CN115015912A - Rotating target space angle estimation method based on vortex electromagnetic waves - Google Patents

Abstract

The invention relates to a method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves, comprising: acquiring echo signals to be measured; extracting characteristic values of the echo signals to be measured; inputting the characteristic values into a trained neural network to obtain echo signals to be measured Off-axis angle estimates of the wave signal; where the neural network is trained based on the training dataset and the off-axis angle labels for each training sample. The method for estimating the spatial angle of a rotating target based on the vortex electromagnetic wave of the present invention can provide more features of the rotating target, and combine the neural network to analyze the law of the echo spectrum under different off-axis angles to predict the off-axis angle. The method can get rid of the complex formula derivation problem of traditional parameter estimation, and finally achieve a more accurate estimation of the angle by using the method of machine learning, which also provides a reference for the estimation of radar target parameters based on orbital angular momentum.

Description

A Method for Estimating Spatial Angle of Rotating Target Based on Vortex Electromagnetic Waves

technical field

The invention belongs to the technical field of radar detection, and in particular relates to a method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves.

Background technique

According to classical electrodynamics, the far-field radiation of electromagnetic waves is not only energy transfer, but also carries angular momentum characteristics. Angular momentum can be divided into spin angular momentum and orbital angular momentum. Spin angular momentum corresponds to the polarization of the electromagnetic field, and orbital angular momentum is linked to changes in the phase wavefront. The orbital angular momentum describes the orbital characteristics of the electromagnetic field rotating around the propagation axis. The rotation phase factor e ^iαφ is superimposed on the basis of the plane wave, where α is the modal number, which represents the magnitude of the orbital angular momentum, and φ is the azimuth angle around the propagation axis. . It is obvious that the modal combination for which α is an integer is orthogonal in φ∈[0,2π]. Therefore, orbital angular momentum can be used as an independent signal measurement dimension.

For plane waves, the Doppler effect occurs only when the target moves radially to the radar. For vortex waves, even the motion of the target in the azimuth dimension will also produce the Doppler effect, which is completely independent of the radial Doppler, which provides the possibility for more detailed parameter estimation of the rotating target.

The off-axis angle of the rotating target is an important target feature, and accurate positioning of the rotating target can be achieved through this parameter, so it is very necessary to estimate this parameter in the process of detecting the rotating target. However, there are complex mathematical formula derivation and calculation problems with traditional parameter estimation methods, which make it very difficult to estimate off-axis angle parameters.

SUMMARY OF THE INVENTION

In order to solve the above problems in the prior art, the present invention provides a method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves. The technical problem to be solved by the present invention is realized by the following technical solutions:

The present invention provides a method for estimating the space angle of a rotating target based on vortex electromagnetic waves, including:

Obtain the echo signal to be measured;

extracting the characteristic value of the echo signal to be measured;

Inputting the eigenvalues into the trained neural network to obtain the off-axis angle estimation value of the echo signal to be measured; wherein,

The neural network is obtained by training based on the training data set and the off-axis angle labels of each training sample.

In an embodiment of the present invention, the characteristic value is a modulus value or real imaginary part data of spectral data corresponding to the echo signal to be measured.

In an embodiment of the present invention, extracting the characteristic value of the echo signal to be measured includes:

Establish a mathematical model based on vortex electromagnetic wave rotating target detection;

According to the mathematical model, the expression of the echo signal to be measured under the mathematical model is obtained;

According to the expression under the mathematical model of the echo signal to be measured, perform fast Fourier transform on it to obtain corresponding spectral data;

According to the spectrum data, the characteristic value of the echo signal to be measured is extracted and obtained.

In an embodiment of the present invention, the mathematical model based on vortex electromagnetic wave rotating target detection includes:

A circular array composed of N identical array elements arranged at equal intervals is used as a transmitting antenna, wherein the radius of the circular array is a, and the receiving antenna is located at the center of the circle O;

A radar coordinate system OXYZ is established with the center O of the circular array as the origin;

The rotation center O' of the rotating target is located on the XOZ plane, and the coordinates of the rotation center O' in the radar coordinate system are (x, 0, z), where the rotation radius is r, the rotation speed is Ω, the rotation center O' and the radar coordinates The angle between the connecting line of the system and the positive direction of the Z axis is the off-axis angle θ, and the length from the center of rotation O' to the origin of the radar coordinate system is L;

A local coordinate system O'X'Y'Z' of the rotation target is established with the rotation center O' as the origin, wherein the coordinates of the rotation target P in the local coordinate system are (x', y', z').

In an embodiment of the present invention, according to the mathematical model, the expression of the echo signal to be measured under the mathematical model is obtained, including:

则所述局部坐标系下的坐标转换到所述雷达坐标系下的坐标表达式为：Let the Euler angle between the radar coordinate system and the local coordinate system be

Then the coordinate expression from the coordinates in the local coordinate system to the radar coordinate system is:

(X, Y, Z) ^T = R(x', y', z') ^T +(x, 0, z) ^T ;

In the formula, (x, 0, z) is the coordinate of the rotation center O' in the radar coordinate system, (x', y', z') is the coordinate of the rotating target P in the local coordinate system at any time, and R is transformation matrix, where,

(x, 0, z) = (Lsinθ, 0, Lcosθ);

(x', y', z') = (rcosΩt, rsinΩt, 0);

Then, the coordinates of the rotating target P in the radar coordinate system at any time are:

(X(t), Y(t), Z(t)) ^T = R(rcosΩt, rsinΩt, 0) ^T +(Lsinθ, 0, Lcosθ) ^T ;

The coordinates of the rotating target P in the radar coordinate system are expressed in spherical coordinates as:

According to the spherical coordinate expression, the expression of the echo signal to be measured under the mathematical model is obtained as:

where σ is the scattering coefficient, N is the number of array elements, f _c is the signal carrier frequency, k is the wave number, l is the number of modes, a is the radius of the circular array, t is the slow time, and J _l is the Bessel function, i is a complex number symbol.

In an embodiment of the present invention, the training method of the neural network includes:

S1: Generate training data set;

S2: Build a neural network;

S3: Use the training data set to train the neural network to obtain a trained neural network.

In an embodiment of the present invention, the S1 includes:

Obtain echo signals corresponding to different off-axis angles and rotation angles;

Extract the eigenvalues of each group of echo signals as training samples;

A corresponding off-axis angle label is added to each of the training samples to obtain the training data set.

In an embodiment of the present invention, the neural network includes an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer connected in sequence, wherein,

The input layer is used to input the eigenvalues of the echo signal;

The output layer is used to output the off-axis angle prediction value of the echo signal;

The activation functions of the first hidden layer, the second hidden layer and the third hidden layer are sigmoid functions.

Compared with the prior art, the beneficial effects of the present invention are:

The method for estimating the spatial angle of a rotating target based on the vortex electromagnetic wave of the present invention can provide more features of the rotating target, and combine the neural network to analyze the law of the echo spectrum under different off-axis angles to predict the off-axis angle. The method can get rid of the complex formula derivation problem of traditional parameter estimation, and finally achieve a more accurate estimation of the angle by using the method of machine learning, which also provides a reference for the estimation of radar target parameters based on orbital angular momentum.

The above description is only an overview of the technical solutions of the present invention, in order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand , the following specific preferred embodiments, and in conjunction with the accompanying drawings, are described in detail as follows.

Description of drawings

1 is a schematic diagram of a method for estimating a space angle of a rotating target based on a vortex electromagnetic wave provided by an embodiment of the present invention;

2 is a schematic diagram of a mathematical model for detecting a rotating target based on a vortex electromagnetic wave provided by an embodiment of the present invention;

Fig. 3a is the amplitude value of the frequency spectrum under different angles provided by the embodiment of the present invention;

Fig. 3b is the real and imaginary part of the frequency spectrum under different angles provided by the embodiment of the present invention;

4 is a schematic structural diagram of a neural network provided by an embodiment of the present invention;

5a is a loss function curve when the real and imaginary parts of the spectral data provided by the embodiment of the present invention are used as a data set;

5b is a loss function curve when the modulus value of the spectral data provided by the embodiment of the present invention is used as a data set;

6a is a prediction error diagram when the real and imaginary parts of the spectral data provided by the embodiment of the present invention are used as a data set;

6b is a prediction error diagram when the modulus value of the spectral data provided by the embodiment of the present invention is used as a data set;

Fig. 7a is the relation curve between the threshold value and the accuracy rate when the real and imaginary parts of the spectral data provided by the embodiment of the present invention are used as the data set;

FIG. 7b is a relationship curve between the threshold value and the accuracy rate when the modulus value of the spectral data provided by the embodiment of the present invention is used as the data set.

Detailed ways

In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, a method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves proposed by the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

The foregoing and other technical contents, features and effects of the present invention can be clearly presented in the following detailed description of the specific implementation with the accompanying drawings. Through the description of the specific embodiments, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the accompanying drawings are only for reference and description, and are not used for the technical description of the present invention. program is restricted.

Example 1

Please refer to FIG. 1. FIG. 1 is a schematic diagram of a method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave provided by an embodiment of the present invention. As shown in the figure, the method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave in this embodiment ,include:

Step 1: Obtain the echo signal to be measured;

Step 2: Extract the eigenvalues of the echo signal to be measured;

In this embodiment, the characteristic value is the modulus value or real and imaginary part data of the spectral data corresponding to the echo signal to be measured.

Step 3: Input the feature value into the trained neural network to obtain the off-axis angle estimation value of the echo signal to be measured; wherein, the neural network is obtained by training based on the training data set and the off-axis angle label of each training sample.

It should be noted that, in this embodiment, if the neural network is obtained by training based on the training samples of the modulo value of the spectral data corresponding to the echo signal, the modulo value of the spectral data corresponding to the echo signal to be measured is extracted as the eigenvalue, and input The trained neural network realizes the estimation of off-axis angle. If the neural network is trained based on the training samples of the real and imaginary data of the spectral data corresponding to the echo signal, extract the real and imaginary data of the spectral data corresponding to the echo signal to be measured as the eigenvalue, and input the trained neural network to realize Estimated off-axis angle.

Further, step 2 includes:

Step 2.1: Establish a mathematical model based on vortex electromagnetic wave rotating target detection;

Please refer to FIG. 2 , which is a schematic diagram of a mathematical model for detecting a rotating target based on a vortex electromagnetic wave provided by an embodiment of the present invention; as shown in the figure, in this implementation, the mathematical model for detecting a rotating target based on a vortex electromagnetic wave includes: A circular array composed of N identical array elements arranged at equal intervals is used as a transmitting antenna, wherein the radius of the circular array is a, and the receiving antenna is located at the center O; the radar coordinate system OXYZ is established with the center O of the circular array as the origin; The rotation center O' of the rotating target is located on the XOZ plane, and the coordinates of the rotation center O' in the radar coordinate system are (x, 0, z), where the rotation radius is r, the rotation speed is Ω, the rotation center O' and the radar coordinates The angle between the connection line of the system and the positive direction of the Z axis is the off-axis angle θ, and the length from the center of rotation O' to the origin of the radar coordinate system is L; the local coordinate system O'X of the rotating target is established with the center of rotation O' as the origin 'Y'Z', wherein the coordinates of the rotation target P in the local coordinate system are (x', y', z').

Step 2.2: According to the mathematical model, obtain the expression of the echo signal to be measured under the mathematical model;

Specifically, including:

则局部坐标系下的坐标转换到雷达坐标系下的坐标表达式为：Let the Euler angle between the radar coordinate system and the local coordinate system be

Then the coordinate expression in the local coordinate system converted to the radar coordinate system is:

(X, Y, Z) ^T = R(x', y', z') ^T + (x, 0, z) ^T (1);

In the formula, (x, 0, z) is the coordinate of the rotation center O' in the radar coordinate system, (x', y', z') is the coordinate of the rotating target P in the local coordinate system at any time, and R is transformation matrix, where,

(x, 0, z) = (Lsinθ, 0, Lcosθ) (2);

(x', y', z') = (rcosΩt, rsinΩt, 0) (4);

Then, according to formulas (1)-(4), the coordinates of the rotating target P in the radar coordinate system at any time are:

(X(t), Y(t), Z(t)) ^T = R(rcosΩt, rsinΩt, 0) ^T + (Lsinθ, 0, Lcosθ) ^T (5);

The coordinates of the rotating target P in the radar coordinate system are expressed in spherical coordinates as:

According to the spherical coordinate expression, the expression of the echo signal to be measured under the mathematical model is obtained as:

where σ is the scattering coefficient, N is the number of array elements, f _c is the signal carrier frequency, k is the wave number, l is the number of modes, a is the radius of the circular array, t is the slow time, and J _l is the Bessel function, i is a complex number symbol.

Step 2.3: According to the expression under the mathematical model of the echo signal to be measured, perform fast Fourier transform on it to obtain corresponding spectral data;

Step 2.4: According to the spectrum data, extract the characteristic value of the echo signal to be measured.

Further, through simulation, it can be found that the Doppler frequency (radial micro-Doppler + rotational Doppler) exhibits regularity with the change of the off-axis angle. Please refer to FIG. 3a and FIG. 3b in combination. FIG. 3a is the amplitude of the spectrum at different angles provided by the embodiment of the present invention; FIG. 3b is the real and imaginary parts of the spectrum at different angles provided by the embodiment of the present invention. It can be seen from the figure that as the angle increases, the spectral width gradually becomes larger, and the amplitude gradually becomes smaller. Therefore, in this embodiment, the neural network is used to learn the above-mentioned characteristic law to predict the off-axis angle.

In this embodiment, the training method of the neural network includes:

S1: Generate training data set;

Specifically, S1 includes:

S11: Obtain echo signals corresponding to different off-axis angles and rotation angles;

In this embodiment, 100,000 angles are randomly selected from the off-axis angle and the rotation angle from 0° to 10° to obtain corresponding 100,000 sets of echo signal data.

S12: Extract the eigenvalues of each group of echo signals as training samples;

The specific extraction method of the eigenvalue is similar to the above-mentioned extraction method of the eigenvalue of the echo signal to be measured, and will not be repeated here.

It should be noted that the modulus values of the spectral data corresponding to each group of echo signals are stored in the same .csv file, and the real and imaginary data of the spectral data corresponding to each group of echo signals are stored in the same .csv file. . Store the off-axis angle corresponding to each group of echo signals in another .csv file.

S13: Add a corresponding off-axis angle label to each training sample to obtain a training data set.

It should be noted that the .csv file storing the modulus value and the .csv file storing the off-axis angle form a training data set, and the .csv file storing the real and imaginary part data and the .csv file storing the off-axis angle form another training data set set. The above two training data sets can be used to train the neural network respectively, and the two trained neural networks can be obtained, so as to realize the estimation of the off-axis angle. When the above two types of trained neural networks are used for prediction and estimation of off-axis angle, their inputs are correspondingly the modulus value of the spectral data corresponding to the echo signal to be measured, and the real and imaginary data of the spectral data corresponding to the echo signal to be measured.

S2: Build a neural network;

Please refer to FIG. 4. FIG. 4 is a schematic structural diagram of a neural network provided by an embodiment of the present invention. As shown in the figure, the neural network of this embodiment includes an input layer, a first hidden layer, a second hidden layer, and a third Hidden layer and output layer, where the input layer is used to input the eigenvalues of the echo signal; the output layer is used to output the off-axis angle prediction value of the echo signal; since the final problem is to predict the angle, the applied neural network It is aimed at the regression problem. At this time, the activation function is not set for the output layer, and the activation functions of the first hidden layer, the second hidden layer and the third hidden layer are sigmoid functions.

Optionally, the optimizer adopts Adam optimizer or SGD optimizer.

Optionally, the loss function (also known as the objective function) adopts a mean square error loss function, a logarithmic loss function or a multi-class logarithmic loss function, or the like.

Since the Adam optimizer converges faster than the SGD optimizer, in this embodiment, the Adam optimizer is chosen and the learning rate is set to 0.0001. The mean squared error loss function is chosen as the loss function of the neural network.

S3: Use the training data set to train the neural network to obtain the trained neural network.

Specifically, first randomly initialize the neural network parameters, then input the training data set into the initialized neural network in batches, use the mean square error loss function to calculate the current training error, and use the ADAM optimizer to update the network parameters until the network converges, End the training and get the trained neural network.

The method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave in this embodiment can provide more features of the rotating target, and combine the neural network to analyze the law of the echo spectrum under different off-axis angles to predict the off-axis angle. The method of this example can get rid of the complex formula derivation problem of traditional parameter estimation, and finally achieve a more accurate estimation of the angle by using the method of machine learning, which also provides a reference for the estimation of radar target parameters based on orbital angular momentum.

Embodiment 2

This embodiment describes the effect of the method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave in the first embodiment through a simulation experiment.

This embodiment provides simulation experiments under the conditions of two training data sets and two test data. The first case is to use the real and imaginary data of the spectral data as the training data set for neural network training, and the corresponding test data set is the real and imaginary data of the spectral data corresponding to the echo signal; the second case is to use the spectral data The modulo value of the echo signal is used as the training data set for neural network training, and the corresponding test data set is the modulo value of the spectral data corresponding to the echo signal.

In the process of training the neural network, the loss curves in two cases are obtained, please refer to Fig. 5a and Fig. 5b, Fig. 5a is the loss function curve when the real part and imaginary part of the spectral data provided by the embodiment of the present invention is used as the data set; Fig. 5b is the loss function curve when the modulus value of the spectral data provided by the embodiment of the present invention is used as the data set. As can be seen from the figure, when the training round is 40 times, the loss function value of the training data set in the first case can reach 0.00045, and the loss function value of the test data set can reach 0.0009. In the second case, the loss function value of the training data set can reach 0.00069, and the loss function value of the test data set can reach 0.0063.

10,000 groups of test sets are used for testing, and the difference curves between the obtained predicted values and the real values are shown in Figure 6a and Figure 6b. Figure 6a is the prediction error when the real part and imaginary part of the spectral data provided by the embodiment of the present invention are used as the data set. Fig. 6b is a prediction error diagram when the modulus value of the spectral data provided by the embodiment of the present invention is used as a data set. As can be seen from the figure, the prediction error in the first case is below 0.1 degrees, and the prediction error in the second case is only below 0.2 degrees.

Setting the corresponding threshold difference within the threshold is equivalent to correct prediction, and the relationship between the threshold and the accuracy is obtained as shown in Figure 7a and Figure 7b, Figure 7a is the real part and imaginary part of the spectral data provided by the embodiment of the present invention. The relationship curve between the threshold value and the accuracy rate when set; FIG. 7b is the relationship curve between the threshold value and the accuracy rate when the modulus value of the spectrum data provided by the embodiment of the present invention is used as the data set. It can be seen from the figure that in the first case, when the threshold is 0.05, the accuracy rate has reached more than 90%, while in the second case, the accuracy rate only reaches more than 90% when the threshold is 0.15.

It should be noted that, herein, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any relationship between these entities or operations. any such actual relationship or sequence exists. Moreover, the terms "comprising", "comprising" or any other variation are intended to encompass a non-exclusive inclusion such that an article or device comprising a list of elements includes not only those elements, but also other elements not expressly listed. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the article or device that includes the element. Words like "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be considered that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field of the present invention, without departing from the concept of the present invention, some simple deductions or substitutions can be made, which should be regarded as belonging to the protection scope of the present invention.

Claims (8)

1. a rotation target space angle estimation method based on vortex electromagnetic wave, is characterized in that, comprises: Obtain the echo signal to be measured; extracting the characteristic value of the echo signal to be measured; Inputting the eigenvalues into the trained neural network to obtain the off-axis angle estimation value of the echo signal to be measured; wherein, The neural network is obtained by training based on the training data set and the off-axis angle labels of each training sample. 2 . The method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave according to claim 1 , wherein the eigenvalue is the modulus value or the real and imaginary part data of the spectral data corresponding to the echo signal to be measured. 3 . 3. The method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave according to claim 1, wherein extracting the eigenvalue of the echo signal to be measured comprises: Establish a mathematical model based on vortex electromagnetic wave rotating target detection; According to the mathematical model, the expression of the echo signal to be measured under the mathematical model is obtained; According to the expression under the mathematical model of the echo signal to be measured, perform fast Fourier transform on it to obtain corresponding spectral data; According to the spectrum data, the characteristic value of the echo signal to be measured is extracted and obtained. 4. The method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave according to claim 3, wherein the mathematical model for detecting a rotating target based on a vortex electromagnetic wave comprises: A circular array composed of N identical array elements arranged at equal intervals is used as a transmitting antenna, wherein the radius of the circular array is a, and the receiving antenna is located at the center of the circle O; A radar coordinate system OXYZ is established with the center O of the circular array as the origin; The rotation center O' of the rotating target is located on the XOZ plane, and the coordinates of the rotation center O' in the radar coordinate system are (x, 0, z), where the rotation radius is r, the rotation speed is Ω, and the rotation center O' is related to the radar coordinates The angle between the connecting line of the system and the positive direction of the Z axis is the off-axis angle θ, and the length from the center of rotation O' to the origin of the radar coordinate system is L; A local coordinate system O'X'Y'Z' of the rotation target is established with the rotation center O' as the origin, wherein the coordinates of the rotation target P in the local coordinate system are (x', y', z'). 5. The method for estimating the space angle of a rotating target based on a vortex electromagnetic wave according to claim 4, wherein, according to the mathematical model, the expression of the echo signal to be measured under the mathematical model is obtained, including : Let the Euler angle between the radar coordinate system and the local coordinate system be

Then the coordinate expression from the coordinates in the local coordinate system to the radar coordinate system is: (X, Y, Z) ^T = R(x', y', z') ^T +(x, 0, z) ^T ; In the formula, (x, 0, z) are the coordinates of the rotation center O' in the radar coordinate system, (x', y', z') are the coordinates of the rotating target P in the local coordinate system at any time, and R is transformation matrix, where, (x,0,z)=(Lsinθ,0,Lcosθ);

(x', y', z')=(rcosΩt,rsinΩt,0); Then, the coordinates of the rotating target P in the radar coordinate system at any time are: (X(t), Y(t), Z(t)) ^T =R(rcosΩt,rsinΩt,0) ^T +(Lsinθ,0,Lcosθ) ^T ; The coordinates of the rotating target P in the radar coordinate system are expressed in spherical coordinates as:

According to the spherical coordinate expression, the expression of the echo signal to be measured under the mathematical model is obtained as:

where σ is the scattering coefficient, N is the number of array elements, f _c is the signal carrier frequency, k is the wave number, l is the number of modes, a is the radius of the circular array, t is the slow time, and J _l is the Bessel function, i is a complex number symbol. 6. The method for estimating the space angle of a rotating target based on a vortex electromagnetic wave according to claim 1, wherein the training method of the neural network comprises: S1: Generate training data set; S2: Build a neural network; S3: Use the training data set to train the neural network to obtain a trained neural network. 7. The method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave according to claim 6, wherein the S1 comprises: Obtain echo signals corresponding to different off-axis angles and rotation angles; Extract the eigenvalues of each group of echo signals as training samples; A corresponding off-axis angle label is added to each of the training samples to obtain the training data set. 8. The method for estimating the spatial angle of a rotating target based on a vortex electromagnetic wave according to claim 6, wherein the neural network comprises an input layer, a first hidden layer, a second hidden layer, and a third hidden layer which are connected in sequence and the output layer, where, The input layer is used to input the eigenvalues of the echo signal; The output layer is used to output the off-axis angle prediction value of the echo signal; The activation functions of the first hidden layer, the second hidden layer and the third hidden layer are sigmoid functions.

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