ionosphere as described in claim 7.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the method for establishing the autocorrelation model of the random error of the Beidou ionosphere as described in any one of claims 1 to 6 or the method for correcting the random error of the Beidou ionosphere as described in claim 7.

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