CN115015912B - Vortex electromagnetic wave-based rotation target space angle estimation method - Google Patents

Abstract

The present invention relates to a method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves, comprising: obtaining an echo signal to be measured; extracting a characteristic value of the echo signal to be measured; inputting the characteristic value into a trained neural network to obtain an estimated value of the off-axis angle of the echo signal to be measured; wherein the neural network is trained based on a training data set and an off-axis angle label of each training sample. The method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves of the present invention can provide more features of rotating targets, and can predict the off-axis angle by combining a neural network to analyze the laws of echo spectra under different off-axis angles. The method of the present invention 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 a machine learning method, and also provides a reference for the estimation of radar target parameters based on orbital angular momentum.

Description

A method for estimating the spatial angle of a 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 transmission, 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 related to the change of the phase wave front. Orbital angular momentum describes the orbital characteristics of the electromagnetic field rotating around the propagation axis. On the basis of the plane wave, a rotation phase factor e ^iαφ is superimposed, where α is the mode number, which characterizes the magnitude of the orbital angular momentum, and φ is the azimuth angle around the propagation axis. It is obvious that the mode combination with an integer α is orthogonal within 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 relative to the radar. For vortex waves, the Doppler effect occurs even when the target moves in the azimuth dimension, and is completely independent of the radial Doppler, which makes it possible to estimate the parameters of rotating targets in more detail.

The off-axis angle of a rotating target is an important target feature. This parameter can be used to accurately locate the rotating target. Therefore, it is very necessary to estimate this parameter in the process of rotating target detection. However, the traditional parameter estimation method has complex mathematical formula derivation and calculation problems, which makes it very difficult to estimate the off-axis angle parameter.

Summary of the invention

In order to solve the above problems existing 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 achieved by the following technical solutions:

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

Acquire the echo signal to be measured;

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

The characteristic value is input 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 trained based on a training data set and an off-axis angle label of each training sample.

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

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

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

According to the mathematical model, an 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, a fast Fourier transform is performed on it to obtain corresponding spectrum data;

The characteristic value of the echo signal to be measured is extracted according to the frequency spectrum data.

In one embodiment of the present invention, the mathematical model for detecting rotating targets based on vortex electromagnetic waves includes:

A circular array consisting of N equally spaced identical array elements is used as the transmitting antenna, where the radius of the circular array is a and the receiving antenna is located at the center O;

Establishing a radar coordinate system OXYZ 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. 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 angle between the line connecting the rotation center O’ and the radar coordinate system and the positive direction of the Z axis is the eccentric angle θ, and the length from the rotation center O’ to the origin of the radar coordinate system is L;

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

In one embodiment of the present invention, according to the mathematical model, obtaining an expression of the echo signal to be measured under the mathematical model includes:

Assume that the Euler angle between the radar coordinate system and the local coordinate system is The coordinate expression for converting 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 ;

Where (x, 0, z) is the coordinate of the rotating 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 the 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 follows:

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

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 mode number, a is the radius of the circular array, t is the slow time, J _l is the Bessel function, and i is the complex number symbol.

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

S1: Generate training dataset;

S2: Build a neural network;

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

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

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

Extract the characteristic values 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 one embodiment of the present invention, the neural network comprises 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 characteristic value 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 present invention has the following beneficial effects:

The rotating target spatial angle estimation method based on vortex electromagnetic waves of the present invention can provide more features of rotating targets, and combine neural network analysis to analyze the laws of echo spectra under different off-axis angles to predict the off-axis angle. The method of the present invention 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 machine learning methods, which also provides a reference for radar target parameter estimation based on orbital angular momentum.

The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following specifically cites a preferred embodiment and describes it in detail with the accompanying drawings as follows.

BRIEF DESCRIPTION OF THE DRAWINGS

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

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

FIG3a is a diagram showing the amplitude of a spectrum at different angles provided by an embodiment of the present invention;

FIG3b is the real and imaginary parts of the spectrum at different angles provided by an embodiment of the present invention;

FIG4 is a schematic diagram of a neural network structure provided by an embodiment of the present invention;

FIG5a is a loss function curve when the real and imaginary parts of the spectrum data provided by an embodiment of the present invention are used as a data set;

FIG5b is a loss function curve when the modulus of the spectrum data provided by an embodiment of the present invention is used as a data set;

FIG6a is a prediction error diagram when the real and imaginary parts of the spectrum data provided by an embodiment of the present invention are used as a data set;

FIG6b is a prediction error diagram when the modulus of the spectrum data provided by an embodiment of the present invention is used as a data set;

FIG7a is a curve showing the relationship between the threshold and the accuracy rate when the real and imaginary parts of the spectrum data provided by an embodiment of the present invention are used as a data set;

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

Detailed ways

In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, a rotating target space angle estimation method based on vortex electromagnetic waves proposed by the present invention is described in detail below in combination with the accompanying drawings and specific implementation methods.

The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

Embodiment 1

Please refer to FIG. 1 , which is a schematic diagram of a rotating target space angle estimation method based on vortex electromagnetic waves provided by an embodiment of the present invention. As shown in the figure, the rotating target space angle estimation method based on vortex electromagnetic waves of this embodiment includes:

Step 1: Obtain the echo signal to be measured;

Step 2: Extract the characteristic value 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 frequency spectrum data corresponding to the echo signal to be measured.

Step 3: Input the characteristic 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 trained 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 trained based on the training samples of the modulus value of the spectrum data corresponding to the echo signal, the modulus value of the spectrum data corresponding to the echo signal to be measured is extracted as the characteristic value, and the trained neural network is input to realize the estimation of the off-axis angle. If the neural network is trained based on the training samples of the real and imaginary part data of the spectrum data corresponding to the echo signal, the real and imaginary part data of the spectrum data corresponding to the echo signal to be measured is extracted as the characteristic value, and the trained neural network is input to realize the estimation of the off-axis angle.

Furthermore, step 2 includes:

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

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

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

Specifically, it includes:

Assume the Euler angle between the radar coordinate system and the local coordinate system is The coordinate expression of 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);

Where (x, 0, z) is the coordinate of the rotating 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 the 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 obtained as follows:

(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 follows:

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

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 mode number, a is the radius of the circular array, t is the slow time, J _l is the Bessel function, and i is the complex number symbol.

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

Step 2.4: Extract the characteristic value of the echo signal to be measured based on the spectrum data.

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

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

S1: Generate training dataset;

Specifically, S1 includes:

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

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

S12: extracting the characteristic values of each group of echo signals as training samples;

Specifically, the method for extracting the characteristic value is similar to the above-mentioned method for extracting the characteristic value of the echo signal to be measured, and will not be described in detail here.

It should be noted that the modulus value of the spectrum data corresponding to each set of echo signals is stored in the same .csv file, the real and imaginary part data of the spectrum data corresponding to each set of echo signals is stored in the same .csv file, and the off-axis angle corresponding to each set of echo signals is stored 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 constitute a training data set, and the .csv file storing the real and imaginary part data and the .csv file storing the off-axis angle constitute another training data set. The two training data sets mentioned above can be used to train the neural network respectively to obtain two trained neural networks to achieve the estimation of the off-axis angle. When the two trained neural networks perform off-axis angle prediction and estimation, their inputs are correspondingly the modulus value of the spectrum data corresponding to the echo signal to be measured, and the real and imaginary part data of the spectrum data corresponding to the echo signal to be measured.

S2: Build a neural network;

Please refer to Figure 4, which is a schematic diagram of the neural network structure 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, a third hidden layer and an output layer connected in sequence, wherein the input layer is used to input the characteristic value of the echo signal; the output layer is used to output the off-axis angle prediction value of the echo signal; since the ultimate problem is to predict the angle, the applied neural network 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 an Adam optimizer or an SGD optimizer.

Optionally, the loss function (also called the objective function) adopts a mean square error loss function, a logarithmic loss function, or a multi-classification logarithmic loss function.

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

S3: Train the neural network using the training data set to obtain a trained neural network.

Specifically, the neural network parameters are first randomly initialized, and then the training data set is input into the initialized neural network in batches. The mean square error loss function is used to calculate the current training error, and the ADAM optimizer is used to update the network parameters until the network converges. The training is ended to obtain a trained neural network.

The rotating target spatial angle estimation method based on vortex electromagnetic waves of this embodiment can provide more features of rotating targets, and combine neural networks to analyze the laws of echo spectra under different off-axis angles to predict the off-axis angle. The method of this embodiment 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 machine learning methods, which also provides a reference for radar target parameter estimation based on orbital angular momentum.

Embodiment 2

This embodiment illustrates the effect of the rotating target space angle estimation method based on vortex electromagnetic waves of the first embodiment through simulation experiments.

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

During the neural network training process, loss curves in two cases are obtained, see Figure 5a and Figure 5b. Figure 5a is a loss function curve when the real and imaginary parts of the spectrum data provided by the embodiment of the present invention are used as a data set; Figure 5b is a loss function curve when the modulus value of the spectrum data provided by the embodiment of the present invention is used as a data set. It can be seen from the figure that when the training rounds are 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.

The difference curves between the predicted value and the true value obtained by testing with 10,000 test sets are shown in Figures 6a and 6b. Figure 6a is a prediction error diagram when the real and imaginary parts of the spectrum data provided by the embodiment of the present invention are used as the data set; Figure 6b is a prediction error diagram 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 the prediction error in the first case is less than 0.1 degrees, and the prediction error in the second case is only less than 0.2 degrees.

Setting the corresponding threshold difference within the threshold is equivalent to correct prediction, and the relationship curve between the threshold and the accuracy is shown in Figure 7a and Figure 7b. Figure 7a is the relationship curve between the threshold and the accuracy when the real and imaginary parts of the spectrum data provided by the embodiment of the present invention are used as the data set; Figure 7b is the relationship curve between the threshold and the accuracy 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, the accuracy has reached more than 90% when the threshold is 0.05, while in the second case, the accuracy reaches more than 90% when the threshold is 0.15.

It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants are intended to cover non-exclusive inclusion, so that an article or device including a series of elements includes not only those elements, but also other elements that are not explicitly listed. In the absence of further restrictions, the elements defined by the statement "including one..." do not exclude the existence of other identical elements in the article or device including the elements. Similar words such as "connect" or "connected" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims (4)

1. A method for estimating the spatial angle of a rotating target based on vortex electromagnetic waves, comprising: Acquire the echo signal to be measured; Extracting a characteristic value of the echo signal to be measured, wherein the characteristic value is a modulus value or real and imaginary part data of spectrum data corresponding to the echo signal to be measured; extracting the characteristic value of the echo signal to be measured includes: A mathematical model for detecting rotating targets based on vortex electromagnetic waves is established; the mathematical model for detecting rotating targets based on vortex electromagnetic waves includes: A circular array consisting of N equally spaced identical array elements is used as the transmitting antenna, where the radius of the circular array is a and the receiving antenna is located at the center O; Establishing a radar coordinate system OXYZ 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. 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 angle between the line connecting the rotation center O’ and the radar coordinate system and the positive direction of the Z axis is the eccentric angle θ, and the length from the rotation center O’ to the origin of the radar coordinate system is L; A local coordinate system O′X′Y′Z′ of the rotating target is established with the rotating circle center O′ as the origin, wherein the coordinates of the rotating target P in the local coordinate system are (x′, y′, z′); According to the mathematical model, an expression of the echo signal to be measured under the mathematical model is obtained, including: Assume that the Euler angle between the radar coordinate system and the local coordinate system is The coordinate expression for converting 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 ; Where (x, 0, z) is the coordinate of the rotating 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 the 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 follows: According to the spherical coordinate expression, the expression of the echo signal to be measured under the mathematical model is obtained as follows: 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 mode number, a is the radius of the circular array, t is the time, J _l is the Bessel function, and i is the complex number symbol; According to the expression under the mathematical model of the echo signal to be measured, a fast Fourier transform is performed on it to obtain corresponding spectrum data; Extracting the characteristic value of the echo signal to be measured according to the frequency spectrum data; The characteristic value is input 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 trained based on a training data set and an off-axis angle label of each training sample. 2. The rotating target space angle estimation method based on vortex electromagnetic waves according to claim 1 is characterized in that the training method of the neural network comprises: S1: Generate training dataset; S2: Build a neural network; S3: Using the training data set to train the neural network to obtain a trained neural network. 3. The rotating target space angle estimation method based on vortex electromagnetic waves according to claim 2, characterized in that S1 comprises: Obtain echo signals corresponding to different off-axis angles and rotation angles; Extract the characteristic values 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. 4. The rotating target space angle estimation method based on vortex electromagnetic waves according to claim 2 is characterized in that the neural network comprises 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 characteristic value 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.