Variational mode decomposition enhanced gated attention bidirectional circulation ionosphere prediction method

Abstract

The invention discloses a variational mode decomposition enhanced gated attention two-way circulation ionosphere prediction method, which comprises the following steps of: decomposing TEC historical data by adopting a variational mode decomposition method to obtain information of different frequency bands and simplify the complexity of an original sequence; then, each decomposed sub-sequence is subjected to bidirectional learning through BiGRU, an internal time change rule is extracted to capture time change characteristics in the data, and an attention mechanism is applied, and according to contribution of each time node in a hidden state to a prediction result, different weights are given to BiGRU output, and the influence of information of a key time point on a prediction model is strengthened; and finally, successfully predicting the output value of the ionosphere parameter at the next moment through linear calculation, and improving the overall prediction precision of the model.

Description

Technical Field

[0001] The present invention belongs to the technical field of ionosphere research and application, and in particular relates to a variational mode decomposition enhanced gated attention bidirectional cyclic ionosphere prediction method. Background Art

[0002] The Beidou navigation satellite positioning system determines the position of the receiver by measuring the propagation time of satellite signals. During the transmission process, the signal is affected by the changes in the ionosphere, resulting in refraction of the signal, which affects the propagation path and time of the signal. Ionospheric delay is one of the main sources of error in positioning accuracy. The distance error caused by ionospheric delay is usually represented by the product of the ionospheric parameter Total Electron Content (TEC) and a constant representing the signal frequency and the geometric relationship of the earth; TEC is a major factor affecting the positioning accuracy of the satellite navigation system. For this error, usually only historical data can be obtained. In order to reduce the impact of delay error on positioning accuracy, it is necessary to accurately predict and correct the error at future times to improve the positioning accuracy of the navigation system.

[0003] Therefore, the study of the ionosphere has important theoretical significance and practical application value in many fields such as space weather forecasting, communication and navigation. Summary of the invention

[0004] The purpose of the present invention is to provide a variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method, which requires mathematical modeling and algorithm optimization, based on historical data, combined with real-time observation data, to accurately predict the ionospheric delay error at future times, so as to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a variational mode decomposition enhanced gated attention bidirectional cyclic ionosphere prediction method, comprising the following steps:

[0006] 1) Collect TEC short-term variation data and preprocess the data to a given range;

[0007] 2) Perform signal decomposition based on variational equations on the preprocessed data to obtain optimized conversion of IMFs in different frequency bands; encode the intrinsic mode function through BiGRU to obtain the feature representation of each historical parameter trajectory;

[0008] 3) Input the encoded input matrices independently into the temporal attention module to predict the TEC values ​​at several future time points. For each IMFs, the prediction results are summed and reconstructed to obtain the TEC prediction results.

[0009] 4) The output layer of the model receives the weighted sequence output by the attention mechanism and linearly transforms it to generate the final prediction result.

[0010] Preferably, it is characterized in that: the specific steps of step 1) are:

[0011] Collect TEC short-term change data, trajectory data f t It can be expressed as <x1,x2,......x t >, where x t is the TEC observation value at time t. The abnormal values ​​in the data are processed by blanking and directly deleting. The missing data are filled by linear interpolation to obtain a complete historical parameter time series. Since the numerical range of ionospheric parameters varies greatly, in order to make the data suitable for training the prediction model, the Min-Max Scaler method is used to standardize the data and scale the data to a given minimum and maximum value, as follows:

[0012] x'=(x-Min(x)) / (Max(x)-Min(x))

[0013] Where x is the data to be normalized, Min(x) is the minimum value of the sequence x, Max(x) represents the maximum value of the sequence x, and x' represents the data after Min-Max normalization.

[0014] Preferably, it is characterized in that the data is scaled to given minimum and maximum values ​​of 0 and 1 respectively.

[0015] Preferably, the specific steps of step 2) are as follows:

[0016] Set the number of intrinsic mode functions, that is, the number of IMFs to be decomposed, as well as the center frequency and bandwidth of each IMF;

[0017] Denote the estimate of each IMF as u k , represented by the kth mode; the center frequency is represented by ω k ; To find the partial derivative; δ(t) represents the Dirac distribution; is the convolution calculation, f t The original TEC data is preprocessed with trajectory data, and a variational problem is constructed so that each u k It has sparseness in its corresponding frequency band and minimizes u k With its center frequency ω k The variational problem is constructed as follows:

[0018]

[0019] Among them, st is a mathematical symbol, which means constrained; j is an imaginary unit; K is the total number of modes; u k (t) represents the function value of the kth component at time t;

[0020] By introducing the quadratic penalty coefficient α and the Lagrange multiplication operator λ(t), the constrained variational problem is transformed into an unconstrained variational problem:

[0021]

[0022] Where f(t) refers to the original signal to be decomposed at time t; λ is the Lagrange multiplier;

[0023] The alternating direction multiplier method is used to solve the above variational problem. By alternating update calculations, u k and ω k The update formula is:

[0024]

[0025] n is the number of iterations, ω represents the conversion of the signal from the time domain to the frequency domain, are the Fourier transforms of f(t), u(t), and λ(t), respectively, where u(t) is the time domain representation of the mode. The variational problem is solved by ADMM, and u of each IMFs is iteratively updated. k and the center frequency ω k , until the convergence condition is met. During the iteration process, each IMFs gradually focuses on a specific frequency band of the original TEC signal, realizing the frequency domain division of the original signal, which greatly reduces the complexity of the original signal and obtains the value U(t)=[u 1t ,u 2t ,…,u kt )], U(t) is the set of u(t), u kt is the time domain of the kth mode.

[0026] Preferably, the specific steps of step 3) are as follows:

[0027] The temporal attention module encodes the historical sequence of TEC ionospheric parameters through BiGRU. The network consists of two GRU networks: one processes the sequence in chronological order, inputs the time series into the network training through forward propagation, and mines the forward correlation of the data; the other processes the sequence in reverse chronological order, and the input sequence is trained through back propagation to mine the reverse correlation of the data; the model can extract the past and future time series features at each time point at the same time, and better capture the contextual information of the sequence; it can be formally expressed as:

[0028]

[0029] Represents the forward hidden layer state of IMFs in different frequency bands at time t, represents the state of the reverse hidden layer at time t, w t 、v t are the weights of the positive and reverse hidden layer states at time t, b t is the bias of the hidden layer state. Each IMFs represents the components of different frequencies in the original signal. t is the encoded vector, the length of which is the same as the input sequence u t The length of is the same, that is, at each time point position, a hidden state code of the corresponding position will be generated, and the hidden state code enters the global attention mechanism to perform attention calculation on the hidden state features;

[0030] Different weights are assigned to the hidden states of the temporal attention module. The weight assignment formula of the attention mechanism is as follows:

[0031] e t =u a tanh(w a h t +b a )

[0032]

[0033] Among them: a t represents the weight assigned to the feature by the temporal attention module, w a is the weight matrix, b a is the bias, e t is the probability distribution;

[0034] The attention mechanism assigns different weights to the BiGRU output hidden states according to the influence of each time node in the hidden layer state on the prediction results, and strengthens the influence of the state information at the relevant moment. The formula is as follows:

[0035]

[0036] Among them, s t is the output of the temporal attention module at time t.

[0037] Preferably, the formula for further processing the weighted sequence by linear change in step 4) is as follows:

[0038]

[0039] in, Represents the output value of the predicted ionospheric parameters at the next moment, y t is the true value, w o is the weight coefficient, b ois bias.

[0040] Preferably, in step 4), the prediction accuracy of the model is improved by introducing a loss function, and the parameters of the model are adjusted to minimize the loss function and improve the model performance; the loss function is:

[0041]

[0042] The technical effects and advantages of the present invention are as follows: the variational mode decomposition method is used to decompose the TEC historical data, the information of different frequency bands is obtained, and the complexity of the original sequence is simplified; then, each decomposed subsequence is subjected to bidirectional learning through BiGRU to extract the internal time variation law so as to capture the time variation characteristics within the data, and the attention mechanism is applied to assign different weights to the BiGRU output according to the contribution of each time node in the hidden state to the prediction result, so as to strengthen the influence of the information of the key time point on the prediction model; finally, the output value of the ionospheric parameter at the next moment is successfully predicted through linear calculation, so as to improve the overall prediction accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a model architecture diagram of the present invention. DETAILED DESCRIPTION

[0044] The specific embodiments of the present invention are further described below in conjunction with the accompanying drawings. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0045] The present invention provides Figure 1 A variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method is shown, which specifically includes the following steps

[0046] 1. Data acquisition and preprocessing

[0047] Collect TEC short-term change data, trajectory data f t It can be expressed as<x1,x2,......xt> , where xt is the TEC observation value at time t. For abnormal values ​​in the data, methods such as blanking and direct deletion are used to process, and the missing data are filled using linear interpolation to obtain a complete historical parameter time series. Since the numerical ranges of ionospheric parameters vary greatly, in order to make the data suitable for training prediction models, the present invention uses the Min-Max Scaler method to standardize the data and scale the data to a given minimum and maximum value, usually between 0 and 1. This ensures that the importance of each feature in the model will not be affected by different numerical ranges.

[0048] x'=(x-Min(x)) / (Max(x)-Min(x))

[0049] Where x is the data to be normalized, Min(x) is the minimum value of the sequence x, Max(x) represents the maximum value of the sequence x, and x' represents the data after Min-Max normalization.

[0050] 2. Variational Mode Decomposition Module

[0051] Since any signal may have frequency components that cannot be explained and lack practical meaning after Hilbert transformation, only the instantaneous frequency of the signal that meets specific conditions has physical meaning. The TEC time series data is decomposed based on the variational equation. The signal decomposition process is transformed into the process of solving the variational equation to obtain k sub-modal components of different frequencies, namely the intrinsic mode function (IMFs) optimization conversion. The specific process is as follows:

[0052] AInitialization process

[0053] Decompose a time series data into several sub-signals of different frequency bands. The decomposition effect is determined by two parameters: the number of decomposition layers k and the quadratic penalty coefficient α. Set the number of intrinsic mode functions, that is, the number of IMFs to be decomposed, as well as the center frequency and bandwidth of each IMF. Usually, the number of IMFs can be determined by observing the spectral characteristics of TEC data.

[0054] B. Establishing the variational problem

[0055] The original TEC signal is the f after data preprocessing t ; Denote the estimate of each IMFs as u k , denoted as the kth mode; the center frequency is denoted as ω k ; To find the partial derivative; δ(t) represents the Dirac distribution; For convolution calculation, construct a variational problem so that each u k It has sparseness in its corresponding frequency band and minimizes u k With its center frequency ω k The variational problem is constructed as follows:

[0056]

[0057] C variation problem solution

[0058] By introducing the quadratic penalty coefficient α and the Lagrange multiplication operator λ(t), the constrained variational problem is transformed into an unconstrained variational problem:

[0059]

[0060] The alternating direction multiplier method (ADMM) is used to solve the above variational problem. By alternating the update calculation, u k and ω k The update formula is:

[0061]

[0062] n is the number of iterations, ω represents the conversion of the signal from the time domain to the frequency domain, are the Fourier transforms of f(t), u(t), and λ(t), respectively. The variational problem is solved by ADMM, and u of each IMFs is iteratively updated. k and the center frequency ω k , until the convergence condition is met; in the iterative process, each IMFs gradually focuses on a specific frequency band of the original TEC signal, realizing the frequency domain division of the original signal, which greatly reduces the complexity of the original signal and obtains the value U(t)=u containing all IMFs at time t 1t ,u 2t ,…,u kt )].

[0063] 3. Temporal Attention Module (BiGRU-Attention)

[0064] The input matrices of each submodal component are independently input into the time series attention module to predict the TEC values ​​at several future time points. The prediction results of each IMFs are added and reconstructed to obtain the final TEC prediction results. The addition and reconstruction can assign different weights to the time series data at different time points to highlight the time points that are more important to the prediction results; the prediction results from different submodal components are added at the corresponding time points to obtain a prediction vector that integrates all submodal information. The purpose is to use the complementary information of different submodal components to generate more accurate and robust TEC prediction values; the architecture design of the model fully considers the characteristics of time series data, and can effectively capture long-distance dependencies and local features in the sequence, thereby improving the accuracy of prediction;

[0065] A Bidirectional Gated Recurrent Unit (BiGRU)

[0066] The temporal attention module encodes the historical sequence of TEC ionospheric parameters through BiGRU. The network consists of two GRU (Gated Recurrent Unit) networks: one processes the sequence in chronological order, inputs the time series into the network training through forward propagation, and mines the forward correlation of the data; the other processes the sequence in reverse chronological order, and the input sequence is trained through back propagation to mine the reverse correlation of the data. The model can extract the past and future time series features at each time point at the same time, better capture the contextual information of the sequence, and can be formally expressed as:

[0067]

[0068] Represents the forward hidden layer state of IMFs in different frequency bands at time t, represents the state of the reverse hidden layer at time t, w t 、v t are the weights of the positive and reverse hidden layer states at time t, b t is the bias of the hidden layer state; each IMFs represents the components of different frequencies in the original signal, h t is the encoded vector, and its length is the same as that of the input sequence ft. That is, at each time point, a hidden state code of the corresponding position will be generated, and then this code will enter the global attention mechanism to perform attention calculation on the hidden state features.

[0069] B. Attention Mechanism

[0070] The global attention mechanism allows the temporal attention module to adaptively weight each position in the sequence according to the needs of the prediction, so that it can pay more attention to the more important parts of the current prediction when predicting. By reasonably allocating attention to different input information, different weights are given to the hidden states of the temporal attention module, and elements are merged according to their importance. The formula for allocating weights by the attention mechanism is as follows:

[0071] e t =u a tanh(w a h t +b a )

[0072]

[0073] Where: h t is the hidden state vector of the network at time t, a t represents the weight assigned to the feature by the temporal attention module, w a is the weight matrix, b a is the bias, e t is a probability distribution.

[0074] In order to study the degree to which the current prediction results are affected by historical inputs, an attention mechanism is introduced after the BiGRU network output results to form a temporal attention module. The attention mechanism assigns different weights to the BiGRU output hidden states according to the influence of each time node in the hidden layer state on the prediction results, and strengthens the influence of the state information at the relevant moment. The formula is expressed as follows:

[0075]

[0076] Among them, h t is the output of the BiGRU module at time t, s t is the output of the temporal attention module at time t, which can better capture the overall characteristics of the sequence, including periodic and non-periodic parts.

[0077] 4. Output module

[0078] The output layer of the model receives the weighted sequence output by the attention mechanism and further processes its linear changes to generate the final prediction result. The formula is as follows:

[0079]

[0080] in, Represents the output value of the predicted ionospheric parameters at the next moment, w o is the weight coefficient, b o is bias.

[0081] The loss function is:

[0082]

[0083] The variational mode decomposition enhanced gated attention bidirectional recurrent ionosphere prediction method first uses variational mode decomposition (VMD) to decompose TEC into a set of intrinsic mode functions (IMFs) of different frequency bands representing the original signal, effectively reducing the complexity of the original sequence and extracting the periodic and trend components in the TEC data; then each subsequence is input into a bidirectional bidirectional gated recurrent unit (BiGRU) for feature extraction and time series learning, and by simultaneously capturing the forward and backward long-term dependencies in the sequence data, the time variation law within the TEC data is learned to improve the prediction accuracy; finally, the attention mechanism is introduced to enhance the model's attention to key time points. According to the influence of each time node in the hidden state on the prediction result, different weights are assigned to the hidden state of the BiGRU output, paying more attention to the time points that have a greater impact on the prediction result, suppressing unimportant information, thereby strengthening the influence of the state information at the relevant moment and improving the overall prediction accuracy of the model.

[0084] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A gated attention bidirectional recurrent ionospheric prediction method enhanced by variational mode decomposition, characterized in that: The steps include: 1) Collect TEC short-term variation data and preprocess the data to a given range; 2) Perform signal decomposition based on variational equations on the preprocessed data to obtain optimized conversion of IMFs in different frequency bands; encode the intrinsic mode function through BiGRU to obtain the feature representation of each historical parameter trajectory; 3) Input the encoded input matrices independently into the temporal attention module to predict the TEC values ​​at several future time points. For each IMFs, the prediction results are summed and reconstructed to obtain the TEC prediction results. 4) The output layer of the model receives the weighted sequence output by the attention mechanism and linearly transforms it to generate the final prediction result.

2. The variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method according to claim 1, characterized in that: The specific steps of step 1) are: Collect TEC short-term change data, trajectory data f t It can be expressed as <x1,x2,......x t >, where x t is the TEC observation value at time t. The abnormal values ​​in the data are processed by blanking and directly deleting. The missing data are filled by linear interpolation to obtain a complete historical parameter time series. Since the numerical range of ionospheric parameters varies greatly, in order to make the data suitable for training the prediction model, the Min-Max Scaler method is used to standardize the data and scale the data to a given minimum and maximum value, as follows: x'=(x-Min(x)) / (Max(x)-Min(x)) Where x is the data to be normalized, Min(x) is the minimum value of the sequence x, Max(x) represents the maximum value of the sequence x, and x' represents the data after Min-Max normalization.

3. The variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method according to claim 2, characterized in that: Scale the data to the given minimum and maximum values ​​of 0 and 1 respectively.

4. The variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method according to claim 1, characterized in that: The specific steps of step 2) are as follows: Set the number of intrinsic mode functions, that is, the number of IMFs to be decomposed, as well as the center frequency and bandwidth of each IMF; Denote the estimate of each IMF as u k , represented by the kth mode; the center frequency is represented by ω k ; To find the partial derivative; δ(t) represents the Dirac distribution; is the convolution calculation, f t The original TEC data is preprocessed with trajectory data, and a variational problem is constructed so that each u k It has sparseness in its corresponding frequency band and minimizes u k With its center frequency ω k The variational problem is constructed as follows: Among them, st is a mathematical symbol, which means constrained; j is an imaginary unit; K is the total number of modes; u k (t) represents the function value of the kth component at time t; By introducing the quadratic penalty coefficient α and the Lagrange multiplication operator λ(t), the constrained variational problem is transformed into an unconstrained variational problem: Where f(t) refers to the original signal to be decomposed at time t; λ is the Lagrange multiplier; The alternating direction multiplier method is used to solve the above variational problem. By alternating update calculations, u k and ω k The update formula is: n is the number of iterations, ω represents the conversion of the signal from the time domain to the frequency domain, are the Fourier transforms of f(t), u(t), and λ(t), respectively, where u(t) is the time domain representation of the mode. The variational problem is solved by ADMM, and u of each IMFs is iteratively updated. k and the center frequency ω k , until the convergence condition is met. During the iteration process, each IMFs gradually focuses on a specific frequency band of the original TEC signal, realizing the frequency domain division of the original signal, which greatly reduces the complexity of the original signal and obtains the value U(t)=[u 1t ,u 2t ,…,u kt )], U(t) is the set of u(t), u kt is the time domain of the kth mode.

5. The variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method according to claim 1, characterized in that: The specific steps of step 3) are as follows: The temporal attention module encodes the historical sequence of TEC ionospheric parameters through BiGRU. The network consists of two GRU networks. Composition: A time-ordered sequence processing, which inputs the time series into the network training through forward propagation and mines the forward correlation of the data; The other one processes the sequence in reverse time order. The input sequence is trained through back propagation to mine the inverse correlation of the data. The model can extract the past and future time series features at each time point to better capture the contextual information of the sequence. It can be formally expressed as: Represents the forward hidden layer state of IMFs in different frequency bands at time t, represents the state of the reverse hidden layer at time t, w t 、v t are the weights of the positive and reverse hidden layer states at time t, b t is the bias of the hidden layer state. Each IMFs represents the components of different frequencies in the original signal. t is the encoded vector, the length of which is the same as the input sequence u t The length of is the same, that is, at each time point position, a hidden state code of the corresponding position will be generated, and the hidden state code enters the global attention mechanism to perform attention calculation on the hidden state features; Different weights are assigned to the hidden states of the temporal attention module. The weight assignment formula of the attention mechanism is as follows: e t =u a tanh(w a h t +b a ) Among them: a t represents the weight assigned to the feature by the temporal attention module, w a is the weight matrix, b a is the bias, e t is the probability distribution; The attention mechanism assigns different weights to the BiGRU output hidden states according to the influence of each time node in the hidden layer state on the prediction results, and strengthens the influence of the state information at the relevant moment. The formula is as follows: Among them, s t is the output of the temporal attention module at time t.

6. The variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method according to claim 1, characterized in that: The formula for further processing the weighted sequence by linear change in step 4) is as follows: in, Represents the output value of the predicted ionospheric parameters at the next moment, y t is the true value, w o is the weight coefficient, b o is bias.

7. The variational mode decomposition enhanced gated attention bidirectional cyclic ionospheric prediction method according to claim 6, characterized in that: In step 4), the prediction accuracy of the model is improved by introducing a loss function, and the parameters of the model are adjusted to minimize the loss function and improve the model performance; the loss function is:

Images