Electromagnetic vector sensor 2D-DOA estimation method based on convolutional neural network

Abstract

The invention provides an electromagnetic vector sensor 2D-DOA estimation method based on a convolutional neural network, and the method comprises the steps: receiving an incident signal from a space signal source through an electromagnetic vector sensor, enabling the incident signal to impact the electromagnetic vector sensor to generate a receiving signal, and carrying out the preprocessing of the receiving signal; extracting a feature vector of an upper triangular part from the covariance matrix because the part contains sufficient information about an incident signal direction, and eliminating redundant or irrelevant information; carrying out normalization processing on the extracted feature vectors by using Min-Max scaling, separating a real part and an imaginary part of a covariance matrix, and forming a directional image by using the real part and the imaginary part; constructing a convolutional neural network model comprising a plurality of convolutional layers and a full connection layer, and training the convolutional neural network model by taking the directional image as input data until a loss function reaches a predetermined threshold value; and performing 2D-DOA estimation on the new electromagnetic wave signal data by using the trained convolutional neural network model, and outputting high-precision estimation results of the azimuth angle and the pitch angle of the signal source.

Description

Technical Field

[0001] The present invention relates to the field of array signal processing, and in particular to a 2D-DOA estimation method for an electromagnetic vector sensor based on a convolutional neural network. Background Art

[0002] In recent years, deep learning methods have also been widely studied and applied in the DOA estimation problem. Some scholars have proposed an efficient model based on convolutional neural networks to estimate the elevation and azimuth angles of multiple sources with high accuracy, high speed and high resolution. It can maintain its good performance even in the presence of array defects and significantly reduced signal-to-noise ratio. Other scholars have proposed a joint DOA estimation method based on CAE (convolutional autoencoder) and CNN for DOA estimation of low-elevation targets under the influence of multipath effects. It can effectively remove multipath and accurately estimate DOA when the DOA of the target is in a lower range. Some scholars have also constructed a deep neural network framework with feasible computational complexity to significantly reduce position gain and phase error, improve the accuracy of mutual coupling DOA estimation, and handle the DOA estimation problem when multiple types of array disturbances coexist. However, most of the above studies are based on traditional scalar sensor arrays, and there is no relevant literature report on deep learning DOA estimation based on electromagnetic vector sensors. Polarization sensor array - Electromagnetic Vector Sensor (EMVS) is different from traditional scalar sensors. A single electromagnetic vector sensor itself embodies the properties of a six-element array, extending the signal processing field from the traditional time domain, space domain and frequency domain to the polarization domain, where the polarization state is not only an inherent characteristic of electromagnetic waves, but also carries important information about the signal.

[0003] Therefore, it is urgent to propose a 2D-DOA estimation method for electromagnetic vector sensor based on convolutional neural network on the basis of electromagnetic vector sensor model and received signal, analyze the influence of factors such as different snapshot numbers and signal-to-noise ratio on the DOA estimation level, and improve the estimation accuracy. Summary of the invention

[0004] The purpose of the present invention is to solve the technical problems in the above background and propose a 2D-DOA estimation method for an electromagnetic vector sensor based on a convolutional neural network, comprising the following steps:

[0005] S1. Using an electromagnetic vector sensor to receive an incident signal from a spatial signal source, the incident signal hits the electromagnetic vector sensor to generate a receiving signal, and the receiving signal is pre-processed;

[0006] S2, extract the eigenvectors of the upper triangular part from the covariance matrix, because this part contains sufficient information about the direction of the incident signal and eliminates redundant or irrelevant information;

[0007] S3, normalizing the eigenvectors extracted in step S2 using Min-Max scaling, separating the real and imaginary parts of the covariance matrix and composing them into a directional image;

[0008] S4, constructing a convolutional neural network model including several convolutional layers and fully connected layers, taking the orientation image obtained in step S3 as input data, and training the convolutional neural network model until the loss function reaches a predetermined threshold;

[0009] S5. Use the trained convolutional neural network model to perform 2D-DOA estimation on the new electromagnetic wave signal data, and output the azimuth and elevation angle estimation results of the spatial signal source.

[0010] In the preferred solution, in step S1, the spatial signal source transmits an incident signal of unit power, which is incident on the electromagnetic vector sensor. In the spherical coordinates, the electric field vector e k and the magnetic field vector h k It is expressed as:

[0011]

[0012] Where k = 1, 2, ... K is the number of information sources, j is an imaginary unit, 0 ≤ γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, Z0 is a real number, representing the inherent impedance of the transmission medium, represents the unit vector along the azimuth direction, represents the unit vector along the pitch angle direction;

[0013] For linearly polarized transverse electromagnetic waves, we have: k =0; for circularly polarized waves: γ k =45°、η k = ±90°, “+” indicates left circular polarization, “-” indicates circular polarization. After normalization, the electric field vector e k and the magnetic field vector h k Expressed in Cartesian coordinates:

[0014]

[0015] Where k = 1, 2, ... K is the number of sources, j is an imaginary unit, and the pitch angle range is 0 ≤ θ k <π, the azimuth range is 0≤φ k <2π,0≤γ k<π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, Z0 is a real number, representing the inherent impedance of the transmission medium, represents the unit vector along the X-axis direction, represents the unit vector along the Y coordinate axis, Represents a unit vector along the Z axis.

[0016] In the preferred solution, the formula of the incident signal is:

[0017]

[0018] where x k (t) is the incident signal, j is the imaginary unit, t is the time function, and the kth signal s k (t) is given by a frequency f k The complex carrier modulation and a uniformly distributed phase offset ψ k composition.

[0019] In a preferred solution, the received signal is a six-element column vector, including the electric field and magnetic field measurement values ​​from the electromagnetic vector sensor element, and the formula of the received signal is:

[0020]

[0021] Where (t) represents the received signal, k = 1, 2, ... K is the number of signal sources, and the pitch angle range is 0 ≤ θ k <π, the azimuth range is 0≤φ k <2π,0≤γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, y e (t0 represents the electric field component of the received signal, y h (t) represents the magnetic field component of the received signal, n(t) is the spatial Gaussian white noise vector of each antenna element, and n e (t) represents the electric field component of the noise, n h (t) represents the magnetic field component of the noise.

[0022] In the preferred solution, the data y(t) received by the electromagnetic vector sensor is first compressed and converted into data that can be used by the neural network. The covariance matrix of the signal suppresses additive Gaussian white noise. The longer the snapshot number, the more accurate the covariance matrix. The covariance matrix is ​​defined as:

[0023]

[0024] Wherein, R represents the covariance matrix of the received signal, y represents the received signal, a represents the array manifold of the received signal, x represents the incident signal, n represents the noise, H represents the complex conjugate transpose, δ and δ s are the noise levels, I is the unit vector, aa H is the data feature that can uniquely determine the DOA.

[0025] In a preferred solution, the preprocessing refers to the linear algebra calculations of matrix-matrix and matrix-vector multiplications.

[0026] In a preferred solution, the real and imaginary parts of the covariance matrix are separated and combined into a direction image as the input data, which is converted from the covariance matrix to the direction image, specifically including the following steps:

[0027] A1. R ij is the element in the i-th column and j-th row of the covariance matrix R, and M is the number of array receiving units;

[0028] A2. Combine the real part Re(R ij ) (i < j) and the imaginary part Im(R ij ) into a single vector; ij

[0029]

[0030] A3. Normalize the vector r using Min-Max scaling:

[0031]

[0032] A4. Restore the normalized vector r norm to an (M + 1) × M matrix, and regard the (M + 1) × M matrix as the direction image;

[0033] A5. The input / output pair for the convolutional neural network model to perform training is {r norm , (θ, φ)}.

[0034] In a preferred solution, in the training stage of step S4, the training data is input into the convolutional neural network model, and the neural network weights are updated according to the loss function. The update will be repeated several times until the loss reaches the specified threshold; when the convolutional neural network model is trained, the desired input / output mapping relationship is established.

[0035] In a preferred solution, the convolutional neural network model structure contains 3 convolutional layers, the fully connected layer has 512 neurons, no pooling layer is adopted, and the output layer adopts the Softmax activation function and the Adam optimizer.

[0036] The beneficial effects of the present invention are as follows: for a single source scenario, the present invention proposes a 2D-DOA estimation method for an electromagnetic vector sensor based on a convolutional neural network, when the auxiliary polarization angle and the polarization phase difference are set to non-zero constants. The real and imaginary parts of the covariance matrix of the received signal are converted into directional images, and then input into the convolutional neural network for training, thereby realizing the inverse mapping from the covariance matrix to the signal incident direction. Simulation results show that compared with classical machine learning methods and traditional array signal processing algorithms, convolutional neural networks have higher estimation accuracy. Even in the case of low snapshot numbers and low signal-to-noise ratios, the method of the present invention can make relatively accurate estimates of DOA. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is the model diagram of the electromagnetic vector sensor.

[0038] Figure 2 Figure 2 is a structural diagram of the convolutional neural network model for two-dimensional DOA estimation.

[0039] Figure 3 Error versus snapshot number mean square error and root mean square error.

[0040] Figure 4 Error curves varying with signal-to-noise ratio mean square error and root mean square error.

[0041] Figure 5 Curves of azimuth estimation using different methods versus snapshot number.

[0042] Figure 6 Azimuth estimation curves of different methods as the signal-to-noise ratio changes.

[0043] Figure 7 Pitch angle estimation curves of different methods changing with the number of snapshots.

[0044] Figure 8 Pitch angle estimation curves of different methods as the signal-to-noise ratio changes. DETAILED DESCRIPTION

[0045] Example 1

[0046] Figure 1 The figure shows a model of an electromagnetic vector sensor unit. A spatial signal source emits an electromagnetic wave of unit power and incidents on the electromagnetic vector sensor unit. This incident unit power fully polarized electromagnetic wave has an electric field vector e k and the magnetic field vector h k , in spherical coordinates, e k 、h k It can be expressed as follows:

[0047]

[0048] Where k=1,2,...K is the number of information sources, 0≤γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, Z0 is the inherent impedance of the transmission medium, which is a real number. is a unit vector along the lower coordinate direction. For linearly polarized transverse electromagnetic waves: k =0; for circularly polarized waves: γ k =45°、η k = ±90°

[0049] (+: left circular polarization, -: right circular polarization). After normalization, it can be expressed in Cartesian coordinates as follows:

[0050]

[0051] The pitch angle range is 0≤θ k <π, the azimuth range is 0≤φ k <2π.

[0052] Assume that the electromagnetic vector sensor array manifold is a(θ k ,φ k ,γ k ,η k ), mapping the given direction and polarization information to the antenna elements of the electromagnetic vector sensor. The array manifold can be interpreted as Θ k (θ k ,φ k ) and g k (γ k ,η k ) is the result of linear transformation, Θ k (θ k ,φ k ) corresponds to the mapping in the spatial domain, g k (γ k ,η k ) corresponds to the mapping in the polarization domain:

[0053]

[0054] Incident signal x k (t) As shown below, the kth signal s k (t) is given by a frequency f k The complex carrier modulation and a uniformly distributed phase offset ψ k composition:

[0055]

[0056] Where j is the imaginary unit and t is the time function.

[0057] The received signal y(t) is a six-element column vector containing the electric and magnetic field measurements from the electromagnetic vector sensor element, as shown in equations (5) and (6):

[0058]

[0059] Where k = 1, 2, ... K is the number of sources, and the pitch angle range is 0 ≤ θ k <π, the azimuth range is 0≤φ k <2π,0≤γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, y e (t) represents the electric field component of the received signal, y h (t) represents the magnetic field component of the received signal, n(t) is the spatial Gaussian white noise vector of each antenna element, and n e (t) represents the electric field component of the noise, n h (t) represents the magnetic field component of the noise.

[0060] The data y(t) received by the electromagnetic vector sensor is too large to be directly fed into the neural network, so data compression is required first. Preprocessing the received data can eliminate irrelevant information and convert it into data that can be used by the neural network. Preprocessing only requires simple linear algebra calculations (matrix-matrix and matrix-vector multiplication). The covariance matrix of the signal can suppress additive Gaussian white noise. The longer the snapshot number, the more accurate the covariance matrix. The covariance matrix R is defined as follows:

[0061]

[0062] Where R represents the covariance matrix of the received signal, y represents the received signal, a is the array manifold of the received signal, x represents the incident signal, n represents the noise, H represents the complex conjugate transpose, δ and δ s is the noise level, I is the unit vector, aa H It is the only data feature that can determine DOA.

[0063] The covariance matrix is ​​conjugate symmetric with respect to the diagonal, and its upper triangle is selected as the input of the network because it contains sufficient information about the direction of the incident signal, and the cross-correlation of the signals received by different array elements eliminates redundant or irrelevant information. The real and imaginary parts of the covariance matrix R are separated and combined into a matrix as input data. This input data is called a directional image. The conversion from R to the directional image is completed by the following steps:

[0064] Step 1: R ijis the element in the i-th column and j-th row of the covariance matrix R, and M is the number of array receiving units. For example, when using a six-component electromagnetic vector sensor, M = 6.

[0065]

[0066] Step 2: Take R ij (where i < j), and form a separate vector from the real part Re(R ij ) and the imaginary part Im(R ij ).

[0067]

[0068] Step 3: Normalize the vector r using Min - Max scaling as shown in Equation (10), and then restore the normalized vector r norm to an (M + 1)×M matrix, and regard the (M + 1)×M matrix as the direction image. The input / output pairs for the final convolutional neural network to perform training are {r norm , (θ, φ)}.

[0069]

[0070] Convolutional Neural Networks (CNN) is a deep - structured feed - forward neural network architecture, which consists of multiple convolutional layers, pooling layers, fully - connected layers, etc. The convolutional structure can reduce the memory occupied by the deep network. The network structure with multiple hidden layers has excellent feature - learning ability and can better reflect the essential features of the data. The weights of the convolutional kernels are learned through the training process and remain constant during the convolution operation. The convolutional neural network model simplifies the complexity of the network model by simulating certain aspects of the biological neural network through the structural feature of parameter sharing, promotes the optimization process of the network, and effectively reduces the risk of overfitting.

[0071] The structure of the convolutional neural network model is as Figure 2 shown. It contains 3 convolutional layers, the fully - connected layer has 512 neurons. Since the input data volume is not too large, the pooling layer is not used, and the output layer uses the Softmax activation function and the Adam optimizer. In the training stage, the training data is input into the neural network, and the weights of the neural network are updated according to the loss function. The update will be repeated multiple times until the loss reaches the specified threshold; once the CNN training is completed, it establishes the desired input / output mapping relationship. Table 1 below gives the specific relevant parameters of the convolutional neural network:

[0072] Table 1 Convolutional Neural Network Parameters

[0073]

[0074] In order to better train the neural network and prevent overfitting, two training techniques can be used: (1) Dropout: During the forward propagation process, the activation values ​​of some neurons are randomly stopped with a certain probability. This can reduce the interaction between feature detectors (hidden layer nodes). Detector interaction means that some detectors rely on other detectors to work, thereby enhancing the generalization ability of the model. (2) Batch Normalization (BN): Through normalization, ensure that each hidden layer input is adjusted to a standard normal distribution with a mean of 0 and a variance of 1. This can make the input value of the activation function fall in the area where its gradient is sensitive to change, effectively prevent the occurrence of gradient vanishing, and significantly improve training efficiency. In addition, the scaling factor of BN can effectively identify neurons that do not contribute much to the network, and automatically weaken or eliminate some neurons after the activation function, thereby improving the generalization ability of the model.

[0075] Example 2

[0076] For the generation of the data set, an ideal channel condition is considered, that is, there is no channel fading, multipath, and no other interference except white noise. A digital signal source is used. Since this embodiment only estimates the signal source DOA, it is assumed that the auxiliary polarization angle and polarization phase difference are non-zero constants, such as γ = 45° and η = 90°. The azimuth and elevation angles are randomly generated within the range, and each angle is sampled 500 times. Use MATLAB to generate a 8.16×10 5 The dataset is divided into training and test datasets in a ratio of 8:2, and a 3-layer convolutional feedforward convolutional neural network is built based on the Tensorflow framework. The mean square error (MAE) and root mean square error (RMSE) are used as the main indicators of estimation error:

[0077]

[0078] Where N T is the total number of instances in the test set, θ est and φ est are the estimated values ​​of azimuth and elevation angles, θ ac t and φ ac t is the actual value.

[0079] Figure 3 This is the error analysis of the DOA estimation results of the convolutional neural network model when the number of snapshots is in the range of [50,500] and the signal-to-noise ratio SNR = 10dB. From the results, it can be seen that the convolutional neural network model constructed by this method has achieved a good inverse mapping from the covariance matrix to DOA. The estimation errors for both the pitch angle and the azimuth angle are generally in a small range (for example, 1 0), even when the number of snapshots is very small (such as 50), the DOA estimation result is close to the true value. The results also show that the number of snapshots does not have a significant impact on the deep learning DOA estimation, which is different from the traditional DOA estimation method. Figure 3 It also shows that the estimated result of the pitch angle is slightly better than the estimated result of the azimuth angle, but the difference between the two is not large. Analysis may be due to the more intensive sampling of the pitch angle.

[0080] Figure 4 The relationship curve of the DOA estimation result of the convolutional neural network model with the change of the signal-to-noise ratio is given when the number of snapshots is 500. It can be seen that with the increase of the signal-to-noise ratio, the DOA estimation error of the convolutional neural network model gradually decreases and the estimation accuracy gradually improves. When the signal-to-noise ratio is greater than 2dB, the estimation performance of the convolutional neural network model gradually stabilizes, and even if the signal-to-noise ratio is further increased, the DOA estimation accuracy will not be significantly improved.

[0081] As shown in Table 2 below, when the number of snapshots is 400 and the signal-to-noise ratio is SNR=10dB, the comparison between the true values ​​of any 13 DOAs in the test set and the CNN estimated values ​​is shown.

[0082] Table 2 Comparison between actual and predicted DOA values

[0083]

[0084] It can be seen from the table that the estimated value of the convolutional neural network model is very close to the true value, and its maximum absolute error does not exceed 1°, which shows the effectiveness of the constructed convolutional neural network for DOA estimation.

[0085] To further verify the effectiveness of this method, classical machine learning methods (such as support vector machine SVM, decision tree DT, etc.) were used to study DOA estimation under the same training set and test set conditions. At the same time, the traditional array signal processing ESPRIT algorithm was also used for simulation research. Figure 5 , 6 The curves of the estimation errors of the azimuth angle with the number of snapshots and the signal-to-noise ratio are given respectively. Figure 7 , 8 The following are the curves of the pitch angle estimation errors of the four methods with the number of snapshots and signal-to-noise ratio. The results show that under the same parameter conditions, the three machine learning algorithms are better than the traditional array signal processing ESPRIT algorithm, which confirms the effectiveness of applying machine learning methods to the DOA estimation problem of electromagnetic vector sensors. In addition, the CNN model used has more obvious advantages, and still has stable performance under low snapshot numbers and low signal-to-noise ratios. The error accuracy is significantly lower than other methods, and it has stronger robustness.

[0086] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A 2D-DOA estimation method for electromagnetic vector sensors based on convolutional neural networks, characterized by: The following steps are involved: S1. Using an electromagnetic vector sensor to receive an incident signal from a spatial signal source, the incident signal hits the electromagnetic vector sensor to generate a receiving signal, and the receiving signal is pre-processed; S2, extract the eigenvectors of the upper triangular part from the covariance matrix, because this part contains sufficient information about the direction of the incident signal and eliminates redundant or irrelevant information; S3, normalizing the eigenvectors extracted in step S2 using Min-Max scaling, separating the real and imaginary parts of the covariance matrix and composing them into a directional image; S4, constructing a convolutional neural network model including several convolutional layers and fully connected layers, taking the orientation image obtained in step S3 as input data, and training the convolutional neural network model until the loss function reaches a predetermined threshold; S5. Use the trained convolutional neural network model to perform 2D-DOA estimation on the new electromagnetic wave signal data, and output the azimuth and elevation angle estimation results of the spatial signal source.

2. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 1 is characterized by: In step S1, the spatial signal source transmits an incident signal of unit power, which is incident on the electromagnetic vector sensor. In the spherical coordinates, the electric field vector e k and the magnetic field vector h k It is expressed as: Where k = 1, 2, ... K is the number of information sources, j is an imaginary unit, 0 ≤ γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, Z0 is a real number, representing the inherent impedance of the transmission medium, represents the unit vector along the azimuth direction, represents the unit vector along the pitch angle direction; For linearly polarized transverse electromagnetic waves, we have: k =0; for circularly polarized waves: γ k =45°、η k = +90°, "+" indicates left circular polarization, "-" indicates circular polarization, after normalization, the electric field vector e k and the magnetic field vector h k Expressed in Cartesian coordinates: Where k = 1, 2, ... K is the number of sources, j is an imaginary unit, and the pitch angle range is 0 ≤ θ k <π, the azimuth range is 0≤φ k <2π,0≤γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, Z0 is a real number, representing the inherent impedance of the transmission medium, represents the unit vector along the X-axis direction, represents the unit vector along the Y coordinate axis, Represents a unit vector along the Z axis.

3. The 2D-DOA estimation method of the electromagnetic vector sensor based on the convolutional neural network according to claim 1 is characterized by: The formula for the incident signal is: where x k (t) is the incident signal, j is the imaginary unit, t is the time function, and the kth signal s k (t) is given by a frequency f k The complex carrier modulation and a uniformly distributed phase offset ψ k composition.

4. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 1 is characterized by: The received signal is a six-element column vector containing the electric and magnetic field measurements from the electromagnetic vector sensor element. The formula for the received signal is: Where (t) represents the received signal, k = 1, 2, ... K is the number of signal sources, and the pitch angle range is 0 ≤ θ k <π, the azimuth range is 0≤φ k <2π,0≤γ k <π / 2 is the auxiliary polarization angle, -π≤η k <π is the polarization phase difference, y e (t) represents the electric field component of the received signal, y h (t) represents the magnetic field component of the received signal, n(t) is the spatial Gaussian white noise vector of each antenna element, and n e (t) represents the electric field component of the noise, n h (t) represents the magnetic field component of the noise.

5. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 1 is characterized by: The data y(t) received by the electromagnetic vector sensor is first compressed and converted into data that can be used by the neural network. The covariance matrix of the signal suppresses additive Gaussian white noise. The longer the snapshot number, the more accurate the covariance matrix. The covariance matrix is ​​defined as: Where R represents the covariance matrix of the received signal, y represents the received signal, a is the array manifold of the received signal, x represents the incident signal, n represents the noise, H represents the complex conjugate transpose, δ and δ s is the noise level, I is the unit vector, aa H It is the only data feature that can determine DOA.

6. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 1 is characterized by: Preprocessing refers to linear algebra calculations of matrix-matrix and matrix-vector multiplications.

7. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 5 is characterized by: The real and imaginary parts of the covariance matrix are separated and combined into a directional image as input data, and the covariance matrix is ​​converted into a directional image, which specifically includes the following steps: A1, R ij is the element in the i-th column and j-th row of the covariance matrix R, and M is the number of array receiving units; A2. Combine the real part Re(R ij (where i < j)) and the imaginary part Im(R ij ) into a single vector; ij ) A3. Normalize the vector r using Min-Max scaling: A4. Normalize the vector r norm Restore to a (M+1)×M matrix and regard the (M+1)×M matrix as a direction image; A5. The input / output pair of the convolutional neural network model for training is {r norm , (θ, φ)}.

8. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 1 is characterized in that: In the training phase in step S4, the training data is input into the convolutional neural network model, and the neural network weights are updated according to the loss function. The update is repeated several times until the loss reaches a specified threshold. When the convolutional neural network model training is completed, the desired input / output mapping relationship is established.

9. The 2D-DOA estimation method of electromagnetic vector sensor based on convolutional neural network according to claim 1 is characterized by: The convolutional neural network model contains 3 convolutional layers, the fully connected layer has 512 neurons, no pooling layer is used, and the output layer uses the Softmax activation function and Adam optimizer.

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