CN117973440A - Regional ionosphere delay prediction method based on LSTM-transducer model - Google Patents
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Abstract
The regional ionosphere delay prediction method based on the LSTM-transducer model comprises the following steps of: step 1: acquiring an ionized layer TEC value, and calculating to obtain a VTEC value through a projection function; step 2: processing the VTEC value by wavelet transformation, and dividing the VTEC value into a low-frequency part and a high-frequency part by a pair of conjugated low-pass and high-pass filters; step 3: introducing solar radiation index and geomagnetic index information as high-frequency part information training data; step 4: putting the data in the step 2 and the step 3 into an LSTM-transducer model for training to obtain an LSTM-Transfomer combined prediction model; step 5: and (3) training the LSTM-Transfomer combined prediction model in the step (4) by using a training set, optimizing the model by using a loss function, and predicting the VTEC value. The VTEC value accuracy obtained by the method is superior to that of the traditional ionosphere empirical model and the general neural network model, and the forecasting speed is higher.
Description
Technical Field
The invention relates to the technical field of ionosphere delay prediction, in particular to a regional ionosphere delay prediction method based on an LSTM-transducer model.
Background
Ionospheric delay of the earth refers to the propagation delay of an electromagnetic signal across the earth's ionosphere (a portion of the atmosphere, located between about 60 km and 1000 km from the earth's surface) due to changes in the concentration of electrons in the ionosphere. Ionospheric delay typically affects the accuracy and reliability in the areas of wireless communications, satellite navigation, and ground-based measurements.
Total Electron Content (TEC) is a characteristic of the ionosphere and total vertical electron content (VTEC) is its main manifestation. The forecasting of the ionized layer TEC value has important significance for radio propagation and navigation positioning. In the past, a learner studied and utilized a large number of observation data sets to build an ionospheric experience model, including an IRI model, a Bent model, a Klobuchar model, and the like. Ionospheric empirical models can better describe the average behavior of global changes, but lack accuracy for small scale changes in regions. The scholars also put forward an autoregressive model according to a time sequence analysis means, so that the periodicity and the trending can be fitted well. However, because the ionosphere is greatly influenced by environmental factors such as geomagnetic disturbance, solar activity, relative distance between the sun and the earth, the accuracy of the autoregressive model is also influenced to a certain extent, and the effect is poor.
The IGS center also issues ionosphere products in the form of grids, and although the grids cover the world, products issued by different institutions all have corresponding systematic errors, and the precision is not very high.
Based on the above analysis, ionospheric delay prediction in the prior art suffers from the following drawbacks: 1) The traditional experience model has low precision and is greatly influenced by environmental changes; 2) The ionosphere product released by the IGS is low in precision and has hysteresis; 3) The ionosphere forecasting scheme of the time sequence model has low precision, long-term change and special conditions are difficult to consider, and the anti-interference performance is weak.
In recent years, as an emerging technology, a neural network can build an effective model aiming at complex and nonlinear data, wherein the model has a certain effect on the prediction of a data set, can accurately represent the rule of dynamic change of a time sequence, provides a new method for forecasting ionospheric delay, and has the advantages that an LSTM-transducer model combination can process the ionospheric sequence, long-term change rule and global information can be considered at the same time, and the model training efficiency is higher.
Disclosure of Invention
The invention provides a regional ionosphere delay prediction method based on an LSTM-transducer model, which combines the LSTM model and the transducer model to process an ionosphere sequence, can simultaneously consider long-term change rules and global information, has higher model training efficiency, and has higher VTEC value accuracy than that of a traditional ionosphere empirical model and a common neural network model, and the prediction speed is higher.
The technical scheme adopted by the invention is as follows:
the regional ionosphere delay prediction method based on the LSTM-transducer model comprises the following steps of:
step 1: acquiring an ionized layer TEC value, and calculating to obtain a VTEC value through a projection function;
step 2: processing the VTEC value by wavelet transformation, and dividing the VTEC value into a low-frequency part and a high-frequency part by a pair of conjugated low-pass and high-pass filters;
step 3: introducing solar radiation index and geomagnetic index information as high-frequency part information training data;
Step 4: putting the data in the step 2 and the step3 into an LSTM-transducer model for training to obtain an LSTM-Transfomer combined prediction model;
Step 5: and (3) training the LSTM-Transfomer combined prediction model in the step (4) by using a training set, optimizing the model by using a loss function, and predicting the VTEC value.
In the step 1, historical ionospheric delay data are collected, ionospheric TEC values obtained through calculation of a global navigation satellite system GNSS are collected, VTEC values are obtained through calculation of a projection function, and the following formula is shown:
；
wherein Z is a height angle, R is the earth radius, and H is the height of the puncture point; at this time, storing longitude and latitude and time related information of the puncture point, and data according to 8: and 2, dividing the training set and the verification set.
In step 2, the VTEC value is processed by wavelet transform, using a pair of conjugate low-pass and high-pass filters, as shown in the following formula:
；
In the above formula, the VTEC value is divided into two parts, and is decomposed into an approximation value and a detail value, wherein the approximation value is a low-frequency part The detail value is the high frequency partThe low frequency part contains trend information and long period information, the high frequency part contains more detailed information such as influence information of solar activity, geomagnetic activity, magnetic storm and the like, and the part contains more information of sunday transformation.
In the step 3, the solar radiation index is calculatedAnd geomagnetic index、A corresponding data set is constructed.
1）.The index indicates the solar activity intensity, and refers to the radiant flux of solar radiation at the wavelength of 10.7cm, and the radiant flux is divided into three grades of strong, medium and weak according to the difference of the index values. Summarizing daily solar radiation indexes, and establishing a solar radiation index data set；
；
In the above-mentioned method, the step of,Solar radiation indexes on the i-th day are respectively represented, wherein i represents the corresponding number of days and n represents the total number of days.
2）.For the hour geomagnetic index, the method is used for describing the process of the magnetic storm, reflecting the change of the equatorial western ring current, monitoring the intensity and the space-time range of the magnetic storm, generally utilizing the horizontal components of the geomagnetic field of four stations with middle and low latitude, correcting and eliminating the ring current latitude, calculating the ring current latitude, and constructing a data set/>, by the obtained geomagnetic indexWherein each subscript represents a time of modeling choice, there are a total of c times:
；
In the above-mentioned method, the step of, Respectively, the geomagnetic indexes at the a-th time, wherein a represents the a-th time, and c represents the total number of times.
3）.The index is calculated according to magnetic field change data of a plurality of geomagnetic observation stations, and shows the influence of solar activity on geomagnetism, and the calculation mode is as follows:
；
；
Wherein, Respectively represent the kthAn index, where s represents the total number of observations and k represents the kth time instant.
The step 4 specifically includes the following steps:
① Since LSTM can capture long-term dependency in time series, low frequency series after wavelet transformation As the input of the model, training LSTM model, longitude and latitude, time,As a feature, performing feature scaling (normalization) to construct an LSTM model, including constructing an input layer, an LSTM layer, and an output layer, and evaluating the model after model training is completed;
wherein, the feature scaling is as follows:
；
；
Wherein, Representing the t-th value in the initial data,Representing the mean of the original time series,Is the standard deviation of the original time series,VTEC value for ith puncture point at time t,Is the VTEC average value at time t-Representing the normalized data. And the time information is converted into proper codes, and the time is converted into characteristics of year, month, hour and the like.
And then adopting principal component analysis to reduce the dimension of the model data, wherein the method specifically comprises the following steps:
a) Defining an initial matrix X, i.e. a parameter that can affect the VTEC value
；
B) Calculating a correlation coefficient matrix:
；
wherein: Representing the correlation coefficient of the 1 st parameter with the 1 st parameter,/> Representing the correlation coefficient of the 1 st parameter and the 2 nd parameter,A correlation coefficient representing the 1 st parameter and the p-th parameter; /(I)Representing the correlation coefficient of the 2 nd parameter with the 1 st parameter,Representing the correlation coefficient of the 2 nd parameter and the 2 nd parameter,Representing the correlation coefficient of the 2 nd parameter and the p-th parameter,Representing the correlation coefficient of the p-th parameter and the 1 st parameter,Representing the correlation coefficient of the p-th parameter and the 2 nd parameter,Representing the correlation coefficient of the p-th parameter and the p-th parameter.
C) According to the characteristic equationSolving eigenvectors, lambda representing eigenvalues,Representing an identity matrix,Representing a correlation coefficient matrix, arranging the characteristic values in sequence from large to small, and selecting the main components actually needed according to the requirements.
The LSTM model has an input gate, a forgetting gate, and an output gate to control the flow of information, thereby realizing an effective time memory function and preventing the gradient vanishing problem. The input gate is similar to the attention of the brain, which determines which parts of the new input data should be added to the current state; forget gate is similar to a sieve, which decides which information should be kept in the current state and which information should be forgotten; the output gate determines which information in the current state should be passed to the state at the next time and the output of the network.
The LSTM model structure is schematically shown in fig. 2, in which the input layer represents the eigenvalues at each time,Memory cell status information indicating the last time,Representing the memory cell status information at this time,Representing forgetful door,Representing the output of the input gate,Representing updated memory cell state information,Representing the output of the output gate,AndRespectively represent an activation function,Output representing last time,Indicating the output at this time.
Constructing an input layer, an LSTM layer and an output layer of the LSTM model:
(i) Creating an input layer, and matching the characteristic dimension of the data dimension;
(ii) Adding an LSTM layer for capturing modes and dependency relations in the time sequence, and setting the number of LSTM units and other super parameters;
(iii) Output layer: and adding a full connection layer, and outputting the mapping relation f (x 1,x2,…,xp) of the features and the VTEC L.
② High frequency sequence after wavelet transformationAs input of the model, high frequency information is usedGeomagnetic index、Solar radiation indexThe data are integrated to form a high-frequency characteristic matrix H, wherein each row represents a time step, each column represents a characteristic, a transducer model is trained, and the training effect is evaluated. The feature matrix is as follows:
；
Wherein F represents solar radiation index, dst and K represent geomagnetic index, S represents random noise; a solar radiation index sequence representing a u-th time step; /(I) AndRespectively representing geomagnetic indexes of a u-th time step, wherein Dst is a magneto-riot loop current index, and Kp is a three-hour magnetic emotion index; /(I)A random noise sequence representing the u-th time step, N representing the total number of time steps.
A Transfomer model is constructed, and a schematic diagram of the Transfomer model structure is shown in fig. 3.
(I) Input layer: input feature matrix；
(Ii) Encoder and decoder layers: a plurality of encoder layers are created, each encoder layer containing a self-attention mechanism and a feed-forward neural network. The self-attention mechanism helps to capture the relationship of different positions in the sequence, and the feedforward neural network is used for processing the characteristics of each position; the encoder takes as input the characteristics of the received solar radiation index, geomagnetic index and the like, and encodes them into a context vector, which contains a representation of the input characteristics;
The decoder takes as input the context vector generated by the receiving encoder and predicts the high frequency part of the TEC from this context vector; the output of the decoder is a prediction of the TEC high frequency portion.
(Iii) Output layer: a fully connected layer is added after the encoder layer for outputting the characteristic representation, and the size of the output layer and the activation function are adjusted according to the task requirement.
In step 4, the high-frequency characteristic matrix H is combined with the observedThe model can dynamically pay attention to information among different features in an input feature sequence through a multi-head attention layer and standardization, understand modes and trends among the features and capture complex relations among solar radiation indexes, geomagnetic indexes and noise.
Multiple attention layers for each time point for the solar radiation indexGeomagnetic indexAndNoiseLinearization is performed to obtain Query vectorKey vectorValue vector，Representing the ith feature;
；
；
；
wherein: 、、 the weight matrix is a linear transformation weight matrix, is a model parameter, and is updated step by step in model training;
normalization refers to: for each feature, a process is adopted in which Is characterized byIs the characteristic mean valueIs the standard deviation of the characteristics,、、For the standardized result, the step can alleviate the problem of gradient disappearance or explosion, and the original characteristic information is reserved, and each characteristic has the same scale in the subsequent splicing process.
；
For the normalized results, after inputting three vectors for each feature, the attention score is calculated, where softmax is the normalization function,For vector dimension, the vector is weighted and summed with the value vector to obtain the attention outputThe output reflects the weight information among different characteristics, and then each is spliced to obtain the total attention output，Is a splicing function;
；
；
；
The feedforward nerve layer can help the model map the characteristic representation generated by the multi-head attention layer into a higher-dimensional characteristic space, and consists of a hidden layer and an output layer, wherein the hidden layer outputs attention by using an activation function And nonlinear transformation is performed, so that the feature dimension is increased, and the expression capacity and adaptability of the model are improved. The result of the hidden layer is subjected to linear transformation at the output layer, and the result is mapped from the original feature space to the new feature space, so that the fitting capacity of the model is enhanced, and the complex relation and mode between the features are better captured.
Then, the characteristic information extracted by the encoder and the previous output sequence are input into a decoder, and under the limitation of a mask multi-head attention layer, only the generated sequence is accessed to establish the characteristic information and the characteristic informationThe mapping relation F (H) of (c) is as follows:
；
wherein: New features trained for models.
Training Transfomer the model by using training set data, optimizing model parameters by minimizing a proper loss function, and helping the model to better predict ionospheric delay high-frequency information; and then evaluating the performance of the model by adopting a verification set, measuring the accuracy of the model according to the difference between the prediction result and the actual value, and performing operations such as super-parameter adjustment, model structure adjustment and the like according to the requirement so as to optimize the performance of the model.
In the step 4, the concrete structure of the Transfomer combined prediction model is shown in fig. 4. Transfomer combining the prediction models according to the relation between the low-frequency characteristic sequences and the high-frequency characteristic sequences, according to the solar activity intensity and the geomagnetic intensity on the same day, training the relation between the characteristic sequences through a feedforward neural network at the full-connection layer, fusing the results, and finally outputting the predicted VTEC value.
In the step 5, for the LSTM-Transfomer combined prediction model in the step 4, training the combined prediction model by using a training set, and optimizing the combined prediction model by using a loss function;
；
；
Wherein, Representing a bias-indexed loss function,Representing a loss function with Rms as an indicator,Representing a GNSS-VTEC value; /(I)The VTEC value of the model prediction is represented by i, i represents the ith puncture point, and n is the total number of puncture points.
As shown in fig. 5, in step 5, the VTEC is obtained by inputting GNSS-VTEC values, performing wavelet transformation on the VTEC to obtain low-frequency and high-frequency portions, and entering an LSTM-transducer model for training to obtain a mapping relationship between the VTEC and the feature information, so that the VTEC can be predicted.
In the step 5, the historical VTEC value and the solar radiation index are utilizedGeomagnetic Activity index、And predicting the future VTEC value and outputting the VTEC value predicted by the model.
The invention discloses a regional ionosphere delay prediction method based on an LSTM-transducer model, which has the following technical effects:
1) Because ionosphere delay data has complex composition, is influenced by various factors, such as geomagnetic indexes, solar radiation, longitude and latitude, and the like, has annual changes, month changes, sunday changes and the like, and is difficult to directly participate in model training as an initial value of training. Therefore, the invention utilizes wavelet transformation to process the VTEC value, and wavelet decomposition can effectively separate and extract the periodicity, nonlinearity and variation trend of the time sequence data, so that the prediction model can better fit and model the periodic variation point information and trend item of the time sequence data, thereby obtaining more accurate prediction results.
2) The method has the advantages of high accuracy and quick resolving, the model combines the two advantages, the long-term change rule and the global information can be considered at the same time, and the model training efficiency is higher.
3) The VTEC value accuracy obtained by the method is superior to that of the traditional ionosphere empirical model and the general neural network model, and the forecasting speed is higher.
4) According to the method, additional fund investment is not needed, a new observation station is not needed to be constructed based on the existing GNSS observation station, additional equipment is used for collecting data, and predicted VTEC data can be obtained through processing and training of the data.
Drawings
The following is a further description of embodiments of the invention, taken in conjunction with the accompanying drawings and examples:
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of the LSTM model of the present invention.
FIG. 3 is a schematic diagram of a transducer model according to the present invention.
FIG. 4 is a schematic diagram of the LSTM-Transfomer combined prediction model of the present invention.
FIG. 5 is a schematic diagram of step 5 of the present invention.
Detailed Description
According to the regional ionosphere delay prediction method based on the LSTM-transducer model, GNSS observation data is utilized, the influence of solar activity is considered, short-term VTEC values in a region are predicted, long-term change rules and global information can be considered at the same time, model training efficiency is higher, the accuracy of the obtained VTEC values is superior to that of a traditional ionosphere empirical model and a general neural network model, and the prediction speed is high.
As shown in fig. 1, the specific implementation steps are as follows:
1) Collecting historical ionosphere delay data, collecting TEC values obtained by GNSS calculation, and obtaining VTEC values by projection function calculation, wherein the VTEC values are shown in the following formula:
；
wherein Z is the altitude angle, R is the earth radius, H is the height of the puncture point, the longitude and latitude and time related information of the puncture point are saved at the moment, and the data are calculated according to 8: and 2, dividing the training set and the verification set.
2) Because ionosphere delay data has complex composition and is influenced by various factors, such as geomagnetic indexes, solar radiation, longitude and latitude, and the like, and also has annual changes, lunar changes, sunday changes and the like, and is difficult to directly participate in model training as initial values of training, VTEC values are processed by wavelet transformation, and periodicity, nonlinearity and variation trend of time sequence data can be effectively separated and extracted by wavelet decomposition, so that a prediction model can better fit and model the periodic variation change point information and trend items of the time sequence data, and a more accurate prediction result is obtained.
Using a pair of conjugate low-pass and high-pass filters, as shown in the following equation:
；
dividing VTEC value into two parts, decomposing it into approximation value and detail value, and reconstructing to obtain low-frequency part The detail value is the high frequency partThe low frequency part contains trend information and long period information, the high frequency part contains more detailed information, such as the influence of solar activity, geomagnetic activity, magnetic storm and the like, and the part contains more information of sunday transformation.
3) Information such as solar radiation index, geomagnetic index and the like is introduced as high-frequency part information training data.
Index of solar radiationAnd geomagnetic index、A corresponding data set is constructed.
The index indicates the solar activity intensity, and refers to the radiant flux of solar radiation at the wavelength of 10.7cm, and the radiant flux is divided into three grades of strong, medium and weak according to the difference of the index values. Summarizing daily solar radiation indexes, and establishing a solar radiation index data setWherein the following table is the corresponding days;
；
wherein: For the hour geomagnetic index, the method is used for describing the process of the magnetic storm, reflecting the change of the equatorial western ring current, monitoring the intensity and the space-time range of the magnetic storm, generally utilizing the horizontal components of the geomagnetic field of four stations with middle and low latitude, correcting and eliminating the ring current latitude, calculating the ring current latitude, and constructing a data set/>, by the obtained geomagnetic index Wherein each subscript represents a time of modeling selection, for a total of n times
；
The index is calculated according to magnetic field change data of a plurality of geomagnetic observation stations, and shows the influence of solar activity on geomagnetism, and the calculation mode is as follows:
；
；
Wherein the method comprises the steps of Global/>, for time kIndex, i, is the i-th site.
4) For the data in 2) and 3), put into LSTM-transducer model for training, the specific steps are as follows
① Since LSTM can capture long-term dependence in time series, low-frequency sequence after wavelet transformationAs input to the model. First, latitude and longitude, time,As a feature, feature scaling (normalization) is performed as shown in the following formula:
；
；
Wherein, Representing the t-th value in the initial data,Representing the mean of the original time series,Is the standard deviation of the original time series,VTEC value for ith puncture point at time t,Is the VTEC average value at time t-Representing the normalized data. And the time information is converted into proper codes, and the time is converted into characteristics of year, month, date, hour and the like.
And the principal component analysis is adopted, so that the dimension of the model data is reduced, the data redundancy is avoided, the influence among related elements is eliminated, and the subsequent modeling is convenient. The principal component analysis steps are as follows:
a) An initial matrix X is defined, i.e., parameters that may have an effect on VTEC values, including, but not limited to, time feature years, months, days, hours, longitudes, latitudes, elevations, and the like.
；
B) Calculating a correlation coefficient matrix, firstly calculating a covariance value among features, and then calculating the correlation matrix
；
；
Wherein the method comprises the steps of、And r is a correlation coefficient for the ith and jth feature quantities. And obtaining the eigenvector and the eigenvalue by decomposing the eigenvalue of the correlation matrix. The eigenvector represents the direction of the principal component, and the eigenvalue represents the magnitude of variability of the data in this direction.
C) According to the characteristic equationAnd solving the feature vector, arranging the feature values in sequence from large to small, and selecting the main components actually needed according to the requirement to finish the dimension reduction of the features.
Meanwhile, the data are classified into subsets according to different characteristics, and training effects of the model on the subsets are improved.
LSTM has input gate, forget gate, output gate control information flow, thus achieving an effective time memory function and preventing gradient vanishing problems. The input gate is similar to the attention of the brain, which determines which parts of the new input data should be added to the current state; forget gate is similar to a sieve, which decides which information should be kept in the current state and which information should be forgotten; the output gate determines which information in the current state should be passed to the state at the next time and the output of the network.
Building an input layer, an LSTM layer and an output layer:
(i) Input layer: an input layer is created that matches the feature dimensions of the data dimensions, inputting the various feature vectors associated with VTEC L.
(Ii) LSTM layer: an LSTM layer is added for capturing patterns and dependencies in the time series, and the number of LSTM units and other super parameters are set.
(Iii) Output layer: and adding a full connection layer, outputting a mapping relation f (x 1,x2,…,xp) of the features and the VTEC L, and fitting the periodicity and the trend of the VTEC.
② Information for high frequencies using a transducer modelModeling processing:
Will high frequency information Geomagnetic index、Solar radiation indexThe data are integrated to form a high-frequency characteristic matrix H.
；
Wherein each row represents a time step and each column represents a feature, and the following table represents different moments in time. F represents the solar radiation index, dst and K represent the geomagnetic index, and S represents the random noise.
Constructing Transfomer models:
(i) Input layer: and inputting a feature matrix.
(Ii) Encoder and decoder layers: a plurality of encoder layers are created, each encoder layer containing a self-attention mechanism and a feed-forward neural network. The self-attention mechanism helps to capture the relationship of the different positions in the sequence, and the feedforward neural network is used to process the characteristics of each position.
(Iii) Output layer: a fully connected layer is added after the encoder layer for outputting the characteristic representation, and the size of the output layer and the activation function are adjusted according to the task requirement.
Training a transducer model by using training data, optimizing model parameters by minimizing a proper loss function, and helping the model to better predict ionospheric delay high-frequency information; and then evaluating the performance of the model by adopting a verification set, measuring the accuracy of the model according to the difference between the prediction result and the actual value, and performing operations such as super-parameter adjustment, model structure adjustment and the like according to the requirement so as to optimize the performance of the model.
③ Model feature fusion:
The method comprises the steps of establishing a full-connection layer, fusing the characteristics of an LSTM model and a Transfomer model, inputting the fused characteristics, giving different weights to the characteristics by utilizing a feedforward neural network according to geomagnetic activity and solar activity intensity, establishing a total mapping relation, obtaining an LSTM-Transfomer combined prediction model, and outputting a result which is a predicted VTEC value.
5) For the LSTM-Transfomer model in 4), training the whole combined model by using a training set, establishing a loss function by combining the VTEC value calculated by GNSS and the predicted VTEC value to optimize model parameters, and setting the absolute error and the root mean square error as the loss function.
；/>
；
Wherein,Represent GNSSVTEC values,The VTEC value of the model prediction is represented by i, i represents the ith puncture point, and n is the total number of puncture points.
6) For the model of 5), historical VTEC values and solar radiation indices are usedGeomagnetic Activity index、And predicting the future VTEC value and outputting the VTEC value predicted by the model.
Throughout the training process, the parameters of the model will be updated by back-propagation and optimization algorithms to minimize the loss function. After the model prediction precision reaches a satisfactory level, a precision threshold can be set according to the requirement so as to meet the requirement of practical application. Once the model reaches this accuracy threshold, training can be completed, completing the creation of a regional ionosphere model.
According to the invention, the ionosphere delay data is predicted by using the high-precision GNSS data and adopting the LSTM-Transfomer combined model, the ionosphere delay is divided into a low frequency part and a high frequency part for training, the long-term change rule and global information can be considered at the same time, the model training efficiency is higher, and the model training precision is better.
Verification example:
the invention selects the performance of 5 stations in the year A and the year B, wherein the year A is the high solar activity year and the year B is the low solar activity year. Five of these sites and their longitudes and latitudes are shown in table 1 below.
Table 1 five stations and longitude and latitude thereof
Table 2 VTEC prediction accuracy for each model of year a
TABLE 3 VTEC forecast accuracy for each model of year B
Tables 2 and 3 show statistics of the accuracy of the LSTM-transducer model, the transducer model and the LSTM model, and MAE and RMS were calculated in tecu units using the model predicted values and the GNSS calculated VTEC. It can be seen that the three models of model a have lower accuracy than the model a in the high years of solar activity than in the low years of solar activity, and the LSTM-transducer model is equivalent to a certain improvement in accuracy of a single model as a whole, and also has a certain improvement in the high years of solar activity.
Claims (10)
1. The regional ionosphere delay prediction method based on the LSTM-transducer model is characterized by comprising the following steps of:
step 1: acquiring an ionized layer TEC value, and calculating to obtain a VTEC value through a projection function;
step 2: processing the VTEC value by wavelet transformation, and dividing the VTEC value into a low-frequency part and a high-frequency part by a pair of conjugated low-pass and high-pass filters;
step 3: introducing solar radiation index and geomagnetic index information as high-frequency part information training data;
Step 4: putting the data in the step 2 and the step3 into an LSTM-transducer model for training to obtain an LSTM-Transfomer combined prediction model;
Step 5: and (3) training the LSTM-Transfomer combined prediction model in the step (4) by using a training set, optimizing the model by using a loss function, and predicting the VTEC value.
2. The regional ionospheric delay prediction method based on LSTM-transducer model of claim 1, wherein: in the step 1, historical ionospheric delay data are collected, ionospheric TEC values obtained through calculation of a global navigation satellite system GNSS are collected, VTEC values are obtained through calculation of a projection function, and the following formula is shown:
；
wherein Z is a height angle, R is the earth radius, and H is the height of the puncture point; at this time, storing longitude and latitude and time related information of the puncture point, and data according to 8: and 2, dividing the training set and the verification set.
3. The regional ionospheric delay prediction method based on LSTM-transducer model of claim 1, wherein: in step 2, the VTEC value is processed by wavelet transform, using a pair of conjugate low-pass and high-pass filters, as shown in the following formula:
；
In the above formula, the VTEC value is divided into two parts, and is decomposed into an approximation value and a detail value, wherein the approximation value is a low-frequency part The detail value is the high frequency partThe low frequency part contains trend information and long period information, and the high frequency part contains influence information of solar activity, geomagnetic activity and magnetic storm.
4. The regional ionospheric delay prediction method based on LSTM-transducer model of claim 1, wherein: in the step 3, the solar radiation index is calculatedAnd geomagnetic index、Constructing a corresponding data set;
1）. the index represents the solar activity intensity, and refers to the radiant flux of solar radiation at the wavelength of 10.7cm, and the solar radiation is divided into three grades of strong, medium and weak according to the difference of the index values; summarizing daily solar radiation indexes, and establishing a solar radiation index data set/> ；
；
In the above-mentioned method, the step of,Solar radiation indexes on the i-th day are respectively represented, wherein i represents the corresponding number of days, and n represents the total number of days;
2）. for the hour geomagnetic index, the method is used for describing the process of the magnetic storm, reflecting the change of the equatorial western ring current, monitoring the intensity and the space-time range of the magnetic storm, calculating the latitude correction and rejection of the ring current by utilizing the horizontal components of the geomagnetic field of four stations with middle and low latitude, and constructing a data set/>, by the obtained geomagnetic index Wherein each subscript represents a time of modeling choice, there are a total of c times:
；
In the above-mentioned method, the step of, Respectively representing geomagnetic indexes at a time a, wherein a represents the time a, and c represents the total number of times;
3）. the index is calculated according to magnetic field change data of a plurality of geomagnetic observation stations, and shows the influence of solar activity on geomagnetism, and the calculation mode is as follows:
；
；
Wherein, Respectively represent the kthAn index, where s represents the total number of observations and k represents the kth time instant.
5. The regional ionospheric delay prediction method based on LSTM-transducer model of claim 1, wherein: in the step 4, the method specifically includes:
low frequency sequence after wavelet transformation As the input of the model, training LSTM model, longitude and latitude, time,As a feature, performing feature scaling, constructing an LSTM model, including constructing an input layer, an LSTM layer and an output layer, and evaluating the model after model training is completed;
wherein, the feature scaling is as follows:
；
；
Wherein, Representing the t-th value in the initial data,Representing the mean of the original time series,Is the standard deviation of the original time series,VTEC value for ith puncture point at time t,Is the VTEC average value at time t-Representing the standardized various data; and the time information is converted into proper codes, and the time is converted into year, month and hour characteristics;
And then adopting principal component analysis to reduce the dimension of the model data, wherein the method specifically comprises the following steps:
a) Defining an initial matrix X, i.e. a parameter that can affect the VTEC value
；
B) Calculating a correlation coefficient matrix:
；
wherein: Representing the correlation coefficient of the 1 st parameter with the 1 st parameter,/> Representing the correlation coefficient of the 1 st parameter and the 2 nd parameter,A correlation coefficient representing the 1 st parameter and the p-th parameter; /(I)Representing the correlation coefficient of the 2 nd parameter with the 1 st parameter,Representing the correlation coefficient of the 2 nd parameter and the 2 nd parameter,Representing the correlation coefficient of the 2 nd parameter and the p-th parameter,Representing the correlation coefficient of the p-th parameter and the 1 st parameter,Representing the correlation coefficient of the p-th parameter and the 2 nd parameter,A correlation coefficient representing the p-th parameter and the p-th parameter;
c) According to the characteristic equation Solving eigenvectors, lambda representing eigenvalues,Representing an identity matrix,Representing a correlation coefficient matrix, arranging the characteristic values in sequence from large to small, and selecting the main components actually needed according to the requirements.
6. The method for regional ionospheric delay prediction based on LSTM-transducer model as claimed in claim 5, wherein: constructing an input layer, an LSTM layer and an output layer of the LSTM model:
(i) Creating an input layer, and matching the characteristic dimension of the data dimension;
(ii) Adding an LSTM layer for capturing modes and dependency relations in the time sequence, and setting the number of LSTM units and other super parameters;
(iii) Output layer: adding a full connection layer, and outputting a mapping relation f (x 1,x2,…,xp) of the features and the VTEC L;
② High frequency sequence after wavelet transformation As an input to the model, high frequency informationGeomagnetic index、Solar radiation indexData integration is carried out to form a high-frequency characteristic matrix H, wherein each row represents a time step, each column represents a characteristic, a transducer model is trained, and training effect is evaluated; the feature matrix is as follows:
；
Wherein F represents solar radiation index, dst and K represent geomagnetic index, S represents random noise; a solar radiation index sequence representing a u-th time step; /(I) AndRespectively representing geomagnetic indexes of a u-th time step, wherein Dst is a magneto-riot loop current index, and Kp is a three-hour magnetic emotion index; /(I)A random noise sequence representing the u-th time step, N representing the total number of time steps.
7. The method for regional ionospheric delay prediction based on LSTM-transducer model as claimed in claim 6, wherein: constructing Transfomer models:
(i) Input layer: input feature matrix ；
(Ii) Encoder and decoder layers: creating a plurality of encoder layers, each encoder layer comprising a self-attention mechanism and a feed-forward neural network; the self-attention mechanism helps to capture the relationship of different positions in the sequence, and the feedforward neural network is used for processing the characteristics of each position; the encoder takes as input the received solar radiation index, geomagnetic index features, and encodes them into a context vector that contains a representation of the input features;
the decoder takes as input the context vector generated by the receiving encoder and predicts the high frequency part of the TEC from this context vector; the output of the decoder is a prediction of the TEC high frequency part;
(iii) Output layer: a fully connected layer is added after the encoder layer for outputting the characteristic representation, and the size of the output layer and the activation function are adjusted according to the task requirement.
8. The method for regional ionospheric delay prediction based on LSTM-transducer model as claimed in claim 7, wherein: in step4, the high-frequency characteristic matrix H is combined with the observedInputting the information into an encoder, and enabling a model to dynamically pay attention to information among different features in an input feature sequence through a multi-head attention layer and standardization;
Multiple attention layers for each time point for the solar radiation index Geomagnetic indexAndNoise andLinearizing to obtain a Query vectorKey vectorValue vector，Representing the ith feature;
；
；
；
wherein: 、、 the weight matrix is a linear transformation weight matrix, is a model parameter, and is updated step by step in model training;
normalization refers to: for each feature, a process is adopted in which Is characterized byIs the characteristic mean valueIs the standard deviation of the characteristics,、、Is the result after normalization;
original characteristic information is reserved, and all the characteristics have the same scale in the subsequent splicing process;
；
For the normalized results, after inputting three vectors for each feature, the attention score is calculated, where softmax is the normalization function, For vector dimension, the vector is weighted and summed with the value vector to obtain the attention outputThe output reflects the weight information among different characteristics, and then each is spliced to obtain the total attention output;
Is a splicing function;
；
；
；
then, the characteristic information extracted by the encoder and the previous output sequence are input into a decoder, and under the limitation of a mask multi-head attention layer, only the generated sequence is accessed to establish the characteristic information and the characteristic information The mapping relation F (H) of (c) is as follows:
；
wherein: New features trained for models.
9. The method for regional ionospheric delay prediction based on LSTM-transducer model of claim 8, wherein: in the step 5, for the LSTM-Transfomer combined prediction model in the step 4, training the combined prediction model by using a training set, and optimizing the combined prediction model by using a loss function;
；
；
Wherein, Representing a bias-indexed loss function,Representing a loss function with Rms as an indicator,Representing a GNSS-VTEC value; /(I)The VTEC value of the model prediction is represented by i, i represents the ith puncture point, and n is the total number of puncture points.
10. The method for regional ionospheric delay prediction based on LSTM-transducer model of claim 9, wherein: in the step 5, the historical VTEC value and the solar radiation index are utilizedGeomagnetic Activity index、And predicting the future VTEC value and outputting the VTEC value predicted by the model.
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