A regional ionospheric electron content prediction method based on ensemble learning

Abstract

The present invention discloses a method for predicting ionospheric electron content based on integrated learning, including: extracting the geographic longitude and latitude and vertical electron content at the ionospheric puncture point of the navigation satellite signal; constructing a regional ionospheric electron content model using spherical harmonics and polynomial functions respectively; using the spherical harmonics model and polynomial model parameters and the 27-day ionospheric electron content reference value as neural network model input parameters respectively, constructing BPNN‑SH and BPNN‑POLY; training a number of BPNN‑SH models and BPNN‑POLY models respectively, and integrating them respectively, and then weighted summing the two integrated results to obtain an integrated model ENN. The present invention combines the advantages of the polynomial model and the spherical harmonics model in regional ionosphere fitting, takes into account the electron content background reference value parameters, ensures the prediction accuracy of the ionospheric electron content of the model under the conditions of daily geomagnetic activity, overcomes the disadvantage of the unstable neural network, better simulates the temporal and spatial variation characteristics of the regional ionosphere, and effectively improves the model accuracy.

Description

Technical Field

[0001] The invention relates to the field of ionospheric total electron content detection, and in particular to an ionospheric electron content prediction method based on an integrated learning method. Background Art

[0002] In the research and application of GNSS ionosphere modeling, the commonly used ionosphere correction models are generally divided into two categories: one is the empirical model, including the Klobuchar model, IRI model, Bent model, etc. used in GPS. Since the establishment of the empirical model is based on long-term data collection, some models are more complex and less applicable. Usually, they cannot meet the requirements when the ionosphere modeling and GNSS positioning accuracy are high. The other is the fitting ionosphere model based on high-precision GNSS dual-frequency observation data, such as polynomial model, spherical harmonic function model, and generalized trigonometric series model. When the stations are evenly distributed and the observation data quality is high, this type of model can correct about 80% of the ionosphere delay. With the development of neural network algorithms and their excellent performance in solving nonlinear problems, the ionosphere delay correction model based on BPNN has attracted people's attention. However, the simple BP neural network model has the disadvantage of instability, and the model effect is highly dependent on the data quality and the setting of initial parameters. At the same time, under the conditions of active solar geomagnetic activity, the electron content in the ionosphere changes dramatically, and it is difficult for the neural network model to accurately fit the TEC change trend. In addition to the significant daily periodic characteristics, the changes in the electron content in the ionosphere also have a 27-day periodic characteristic. Summary of the invention

[0003] Purpose of the invention: Based on the above background technology, in view of the shortcomings of the existing prediction methods, the purpose of the present invention is to propose an ionospheric electron content prediction method based on ensemble learning. The traditional mathematical fitting model does not fully consider the daily variation trend of the ionospheric electron content, and the simple neural network is not stable enough when dealing with nonlinear fitting problems. This method can effectively improve the accuracy and stability of regional ionospheric electron content prediction by increasing the Beijing reference value of ionospheric electron content and integrating multiple simple neural network models.

[0004] Technical solution: To achieve the above-mentioned invention object, the technical solution adopted by the present invention is:

[0005] A regional ionospheric electron content prediction method based on ensemble learning comprises the following steps:

[0006] S1: Extract the geographic longitude and latitude and vertical electron content VTEC at the ionospheric puncture point IPP of the navigation satellite signal using phase smoothed pseudorange;

[0007] S2: Construct the spherical harmonic model and polynomial model of the regional ionospheric electron content based on spherical harmonic functions and polynomial functions respectively;

[0008] S3: The parameters of the spherical harmonic model and the mean value of the ionospheric electron content 27 days before the modeling time are used as the input of the BP neural network, and the current value of the ionospheric electron content is used as the output of the BP neural network to construct the neural network model BPNN-SH; the parameters of the polynomial model and the mean value of the ionospheric electron content 27 days before the modeling time are used as the input of the neural network, and the current value of the ionospheric electron content is used as the output of the BP neural network to construct the BP neural network model BPNN-POLY;

[0009] S4: Train Count BPNN-SH models and Count BPNN-POLY models respectively;

[0010] S5: Integrate the trained Count BPNN-SH models and Count BPNN-POLY models respectively to obtain the integrated model ENN;

[0011] S6: Use the integrated model ENN to predict the regional ionospheric electron content.

[0012] Furthermore, in S1, the phase smoothed pseudorange is used to extract the geographic longitude and latitude and VTEC at the navigation satellite signal IPP.

[0013] Furthermore, in S1, the geographical longitude and latitude of the IPP is:

[0014]

[0015]

[0016] Where λ is the geographical longitude at IPP, λ0 is the geographical longitude of the receiver at the observation station, and Ψ pp is the geocentric angle, A is the satellite azimuth, is the geographical latitude of the IPP, is the geographical latitude of the receiver of the observation station, E is the satellite altitude angle, R is the radius of the earth, and H is the equivalent height of the ionosphere single layer model;

[0017] The vertical electron content VTEC is:

[0018]

[0019] Where STEC is the total electron content of the ionosphere along the GPS signal propagation path, f1, f2 are GPS satellite signal frequencies, p 4,smis the pseudorange observation value after phase smoothing, c is the speed of light, DCB j is the receiver differential code deviation, DCB i is the satellite differential code bias.

[0020] Furthermore, in S2, the order of spherical harmonic functions and the order of polynomial functions are selected, and the spherical harmonic model and the polynomial model of the regional ionospheric electron content are constructed based on the observation data of the GPS observation station in the area to be modeled.

[0021] Furthermore, the order of the spherical harmonic function is selected as N, and the spherical harmonic model is established:

[0022]

[0023] In the formula, are the coefficients of the spherical harmonics model, is the geographical latitude of IPP, λ′ is the sun’s longitude, λ IPP is the geographical longitude of the IPP, λ SUN is the solar longitude, is the fully normalized nth-order kth-order Legendre function;

[0024] Select the polynomial function order M, N' and establish the polynomial model:

[0025]

[0026] In the formula, E mn′ are the model coefficients to be solved, and S are the geographical latitude and solar hour angle at IPP, and S0 are the geographical latitude and solar hour angle of the center of the area to be modeled, λ and λ′0 are the geographical longitude at the IPP and the geographical longitude of the center of the area to be modeled, and (t-t0) is the time difference between the observation epoch t and the intermediate epoch t0.

[0027] Furthermore, when k=0, n=0, When k=0,n=1, When k=0,n>1, When k=1,n=1, When k=n>1, When k = n-1, When k<n-1,

[0028] Furthermore, in S4, Count is greater than 10.

[0029] Furthermore, the integration method described in S5 is: averaging the outputs of Count BPNN-SH models and Count BPNN-POLY models respectively to obtain a preliminary integration result Y BP-SH and Y BP-POLY , and then Y BP-SH and Y BP-POLY The weighted summation is performed to obtain the final integrated result.

[0030] Furthermore, the weighted average is specifically:

[0031] Y ENN =Y BP-SH ·W SH +Y BP-POLY ·W POLY

[0032] Where Y ENN is the output of the integrated model ENN, M SH and M POLY are the errors of the spherical harmonic model and the polynomial model.

[0033] Beneficial effects: The method proposed in the present invention combines the advantages of the polynomial model and the spherical harmonic function model in regional ionosphere fitting, takes into account the electron content background reference value parameters, ensures the prediction accuracy of the model's ionospheric electron content under the conditions of daily geomagnetic activity, and overcomes the shortcomings of the neural network's instability through single neural network model training and model integration, better simulates the temporal and spatial variation characteristics of the regional ionosphere, and effectively improves the model accuracy. The prediction accuracy of the ionospheric electron content is improved compared with the traditional mathematical model, with MAE of about 37%, RMSE of about 30%, STD of about 31%, and MAPE of about 32%, and the integrated model is more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flow chart of the method implemented by the present invention;

[0035] Figure 2 It is a schematic diagram of the structure of the neural network model BPNN-SH;

[0036] Figure 3 It is a schematic diagram of the structure of the neural network model BPNN-POLY;

[0037] Figure 4 It is the distribution map of the survey area and survey stations;

[0038] Figure 5 This is a comparison chart of the effects of the simple BPNN model and the integrated model, where (a) is the MAE indicator, (b) is the RMSE indicator, (c) is the STD indicator, and (d) is the MAPE indicator;

[0039] Figure 6 It is a performance comparison chart of spherical harmonic function model, polynomial model and integrated model, where (a) is MAE index, (b) is RMSE index, (c) is STD index, and (d) is MAPE index; DETAILED DESCRIPTION

[0040] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific examples.

[0041] This specific embodiment discloses a method for predicting ionospheric electron content based on ensemble learning, such as Figure 1 As shown, it mainly includes the following steps:

[0042] Step 1: Use 31 GPS observation stations in southwest my country. The distribution of the stations is as follows: Figure 4 As shown in the figure, the triangle represents the test site and the circle represents the verification site. Based on the observation data for 24 hours on September 8, 2017 (when the geomagnetic activity was active, F10.7>100sfu, Kp>4, Dst<-30nT), the geographic longitude and latitude and vertical electron content of the satellite signal ionosphere puncture point were calculated; some of the data are shown in Table 1:

[0043] Table 1 Part of the measured data

[0044]

[0045] Step 2: Using the measured data of 25 observation stations in step 1 as modeling data, the ionospheric spherical harmonics model and polynomial model were constructed for each period on September 8. The measured data of the remaining 6 stations were used as verification data. The station distribution is as follows: Figure 2 As shown; then the mean absolute deviation (MAE), root mean square error (RMSE), correlation coefficient (R), and standard deviation (STD) are used to evaluate the model accuracy:

[0046]

[0047]

[0048]

[0049]

[0050] In the formula, is the model output value and true value of the i-th observation, The average of the model output and the true value for all observations.

[0051] Step 3: The parameters of the spherical harmonic function model and the polynomial model are used as the input of the neural network model respectively. Considering that the ionospheric electron content has a periodic characteristic of 27 days, the average value of the ionospheric electron content in the previous 27 days at the same time is used as the reference value and also as the input of the neural network model. Two neural network models BPNN-SH and BPNN-POLY that consider the reference value of the ionospheric electron content are constructed. The number of nodes in the hidden layer of the model is determined by the ten-cross validation method. In this experiment, the number of nodes in the hidden layer of the model is 11. The structure of the BPNN-SH and BPNN-POLY models is as follows: Figure 2 and Figure 3 shown.

[0052] Step 4: Train Count BPNN-SH and Count BPNN-POLY models respectively, and generally take Count as a number greater than 10. Take the average of the results calculated by Count models as the preliminary integration results of BPNN-SH and BPNN-POLY. In this embodiment, take Count=10, and the preliminary integration model result is recorded as Y BP-SH and Y BP-POLY .

[0053] Step 5: The calculation results Y of BPNN-SH and BPNN-POLY BP-SH and Y BP-POLY Perform weighted summation as the result of the final integrated model ENN, the output of the model Y ENN The error between the spherical harmonics model and the polynomial model is denoted by M SH and M POLY , the weight in the integrated model is: and The output of the integrated model is recorded as Y ENN =Y SH ·W SH +Y POLY ·W POLY .

[0054] In this embodiment, the number of simple neural network models is 10 (Count=10), and the performance comparison between each simple neural model and the integrated model is as follows: Figure 5 As shown in (a) to (d), they represent the four indicators of MAE, RMSE, STD, and MAPE of the model respectively. The horizontal axis represents the neural network model number. 1-20 (the first 10 BPNN-POLY 1-10, the last 10 BPNN-SH 1-10) represents the simple neural network model number, and the 21st is the result of the final integrated model. Figure 5It can be seen that the simple neural network model is extremely unstable and the output results are very jumpy. The output results of the integrated model are the optimal values ​​or very close to the optimal simple neural network model output values ​​in the four indicators of MAE, RMSE, R, and STD, which proves that the integrated learning model has high accuracy, good stability, high degree of fitting, and the output results deviate little from the true value.

[0055] The average values ​​of the six time periods predicted by the integrated model are compared with those predicted by the spherical harmonic function and polynomial models. The results are as follows: Figure 6 As shown in (a) to (d) and Table 2. Figure 6 (a) to (d) in the figure represent the four indicators of MAE, RMSE, STD, and MAPE of the model respectively, and the horizontal axis represents the UTC time (universal time) on the day of modeling. Figure 6 It can be seen that the MAE, RMSE, STD, and MAPE of the integrated model are all smaller than those of the POLY model and the SH model in 24 hours, so the effect is the best.

[0056] As shown in Table 2, the integrated model improves MAE by about 37%, RMSE by about 30%, STD by about 31%, and MAPE by about 32% compared with the SH model and the POLY model. Experiments have shown that this method can stably and accurately predict the ionospheric electron content.

[0057] Table 2 Comparison of model accuracy

[0058] MAE RMSE STD MAPE POLY 2.32 2.86 2.81 16.92 SH 2.31 2.84 2.81 16.87 ENN 1.44 1.99 1.94 11.47

[0059] The above description is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or substitutions within the technical scope disclosed by the present invention, which should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A regional ionospheric electron content prediction method based on ensemble learning, characterized in that: The following steps are involved: S1: Extract the geographic longitude and latitude and vertical electron content VTEC at the ionospheric puncture point IPP of the navigation satellite signal using phase smoothed pseudorange; S2: Construct the spherical harmonic model and polynomial model of the regional ionospheric electron content based on spherical harmonic functions and polynomial functions respectively; S3: The parameters of the spherical harmonic model and the mean value of the ionospheric electron content 27 days before the modeling time are used as the input of the BP neural network, and the current value of the ionospheric electron content is used as the output of the BP neural network to construct the neural network model BPNN-SH; the parameters of the polynomial model and the mean value of the ionospheric electron content 27 days before the modeling time are used as the input of the neural network, and the current value of the ionospheric electron content is used as the output of the BP neural network to construct the BP neural network model BPNN-POLY; S4: Train Count BPNN-SH models and Count BPNN-POLY models respectively; S5: Integrate the trained Count BPNN-SH models and Count BPNN-POLY models respectively to obtain the integrated model ENN; S6: Predict the regional ionospheric electron content using the integrated model ENN; In said S2, the spherical harmonic function order and the polynomial function order are selected, and the spherical harmonic model and the polynomial model of the regional ionospheric electron content are constructed based on the observation data of the GPS observation station in the area to be modeled; Select the spherical harmonic function order as N and establish the spherical harmonic model: In the formula, are the coefficients of the spherical harmonics model, is the geographical latitude of IPP, λ′ is the sun’s longitude, λ IPP is the geographical longitude of the IPP, λ SUN is the solar longitude, is the fully normalized nth-order kth-order Legendre function; Select the polynomial function order M, N' and establish the polynomial model: In the formula, E mn′ are the model coefficients to be solved, and S are the geographical latitude and solar hour angle at IPP, and S0 are the geographical latitude and solar hour angle of the center of the area to be modeled, respectively; λ and λ′0 are the geographical longitude at the IPP and the geographical longitude of the center of the area to be modeled, respectively; (t-t0) is the time difference between the observed epoch t and the intermediate epoch t0; When k=0,n=0, When k=0,n=1, When k=0,n>1, When k=1,n=1, When k=n>1, When k = n-1, When k<n-1, 2. The ionospheric electron content prediction method based on ensemble learning according to claim 1, characterized in that: In S1, the phase smoothed pseudorange is used to extract the geographic longitude and latitude and VTEC at the navigation satellite signal IPP.

3. The method for predicting ionospheric electron content based on ensemble learning according to claim 2, characterized in that: In S1, the geographical longitude and latitude of the IPP are: Where λ is the geographical longitude at IPP, λ0 is the geographical longitude of the receiver at the observation station, and Ψ pp is the geocentric angle, A is the satellite azimuth, is the geographical latitude of the IPP, is the geographical latitude of the receiver of the observation station, E is the satellite altitude angle, R is the radius of the earth, and H is the equivalent height of the ionosphere single layer model; The vertical electron content VTEC is: Where STEC is the total electron content of the ionosphere along the GPS signal propagation path, f1, f2 are GPS satellite signal frequencies, p 4,sm is the pseudorange observation value after phase smoothing, c is the speed of light, DCB j is the receiver differential code deviation, DCB i is the satellite differential code bias.

4. The method for predicting ionospheric electron content based on ensemble learning according to claim 1, characterized in that: In S4, Count is greater than 10.

5. The method for predicting ionospheric electron content based on ensemble learning according to claim 1, characterized in that: The integration method described in S5 is: averaging the outputs of Count BPNN-SH models and Count BPNN-POLY models respectively to obtain the preliminary integration result Y BP-SH and Y BP-POLY , and then Y BP-SH and Y BP-POLY The weighted summation is performed to obtain the final integrated result.

6. The method for predicting ionospheric electron content based on ensemble learning according to claim 1, characterized in that: The weighted average is specifically: Y ENN =Y BP-SH ·W SH +Y BP-POLY ·W POLY Where Y ENN is the output of the integrated model ENN, M SH and M POLY are the errors of the spherical harmonic model and the polynomial model.

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