Meter-wave Radar Low Elevation Angle Estimation Method Based on Deep Learning

Abstract

The present invention discloses a method for estimating the low elevation angle of a meter-wave radar based on deep learning, belonging to the technical field of meter-wave radars. Aiming at the serious multipath effect existing when the meter-wave radar detects low-altitude targets, the direct wave and the reflected wave are equivalent to two strong coherent point sources with relatively close distances. At this time, there is mutual penetration between the noise subspace and the signal subspace in the echo signal covariance matrix, resulting in the problem of poor elevation angle estimation accuracy for physical algorithms based on subspace decomposition or signal fitting. The method for estimating the low elevation angle of the meter-wave radar proposed in the present invention extracts the real part, imaginary part and phase characteristics of the signal covariance matrix with mutual penetration between the signal and the noise subspace under multipath reflection conditions as the input features of the network, constructs a deep learning network using DNN and FCN for estimating the low elevation angle of the meter-wave radar, and utilizes the non-linear mapping and generalization ability of DNN to improve the performance of measuring the low elevation angle of the meter-wave radar and achieve a lower computational complexity.

Description

Technical Field

[0001] The present invention relates to the technical field of meter-wave radar, and in particular to a method for estimating the low elevation angle of a meter-wave radar based on deep learning. Background Art

[0002] DOA (Direction Of Arrival) estimation, as one of the research contents of array signal processing, has wide applications in military and economic fields such as radar, sonar, and communication. Meter-wave radar has become an important support for anti-stealth technology due to its advantages such as a long detection range, good anti-radiation missile (ARM) resistance ability, and natural anti-stealth performance. However, due to its lower frequency band, longer wavelength, and wider beam, there are serious multipath effects when detecting low-altitude targets, and there is strong coherence between the direct wave and the reflected wave, resulting in a sharp decline in the angle resolution and angle measurement accuracy when tracking and measuring low-altitude targets, making the low elevation angle estimation of meter-wave radar a major problem.

[0003] To solve this problem, currently, super-resolution algorithms such as the spatial smoothing (SS) decoherence algorithm, the generalized multiple signal classification (MUSIC) algorithm without decoherence, and the maximum likelihood (ML) estimation algorithm can be used to improve the angle resolution and angle measurement accuracy of meter-wave radar for detecting low-altitude targets. However, in the problem of low elevation angle height measurement of a meter-wave array, even under the condition that the received signal covariance matrix is full rank, the forward-backward spatial smoothing (FBSS) decoherence algorithm will still show the phenomenon of decoherence failure and a large elevation angle error. The low elevation angle estimation technology of meter-wave radar based on a uniform linear array (ULA) is relatively mature and is the most commonly used method. However, its array aperture is small, and the angle measurement accuracy is not high when the signal-to-noise ratio and the number of snapshots are low, and the computational complexity is relatively high. The low elevation angle estimation technology of meter-wave radar based on a sparse array is not yet mature. In particular, for the method based on a virtual array

[16] , due to the approximate equivalent model, the angle measurement error is large. For the method based on a physical array, due to the non-uniformity of the sparse array, traditional decoherence algorithms cannot be used, and currently, only the generalized MUSIC algorithm and the ML algorithm without decoherence can be used for processing. Although the above methods have improved the angle measurement accuracy, they still have the problem of large computational complexity. It can be found that traditional physical methods have bottlenecks in solving the problem of low elevation angle estimation of meter-wave radar. Summary of the Invention

[0004] Aiming at the above problems, the present invention aims to provide a method for estimating the low elevation angle of a meter-wave radar based on deep learning. By extracting the real part, imaginary part, and phase characteristics of the signal covariance matrix where the signal and noise subspaces penetrate each other under multipath reflection conditions as the input features of the network, a deep learning network is constructed using DNN and FCN for estimating the low elevation angle of the meter-wave radar. Utilizing the nonlinear mapping and generalization capabilities of DNN, the performance of the low elevation angle measurement of the meter-wave radar is improved, and a relatively low computational complexity is achieved.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A method for estimating the low elevation angle of a meter-wave radar based on deep learning, characterized by including the following steps:

[0007] S1: Establish a signal model of the meter-wave radar system;

[0008] S2: Based on the signal model of the meter-wave radar system in step S1, construct a deep learning neural network for estimating the elevation angle of low-altitude targets of the meter-wave radar;

[0009] S3: Use the deep learning neural network established in step S2 to perform DOA estimation on low elevation angle targets.

[0010] Further, the specific operations of step S1 include the following steps:

[0011] S101: Under the condition that the meter-wave radar system is vertically placed, establish a classical mirror multipath propagation model of the meter-wave radar;

[0012] S102: Calculate the path difference ΔR between the direct wave and the reflected wave of the radar system's transmitted signal;

[0013] S103: Establish a data model of the radar system's received signal.

[0014] Further, the specific operations of step S102 include the following steps:

[0015] S1021: According to the classical mirror multipath propagation model of the meter-wave radar established in step S101, the direct wave path length R between the meter-wave radar and the target d and the reflected wave path length R i are respectively

[0016]

[0017]

[0018] where h a and h t are the radar antenna height and the target height respectively, and R is the horizontal distance between the radar and the target.

[0019] S1022: The binomial expansion of equations (1) and (2) gives

[0020]

[0021] S1023: When the target flight altitude is low, R >> h a , h t , so the high-order terms are discarded, and only the first two terms in the binomial are retained to obtain the direct wave path length R d and the reflected wave path length R i The approximate values are

[0022]

[0023] S1024: Calculate the wave path difference ΔR between the direct wave and the reflected wave,

[0024]

[0025] Then the phase difference between the reflected wave and the direct wave is expressed as

[0026]

[0027] In the formula, λ is the wavelength.

[0028] Furthermore, the specific operations of step S103 include the following steps

[0029] S1031: Treat the low-altitude target and the mirror target as targets within a distance unit, only consider the received multipath, and regard it as two reflection paths, namely the direct-direct path and the direct-reflection path. Then, the data received by the m-th array element of the radar antenna at time t is

[0030]

[0031] In the formula, s(t) is the signal complex envelope, n m (t) is the additive Gaussian white noise; ρ is the reflection coefficient. When the radar signal is a horizontally polarized wave, the value of ρ is -1; θ d is the incident angle of the target direct wave, θ s is the incident angle of the target reflected wave, j = (-1) 0.5 , which is the imaginary part of the complex number, d m is the position of the m-th array element, that is, the distance from the reference array element;

[0032]

[0033] S1032: Assume that the number of antenna array elements of the meter-wave radar system is M. Then, the data model of the received signal of the entire meter-wave radar system is

[0034]

[0035] where N(t) is an additive white Gaussian noise vector with a mean of 0 and a variance of 1; t ∈ (t1,...t L ), L is the number of snapshots; ε = ρe -jα represents the multipath attenuation coefficient, T represents matrix transpose, Γ = [1, ε] T ; a(θ d ) and a(θ s ) represent the steering vectors of the direct wave and the reflected wave respectively, A = [a(θ d ), a(θ s )] is the signal composite steering vector;

[0036] S1033: Calculate the signal covariance matrix according to Equation (10) as

[0037]

[0038] where * is the conjugate processing of the matrix; is the power of the signal; is the power of the noise; E[] represents the mathematical expectation; H represents the conjugate transpose of the matrix; I M represents the M×M dimensional identity matrix;

[0039] S1034: According to the classical mirror multipath propagation model of the meter-wave radar,

[0040] sin(θ d ) = (h t - h a ) / R d (12)

[0041] sin(θ s ) = -(h t + h a ) / R d (13)

[0042] Since R ≈ R d ≈ R i , then the relationship between the incident angle θ d of the direct wave and the incident angle θ s of the reflected wave is expressed as

[0043] θ s = -arcsin(sin(θ d ) + 2h a / R) ≈ -θ d (14) ​

[0044] S1035: According to the relationship between the incident angle θ of the wave d and the incident angle θ of the reflected wave s , the signal composite steering vector A = [a(θ d ), a(θ s )] is reduced from two-dimensional to one-dimensional, and the steering vector after dimensionality reduction is expressed as

[0045] A1 = [a(θ d ), a(-arcsin(sin(θ d ) + 2h a / R))]

[0046] (15).

[0047] Furthermore, the specific operations of step S2 include the following steps.

[0048] S201: Based on the signal model of the meter wave radar system in step S1, construct the main structure of the deep learning neural network for estimating the elevation angle of low-altitude targets of the meter wave radar;

[0049] S202: Use the real part, imaginary part, and phase characteristics of the signal covariance matrix data where the signal and noise subspaces penetrate each other under multipath reflection conditions to form a dataset Y as the input of the deep learning network to construct a dataset;

[0050] S203: Design the operation methods of the convolutional layer and the fully connected layer, perform operations on the input of the deep learning network, and make its output result be the target elevation angle, thereby constructing a complete deep learning neural network;

[0051] S204: Train and learn the deep learning neural network obtained in step S203.

[0052] Furthermore, the main structure of the deep learning neural network described in step S201 includes six convolutional layers and two fully connected layers. Each convolutional layer has 256 convolutional kernels. The convolutional kernel sizes of the first two convolutional layers are 3×3, and the convolutional kernel sizes of the last four convolutional layers are 2×2. Behind each convolutional layer is a batch normalization layer and a ReLU layer; after all convolutional layers, there are two fully connected layers. After the first fully connected layer, there is a ReLU activation function and a dropput layer, and after the second fully connected layer, a sigmoid activation function is used to induce classification probabilities and output.

[0053] Furthermore, the network parameters of the convolutional layer described in step S203 are where W e represents a convolutional kernel with a dimension of c e ×f e ×f e ×n e , ce represents the number of input channels, f e represents the length and width of the convolutional kernel, n e represents the number of convolutional kernels, b e represents the bias vector of dimension n e represents the convolutional operation. The operations of each convolutional layer are as follows:

[0054] ① The convolutional layer Conv-1 is used to extract features from the input data. It uses the ReLU activation function. At this time, c e = 3, n e = 256. The specific operation is expressed as

[0055]

[0056] ② The convolutional layers Conv-2 to Conv-5 implement the non-linear mapping of features and all use the ReLU activation function. At this time, c e = 256, n e = 256. The specific operation is expressed as

[0057]

[0058] ③ The convolutional layer Conv-6 is the data reconstruction layer, obtaining a data output of dimension M×M×256. At this time, c e = 256, n e = 256. The specific operation is expressed as

[0059]

[0060] Furthermore, the network parameters of the fully connected layer described in step S203 are where W 0f represents the weight matrix of dimension c f ×n f , c f represents the number of input channels, n f represents the number of neurons in the fully connected layer, b 0f represents the bias vector of dimension n f . * represents the matrix multiplication operation. The operations of each fully connected layer are respectively

[0061] ① The fully connected layer FC-1 is used to integrate the information of the convolutional layer. It uses the ReLU activation function. At this time, c f = M×M×256, n f = 1024. The specific operation is expressed as:

[0062]

[0063] ​② The fully connected layer FC-2 is used to induce classification probabilities and output, using the sigmoid activation function. At this time, c f = 1024, n f = N, and the specific operation is expressed as

[0064]

[0065] Furthermore, the specific operations of step S204 include the following steps

[0066] S2041: Take the positions of non-zero elements in the signal vector as labels, denoted as γ; the training set of the network is expressed as

[0067] D train = {(Υ 1 , Y 1 ), (Υ 2 , Y 2 ), …, (Υ l , Y l )} (21)

[0068] where Y represents the network input of the training sample size

[0069] S2042: In the spatial angle range, evenly divide the spatial angle to form a discrete angle set, with an angle interval of 0.1°

[0070] S2043: Randomly set a position in the discrete angle set to be non-zero as the incident angle of the direct wave signal According to equation (9), obtain the array received signal data x m (t), obtain the array received data X(t) of multiple snapshots according to equation (10), calculate the signal covariance matrix R according to equation (11) x and perform dimensionality reduction using equation (15) to obtain the real part, imaginary part, and phase characteristics of R x as the multi-channel input Y of the network

[0071] S2044: Corresponding to the position of the non-zero element in , set the value of this position in Υ to 1 in Υ to obtain the label Υ, thereby generating the data samples for training the network and the corresponding labels

[0072] S2045: Divide the data samples for training the network and the corresponding labels into a training set and a test set. The training set data Y passes through the deep learning network to obtain the network output At this time The position of the larger value in represents the estimated signal arrival direction

[0073] S2046: During the network training process, use the cross-entropy between the label and the network output as the loss function

[0074]

[0075] Wherein, is the actual output of the deep learning network;

[0076] S2047: Use the backpropagation algorithm to minimize the loss function to train the network parameters. After each forward propagation of the neural network, backpropagate the error and update the network weights until the network objective function converges to determine the network weights and parameters;

[0077] S2048: After the network training is completed, use the test data to test the network.

[0078] The beneficial effects of the present invention are:

[0079] In the present invention, the VHF radar low elevation angle estimation method constructs a VHF radar low elevation angle estimation model based on DL, and uses the real part, imaginary part and phase characteristics of the original covariance matrix data with subspace mutual penetration as the input of the deep learning network. A deep learning network is constructed using DNN and FCN for VHF radar low elevation angle estimation. Utilize the non-linear mapping and generalization ability of DNN to solve the DOA estimation problem under the multipath reflection condition of VHF radar. Compared with the calculation methods based on subspace decomposition or signal fitting, the low elevation angle estimation method in the present invention has higher angle estimation accuracy and smaller calculation amount, and has better effect under low snapshots and low signal-to-noise ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a schematic diagram of the classical mirror multipath propagation model of the VHF radar in the present invention.

[0081] Figure 2 is a schematic diagram of the main structure of the deep learning neural network in the present invention.

[0082] Figure 3 is the comparison result of the network convergence situation in the present invention.

[0083] Figure 4 is the low elevation angle estimation spatial spectrogram in Simulation Experiment 1 of the present invention.

[0084] Figure 5 is the influence result of the elevation angle on the elevation angle measurement accuracy in Simulation Experiment 2 of the present invention.

[0085] Figure 6 is the influence result of the signal-to-noise ratio on the elevation angle measurement accuracy in Simulation Experiment 3 of the present invention.

[0086] Figure 7 is the influence result of the number of snapshots on the elevation angle measurement accuracy in Simulation Experiment 4 of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0087] In order to enable those of ordinary skill in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0088] A method for estimating the low elevation angle of a meter-wave radar based on deep learning includes the following steps

[0089] S1: Establish a signal model of the meter-wave radar system;

[0090] S2: Based on the signal model of the meter-wave radar system in step S1, construct a deep learning neural network for estimating the elevation angle of low-altitude targets of the meter-wave radar;

[0091] S3: Use the deep learning neural network established in step S2 to perform DOA estimation on low-elevation targets.

[0092] Specifically, the specific operations of step S1 include the following steps

[0093] S101: Assume that a meter-wave radar antenna is a uniformly or non-uniform linear array placed vertically. Under the condition that the meter-wave radar system is placed vertically, establish a classical mirror multipath propagation model of the meter-wave radar. As shown in the attached Figure 1 figure, the radar is placed at point A, the target is at point T, and B is the multipath reflection point. Among them, h a and h t are the radar antenna height and the target height respectively, R is the horizontal distance between the radar and the target, R d is the direct wave path length (the straight-line distance between the radar and the target), R i is the multipath reflected wave path length, θ d is the direct wave incident angle of the target, and θ s is the reflected wave incident angle of the target.

[0094] Further, S102: Calculate the wave path difference ΔR between the direct wave and the reflected wave of the radar system transmission signal;

[0095] More specifically, S1021: According to the classical mirror multipath propagation model of the meter-wave radar established in step S101 (attached Figure 1 ), it can be obtained that the direct wave path length R d and the reflected wave path length R i between the meter-wave radar and the target are respectively

[0096]

[0097] S1022: Perform binomial expansion on equations (1) and (2) to obtain

[0098]

[0099] S1023: In actual situations, when the target flight altitude is relatively low, R >> h a , h t , h t is relatively small, R >> h a , h t , is approximately equal to 0. Therefore, the higher-order terms can be discarded, and only the first two terms in the binomial are retained to obtain the direct wave path length R d and the approximate value of the reflected wave path length R i is

[0100]

[0101] S1024: Calculate the wave path difference ΔR between the direct wave and the reflected wave

[0102]

[0103] Then the phase difference between the reflected wave and the direct wave is expressed as

[0104]

[0105] where λ is the wavelength

[0106] Furthermore, S103: Establish a data model for the received signal of the radar system

[0107] More specifically, S1031: The signal propagates bidirectionally between the radar and the target. The signal received by the meter-wave radar antenna comes from four propagation paths: namely, the direct-direct path, the direct-reflection path, the reflection-direct path, and the reflection-reflection path. Different from the range high-resolution radar, when the conventional array meter-wave radar estimates the elevation angle of a low-altitude target, due to the limited range resolution ability, the low-altitude target and the mirror target are often regarded as targets within one range cell. Therefore, only the received multipath is considered and regarded as two reflection paths, that is, the direct-direct path and the direct-reflection path. Then, at time t, the data received by the m-th element of the radar antenna is

[0108]

[0109] where s(t) is the complex envelope of the signal, n m (t) is the additive Gaussian white noise; ρ is the reflection coefficient. When the radar signal is a horizontally polarized wave, the value of ρ is -1; θ d is the incident angle of the direct wave of the target, θ s is the incident angle of the reflected wave of the target, j = (-1) 0.5 , which is the imaginary part of the complex number, d m is the position of the m-th element, that is, the distance from the reference element

[0110]

[0111] S1032: Let the number of antenna elements of the meter-wave radar system be M, then the data model of the received signal of the entire meter-wave radar system is

[0112]

[0113] where N(t) is an additive Gaussian white noise vector with a mean of 0 and a variance of 1; t ∈ (t1,...t L ), L is the number of snapshots; ε = ρe -jα represents the multipath attenuation coefficient, T represents matrix transpose, r = [1, ε] T ; a(θ d ) and a(θ s ) respectively represent the steering vectors of the direct wave and the reflected wave, A = [a(θ d ), a(θ s )] is the signal composite steering vector;

[0114] S1033: Calculate the signal covariance matrix according to Equation (10) as

[0115]

[0116] where, * is the conjugate processing of the matrix; is the power of the signal; is the power of the noise; E[] represents the mathematical expectation; H represents the conjugate transpose of the matrix; I M represents the M×M dimensional identity matrix;

[0117] S1034: According to the classical mirror multipath propagation model of the meter-wave radar, it can be obtained that

[0118] sin(θ d ) = (h t - h a ) / R d (12)

[0119] sin(θ s ) = -(h t + h a ) / R d (13)

[0120] Since R ≈ R d ≈ R i , then the relationship between the incident angle θ d of the direct wave and the incident angle θ s of the reflected wave is expressed as​

[0121] θ s =-arcsin(sin(θ d ) + 2h a / R) ≈ -θ d (14)

[0122] S1035: According to the relationship between the incident angle θ of the damped wave and the incident angle θ of the reflected wave, the signal composite steering vector A = [a(θ d ), a(θ s )] is reduced from two - dimensional to one - dimensional, and the steering vector after dimensionality reduction is expressed as d )], a(θ s )] is reduced from two - dimensional to one - dimensional, and the steering vector after dimensionality reduction is expressed as

[0123] A1 = [a(θ d ), a(-arcsin(sin(θ d ) + 2h a / R))](15).

[0124] Furthermore, the specific operations in step S2 include the following steps

[0125] S201: Based on the signal model of the meter - wave radar system in step S1, construct the main structure of the deep - learning neural network for estimating the elevation angle of low - altitude targets of the meter - wave radar;

[0126] The main structure of this deep - learning neural network is as shown in the appendix Figure 2 and includes six convolutional layers and two fully - connected layers. Each convolutional layer has 256 convolutional kernels. The convolutional kernels of the first two convolutional layers are of size 3×3, and the convolutional kernels of the last four convolutional layers are of size 2×2. Behind each convolutional layer is a batch normalization layer and a ReLU layer; after all convolutional layers, there are two fully - connected layers. After the first fully - connected layer, there is a ReLU activation function and a dropout layer, and after the second fully - connected layer, a sigmoid activation function is used to induce the classification probability and output. Since zero padding is used at the edges in each convolutional layer, only the number of channels is changed while keeping the length and width of the data unchanged.

[0127] S202: Use the real part, imaginary part, and phase characteristics of the signal covariance matrix data where the signal and noise sub - spaces penetrate each other under the multipath reflection condition to form a dataset Y as the input of the deep - learning network to construct a dataset, so as to ensure the low - elevation angle estimation performance of the meter - wave radar and the generalization ability of the deep - learning network.

[0128] Specifically, it can be seen from formula (11) that the signal covariance matrix is a complex - number matrix. The real part is the matrix composed of the real parts of each element in the matrix, the imaginary part is the matrix composed of the imaginary parts of each element, and the phase is the matrix composed of the phase angles of the ratio of the real part to the imaginary part of each element in the matrix. It can be expressed by formulas as R real= real[R x , R imag = imag[R x , R phase = phase[R x , Y is the general term for the above three features.

[0129] S203: Design the operation methods of the convolutional layer and the fully connected layer, perform operations on the input of the deep learning network so that its output result is the target elevation angle, thereby constructing a complete deep learning neural network;

[0130] The network parameters of the convolutional layer are Among them, W e represents a convolutional kernel with dimensions of c e × f e × f e × n e ; c e represents the number of input channels, f e represents the length and width of the convolutional kernel, n e represents the number of convolutional kernels, b e represents a bias vector with dimension n e . represents the convolutional operation, and the operations of each convolutional layer are:

[0131] ① The convolutional layer Conv-1 is used to extract features from the input data, and it uses the ReLU activation function. At this time, c e = 3, n e = 256, and the specific operation is expressed as

[0132]

[0133] ② The convolutional layers Conv-2 to Conv-5 implement the non-linear mapping of features, and all use the ReLU activation function. At this time, c e = 256, n e = 256, and the specific operation is expressed as

[0134]

[0135] ③ The convolutional layer Conv-6 is a data reconstruction layer, obtaining a data output with dimensions of M × M × 256. At this time, c e = 256, n e = 256, and the specific operation is expressed as

[0136]

[0137] The network parameters of the fully connected layer are Among them, W 0f represents a dimension of c f × nf weight matrix of c f represents the number of input channels, n f represents the number of neurons in the fully connected layer, b 0f represents the dimension of n f bias vector of, * represents matrix multiplication operation, and the operations of each fully connected layer are respectively

[0138] ① The fully connected layer FC-1 is used to integrate the information of the convolutional layer. It uses the ReLU activation function. At this time, c f = M×M×256, n f = 1024, and the specific operation is expressed as

[0139]

[0140] ② The fully connected layer FC-2 is used to induce classification probabilities and output. It uses the sigmoid activation function. At this time, c f = 1024, n f = N, and the specific operation is expressed as

[0141]

[0142] Similar to most deep neural networks, this paper adopts a supervised learning method, that is, the network is trained based on the pre-given data and its labels. This paper uses the echo signal of the classical mirror multipath propagation model as the data source of the dataset, and constructs a complete dataset with the real part, imaginary part and phase characteristics Y of the signal covariance matrix data where the signal and noise subspaces penetrate each other under the multipath reflection condition, so as to ensure the low elevation angle estimation performance of the meter-wave radar and the generalization ability of the deep learning network. The incident angle varies from 0.1° to 10°, the variation interval is 0.1°, the signal traverses the positioning range of each group, and the number of samples N is 100. The input data dimension is M×M×3, that is, the length×width is M×M, and the number of channels is 3. The output is an N×1-dimensional signal vector, and the position of the largest element is the target elevation angle.

[0143] S204: Train and learn the deep learning neural network obtained in step S203.

[0144] More specifically, S2041: Use the position of the non-zero elements in the signal vector as the label, denoted as Υ; the training set of the network is expressed as

[0145] D train = {(Υ 1 , Y 1 ), (Υ 2 , Y 2 ), …, (Υ l , Y l )} (21)

[0146] Among them, Y represents the input of the training sample capacity network. Taking the one-dimensional array structure as an example, the following operations specifically describe the generation process and method of training samples and labels.

[0147] S2042: In the spatial angle range, evenly divide the spatial angle to form a discrete angle set. For a vertically placed one-dimensional array, evenly divide the spatial angle range of the pitch angle into discrete angles, with an angle interval of 0.1°. If the angle interval is divided too small, it will affect the accuracy of DOA estimation; if the division is too large, the precision will be reduced.

[0148] S2043: Randomly set a non-zero position in the discrete angle set as the incident angle of the direct wave signal. According to Equation (9), obtain the array received signal data x (t). According to Equation (10), obtain the array received data X(t) for multiple snapshots. Calculate the signal covariance matrix R according to Equation (11) m and perform dimensionality reduction using Equation (15) to obtain the real part, imaginary part, and phase characteristics of R as the multi-channel input Y of the network. x and use Equation (15) for dimensionality reduction to obtain the real part, imaginary part, and phase characteristics of R as the multi-channel input Y of the network. x Set the value at this position to 1 in γ (1 indicates that there is a non-zero value signal arriving at this position angle) corresponding to the position of the non-zero element in

[0149] S2044: Corresponding to to obtain the label γ, thereby generating the data samples for training the network and the corresponding labels; the label represents the direction of signal arrival, which is known during training.

[0150] S2045: Divide the data samples for training the network and the corresponding labels into a training set and a test set according to a ratio of 8:2. The training set data Y passes through the deep learning network to obtain the network output At this time The position of the larger value in represents the estimated direction of signal arrival.

[0151] S2046: During the network training process, use the cross-entropy between the label and the network output as the loss function.

[0152]

[0153] In the formula, is the actual output of the deep learning network.

[0154] S2047: Use the backpropagation algorithm to minimize the loss function to train the network parameters. After each forward propagation of the neural network, backpropagate the error and update the network weights until the network objective function converges to determine the network weights and parameters.

[0155] In the present invention, the Adam optimizer is adopted to update the network parameters. After repeatedly updating the network parameters for many times until the network objective function converges. To prevent the problem of network overfitting, the Dropout strategy is adopted to randomly remove neurons with a certain probability to alleviate the dependence of the network on the data distribution of the training set. Through training, the actual output of the network is getting closer and closer to γ; when the network training is completed for testing, similar to the way of generating training samples during the training process, the test samples are also input into the deep learning network in the form of multi-channel data Y (the real part, imaginary part and phase characteristics of the complex signal covariance matrix), and the network output is obtained and it is checked whether it is close to the true label Υ to judge the training level of the network. Since the deep learning network has many parameters and the optimization problem is complex, during the network training process, as the number of iterations increases, the learning rate should be gradually reduced so that the network parameters gradually converge to the optimal or near-optimal.

[0156] S2048: After the network training is completed, use the test data to test the network.

[0157] Under the same conditions of the deep learning network structure, labels and training process in the present invention, the received signals of the ULA with equal number of array elements, the simple coprime array (SCA) and the second-order nested array (NA) are respectively trained by using the above deep learning network, and Figure 3 shows the relationship between the training rounds of each array and the network convergence situation. From Figure 3 it can be found that when using sparse arrays (SCA and second-order NA) for learning and training, the RMSE is smaller than that of the ULA, and among them, the deep learning convergence speed of the SCA is the fastest, and the RMSE fluctuation of the second-order NA deep learning is the smallest.

[0158] Furthermore, when the network completes training and testing, fix the parameters and structure of the network, and then the deep learning network can be used to estimate the DOA of low-elevation targets to obtain the elevation angle estimation value

[0159] Experimental simulation:

[0160] In the simulation experiment, subspace decomposition or signal fitting algorithms such as FBSSMUSIC, RWGMUSIC and ML and the DL-based method proposed in this paper are implemented in the experimental environment of Matlab2020b. Select the ULA, SCA and second-order NA structures with equal number of array elements to compare and analyze the low-elevation estimation performance of different methods.

[0161] The basic conditions of each simulation experiment are the same: Assume three array antennas placed vertically and arranged in a one-dimensional linear array. Antenna 1 is a ULA, Antenna 2 is an SCA, and Antenna 3 is a second-order nested array. The number of array elements of each array is M = 7. The element spacing distance d of Antenna 1 is 0.5λ, where λ is the signal wavelength, and its physical element positions are {0, d, 2d, 3d, 4d, 5d, 6d}; the physical element positions of Antenna 2 are {0, 3d, 5d, 6d, 9d, 10d, 12d}; the physical element positions of Antenna 3 are {0, d, 2d, 3d, 7d, 11d, 15d}; the radar operating frequency is 300 MHz, the number of spatial targets is n = 1, the height of the antenna bottom is 4 m, the ground reflection coefficient is -0.98, and the added noise is Gaussian white noise. The present invention adopts Monte Carlo repeated experiments to compare the angle measurement accuracies of different algorithms and different arrays. The number of Monte Carlo repeated experiments is 100 times. The one-dimensional root mean square error formula is:

[0162]

[0163] In Equation (23), K is the number of Monte Carlo trials, is the elevation angle of the target measured at the k-th time.

[0164] Experiment 1: Spatial spectrum imaging comparison experiment

[0165] The conditions of this group of experiments are: signal-to-noise ratio SNR = 10 dB, number of snapshots L = 100, the incident angle of the target direct wave is 3°, and the target distance is 200 km. The angle search range is from 0.1° to 8°, and the search interval is 0.1°. The FBSSMUSIC, RWGMUSIC, and ML algorithms are respectively used for spectral peak search, and the method based on DL is used for elevation angle prediction. The spatial spectrum diagrams obtained by Matlab simulation are as follows. The elevation angle estimation value is at the peak. The simulation results are as shown in the appendix Figure 4 shown, where (a) is a uniform array, (b) is a simple co-prime array, and (c) is a second-order nested array; it can be seen from Figure 4 that all arrays and all algorithms can accurately estimate the low elevation angle of the target, but the DL-based low elevation angle estimation method proposed in the present invention has a sharper spectral peak of the spatial spectrum than subspace decomposition or fitting algorithms such as FBSSMUSIC, RWGMUSIC, and ML, and has the best performance.

[0166] Experiment 2: Experiment on the influence of elevation angle on angle measurement accuracy:

[0167] The experimental conditions for this group are: signal-to-noise ratio SNR = 10 dB, number of snapshots L = 100, target distance is 200 km. The elevation angle ranges from 0.5° to 8°, with a change interval of 0.1°. The angle search range is from 0.1° to 8°, and the search interval is 0.01°. Monte Carlo repeated experiment errors of the elevation angle estimation values of each array and each algorithm relative to the true angle are simulated and tested at different elevation angles. The relationship between elevation angle and angle RMSE is plotted through Matlab simulation experiments, and the results are as shown in the appendix Figure 5 as shown. In the appendix Figure 5 , (a) is a uniform array, (b) is a simple co-prime array, and (c) is a second-order nested array; it can be seen from the appendix Figure 5 that: ① The DL-based low elevation angle estimation method proposed in the present invention has a smaller angle RMSE than subspace decomposition algorithms or signal fitting algorithms such as FBSSMUSIC, RWGMUSIC, and ML, and has the best performance. ② For each array and each algorithm, there is a certain fluctuation in the measurement accuracy within the interval with the change of elevation angle. The main reason is that the change of elevation angle brings about the periodic change of the phase of the multipath attenuation coefficient, which in turn affects the algorithm effect. When the phases of the direct wave and the reflected wave are opposite, they will cancel each other out, the signal energy will decrease sharply, resulting in a sudden drop in the signal-to-noise ratio and a sudden change in the measurement accuracy. However, the DL-based low elevation angle estimation method proposed in the present invention has the smallest fluctuation and the best performance.

[0168] Experiment 3: Experiment on the influence of signal-to-noise ratio on angle measurement accuracy

[0169] The experimental conditions for this group are: the incident angle of the target direct wave is 4.5°, the target distance is 200 km, the number of snapshots L = 100, the signal-to-noise ratio SNR ranges from 0 dB to 10 dB, with a change interval of 1 dB. The angle search range is from 0.1° to 8°, and the search interval is 0.01°. Monte Carlo repeated experiment errors of the elevation angle estimation values of each array and each algorithm relative to the true angle are simulated and tested under different signal-to-noise ratio conditions. The relationship between signal-to-noise ratio and angle RMSE is plotted through Matlab simulation experiments, and the results are as shown in the appendix Figure 6 as shown. In the appendix Figure 6 , (a) is a uniform array, (b) is a simple co-prime array, and (c) is a second-order nested array; it can be seen from the appendix Figure 6 that: ① The signal-to-noise ratio is positively correlated with the angle measurement accuracy of each array and each algorithm, and after the signal-to-noise ratio is greater than a certain range, the improvement of the angle measurement accuracy tends to be flat; ② When the signal-to-noise ratio is the same (greater than or equal to) condition, the DL-based low elevation angle estimation method proposed in the present invention has a smaller angle RMSE than subspace decomposition algorithms or signal fitting algorithms such as FBSSMUSIC, RWGMUSIC, and ML, and has the best performance.

[0170] Experiment 4: Experiment on the influence of the number of snapshots on angle measurement accuracy:

[0171] The experimental conditions for this group are as follows: the incident angle of the target direct wave is 4.5°, the target distance is 200 km, the signal-to-noise ratio SNR = 10 dB, the number of snapshots L ranges from 10 to 100 times, and the change interval is 10 times. The angle search range is from 0.1° to 8°, and the search interval is 0.01°. The Monte Carlo repeated experiment error of the elevation angle estimation value of each array and each algorithm relative to the true angle is simulated and tested under different numbers of snapshots. The relationship between the number of snapshots and the angle RMSE is plotted through Matlab simulation experiments, and the results are as follows Figure 7 shown. In the appendix Figure 7 , (a) is a uniform array, (b) is a simple co-prime array, and (c) is a second-order nested array. It can be seen from the appendix Figure 7 that: ① The number of snapshots is positively correlated with the angle measurement accuracy of each array and each algorithm, and after the number of snapshots is greater than a certain range, the improvement of the angle measurement accuracy tends to be flat; ② Under the same number of snapshots, the DL-based low elevation angle estimation method proposed in the present invention has a smaller angle RMSE than subspace decomposition or signal fitting algorithms such as FBSSMUSIC, RWGMUSIC, and ML, and has the best performance.

[0172] Table 1 below shows the comparison of the running times consumed by different arrays and different methods when the number of snapshots is 100. The CPU processor for the experiment is Intel Xeon Gold 5218, and the software used is Matlab R2020b. The running time in Table 1 is the average value of the CPU running time consumed by 1000 Monte Carlo experiments. It can be seen from Table 1 that the algorithm complexities based on subspace decomposition and signal fitting are similar, and the CPU running time is about 0.034 s, while the running time of the deep learning method is about 0.005 s, which is about 6 times lower than the FBSSMUSIC, RWGMUSIC, and ML algorithms. Therefore, the deep learning method has obvious advantages in the running time of low elevation angle estimation for meter-wave radars, and this advantage does not change due to different arrays. The main reason is that the training process of the DL method is offline and does not need to consider the time cost. When the network is trained, the computational amount brought by the parameter prediction process is small.

[0173] Table 1 Running times of different estimation methods

[0174] a. Uniform linear array

[0175]

[0176] b. Simple co-prime array

[0177]

[0178] c. Second-order nested array

[0179]

[0180] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification is only to illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the low elevation angle of a meter-wave radar based on deep learning, characterized in that, Including the following steps, S1: Establish a signal model of the meter-wave radar system; S2: Based on the signal model of the meter-wave radar system in step S1, construct a deep learning neural network for estimating the elevation angle of low-altitude targets of the meter-wave radar; S3: Use the deep learning neural network established in step S2 to perform DOA estimation on low-elevation targets; Among them, the specific operations of step S2 include the following steps, S201: Based on the signal model of the meter-wave radar system in step S1, construct the main structure of a deep learning neural network for estimating the elevation angle of low-altitude targets of the meter-wave radar; S202: Using the real part, imaginary part, and phase characteristics of the signal covariance matrix data where the signal and noise subspaces penetrate each other under multipath reflection conditions to form a dataset Y as the input of the deep learning network to construct a dataset; S203: Design the operation methods of the convolutional layer and the fully connected layer to perform operations on the input of the deep learning network so that its output result is the target elevation angle, thereby constructing a complete deep learning neural network; S204: Train and learn the deep learning neural network obtained in step S203; The specific operations of step S204 include the following steps, S2041: Using the positions of non-zero elements in the signal vector as labels, denoted as Υ; the training set of the network is expressed as D train = {(Υ 1 Y 1 ), (Υ 2 ,Y 2 , …, (Υ l ,Y l )} (21) Among them, Y represents the network input of the training sample capacity; S2042: In the spatial angle range, evenly divide the spatial angle to form a discrete angle set with an angle interval of 0.1°; S2043: Randomly set a non-zero position in the discrete angle set as the direct wave signal 's incident angle, and obtain the array received signal data x m (t) according to Equation (9), obtain the array received data X(t) for multiple snapshots according to Equation (10), and calculate the signal covariance matrix R x and perform dimensionality reduction using Equation (15) to obtain R x The real part, imaginary part, and phase characteristics are used as the network multi-channel input Y; S2044: Corresponding to the positions of non-zero elements in Υ, set the value at this position to 1 in Υ to obtain the label γ, thereby generating data samples for training the network and corresponding labels; S2045: Divide the data samples and corresponding labels used for training the network into a training set and a test set. The training set data Y passes through the deep learning network to obtain the network output At this time The position of the larger value represents the estimated direction of arrival of the signal; S2046: During the network training process, use the cross-entropy between the label and the network output as the loss function, In the formula, is the actual output of the deep learning network; S2047: Use the backpropagation algorithm to minimize the loss function to train the network parameters. After each forward propagation of the neural network, backpropagate the error and update the network weights until the network objective function converges to determine the network weights and parameters; S2048: After the network training is completed, use the test data to test the network.

2. The method for estimating the low elevation angle of a meter-wave radar based on deep learning according to claim 1, wherein The specific operations of step S1 include the following steps, S101: Under the condition of vertically placing the meter-wave radar system, establish a classical mirror multipath propagation model of the meter-wave radar; S102: Calculate the path difference ΔR between the direct wave and the reflected wave of the radar system's transmitted signal; S103: Establish a data model of the radar system's received signal.

3. The method for estimating the low elevation angle of a meter-wave radar based on deep learning according to claim 2, wherein The specific operations of step S102 include the following steps, S1021: According to the established classical mirror multipath propagation model of the meter-wave radar in step S101, the direct wave path length R between the meter-wave radar and the target d and the reflected wave path length R i are respectively where h a and h t are the height of the radar antenna and the height of the target respectively, and R is the horizontal distance between the radar and the target S1022: Binomial expansion of equations (1) and (2) gives S1023: When the target flight altitude is relatively low, R >> h a , h t , so the high-order terms are discarded, and only the first two terms in the binomial are retained to obtain the direct wave path length R d and the reflected wave path length R i The approximation is S1024: Calculate the path difference ΔR between the direct wave and the reflected wave, Then the phase difference between the reflected wave and the direct wave is expressed as In the formula, λ is the wavelength.

4. The method for estimating the low elevation angle of a meter-wave radar based on deep learning according to claim 3, wherein The specific operations of step S103 include the following steps, S1031: Regarding the low-altitude target and the mirror target as targets within a distance unit, only considering the received multipath and regarding it as two reflection paths, namely the direct-direct path and the direct-reflection path, then the data received by the m-th array element of the radar antenna at time t is where s(t) is the complex envelope of the signal, and n m (t) is additive white Gaussian noise; ρ is the reflection coefficient, and when the radar signal is a horizontally polarized wave, the value of ρ is -1; θ d is the incident angle of the direct wave of the target, and θ s is the incident angle of the reflected wave of the target, j = (-1) 0.5 , which is the imaginary part of the complex number, and d m is the position of the m-th array element, that is, the distance from the reference array element; S1032: Assuming the number of antenna array elements of the meter-wave radar system is M, then the data model of the received signal of the entire meter-wave radar system is where \(N(t)\) is an additive white Gaussian noise vector with a mean of 0 and a variance of 1; \(t\in(t_1,\cdots,t\) L ), \(L\) is the number of snapshots; \(\varepsilon = \rho e\) -jα represents the multipath attenuation coefficient, \([\) T represents matrix transpose, \(\Gamma=[1,\varepsilon][\) T ; \(a(\theta\) d ) and \(a(\theta\) s ) represent the steering vectors of the direct wave and the reflected wave respectively, \(A = [a(\theta\) d ), \(a(\theta\) s )]\) is the signal composite steering vector; S1033: Calculate the signal covariance matrix according to equation (10) as In the formula, [] * is the conjugate process of the matrix; is the power of the signal; is the power of the noise; E[] represents the mathematical expectation; [] H represents the conjugate transpose of the matrix; I M represents the M×M dimensional identity matrix; S1034: According to the classical mirror multipath propagation model of the meter-wave radar, it can be obtained that sin(θ d )=(h t -h a ) / R d (12) sin(θ s ) = -(h t + h a ) / R d (13) Since R≈R d ≈R i , the relationship between the incident angle θ d of the direct wave and the incident angle θ s of the reflected wave is expressed as θ s = -arcsin(sin(θ d ) + 2h a / R) ≈ -θ d (14) S1035: According to the relationship between the direct wave incident angle θ d and the reflected wave incident angle θ s , the signal composite steering vector A = [a(θ d ), a(θ s )] is reduced from two dimensions to one dimension, and the steering vector after dimension reduction is expressed as A1 = [a(θ d ), a(-arcsin(sin(θ d ) + 2h a / R))] (15).

5. The method for estimating the low elevation angle of a meter-wave radar based on deep learning according to claim 1, wherein The main structure of the deep learning neural network described in step S201 includes six convolutional layers and two fully connected layers. Each convolutional layer has 256 convolutional kernels. The convolutional kernels of the first two convolutional layers are 3×3 in size, and the convolutional kernels of the last four convolutional layers are 2×2 in size. Behind each convolutional layer is a batch normalization layer and a ReLU layer; after all convolutional layers, there are two fully connected layers. After the first fully connected layer, there are a ReLU activation function and a dropout layer. After the second fully connected layer, the sigmoid activation function is used to induce classification probabilities and output.

6. The method for estimating the low elevation angle of a meter-wave radar based on deep learning according to claim 5, characterized in that The network parameters of the convolutional layer described in step S203 are where W e represents a convolution kernel of dimension c e ×f e ×f e ×n e ; c e represents the number of input channels, f e represents the length and width of the convolution kernel, and n e represents the number of convolution kernels; b e represents a bias vector of dimension n e , and represents the convolution operation. The operations of each convolutional layer are as follows: ① The convolutional layer Conv-1 is used to extract features from the input data. It uses the ReLU activation function. At this time, c e = 3, n e = 256. The specific operation is expressed as ②The convolutional layers Conv-2 to Conv-5 implement the non-linear mapping of features, and the ReLU activation function is used. At this time, c e = 256, n e = 256, and the specific operation is expressed as ③ The convolutional layer Conv-6 is a data reconstruction layer, obtaining a data output with dimensions of M×M×256. At this time, c e = 256, n e = 256, and the specific operation is expressed as 7. The method for estimating the low elevation angle of a meter-wave radar based on deep learning according to claim 6, wherein The network parameters of the fully connected layer described in step S203 are where W 0f represents the weight matrix of dimension c f ×n f , c f represents the number of input channels, n f represents the number of neurons in the fully connected layer, b 0f represents the bias vector of dimension n f , * represents matrix multiplication operation, and the operations of each fully connected layer are respectively ① The fully connected layer FC-1 is used to integrate the information of the convolutional layer. It uses the ReLU activation function. At this time, c f = M × M × 256, n f = 1024. The specific operation is expressed as: ②The fully connected layer FC-2 is used to induce classification probabilities and output, and the sigmoid activation function is adopted. At this time, c f = 1024, n f = N, and the specific operation is expressed as

Images