Method and device for reconstructing vertical electron density distribution by using TEC map

Abstract

The invention discloses a method and device for reconstructing vertical electron density distribution by using a TEC map, and the method comprises the steps: obtaining ionosphere frequency-height distribution data from a meridian engineering data center through setting software, and converting the ionosphere frequency-height distribution data into electron density-height distribution data; performing data quality control on the electron density data to obtain quality-controlled electron density data; based on the electron density data after quality control, time-space collaborative TEC data are matched; based on the TEC data, matching space-time collaborative space physical parameters; on the basis of a symbol regression algorithm of genetic programming, calculation is carried out through an empirical formula of station fitting, and TEC physical fitting features are extracted; training a three-hidden-layer full-connection neural network based on the attention mechanism to obtain a trained neural network; and inputting the current time and the set data into the trained neural network for processing to obtain the electron density distribution of the altimeter station position at the current time. According to the invention, real-time reporting can be realized, and the high-precision application requirement is met.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ionosphere detection, and particularly relates to a method and device for reconstructing vertical electron density distribution by using TEC map. BACKGROUND

[0002] As a key region of human space activities, the ionosphere contains a large number of free electrons and ions, which can significantly affect the propagation of radio waves. Therefore, TEC (Total Electron Content) and electron density distribution have become the core physical parameters for studying the structure, state and changes of the ionosphere, and have irreplaceable application value in the fields of short-wave communication frequency selection, satellite navigation error correction, etc. Among them, the electron density can directly describe the characteristics of the ionosphere, and its profile distribution usually follows regular patterns such as Chapman model or Loewe-Rosenberg model. TEC is the integral of electron density along the radio wave propagation path. Global TEC map is mainly obtained by relying on global navigation satellite system (GNSS). The GNSS Ground-based method is commonly used, in which GNSS satellites are used as the transmitting side and ground receivers are used as the receiving side. By analyzing the phase delay and code pseudorange difference of dual-frequency carrier, the slant TEC is calculated and converted into vertical TEC for global distribution and pattern analysis. Representative data sources include the 1998-2025 World-wide GNSS Receiver Network data provided by the Madrigal database hosted by the MIT Haystack Observatory. Such TEC detection technology has become the mainstream method for current ionosphere monitoring.

[0003] However, the process of inverting the vertical profile of electron density from vertical TEC is an ill-posed inverse problem. The existing technology has not formed an efficient and high-precision solution. There are mainly three limitations: first, the ionospheric tomography technology can solve the electron density distribution by establishing equations based on the slant TEC observations of multiple satellites from multiple stations, but it needs to rely on the original satellite signal, and the data acquisition is limited by the release authority of the satellite unit, so the application range is narrow. Second, the empirical model method can describe the change of electron density by exploring the correlation between TEC and peak electron density, and combining a parabolic distribution model or IRI (International Reference Ionosphere) model, but this method relies on empirical formulas and has large errors compared with actual observations. It can only be used as a reference and cannot meet the high-precision application requirements. Third, the ionospheric data assimilation method can combine multiple observation data and physical models to integrate TEC data into the model through Kalman filtering and variational methods, but the accuracy of the final electron density distribution is between the observation and the model. Moreover, the model has high complexity and high computational cost, and it is difficult to realize real-time reporting. It cannot effectively make up for the missing observation data caused by maintenance and failure of the measuring instrument.

[0004] Therefore, there is an urgent need for a method of reconstructing vertical electron density distribution using TEC map to solve the above problems, realize real-time reporting, and meet the demand of high-precision application. SUMMARY

[0005] To this end, the application provides a method and device for reconstructing vertical electron density distribution using TEC map, which solves the problems of the prior art, such as over-reliance on original satellite signals, large error compared with actual observation, and inability to realize real-time reporting, by performing multi-dimensional quality control on electron density data, combining solar cycle TEC data and spatial physical parameters, extracting TEC fitting features using genetic programming, and reducing errors using attention neural network.

[0006] To achieve the above purpose, the application provides the following technical scheme: a method for reconstructing vertical electron density distribution using TEC map, comprising:

[0007] Obtaining ionospheric frequency-height distribution data of a sonde station from the Meridian Project Data Center by setting software, and converting the ionospheric frequency-height distribution data into electron density-height distribution data;

[0008] Performing data quality control on electron density data in the electron density-height distribution data to obtain quality-controlled electron density data;

[0009] Matching spatiotemporally coordinated TEC data based on the quality-controlled electron density data;

[0010] Matching spatial physical parameters based on the TEC data;

[0011] Using a symbolic regression algorithm based on genetic programming to calculate through an empirical formula fitted by the station, so that the TEC data effectively approximates integral TEC data in the quality-controlled electron density data, and extracts TEC physical fitting features;

[0012] Taking universal time, the TEC data, the spatial physical parameters, the TEC physical fitting features, and frequency-height distribution of the IRI2020 model as inputs, and taking sonde observed electron density corresponding to geographical coordinates as outputs, training a three-layer hidden layer fully connected neural network based on an attention mechanism to obtain a trained neural network;

[0013] Inputting current time, the universal time, the TEC data, the spatial physical parameters, the TEC physical fitting features, and frequency-height distribution of the IRI2020 model into the trained neural network for processing to obtain electron density distribution of the sonde station at the current time.

[0014] As a preferred scheme of the method for reconstructing the vertical electron density distribution by using the TEC map, in the process of data quality control on the electron density data in the electron density-altitude distribution data, the quality control process comprises:

[0015] Eliminate samples with a difference of more than twice the IRI2020 empirical model F2 layer critical frequency;

[0016] Retain the altimeter observation data at the height of 90-500km;

[0017] Integrate the electron density with the height to obtain the TEC observed by the altimeter at the height of 90-500km, and remove the extreme values less than 1 TEC or greater than 70 TECU to obtain the integrated TEC data;

[0018] Remove the TEC difference abnormal data by the three-sigma rule.

[0019] As a preferred scheme of the method for reconstructing the vertical electron density distribution by using the TEC map, in the process of removing the TEC difference abnormal data by the three-sigma rule, subtract the integrated TEC data from the TEC product of Madrigal to remove the abnormal data with a difference greater than three times the standard deviation; the expression of the retained TEC data is:

[0020]

[0021] In the formula, X is the difference between the two TECs; μ is the mean of X; σ is the standard deviation of X; TEC Madrigal is the TEC product of Madrigal; is the integrated TEC data.

[0022] As a preferred scheme of the method for reconstructing the vertical electron density distribution by using the TEC map, in the process of matching the spatiotemporal coordination of the TEC data, the extraction data range of the TEC data is one solar cycle of data.

[0023] As a preferred scheme of the method for reconstructing the vertical electron density distribution by using the TEC map, the space physics parameters comprise: lunar phase parameter, lunar local time, three-hour magnetic condition index, magnetic storm ring current index, and solar 10.7cm wavelength radio radiation flux index.

[0024] The application also provides a device for reconstructing the vertical electron density distribution by using the TEC map, based on the above method for reconstructing the vertical electron density distribution by using the TEC map, comprising:

[0025] An electron density-altitude distribution data acquisition module is configured to acquire ionospheric frequency-altitude distribution data of a total electron content (TEC) mapper station from a meridian project data center by setting software, and convert the ionospheric frequency-altitude distribution data into electron density-altitude distribution data;

[0026] An electron density data quality control processing module is configured to perform data quality control on electron density data in the electron density-altitude distribution data to obtain quality-controlled electron density data;

[0027] A TEC data matching module is configured to match spatiotemporally coordinated TEC data based on the quality-controlled electron density data;

[0028] A spatial physical parameter matching module is configured to match spatiotemporally coordinated spatial physical parameters based on the TEC data;

[0029] A TEC physical fitting feature extraction module is configured to calculate by an empirical formula fitted by a station to make the TEC data effectively approximate integral TEC data in the quality-controlled electron density data based on a genetic programming symbolic regression algorithm, and extract TEC physical fitting features;

[0030] A neural network training module is configured to train a three-layer hidden layer fully connected neural network based on an attention mechanism by taking universal time, the TEC data, the spatial physical parameters, the TEC physical fitting features, and frequency-altitude distribution of an IRI2020 model as inputs, and taking electron density observed by a TEC mapper at a corresponding geographic coordinate as output, to obtain a trained neural network;

[0031] A neural network processing module is configured to input current time, the universal time, the TEC data, the spatial physical parameters, the TEC physical fitting features, and the frequency-altitude distribution of the IRI2020 model into the trained neural network to process, and obtain electron density distribution of a TEC mapper station at the current time.

[0032] As a preferred solution of the device for reconstructing vertical electron density distribution by using a TEC map, in the process of performing data quality control on electron density data in the electron density-altitude distribution data, the quality control processing includes:

[0033] Samples with a difference greater than twice a critical frequency of an F2 layer of an IRI2020 empirical model are removed;

[0034] TEC mapper observation data at a height of 90-500 km are retained;

[0035] The TEC data of 90-500km altitude observed by the ionosonde is obtained by integrating the electron density with respect to altitude, and the extreme values less than 1 TECU or greater than 70 TECU are removed to obtain the integral TEC data;

[0036] The abnormal data of TEC difference is removed by the three-sigma rule.

[0037] As a preferred scheme of the device for reconstructing the vertical electron density distribution by using the TEC map, in the process of removing the abnormal data of TEC difference by the three-sigma rule, the TEC product of Madrigal is subtracted from the integral TEC data to remove the abnormal data with the difference greater than three times the standard deviation; the expression of the retained TEC data is:

[0038]

[0039] In the formula, X is the difference between the two TECs; μ is the mean of X; σ is the standard deviation of X; TEC Madrigal is the TEC product of Madrigal; is the integral TEC data.

[0040] As a preferred scheme of the device for reconstructing the vertical electron density distribution by using the TEC map, in the process of matching the TEC data in space-time coordination, the extraction data range of the TEC data is one solar cycle.

[0041] As a preferred scheme of the device for reconstructing the vertical electron density distribution by using the TEC map, in the space physics parameter matching module, the space physics parameters include: lunar phase parameter, local time, three-hour magnetic condition index, magnetic storm ring current index, and solar 10.7cm wavelength radio radiation flux index.

[0042] The present application has the following advantages: the present application obtains ionospheric frequency-height distribution data of the ionosonde station data from the meridian engineering data center through setting software, and converts the ionospheric frequency-height distribution data into electron density-height distribution data; the electron density data in the electron density-height distribution data is subjected to data quality control to obtain post-quality control electron density data; the post-quality control electron density data is matched with spatio-temporal coordinated TEC data; the TEC data is matched with spatio-temporal coordinated spatial physical parameters; the TEC data is effectively approximated to the integral TEC data in the post-quality control electron density data through a station fitting empirical formula based on a genetic programming symbolic regression algorithm to extract TEC physical fitting features; a three-layer hidden layer fully connected neural network based on an attention mechanism is trained with universal time, the TEC data, the spatial physical parameters, the TEC physical fitting features and the frequency-height distribution of the IRI2020 model as inputs and the ionosonde observed electron density corresponding to the geographical coordinates as outputs to obtain a trained neural network; the current time, the universal time, the TEC data, the spatial physical parameters, the TEC physical fitting features and the frequency-height distribution of the IRI2020 model are input into the trained neural network for processing to obtain the electron density distribution of the ionosonde station at the current time. The present application is based on long time series data covering the solar cycle and continuously updated TEC data, combines multi-dimensional data quality control to ensure input reliability, innovatively introduces TEC physical fitting features and fuses spatial physical parameters such as solar activity, geomagnetism and lunar phase, and matches the three-layer fully connected neural network with an attention mechanism that strengthens key features to realize high-precision real-time reporting of ionosonde station electron density, reduce the error between the reconstruction result and the measured value, and far exceed the traditional empirical model. At the same time, the contribution degree of each input feature to the result is sorted through an attribution algorithm to solve the "black box" problem of the deep learning model, give the model good interpretability, and do not need to rely on the original satellite signal, but can run with easily obtained data, effectively make up for the missing observation data caused by ionosonde failure or maintenance, provide real-time and reliable ionospheric parameter support for shortwave communication, satellite navigation and other scenarios, and have stronger practicality and applicability. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only exemplary, and those skilled in the art can also obtain other drawings from the provided drawings without creative labor.

[0044] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0045] Figure 1 This is a flowchart illustrating a method for reconstructing vertical electron density distribution using a TEC map, as provided in Embodiment 1 of the present invention.

[0046] Figure 2 This is a schematic diagram illustrating the specific implementation process of a method for reconstructing vertical electron density distribution using TEC maps, as provided in Embodiment 1 of the present invention.

[0047] Figure 3 This is a schematic diagram of the feature contribution results of the attribution algorithm in one possible embodiment of Embodiment 1 of the present invention;

[0048] Figure 4 This is a radar diagram showing the error comparison between the model of the present invention and the IRI model and the observation in one possible embodiment provided in Embodiment 1 of the present invention;

[0049] Figure 5 This is a schematic diagram comparing the effects of different test time models at the Zuoling Town Station in Wuhan in one possible embodiment of the present invention, as provided in Embodiment 1 of the present invention;

[0050] Figure 6 This is a schematic diagram comparing the effects of different test time models at the Hainan Fukezhen station in one possible embodiment of the present invention, as provided in Embodiment 1 of the present invention;

[0051] Figure 7 This is a schematic diagram of the architecture of a device for reconstructing vertical electron density distribution using TEC maps, as provided in Embodiment 2 of the present invention. Detailed Implementation

[0053] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example 1

[0055] See Figure 1 andFigure 2 Embodiment 1 of the present invention provides a method for reconstructing the vertical electron density distribution using a TEC map, comprising the following steps:

[0056] S1. Obtain ionospheric frequency-height distribution data from the Meridian Engineering Data Center using software settings, and convert the ionospheric frequency-height distribution data into electron density-height distribution data.

[0057] S2. Perform data quality control on the electron density data in the electron density-height distribution data to obtain quality-controlled electron density data;

[0058] S3. Based on the electron density data after quality control, match the spatiotemporally coordinated TEC data;

[0059] S4. Based on the TEC data, match the spatiotemporal coordinated spatial physical parameters;

[0060] S5. A symbolic regression algorithm based on genetic programming is used to calculate the TEC data by means of empirical formulas for station fitting, so that the TEC data can effectively approximate the integral TEC data in the electron density data after quality control, and extract the physical fitting features of TEC.

[0061] S6. Using UTC, the TEC data, the spatial physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model as inputs, and the electron density observed by the altimeter at the corresponding geographic coordinates as output, train the three-layer hidden layer fully connected neural network based on the attention mechanism to obtain the trained neural network.

[0062] S7. Input the current time, the UTC, the TEC data, the spatial physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model into the trained neural network for processing to obtain the electron density distribution of the altimeter station position at the current time.

[0063] In this embodiment, in step S1, the ionospheric frequency-height distribution data of the altimeter station data is obtained from the Meridian Engineering Data Center by setting software, and the ionospheric frequency-height distribution data is converted into electron density-height distribution data.

[0064] Specifically, SAOExplorer software was used as the setting software. Raw observation data from at least two altimeter stations were downloaded from the Meridian Engineering Data Center. The software’s built-in ionospheric parameter inversion function was used to extract the ionospheric frequency-height distribution information contained in the data. Then, based on the conversion relationship between plasma frequency and electron density, the frequency-height distribution data was converted into electron density distribution data that varies with height, forming a dataset containing electron density values ​​corresponding to different heights.

[0065] In this embodiment, in step S2, data quality control is performed on the electron density data in the electron density-height distribution data to obtain quality-controlled electron density data;

[0066] Specifically, data quality control is performed on electron density data:

[0067] First, the observed value samples that deviate too much from the empirical values ​​may also have some problems. Therefore, samples that deviate more than twice the critical frequency of the F2 layer of the IRI2020 empirical model were removed.

[0068] Secondly, only altimeter observation data at altitudes of 90-500km are retained. The top ionosphere observed by the altimeter is an extrapolated value from the model and has little contribution to practical applications.

[0069] Third, the electron density is integrated with altitude to obtain the TEC at altitudes of 90-500km observed by the altimeter, and the extreme values ​​at both ends (less than 1TEC or greater than 70TECU) are removed.

[0070] Fourth, we control data quality using the three-standard-deviation principle, which means subtracting our integral TEC from Madrigal's TEC products and eliminating cases where the difference is greater than three standard deviations:

[0071]

[0072] In the formula, X is the difference between the two TEC values; μ is the mean of X; σ is the standard deviation of X; and TEC is the standard deviation of X. Madrigal For Madrigal's TEC products; This is the integral TEC data.

[0073] In this embodiment, in step S3, based on the quality control electron density data, spatiotemporally coordinated TEC data is matched;

[0074] Specifically, based on the timestamps of the electron density data after quality control and the geographical coordinates of the altimeter station, spatiotemporally matched vertical TEC data are retrieved from the https: / / cedar.openmadrigal.org database. This ensures that the time deviation between the TEC data and the observation time of the altimeter data does not exceed 30 minutes, the spatial coverage includes the latitude and longitude range of the altimeter station within ±0.5°, and the time series of the TEC data must cover at least one complete solar cycle (approximately 11 years) to include the ionospheric variation characteristics under different solar activity levels.

[0075] In this embodiment, in step S4, spatial physical parameters for spatiotemporal coordination are matched based on the TEC data;

[0076] Specifically, based on the temporal and spatial information of TEC data, multiple types of space physics parameters are matched and obtained, including lunar phase parameters (LP), lunar local time (LLT), three-hour magnetic index (Kp), magnetic storm ring current index (Dst), and solar radio flux index at a wavelength of 10.7 cm (F10.7). The temporal resolution of all parameters is consistent with that of TEC data to ensure spatiotemporal coordination.

[0077] In this embodiment, in step S5, a symbolic regression algorithm based on genetic programming is used to calculate the TEC data by means of empirical formulas for station fitting, so that the TEC data can effectively approximate the integral TEC data in the electron density data after quality control, and extract the TEC physical fitting features.

[0078] Specifically, firstly, the electron density data after quality control is integrated along the height to obtain the integrated TEC data corresponding to the altimeter station; then, a symbolic regression algorithm based on genetic programming is used, with the TEC data obtained in step S3 as the input variable, to automatically generate a station-specific empirical fitting formula through evolutionary calculation, so that the error between the formula calculation result and the integrated TEC data is minimized (root mean square error is less than 3 TECU); the coefficients and nonlinear terms of this empirical formula are used as TEC physical fitting features, which can quantify the mapping relationship between TEC data and actual electron density integral values, preserving physical meaning.

[0079] In this embodiment, in step S6, the frequency-height distribution of the IRI2020 model, the TEC data, the spatial physical parameters, the TEC physical fitting features, and the frequency-height distribution of the model are used as inputs, and the electron density observed by the altimeter at the corresponding geographic coordinates is used as output. The three-layer hidden layer fully connected neural network based on the attention mechanism is trained to obtain the trained neural network.

[0080] Specifically, Universal Time (UTC) is decomposed into five independent time features: year, month, day, hour, and minute. These features, along with TEC data, space physics parameters, TEC physics fitting features, and frequency-altitude distribution data of corresponding spatiotemporal points calculated by the IRI2020 model, form the input feature set. The electron density values ​​of each altitude layer in the electron density-altitude distribution observed by an altimeter are used as the output labels. A fully connected neural network with three hidden layers (256, 128, and 64 neurons respectively) is constructed, and an attention mechanism is introduced into the network to manage Hour, TEC, and other time-related parameters. fit Dynamic weights are assigned to the Altitude feature; the training set and validation set are divided in a 4:1 ratio; the last 20% of the data is selected as the test set using a time-series preservation strategy; the network parameters are optimized through backpropagation until the model's error on the validation set converges and stabilizes, thus obtaining a trained neural network.

[0081] In this embodiment, in step S7, the current time, the UTC, the TEC data, the spatial physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model are input into the trained neural network for processing to obtain the electron density distribution of the altimeter station position at the current time.

[0082] Specifically, collect the current time (which must be consistent with the time format used during model training) corresponding to the Universal Time, decompose it into year, month, day, hour, and minute, real-time or near-real-time TEC data, synchronously observed spatial physical parameters, the current TEC physical fitting features calculated by the method in step S5, and the current spatiotemporal point frequency-altitude distribution data output by the IRI2020 model. After organizing these parameters according to the input format in step S6, input them into the trained neural network. The neural network outputs the electron density numerical distribution of the altimeter station position in the 90-500km altitude range at the current time through internal feature weighting and nonlinear mapping, realizing the real-time reconstruction of the vertical electron density distribution.

[0083] In one possible embodiment, verification examples are provided at the mid-latitude Wuhan Zuolingzhen Station (ZLT, 31.0°N, 114.45°E) and the low-latitude Hainan Fuke Station (FKT, 19.52°N, 109.13°E) as follows:

[0084] Madrigal's TEC map marks the geographical locations of the mid-latitude Wuhan Zuolingzhen Station (ZLT, 31.0°N, 114.45°E) and the low-latitude Hainan Fuke Station (FKT, 19.52°N, 109.13°E).

[0085] The purpose of this invention is to output the electron density profile at the corresponding position by inputting TEC (tectic density function), a method named "TEC2Ne". This method is based on a neural network and uses a large amount of data as input to solve ill-posed problems. It requires adding some variables to the equation input to constrain the equation. These variables need to be easily obtainable and indirectly related to the output. The model input includes TEC (tectic density function) downloaded from the Madrigal data center. Madrigal In addition to UT time, lunar phase (LP) and lunar local time (LLT), global geomagnetic activity index (Kp), geomagnetic storm loop current index (Dst), solar 10.7 cm wavelength radio flux index (F10.7), and the critical frequency (f0_IRI) of the IRI2020 model at various altitudes of the site were also selected. It is worth mentioning that TEC digisonde It is derived from the electron density integration of the altimeter, and is related to TEC. Madrigal A certain correlation is exhibited. Utilizing this correlation, the present invention extracts a physical fitting feature (TEC) from each station. fitThis invention uses the critical frequency as the output for supervised learning during neural network training, eliminating the need for standardization and thus preserving its physical meaning. The reconstructed critical frequency can be converted to electron density.

[0086] After decomposing UT time into five independent features—year, month, day, hour, and minute—the model contains a total of 14 input features. A trainable dataset was constructed by strictly aligning the input features with the timestamps of the output critical frequencies. Taking Zuoling Town station as an example, 99,123 valid observation times were matched within a complete solar activity cycle. The ionospheric profile at each time point contains 42 altitude layers, resulting in a total of 4,163,166 training samples for this station. This invention uses a fully connected neural network with three hidden layers as its basic architecture, dividing the training and validation sets in a 4:1 ratio. Based on feature importance analysis using attribution algorithms, the model prioritizes Hour and TEC. fit A focused attention mechanism is applied to the three key features: A, B, C, and A, as well as Alititude. This mechanism dynamically calculates the attention weight distribution, enabling the model to adaptively strengthen the contribution of key features during the feature decoding stage.

[0087] like Figure 3 The image shows the feature contribution results of the attribution algorithm. The IG algorithm (Integrated Gradients) is an attribution method used to interpret predictions from deep neural networks. Its basic idea is to smoothly move the input from a "baseline value" to the actual input and integrate the gradient along the path to calculate the influence of features on the output. Figure 3 (a) and Figure 3 Box plots (c) show the contribution distribution of each feature at Zuolingzhen Station and Fuke Station, respectively. The study found that the spatiotemporal features of the two stations exhibited a completely consistent feature importance ranking: Alt > Hour > Month > Year > Day > Minute, with Alt and Hour contributing more than all non-spatiotemporal features. This result is consistent with the physical characteristics of the ionosphere, where electron density peaks at the F2 layer and exhibits a typical parabolic distribution in the vertical profile; electron density shows significant diurnal variation, with daytime values ​​generally higher than nighttime values. The non-spatiotemporal features were extracted, and the average contribution was taken. After normalization, the histograms of the contribution of each non-spatiotemporal feature were obtained as shown below. Figure 3 (b) and Figure 3 As shown in (d). Key findings include: The most important non-spatiotemporal feature is TEC, f0_IRI, and f10.7. It is worth noting that the contribution of lunar phase LP and lunar local time LLT features (approximately 7.5%) exceeds that of the traditional geomagnetic index (Kp / DST is less than 5%), a first-time finding in electron density reconstruction studies.

[0088] like Figure 4 The image shows a radar chart comparing the errors of the proposed model and the IRI model with observations. During model training, a time-series-preserving data partitioning strategy was adopted, selecting the last 20% of the time-series data as the test set. The radar chart displays the overall model performance statistics for the test set. Figure 4 As shown, the TEC2Ne model significantly outperforms the IRI2020 empirical model across all evaluation metrics at both stations. Specifically, at the ZLT station, the MSE of the IRI2020 is four times that of the TEC2Ne model; while at the FKT station, this gap widens further to more than eight times (to maintain the visibility of the radar chart, ...). Figure 4 (The MSE index of the Zhongfuke station is presented using a separate annotation method.) For the RMSE and MAE indices, IRI2020 performs twice as well as TEC2Ne at the ZLT station and approximately three times better at the FKT station. Notably, TEC2Ne achieved an RMSE of 0.867 MHz and a MAE of 0.582 MHz at the ZLT station, implying an average prediction error of approximately 0.6 MHz for the critical frequency. Considering that typical daytime foF2 values ​​in mid-latitude regions range from 6-12 MHz (reaching over 14 MHz during peak solar activity), this error level corresponds to a relative error of only 5%-10% for NmF2, significantly better than the accuracy of the international reference ionospheric model. Furthermore, TEC2Ne's coefficient of determination... The value reached 0.902 at the ZLT station and 0.862 at the FKT station, significantly higher than the IRI2020 model, which is close to 1. The values ​​fully demonstrate that the model's predictions are highly consistent with the measured data.

[0089] like Figure 5 and Figure 6 As shown, in order to verify the generalization ability of the model, four days of independent data (December 31, 2024 to January 3, 2025) that were not involved in training and testing were additionally selected for verification, and the results of the reconstructed electron density experiment were illustrated. Figure 5 and Figure 6The results show a comparison of electron density profiles from the ZLT and FKT stations at different times. The solid red line in the figure represents the TEC2Ne reconstructed profile after SG smoothing, and the surrounding pink area represents the 95% confidence interval predicted by the model. A comparison with ionospheric altimeter data (blue line) shows that the quasi-parabolic profile reconstructed by TEC2Ne (red line) is closer to the observed values ​​at most altitudes. In contrast, the IRI2020 model (green line) and the results based on empirical formulas (purple asterisks) exhibit systematic bias. Quantitative assessment shows that the average peak electron density ratios of each method to altimeter observations at the ZLT station are: TEC2Ne -0.94, empirical method -0.78, and IRI2020 -0.72; the corresponding values ​​at the FKT station are 0.90, 0.51, and 0.30.

[0090] These results confirm that: first, the reconstruction accuracy of TEC2Ne is sufficient to support the prediction of the strongest ionospheric reflection; second, even in areas where the observed values ​​differ significantly from the empirical model (such as the FKT station, where ΔNmF2>40%), TEC2Ne can still maintain stable performance, with its RMSE reduced by up to 65% compared to IRI2020.

[0091] The application scenarios of this invention are as follows:

[0092] In the field of shortwave communication, it can provide the vertical distribution of electron density at the location of altimeter stations in real time, helping the communication system to dynamically select the optimal operating frequency and avoid signal attenuation or interruption caused by sudden changes in ionospheric electron density. It is especially suitable for scenarios with high requirements for signal stability, such as emergency communication and long-range aviation and maritime communication.

[0093] In the field of satellite navigation, it can accurately invert the electron density distribution of the ionosphere, provide ionospheric delay correction parameters for the Global Navigation Satellite System (GNSS), reduce the impact of the ionosphere on satellite signal propagation, improve navigation and positioning accuracy, and meet the high-precision positioning requirements of autonomous driving, precision mapping, and spacecraft orbit control.

[0094] In the field of space weather monitoring and early warning, based on continuously acquired electron density data and combined with spatiotemporal variation characteristics, it can help judge the occurrence and development trend of space weather events such as ionospheric storms and sudden ionospheric disturbances, and provide risk early warning support for space activities such as satellite operation and manned spaceflight;

[0095] Meanwhile, in the field of ionospheric scientific research, it can make up for the lack of observational data caused by the maintenance and failure of altimeters, and provide continuous and reliable data support for building a more comprehensive ionospheric model and studying the correlation between solar activity and ionospheric changes.

[0096] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0097] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0098] Example 2

[0099] See Figure 7 Embodiment 2 of the present invention also provides an apparatus for reconstructing the vertical electron density distribution using a TEC map, comprising:

[0100] The electron density-height distribution data acquisition module 001 is used to acquire ionospheric frequency-height distribution data from the Meridian Engineering Data Center through setting software, and convert the ionospheric frequency-height data into electron density-height data.

[0101] The electron density data quality control processing module 002 is used to perform data quality control on the electron density data in the electron density-height distribution data to obtain quality-controlled electron density data.

[0102] TEC data matching module 003 is used to match spatiotemporally coordinated TEC data based on the electron density data after quality control;

[0103] The space physics parameter matching module 004 is used to match spatiotemporally coordinated space physics parameters based on the TEC data.

[0104] The TEC physical fitting feature extraction module 005 is used for a genetic programming-based symbolic regression algorithm. It calculates the TEC data by using empirical formulas for station fitting, so that the TEC data can effectively approximate the integral TEC data in the quality control electron density data, and extracts the TEC physical fitting features.

[0105] The neural network training module 006 is used to train a three-layer fully connected neural network based on an attention mechanism, with the UTC, the TEC data, the spatial physical parameters, the TEC physical fitting features and the frequency-height distribution of the IRI2020 model as inputs and the electron density observed by an altimeter at the corresponding geographic coordinates as output, to obtain a trained neural network.

[0106] The neural network processing module 007 is used to input the current time, the UTC, the TEC data, the spatial physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model into the trained neural network for processing, so as to obtain the electron density distribution of the altimeter station position at the current time.

[0107] In this embodiment, the electron density data quality control processing module 002, during the data quality control process of the electron density data in the electron density-height distribution data, includes:

[0108] Samples with a critical frequency in the F2 layer of the IRI2020 empirical model that differs from the critical frequency by more than two times are excluded.

[0109] Retain altimeter observation data at altitudes of 90-500km;

[0110] The electron density is integrated with altitude to obtain the TEC at altitudes of 90-500 km as observed by the altimeter, and extreme values ​​less than 1 TEC or greater than 70 TECU are removed to obtain the integrated TEC data.

[0111] Outlier data with TEC differences were removed using the three-standard-deviation principle.

[0112] In this embodiment, in the electron density data quality control processing module 002, during the process of eliminating abnormal TEC difference data according to the three-standard-deviation principle, the integral TEC data is subtracted from the TEC product of Madrigal to eliminate abnormal data with a difference greater than three standard deviations; the expression for the retained TEC data is:

[0113]

[0114] In the formula, X is the difference between the two TEC values; μ is the mean of X; σ is the standard deviation of X; and TEC is the standard deviation of X. Madrigal For Madrigal's TEC products; This is the integral TEC data.

[0115] In this embodiment, in the TEC data matching module 003, during the process of matching the spatiotemporally coordinated TEC data, the data range of the extracted TEC data is one solar cycle.

[0116] In this embodiment, the space physical parameters in the space physical parameter matching module 004 include: lunar phase parameters, local time, three-hour magnetic index, magnetic storm ring current index, and solar radio flux index at a wavelength of 10.7 cm.

[0117] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0118] Example 3

[0119] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a method of reconstructing a vertical electron density distribution using a TEC map. The program code includes instructions for executing the method of reconstructing a vertical electron density distribution using a TEC map according to Embodiment 1 or any possible implementation thereof.

[0120] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives, SSDs).

[0121] Example 4

[0122] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0123] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can call the program instructions to execute a method for reconstructing the vertical electron density distribution using a TEC map, as described in Embodiment 1 or any possible implementation thereof.

[0124] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0125] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0126] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0127] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for reconstructing the vertical electron density distribution using a TEC map, characterized in that, include: The software is configured to acquire ionospheric frequency-height distribution data from altimeter stations in the Meridian Engineering Data Center, and then convert the ionospheric frequency-height distribution data into electron density-height distribution data. Perform data quality control on the electron density data in the electron density-height distribution data to obtain quality-controlled electron density data; Based on the quality control electron density data, spatiotemporally coordinated TEC data is matched; Based on the TEC data, spatial physical parameters for spatiotemporal coordination are matched; The symbolic regression algorithm based on genetic programming calculates the TEC data by using empirical formulas for station fitting, so that the TEC data can effectively approximate the integral TEC data in the electron density data after quality control, and extract the physical fitting features of TEC. Using UTC, the TEC data, the spatial physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model as inputs, and the electron density observed by an altimeter at the corresponding geographic coordinates as output, a three-layer fully connected neural network based on an attention mechanism is trained to obtain a trained neural network. The current time, the UTC, the TEC data, the space physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model are input into the trained neural network for processing to obtain the electron density distribution of the altimeter station at the current time.

2. The method for reconstructing vertical electron density distribution using a TEC map according to claim 1, characterized in that, In the process of performing data quality control on the electron density data in the electron density-height distribution data, the quality control process includes: Samples with a critical frequency in the F2 layer of the IRI2020 empirical model that differs from the critical frequency by more than two times are excluded. Retain altimeter observation data at altitudes of 90-500km; The electron density is integrated with altitude to obtain the TEC at altitudes of 90-500 km as observed by the altimeter, and extreme values ​​less than 1 TEC or greater than 70 TECU are removed to obtain the integrated TEC data. Outlier data with TEC differences were removed using the three-standard-deviation principle.

3. The method for reconstructing vertical electron density distribution using a TEC map according to claim 2, characterized in that, In the process of eliminating outlier TEC difference data using the three-standard-deviation principle, the integral TEC data is subtracted from Madrigal's TEC products to eliminate outlier data with differences greater than three standard deviations; the expression for the retained TEC data is: In the formula, X is the difference between the two TEC values; μ is the mean of X; σ is the standard deviation of X; and TEC is the standard deviation of X. Madrigal For Madrigal's TEC products; This is the integral TEC data.

4. The method for reconstructing vertical electron density distribution using a TEC map according to claim 3, characterized in that, In the process of matching the spatiotemporally coordinated TEC data, the extracted data range of the TEC data is one solar cycle.

5. The method for reconstructing the vertical electron density distribution using a TEC map according to claim 4, characterized in that, The space physics parameters include: lunar phase parameters, local time, three-hour magnetic index, geomagnetic storm ring current index, and solar radio flux index at a wavelength of 10.7 cm.

6. An apparatus for reconstructing vertical electron density distribution using a TEC map, employing the method for reconstructing vertical electron density distribution using a TEC map as described in any one of claims 1-5, characterized in that, include: The electron density-height distribution data acquisition module is used to acquire ionospheric frequency-height distribution data from the Meridian Engineering Data Center through setting software, and convert the ionospheric frequency-height data into electron density-height data. The electron density data quality control processing module is used to perform data quality control on the electron density data in the electron density-height distribution data to obtain quality-controlled electron density data. The TEC data matching module is used to match spatiotemporally coordinated TEC data based on the electron density data after quality control. The space physics parameter matching module is used to match spatiotemporally coordinated space physics parameters based on the TEC data; The TEC physical fitting feature extraction module is used for a genetic programming-based symbolic regression algorithm. It calculates the TEC data by using empirical formulas for station fitting, so that the TEC data can effectively approximate the integral TEC data in the quality control electron density data, and extracts the TEC physical fitting features. The neural network training module is used to train a three-layer fully connected neural network based on an attention mechanism, with the frequency-height distribution of the IRI2020 model as input, the TEC data, the spatial physical parameters, the TEC physical fitting features, and the frequency-height distribution of the IRI2020 model as input, and the electron density observed by the altimeter at the corresponding geographic coordinates as output, to obtain a trained neural network. The neural network processing module is used to input the current time, the UTC, the TEC data, the spatial physics parameters, the TEC physics fitting features, and the frequency-height distribution of the IRI2020 model into the trained neural network for processing, so as to obtain the electron density distribution of the altimeter station position at the current time.

7. The apparatus for reconstructing vertical electron density distribution using a TEC map according to claim 6, characterized in that, In the electron density data quality control processing module, during the process of performing data quality control on the electron density data in the electron density-height distribution data, the quality control processing includes: Samples with a critical frequency in the F2 layer of the IRI2020 empirical model that differs from the critical frequency by more than two times are excluded. Retain altimeter observation data at altitudes of 90-500km; The electron density is integrated with altitude to obtain the TEC at altitudes of 90-500 km as observed by the altimeter, and extreme values ​​less than 1 TEC or greater than 70 TECU are removed to obtain the integrated TEC data. Outlier data with TEC differences were removed using the three-standard-deviation principle.

8. The apparatus for reconstructing vertical electron density distribution using a TEC map according to claim 7, characterized in that, In the electron density data quality control processing module, during the process of eliminating abnormal TEC difference data according to the three-standard-deviation principle, the integral TEC data is subtracted from the TEC product of Madrigal to eliminate abnormal data with a difference greater than three standard deviations; the expression for the retained TEC data is: In the formula, X is the difference between the two TEC values; μ is the mean of X; σ is the standard deviation of X; and TEC is the standard deviation of X. Madrigal For Madrigal's TEC products; This is the integral TEC data.

9. The apparatus for reconstructing vertical electron density distribution using a TEC map according to claim 8, characterized in that, In the TEC data matching module, during the process of matching spatiotemporally coordinated TEC data, the extracted data range of the TEC data is one solar cycle.

10. The apparatus for reconstructing vertical electron density distribution using a TEC map according to claim 9, characterized in that, The space physics parameter matching module includes the following space physics parameters: lunar phase parameters, local time, three-hour magnetic index, magnetic storm ring current index, and solar radio flux index at a wavelength of 10.7 cm.

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