Low signal-to-noise ratio DOA estimation method based on auto-encoder and deep neural network

Abstract

The invention discloses a low signal-to-noise ratio DOA estimation method based on an auto-encoder and a deep neural network, comprising a low signal-to-noise ratio DOA estimation method and a DOA estimation method combining DAE and CNN, the low signal-to-noise ratio DOA estimation method comprises the following steps: giving parameters such as array radar receiving antenna array element number M, array element position dm, signal-to-noise ratio SNR, input signal sin and the like; obtaining an array receiving data covariance matrix R; taking a real part and an imaginary part of a received signal covariance matrix R in an incidence angle [-60 degrees, 60 degrees] range as input Y1 of the neural network, constructing a data set, and distinguishing a training set and a test set according to a proportion of 8: 2; dAE network parameters are initialized, data in the training set are imported, forward propagation is completed, meanwhile, back propagation is conducted on errors, and network weights are synchronously updated; a DAE network structure is further introduced to optimize signal processing, the DOA estimation accuracy is improved, and the requirement for complex computing resources is lowered.

Description

Technical Field

[0001] The present invention relates to the field of coding sensors, and in particular to a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network. Background Art

[0002] High-resolution Direction-of-Arrive (DOA) estimation of sensor arrays is an important research direction in modern array signal processing. Accurate angle estimation can effectively improve the measurement accuracy of radar targets.

[0003] Although the traditional estimation algorithms such as the multiple signal classification algorithm (MUSIC) can achieve higher measurement accuracy, their estimation accuracy is highly dependent on the environment and is easily affected by noise. In order to solve the problem of high measurement error of traditional estimation algorithms in low signal-to-noise ratio working environment, this paper proposes a hybrid model using denoising autoencoder (DAE) and deep neural network (DNN), modeling DOA estimation as a classification problem, so as to improve the estimation accuracy and anti-interference ability of the algorithm under low signal-to-noise ratio.

[0004] Sensor array direction of arrival (DOA) estimation, as one of the important research contents of array signal processing, has a wide range of applications in economic and military fields such as radar, communication, sonar and astronomy.

[0005] In actual application scenarios, traditional direction finding methods such as MUSIC, ESPIRT, Capon and their various improved algorithms are often required to adapt to complex and changeable signal environments and application environments, and to achieve fast (real-time) direction finding as much as possible. However, the above-mentioned traditional model-driven direction finding methods are usually difficult to achieve real-time, applicability, generalization and other requirements, especially in low signal-to-noise ratio working conditions. The traditional algorithms perform poorly.

[0006] In view of this, the existing problems are studied and improved, and a low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network is provided. The method has a reasonable structural design, extracts the real part, imaginary part and phase characteristics of the array receiving data covariance matrix, and then uses DAE to perform unsupervised training on the noisy array covariance matrix data. Subsequently, the denoised data is connected to the DNN network, and the transfer learning strategy is used to extract features using network models such as Resnet18, VGG and Alexnet. Finally, the proposed DAE-DNN algorithm is compared and verified with other traditional estimation algorithms. The simulation results show that the algorithm proposed in this paper has higher accuracy under low signal-to-noise ratio conditions, and the relative error is 6.39%-23.23% smaller than traditional algorithms such as MUSIC and ESPIRT. The purpose is to solve the problem and improve the practical value through this technology. Summary of the invention

[0007] The purpose of the present invention is to solve the shortcomings existing in the prior art and propose a low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network.

[0008] In order to achieve the above object, the present invention adopts the following technical scheme: a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network, including a low signal-to-noise ratio DOA estimation method and a DOA estimation method combining DAE and CNN, and the low signal-to-noise ratio DOA estimation method has the following steps:

[0009] S1: Given the number of array radar receiving antenna elements M, array element position dm, signal-to-noise ratio SNR, input signal sin and other parameters;

[0010] S2: Get the array received data covariance matrix R;

[0011] S3: Take the real and imaginary parts of the covariance matrix R of the received signal within the range of incident angle [-60°, 60°] as the input Y1 of the neural network, construct a data set, and distinguish between a training set and a test set in a ratio of 8:2;

[0012] S4: Initialize the DAE network parameters, import the data in the training set, complete the forward propagation, and simultaneously backpropagate the error and update the network weights synchronously; repeat this step many times until the network converges, save the network parameters, and obtain the DAE output data

[0013] S5: Initialize the CNN network. Send it to the network, add the angle channel, and start training the CNN network after interpolation, using the actual angle as the label. After the training is completed, save the network parameters;

[0014] S6: Import the test set data into the network to test the network performance;

[0015] S7: After the test is completed, the network structure and parameters are fixed. The network can be used to estimate DOA under low signal-to-noise ratio conditions to obtain the elevation angle estimate.

[0016] As a further description of the above technical solution:

[0017] The steps of the DOA estimation method combining DAE and CNN are as follows:

[0018] S1, first extract the covariance matrix after the signal and noise subspaces permeate each other under low signal-to-noise ratio conditions;

[0019] S2, take the real part, imaginary part and phase of the covariance matrix as network input features, introduce them into DAE to improve the signal-to-noise ratio of the array received signal to improve the subsequent CNN classification accuracy;

[0020] S3, model the DOA estimation problem as a multi-label classification model, add the denoised covariance matrix to CNN, and use CNN to construct a deep learning network for DOA estimation;

[0021] S4. Improve the estimation performance and computational efficiency under low signal-to-noise ratio through the generalization ability and nonlinear mapping ability of CNN; simulation results show that under low signal-to-noise ratio, compared with traditional algorithms such as MUSIC, ESPIRT, and Capon, the method proposed in this paper significantly reduces the mean square error of angle estimation.

[0022] As a further description of the above technical solution:

[0023] Build the signal model:

[0024] Generally speaking, for far-field signals, there is a path difference when the same signal reaches different array elements. This path difference further causes the phase difference of the signal between the receiving array elements. The direction of the signal arrival can be obtained by using the phase difference between the array elements.

[0025] The echo signal can be represented by the following complex envelope form:

[0026]

[0027] In the formula, u i (t) is the received signal amplitude, is the phase of the received signal, ω0 is the frequency of the received signal;

[0028] Considering the distance R>>λ between the target and the antenna array in radar operation, the echo can be regarded as a far-field narrowband signal, so

[0029]

[0030] Then the signal received by the lth array element is

[0031]

[0032] In the formula, represents the gain of the lth array element for the i-th signal, n l (t) is the noise received by the lth array element at time t, τ li It represents the delay of the i-th signal reaching the l-th array element relative to the reference array element;

[0033] Ideally, assuming that each array element is isotropic and does not have the influence of mutual coupling, channel inconsistency and other factors, the gain in equation (3) can be normalized to 1, and then equation (3) can be rewritten as a vector form:

[0034] X(t)=AS(t)+N(t) (4)

[0035] Where X(t) is the M×1-dimensional snapshot data vector, N(t) is the M×1-dimensional noise data vector, A(t) is the N×1-dimensional vector of the received signal, and A is the M×N-dimensional steering vector array.

[0036] A=[a1(w0) a2(ω0) … a N (ω0)] (5)

[0037] The steering vector is

[0038]

[0039] This article takes a typical uniform linear array as an example. The schematic diagram of the array structure is as follows Figure 1 As shown, the array element position is x k (k=1,2,...,M), the signal incident elevation angle and azimuth angle are (i=1,2,...,N), then

[0040]

[0041] (1) To ensure that the columns of the steering vector matrix are linearly independent, the number of signal sources is less than the number of array elements;

[0042] (2) The noise sequence obeys a zero-mean Gaussian process, the noise of each array element is independent of each other, and the signal and noise are independent of each other;

[0043] (3) Each array element is isotropic and there is no inconsistency in the mutual coupling channels;

[0044] From the mathematical model of equation (4), according to the above assumptions, the covariance matrix of the array snapshot data can be obtained as follows:

[0045] R=E{XX H}

[0046] =AE{SS H} H +E{NN H}

[0047] =AR S A H +R N (8)

[0048] Where RS and RN are the covariance matrices of the signal and noise respectively. 2 The ideal white noise sequence is

[0049] R=AR S A H +R N

[0050] =AR S A H +σ 2 I (9).

[0051] As a further description of the above technical solution:

[0052] Establish multiple signal classification algorithms and rotation-invariant subspace algorithms;

[0053] The multiple signal classification algorithm is to decompose the array output covariance matrix eigenvalues ​​to obtain the signal subspace formed by the signal components and the noise subspace orthogonal to the signal components, and then use the orthogonality of the subspaces to estimate the signal parameters (incident direction, signal strength and polarization information, etc.);

[0054] First, the covariance matrix R of the array data in formula (9) is decomposed into

[0055]

[0056] Where Us is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues, and Un is the noise subspace spanned by the eigenvectors corresponding to the small eigenvalues;

[0057] Under ideal conditions, the signal subspace and the noise subspace are orthogonal to each other, that is, the steering vector of the signal subspace is also orthogonal to the noise subspace, then

[0058] a H (θ)U N =0( 11 )

[0059] Formula (11) is also the core solution idea of ​​the MUSIC algorithm. Considering that the actual array output matrix is ​​of finite length, the maximum likelihood estimate of R is

[0060]

[0061] Where L is the number of sampling points for received data;

[0062] right Performing eigendecomposition can obtain the noise subspace eigenvector matrix Due to the presence of noise, If they are not completely orthogonal, the estimated arrival angle in actual engineering is obtained by minimum optimization search, that is,

[0063]

[0064] Then the spatial spectrum estimation formula of the MUSIC algorithm is:

[0065]

[0066] The rotation invariant subspace algorithm is based on the rotation invariance of the signal subspace of the array received data covariance matrix. When estimating signal parameters, it requires that the geometric structure of the array is rotation invariant, that is, the array itself has two or more identical subarrays, or the same subarray can be obtained through some transformation. For the same signal, since the two subarrays are exactly the same, their outputs differ by only φ i , assuming that the outputs of the two sub-arrays are X1 and X2 respectively, according to the array model of formula (4), we have

[0067] X1=[a(θ1) … a(θ N )]S+N1

[0068] =AS+N1 (15)

[0069]

[0070] In the formula, the steering vector matrix of subarray 1 is A, the steering vector matrix of subarray 2 is, and there is

[0071]

[0072] The direction information of the signal is contained in A and Φ, and Φ is a diagonal matrix, so we can get

[0073] φ k =(2π|Δ|sinθ k ) / λ (18)

[0074] Where Δ is the spacing between two sub-arrays;

[0075] Therefore, as long as the relationship Φ between the two sub-arrays is obtained and then substituted into equation (18) to solve, the angle estimation value can be obtained. First, the two sub-array models are merged, that is,

[0076]

[0077] The covariance matrix under ideal conditions is

[0078]

[0079] The characteristic decomposition can be obtained

[0080]

[0081] Where US is the signal subspace spanned by the eigenvectors corresponding to large eigenvalues, and UN is the noise subspace spanned by the eigenvectors corresponding to small eigenvalues. Considering the actual snapshot data, equation (21) is modified to

[0082]

[0083] The signal subspace spanned by the eigenvectors corresponding to the large eigenvalues ​​and the signal subspace spanned by the steering vectors should be equal, then there exists a non-singular matrix T such that

[0084]

[0085] And it holds true for both of the above sub-matrices, that is

[0086]

[0087] Bringing in the relationship between the two arrays, we get

[0088] U S2 =U S1 T -1 ΦT=U S1 Ψ (25)

[0089] Formula (25) reflects the rotation invariance between the signal subspaces of the two subarrays receiving data. If the received signals are incoherent, that is, the steering vector array A is a full-rank matrix, then

[0090] Φ=TΨT -1 (26)

[0091] After obtaining the above rotation invariant relationship matrix Ψ, we can substitute it into equation (18) to get the signal angle;

[0092] The Capon algorithm is also a spectrum peak search algorithm. The DOA estimation value is determined by the angle at which equation (27) reaches its minimum value.

[0093]

[0094] Where θ is the angle estimate, Receives the covariance matrix of the data as an array.

[0095] As a further description of the above technical solution:

[0096] Establishing the DAE network structure: DAE is a variation of the autoencoder (AE). The difference is that DAE learns features by training the corrupted data with added noise, and uses the input original data and the output denoised data to calculate the loss function and perform error back propagation.

[0097] The input data of the DAE network structure is the real and imaginary parts of the array received signal covariance matrix. A data set is created in the interval of [-60°, 60°] with an interval of 1°. The size is 2×M×M, where M is the number of array elements. The encoding layer is composed of 4 layers of two-dimensional convolutional layers, nonlinear activation layers, and pooling layers. The loss function uses the mean square error function (MSE). After denoising, the mean square error function is used again to examine the denoising effect.

[0098] The network can be divided into the encoding part and the decoding part. The encoding part has 4 convolutional layers. The convolution kernel size of each convolutional layer is 4×4, the step size is 2 for downsampling, the edge padding is set to 1, and each convolutional layer is connected to a batch normalization layer and a Tanh nonlinear activation layer. Therefore, the size of the data matrix is ​​reduced to half of its original size after a convolution operation.

[0099] The present invention has the following beneficial effects:

[0100] The present invention further introduces the DAE network structure to optimize signal processing, which not only improves the accuracy of DOA estimation, but also reduces the demand for complex computing resources. Specifically, the DAE network structure enables the network to learn effective features in the data and remove noise interference by training noisy data. This ability is particularly important when processing array received signals, because array received signals often contain a lot of noise and interference.

[0101] In the encoding part, through multi-layer convolution operations, the network can gradually extract the key features of the signal. With the deepening of the convolution layer, the network can learn more abstract and advanced feature representations, which is crucial for subsequent DOA estimation. At the same time, the introduction of batch normalization layer and Tanh nonlinear activation layer makes the network more stable during training and helps to speed up training.

[0102] In the decoding part, the network reconstructs the encoded features to restore the approximate shape of the original signal. In this process, the network decodes and transforms the features to generate outputs similar to the original signal. By comparing the difference between the original signal and the output signal, the network's loss function can be calculated, and then the error backpropagation and parameter update can be performed.

[0103] After being processed by the DAE network structure, the signal-to-noise ratio of the array received signal has been significantly improved, thus providing a more accurate and reliable data basis for subsequent DOA estimation. In the DOA estimation process, by using the signal features extracted by the DAE network and combining it with the traditional spectrum peak search algorithm, the angle information of the signal can be estimated more accurately.

[0104] In addition, the present invention also uses an interval sampling method to produce a data set, which not only reduces the complexity of data processing, but also improves the generalization ability of the algorithm. By training under different angles and noise conditions, the DAE network can learn more robust and universal feature representations, thereby showing better performance in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1This is a schematic diagram of the overall structure of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0106] Figure 2 This is an array model diagram of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0107] Figure 3 A DAE flow chart of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0108] Figure 4 A schematic diagram of the DAE structure of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0109] Figure 5 A DOA estimation flow chart of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0110] Figure 6 A schematic diagram of the DAE+ESPIRT process of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0111] Figure 7 A schematic diagram of the DAE+Capon process of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0112] Figure 8 A schematic diagram of a coordinate system for introducing a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0113] Fig. 9 This is a MUSIC estimation simulation spectrogram under different signal-to-noise ratios of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0114] Fig.10 A schematic diagram of dB MUSIC RMSE of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0115] Fig.11 This is a DAE+ESPIRT simulation diagram of a low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network proposed in the present invention;

[0116] Fig.12 The dB simulation spectra at different angles of a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network proposed in the present invention;

[0117] Fig.13 This is a CNN test result diagram of a low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network proposed in the present invention;

[0118] Fig.14 This is a schematic diagram of the running time of each algorithm of the low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network proposed in the present invention. DETAILED DESCRIPTION

[0119] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0120] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention; the terms "first", "second", and "third" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance. In addition, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0121] Reference Figure 1-14 The present invention provides an embodiment: a low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network, including a low signal-to-noise ratio DOA estimation method and a DOA estimation method combining DAE and CNN, characterized in that: the low signal-to-noise ratio DOA estimation method has the following steps:

[0122] S1: Given the number of array radar receiving antenna elements M, array element position dm, signal-to-noise ratio SNR, input signal sin and other parameters;

[0123] S2: Get the array received data covariance matrix R;

[0124] S3: Take the real and imaginary parts of the covariance matrix R of the received signal within the range of incident angle [-60°, 60°] as the input Y1 of the neural network, construct a data set, and distinguish between a training set and a test set in a ratio of 8:2;

[0125] S4: Initialize the DAE network parameters, import the data in the training set, complete the forward propagation, and simultaneously backpropagate the error and update the network weights synchronously; repeat this step many times until the network converges, save the network parameters, and obtain the DAE output data

[0126] S5: Initialize the CNN network. Send it to the network, add the angle channel, and start training the CNN network after interpolation, using the actual angle as the label. After the training is completed, save the network parameters;

[0127] S6: Import the test set data into the network to test the network performance;

[0128] S7: After the test is completed, the network structure and parameters are fixed. The network can be used to estimate DOA under low signal-to-noise ratio conditions to obtain the elevation angle estimate.

[0129] In the present invention, the steps of the DOA estimation method combining DAE and CNN are as follows:

[0130] S1, first extract the covariance matrix after the signal and noise subspaces permeate each other under low signal-to-noise ratio conditions;

[0131] S2, take the real part, imaginary part and phase of the covariance matrix as network input features, introduce them into DAE to improve the signal-to-noise ratio of the array received signal to improve the subsequent CNN classification accuracy;

[0132] S3, model the DOA estimation problem as a multi-label classification model, add the denoised covariance matrix to CNN, and use CNN to construct a deep learning network for DOA estimation;

[0133] S4. Improve the estimation performance and computational efficiency under low signal-to-noise ratio through the generalization ability and nonlinear mapping ability of CNN; simulation results show that under low signal-to-noise ratio, compared with traditional algorithms such as MUSIC, ESPIRT, and Capon, the method proposed in this paper significantly reduces the mean square error of angle estimation.

[0134] Furthermore, a signal model is established:

[0135] Generally speaking, for far-field signals, there is a path difference when the same signal reaches different array elements. This path difference further causes the phase difference of the signal between the receiving array elements. The direction of the signal arrival can be obtained by using the phase difference between the array elements.

[0136] The echo signal can be represented by the following complex envelope form:

[0137]

[0138] In the formula, u i (t) is the received signal amplitude, is the phase of the received signal, ω0 is the frequency of the received signal;

[0139] Considering the distance R>>λ between the target and the antenna array in radar operation, the echo can be regarded as a far-field narrowband signal, so

[0140]

[0141] Then the signal received by the lth array element is

[0142]

[0143] In the formula, represents the gain of the lth array element for the i-th signal, n l (t) is the noise received by the lth array element at time t, τ li It represents the delay of the i-th signal reaching the l-th array element relative to the reference array element;

[0144] Ideally, assuming that each array element is isotropic and does not have the influence of mutual coupling, channel inconsistency and other factors, the gain in equation (3) can be normalized to 1, and then equation (3) can be rewritten as a vector form:

[0145] x(t)=AS(t)+N(t) (4)

[0146] Where X(t) is the M×1-dimensional snapshot data vector, N(t) is the M×1-dimensional noise data vector, A(t) is the N×1-dimensional vector of the received signal, and A is the M×N-dimensional steering vector array.

[0147] A=[a1(w0) a2(ω0) … a N (ω0)] (5)

[0148] The steering vector is

[0149]

[0150] This article takes a typical uniform linear array as an example. The schematic diagram of the array structure is as follows Figure 1 As shown, the array element position is x k (k=1,2,...,M), the signal incident elevation angle and azimuth angle are (i=1,2,...,N), then

[0151]

[0152] (1) To ensure that the columns of the steering vector matrix are linearly independent, the number of signal sources is less than the number of array elements;

[0153] (2) The noise sequence obeys a zero-mean Gaussian process, the noise of each array element is independent of each other, and the signal and noise are independent of each other;

[0154] (3) Each array element is isotropic and there is no inconsistency in the mutual coupling channels;

[0155] From the mathematical model of equation (4), according to the above assumptions, the covariance matrix of the array snapshot data can be obtained as follows:

[0156] R=E{XX H}

[0157] =AE{SS H} H +E{NN H}

[0158] =AR S A H +R N (8)

[0159] Where RS and RN are the covariance matrices of the signal and noise respectively. 2 The ideal white noise sequence is

[0160] R=AR s A H +R N

[0161] =AR S A H +σ 2 I (9).

[0162] Furthermore, a multiple signal classification algorithm and a rotation-invariant subspace algorithm are established;

[0163] The multiple signal classification algorithm is to decompose the array output covariance matrix eigenvalues ​​to obtain the signal subspace formed by the signal components and the noise subspace orthogonal to the signal components, and then use the orthogonality of the subspaces to estimate the signal parameters (incident direction, signal strength and polarization information, etc.);

[0164] First, the covariance matrix R of the array data in formula (9) is decomposed into

[0165]

[0166] Where Us is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues, and Un is the noise subspace spanned by the eigenvectors corresponding to the small eigenvalues;

[0167] Under ideal conditions, the signal subspace and the noise subspace are orthogonal to each other, that is, the steering vector of the signal subspace is also orthogonal to the noise subspace, then

[0168] a H (θ)U N =0( 11 )

[0169] Formula (11) is also the core solution idea of ​​the MUSIC algorithm. Considering that the actual array output matrix is ​​of finite length, the maximum likelihood estimate of R is

[0170]

[0171] Where L is the number of sampling points for received data;

[0172] right Performing eigendecomposition can obtain the noise subspace eigenvector matrix Due to the presence of noise, a H (θ) and If they are not completely orthogonal, the estimated arrival angle in actual engineering is obtained by minimum optimization search, that is,

[0173]

[0174] Then the spatial spectrum estimation formula of the MUSIC algorithm is:

[0175]

[0176] The rotation invariant subspace algorithm is based on the rotation invariance of the signal subspace of the array received data covariance matrix. When estimating signal parameters, it requires that the geometric structure of the array is rotation invariant, that is, the array itself has two or more identical subarrays, or the same subarray can be obtained through some transformation. For the same signal, since the two subarrays are exactly the same, their outputs differ by only φ i , assuming that the outputs of the two sub-arrays are X1 and X2 respectively, according to the array model of formula (4), we have

[0177] X1=[a(θ1) … a(θ N )]S+N1

[0178] =AS+N1 (15)

[0179]

[0180] In the formula, the steering vector matrix of subarray 1 is A, the steering vector matrix of subarray 2 is, and there is

[0181]

[0182] The direction information of the signal is contained in A and Φ, and Φ is a diagonal matrix, so we can get

[0183] φ k =(2π|Δ|sinθ k ) / λ (18)

[0184] Where Δ is the spacing between two sub-arrays;

[0185] Therefore, as long as the relationship Φ between the two sub-arrays is obtained and then substituted into equation (18) to solve, the angle estimation value can be obtained. First, the two sub-array models are merged, that is,

[0186]

[0187] The covariance matrix under ideal conditions is

[0188]

[0189] The characteristic decomposition can be obtained

[0190]

[0191] Where US is the signal subspace spanned by the eigenvectors corresponding to large eigenvalues, and UN is the noise subspace spanned by the eigenvectors corresponding to small eigenvalues. Considering the actual snapshot data, equation (21) is modified to

[0192]

[0193] The signal subspace spanned by the eigenvectors corresponding to the large eigenvalues ​​and the signal subspace spanned by the steering vectors should be equal, then there exists a non-singular matrix T such that

[0194]

[0195] And it holds true for both of the above sub-matrices, that is

[0196]

[0197] Bringing in the relationship between the two arrays, we get

[0198] U S2 =U S1 T -1 ΦT=U S1 Ψ (25)

[0199] Formula (25) reflects the rotation invariance between the signal subspaces of the two subarrays receiving data. If the received signals are incoherent, that is, the steering vector array A is a full-rank matrix, then

[0200] Φ=TΨT -1 (26)

[0201] After obtaining the above rotation invariant relationship matrix Ψ, we can substitute it into equation (18) to get the signal angle;

[0202] The Capon algorithm is also a spectrum peak search algorithm. The DOA estimation value is determined by the angle at which equation (27) reaches its minimum value.

[0203]

[0204] Where θ is the angle estimate, Receives the covariance matrix of the data as an array.

[0205] Furthermore, a DAE network structure is established: DAE is a variation of the autoencoder (AE). The difference is that DAE learns features by training the damaged data with noise added, and uses the input original data and the output denoised data to calculate the loss function and perform error back propagation.

[0206] The input data of the DAE network structure is the real and imaginary parts of the array received signal covariance matrix. A data set is created in the interval of [-60°, 60°] with an interval of 1°. The size is 2×M×M, where M is the number of array elements. The encoding layer is composed of 4 layers of two-dimensional convolutional layers, nonlinear activation layers, and pooling layers. The loss function uses the mean square error function (MSE). After denoising, the mean square error function is used again to examine the denoising effect.

[0207] The network can be divided into the encoding part and the decoding part. The encoding part has 4 convolutional layers. The convolution kernel size of each convolutional layer is 4×4, the step size is 2 for downsampling, the edge padding is set to 1, and each convolutional layer is connected to a batch normalization layer and a Tanh nonlinear activation layer. Therefore, the size of the data matrix is ​​reduced to half of its original size after a convolution operation.

[0208] Working principle and usage flow: Preprocess the array received signal to obtain the signal covariance matrix. Since the signal will be interfered by various noises in the actual environment, the DAE network structure is used for noise reduction. The input data of the DAE network is the real and imaginary parts of the array received signal covariance matrix, and the data set is produced according to the set interval.

[0209] During the training phase, the noisy data is input into the encoding part of the DAE network. The encoding part extracts features from the input data through four convolutional layers. Each convolutional layer captures local features through the convolution kernel and introduces nonlinear factors through nonlinear activation functions, so that the network can learn more complex features. At the same time, the data of each layer is normalized through the batch normalization layer to speed up the network training process and prevent overfitting.

[0210] After being processed by the encoding part, the network outputs the denoised data. Then, the denoised data is input to the decoding part for reconstruction. The structure of the decoding part is similar to that of the encoding part, but in the opposite direction. The feature map is restored to the size of the original data through the deconvolution operation. Finally, the mean square error between the original data and the reconstructed data is calculated as the loss function, and the weights and biases of the network are updated through the back-propagation algorithm.

[0211] After training, the DAE network has the ability to reduce noise and extract features. In the DOA estimation stage, the covariance matrix of the array received signal is input into the trained DAE network, and the network automatically extracts the signal features and removes noise interference. Then, the Capon algorithm or other DOA estimation algorithms are used to perform angle estimation based on the extracted signal features.

[0212] Specifically, the output of the DAE network can be used as the input of the Capon algorithm, and the angle estimation value of the signal can be obtained by calculating the minimum value of formula (27). Since the DAE network has performed noise reduction on the signal, the accuracy and robustness of DOA estimation can be improved.

[0213] The entire usage process includes data preprocessing, DAE network training, DOA estimation and other steps. In actual applications, it can be adjusted and optimized according to specific needs and scenarios to achieve better performance.

[0214] Embodiment 1: The DAE network is trained using an unsupervised learning method (training without given labels), and the array received signal under the classic array signal model is used as the data set source. The real and imaginary parts of the covariance matrix of the array received signal are used as network inputs to construct a data set. To ensure the generalization of the network, the training set and the test set are distinguished in a ratio of 8:2. The process and method of generating the data set are briefly described below.

[0215] First, the angles are evenly divided in the airspace to form a discrete angle set. Considering the actual working conditions of the radar, the angle is set to [-60°, 60°], the step size is 1°, the number of array elements is 24, the array element spacing is 0.5m, the number of snapshots is set to 1000, the input signal is a Gaussian white noise signal with a mean of 0 and a variance of 1, the number of Monte Carlo times is 100, and the training set and test set are distinguished in a ratio of 8:2. The data dimension is [2×24×24], that is, the number of channels is 2, and the length and width are 24 and 24 respectively. During training, the input data is added with a mean of 0 and a variance of

[0216]

[0217] In the formula, SNR_dB is the signal-to-noise ratio after adding, in decibels, and is set to 0dB here, that is, the signal-to-noise ratio becomes 0dB after adding noise to the original data. Then it is imported into the network for forward propagation, and the output is still 2×24×24. Then the mean square error of the original data without adding noise and the output data is calculated and back propagated. The loss function is set to MSE, and the calculation formula is

[0218]

[0219] In the formula is the output of the noisy data after passing through the network, R is the original data without noise added, and K is the number of Monte Carlo times.

[0220] DAE uses the back-propagation algorithm to minimize the MSE loss function to train the network parameters, and uses Adam to optimize the network parameters. After forward propagation, the error is back-propagated to adjust and update the network parameters. After multiple repetitions, the objective function converges, that is, the loss is minimized.

[0221] To prevent overfitting, a batch normalization layer

[31] is added between the convolutional layer and the nonlinear activation layer to reduce the gradient elimination and gradient explosion problems, improve network training speed and performance, and improve generalization. After multiple rounds of training, the actual output of the network is The training is completed as it gets closer and closer to the original data R. The network performance is then tested through the validation set to determine the network training level and generalization performance. At the same time, since the DAE network has many parameters, in order to make the network converge in the right direction, a strategy of dynamically adjusting the learning rate is adopted. As the training progresses, the learning rate is gradually reduced, that is, the learning rate LR is multiplied by a decay factor of 7 every 10 cycles to avoid oscillation while making it converge to the optimal or suboptimal result as soon as possible.

[0222] Embodiment 2: DOA estimation is performed by combining the traditional physics-driven algorithm and the deep learning data-driven algorithm. After the covariance matrix of the array received signal is denoised, the DOA estimation is performed using traditional estimation algorithms such as MUSIC, ESPIRT and Capon. The algorithm flow is as follows.

[0223] After denoising the covariance matrix with low signal-to-noise ratio, a covariance matrix closer to the original data is obtained, which is then introduced into the classic MUSIC algorithm for DOA estimation.

[0224] The denoised data matrix is ​​connected to CNN using a transfer learning strategy. The CNN network structure draws on the Alexnet

[32] , VGG

[36] and ResNet

[37] network structures. To ensure that the classification results correspond to the dataset labels, a fully connected layer is added after the last output layer of the network to make the output dimension 120.

[0225] Different from the DAE training method, CNN uses supervised learning method for training (given data and labels for training), and uses the covariance matrix of the array received data after DAE network denoising is the input data, is the number of matching network input channels, and is the covariance matrix An angle channel is added with the actual angle as the label, and the image size is expanded to (224, 224)

[38] using the bilinear interpolation method. The steps of the bilinear interpolation algorithm are briefly described below.

[0226] Bilinear interpolation utilizes the correlation of the data around the pixels of the original image (matrix) and is calculated through a bilinear algorithm. This paper maps the real and imaginary parts of the covariance matrix into two channels of image grayscale for processing. For any target coordinates. Through backward mapping, the corresponding floating-point coordinates (i+u,j+v) in the original image are obtained, where i and j are non-negative integers, and u and v are decimals in the interval [0,1]. The pixel value f(i+u,j+v) corresponding to the desired point can be obtained from the original image (i,j), (i+1,j), (i,j+1), The pixel values ​​of the four points (i+1, j+1) are obtained by interpolation, namely:

[0227] Where f(i,j) represents the pixel value at (i,j) in the original image.

[0228] like Figure 5 As shown, given the grayscale values ​​of (0,0), (0,1), (1,0), and (1,1), i.e., the real and imaginary parts of the array received data covariance matrix, we can linearly interpolate f(0,0) and f(0,1) in the X direction to get the grayscale value f(x,0) of (x,0). Similarly, we can get f(x,1). Then, linear interpolation in the Y direction can get the grayscale f(x,y) of (x,y).

[0229] After the training data passes through the CNN network, the actual output is Select CrossEntropyLoss as the loss function, that is

[0230]

[0231] CNN uses the SGD optimizer to update network parameters, and updates network weights through error back propagation after forward propagation, repeating the process multiple times until the objective function converges.

[0232] Embodiment three:

[0233] In the simulation experiment, Python language is used to implement physical algorithms such as MUSIC, ESPIRT and Capon as well as the deep learning algorithm mentioned in this paper in the PyCharm integrated development environment. The pytorch framework is used to implement the deep learning network. Different signal-to-noise ratios and snapshot numbers are selected to compare and analyze the estimation performance of different algorithms under low signal-to-noise ratio.

[0234] The simulation conditions are set to be consistent. The antenna array is a uniform linear array with a one-dimensional linear arrangement. The number of array elements is 24. The physical position of the array elements is {0, d, 2d, ..., 23d}, d = 0.5λ, the wavelength is 1m, the radar transmission signal is a Gaussian white noise with a mean of 0 and a variance of 1, the number of space targets is 1, and the added noise is Gaussian white noise. Monte Carlo repeated experiments are used to compare and analyze the estimation accuracy of different algorithms. The number of experiments is designed to be 100 times, and the DOA estimation RMSE is

[0235]

[0236] Where K represents the Monte Carlo order, is the k-th estimated angle.

[0237] This group of simulation conditions is set to snapshot number L=1000, the signal-to-noise ratio is 0dB after adding noise to the original data in the training set, the training set size is 9600, and the noise [-10,10]dB is added in the test set in sequence. The root mean square error of the covariance matrix after adding noise compared with the original data after passing through the network is examined. The control group is the root mean square error without using DAE denoising under the same conditions. The simulation results show that the DAE denoising performance is relatively good and can significantly improve the signal-to-noise ratio.

[0238] The experimental conditions for this group of experiments were set to the snapshot number L = 1000, and two cases were distinguished: (1) the signal-to-noise ratio was [-10, 10] dB after noise was added to the original data, and the RMSE of angle measurement with and without DAE noise reduction was mainly compared; (2) the signal-to-noise ratio was -10 dB after noise was added to the original data, and the MUSIC spatial spectrum was used as the comparison standard, with the angle search range of [-60°, 60°] and the search interval of 1°.

[0239] When the signal-to-noise ratio is -10dB during training, three angle spatial spectra are randomly selected for investigation, such as Fig.10 The simulation results show that: under the conditions of -10dB, 0dB and 10dB signal-to-noise ratio of the test set, DAE noise reduction processing can effectively improve the estimation accuracy of the MUSIC algorithm, and can effectively improve the sharpness of the spectrum peak while ensuring the correctness of the angle measurement results.

[0240] When the signal-to-noise ratio is [-10, 10] after adding noise to the input signal, the covariance matrix of the array received signal after adding noise in the entire training set is subjected to DAE denoising, and then the spatial spectrum is estimated using the MUSIC algorithm. The control group does not use DAE for denoising, and the root mean square error is calculated. During training, different power noises are added to make the signal-to-noise ratio [-10, 10] dB step size 5, and the impact of different training modes on RMSE is investigated. The simulation results are shown in the figure. Figure 11-14 As shown. The simulation results show that: (1) Using DAE for noise reduction can significantly reduce the RMSE of MUSIC algorithm angle measurement under low signal-to-noise ratio, and the system robustness is improved, the adaptability to low signal-to-noise ratio is improved, and the algorithm performance is improved; (2) When the signal-to-noise ratio of the array received signal is greater than 0dB, using DAE will reduce the measurement accuracy, and the algorithm has limitations when the signal-to-noise ratio is high; (3) The greater the noise power added during training, the worse the DAE network's learning effect on signal features, and the curve intersection moves to the left, and vice versa, the curve intersection moves to the right, but it will not exceed 0dB. The reason is that when the signal power is greater than the noise power, the DAE network will destroy the matrix structure, resulting in a decrease in the angle measurement accuracy of the MUSIC algorithm. However, after checking the spectrum peak, it is found that when the signal-to-noise ratio is high, DAE can still improve the sharpness of the spectrum peak while ensuring a small mean square error.

[0241] During training, different power noises were added to make the signal-to-noise ratio [-10, 10] dB with a step size of 5. The impact of different training modes on RMSE was investigated. The simulation results are shown in the figure. Figure 11-14 The simulation results show that: (1) Using DAE for noise reduction can significantly reduce the RMSE of the ESPIRT algorithm under low signal-to-noise ratio, and the system robustness is improved, the adaptability to low signal-to-noise ratio is improved, and the algorithm performance is improved; (2) When the signal-to-noise ratio of the array received signal is greater than 2dB, the use of DAE will reduce the measurement accuracy, and the algorithm has limitations when the signal-to-noise ratio is high; (3) Unlike the DAE+MUSIC algorithm, the noise power added during training has little effect on the intersection of the curves.

[0242] The experimental conditions for this group of experiments were set to the snapshot number L = 1000, and two cases were distinguished: (1) the signal-to-noise ratio was [-10, 10] dB after noise was added to the original data, and the RMSE of angle measurement with and without DAE noise reduction was mainly compared; (2) the signal-to-noise ratio was -10 dB after noise was added to the original data, and the Capon space spectrum was used as the comparison standard, with the angle search range of [-60°, 60°] and the search interval of 1°.

[0243] When the signal-to-noise ratio is -10dB, three angle spatial spectra are randomly selected for investigation, such as Fig.10The simulation results show that: under the condition of -10dB signal-to-noise ratio, after DAE noise reduction processing, the spatial spectrum is calculated by Capon algorithm. Although the sharpness is improved to a certain extent, the sidelobe amplitude is still high and the minimum value is not easy to observe. The reason for this is that the standard Capon algorithm model mismatch error is very sensitive, resulting in reduced system robustness.

[0244] When the signal-to-noise ratio is [-10,10] after adding noise to the input signal, the covariance matrix of the array received signal after adding noise in the entire training set is processed by DAE for denoising, and then the Capon algorithm is used for spatial spectrum estimation. The control group does not use DAE for denoising, and the root mean square error is calculated. The simulation results show that using DAE for denoising can reduce the RMSE of the Capon algorithm for angle measurement to a certain extent and improve its adaptability to low signal-to-noise ratio, but the angle measurement error is still large and the estimation result is not accurate enough.

[0245] Without changing the experimental conditions, the covariance matrix of the array received signal processed by DAE denoising was imported into CNN for DOA estimation. The number of cycles was set to 30 times, the batch size was set to 128, the loss was set to the cross entropy loss function, the optimizer was set to Adam optimizer, the learning rate was 0.001, the weight decay was 0.0005, the label range was [-60°, 60°], the step size was 1°, the sample value of each angle in the training set was set to 80, and the test set was set to 20. The network structures used were Alexnet, VGG16 and Resnet18 respectively.

[0246] During the training phase, as the number of training rounds increases, the accuracy of angle estimation is effectively improved. Fig.13 The simulation results show that when the signal-to-noise ratio is [-10dB, 10dB], the accuracy of the DAE+CNN algorithm on the test set is higher, that is, the angle measurement accuracy is higher, which proves the effectiveness of the algorithm proposed in this paper in improving the angle measurement accuracy under low signal-to-noise ratio.

[0247] The MUSIC algorithm and the ESPIRT algorithm are superior to various DL algorithms when the number of array elements is small, but the algorithm running time is greatly affected by the number of array elements. When the number of array elements is approximately 30 and 70, the running time is longer than the DL algorithm. The main reason is that in order to adopt the transfer learning strategy and adapt to the network structure at the same time, the covariance matrix needs to be enlarged to (224, 224), which increases the amount of calculation.

[0248] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A low signal-to-noise ratio DOA estimation method based on an autoencoder and a deep neural network, including a low signal-to-noise ratio DOA estimation method and a DOA estimation method combining DAE and CNN, characterized in that: The steps of low signal-to-noise ratio DOA estimation method are as follows: S1: Given the number of array radar receiving antenna elements M, array element position dm, signal-to-noise ratio SNR, input signal sin and other parameters; S2: Get the array received data covariance matrix R; S3: Take the real and imaginary parts of the covariance matrix R of the received signal within the range of incident angle [-60°, 60°] as the input Y1 of the neural network, construct a data set, and distinguish between a training set and a test set in a ratio of 8:2; S4: Initialize the DAE network parameters, import the data in the training set, complete the forward propagation, and simultaneously backpropagate the error and update the network weights synchronously; repeat this step many times until the network converges, save the network parameters, and obtain the DAE output data S5: Initialize the CNN network. Send it to the network, add the angle channel, and start training the CNN network after interpolation, using the actual angle as the label. After the training is completed, save the network parameters; S6: Import the test set data into the network to test the network performance; S7: After the test is completed, the network structure and parameters are fixed. The network can be used to estimate DOA under low signal-to-noise ratio conditions to obtain the elevation angle estimate.

2. The low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network according to claim 1, characterized in that: The steps of the DOA estimation method combining DAE and CNN are as follows: S1, first extract the covariance matrix after the signal and noise subspaces permeate each other under low signal-to-noise ratio conditions; S2, take the real part, imaginary part and phase of the covariance matrix as network input features, introduce them into DAE to improve the signal-to-noise ratio of the array received signal to improve the subsequent CNN classification accuracy; S3, model the DOA estimation problem as a multi-label classification model, add the denoised covariance matrix to CNN, and use CNN to construct a deep learning network for DOA estimation; S4. Improve the estimation performance and computational efficiency under low signal-to-noise ratio through the generalization ability and nonlinear mapping ability of CNN; simulation results show that under low signal-to-noise ratio, compared with traditional algorithms such as MUSIC, ESPIRT, and Capon, the method proposed in this paper significantly reduces the mean square error of angle estimation.

3. The low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network according to claim 2, characterized in that: Build the signal model: Generally speaking, for far-field signals, there is a path difference when the same signal reaches different array elements. This path difference further causes the phase difference of the signal between the receiving array elements. The direction of the signal arrival can be obtained by using the phase difference between the array elements. The echo signal can be represented by the following complex envelope form: In the formula, u i (t) is the received signal amplitude, is the phase of the received signal, ω0 is the frequency of the received signal; Considering the distance R>>λ between the target and the antenna array in radar operation, the echo can be regarded as a far-field narrowband signal, so Then the signal received by the lth array element is In the formula, 1g li represents the gain of the lth array element for the i-th signal, n l (t) is the noise received by the lth array element at time t, τ li It represents the delay of the i-th signal reaching the l-th array element relative to the reference array element; Ideally, assuming that each array element is isotropic and does not have the influence of mutual coupling, channel inconsistency and other factors, the gain in equation (3) can be normalized to 1, and then equation (3) can be rewritten as a vector form: X(t)=AS(t)+N(t)(4) Where X(t) is the M×1-dimensional snapshot data vector, N(t) is the M×1-dimensional noise data vector, A(t) is the N×1-dimensional vector of the received signal, and A is the M×N-dimensional steering vector array. A=[a1(ω0) a2(ω0)…a N (ω0)] (5) The steering vector is This paper takes a typical uniform linear array as an example. The schematic diagram of the array structure is shown in Figure 1. The array element position is x k (k=1,2,...,M), the signal incident elevation angle and azimuth angle are Then there is (1) To ensure that the columns of the steering vector matrix are linearly independent, the number of signal sources is less than the number of array elements; (2) The noise sequence obeys a zero-mean Gaussian process, the noise of each array element is independent of each other, and the signal and noise are independent of each other; (3) Each array element is isotropic and there is no inconsistency in the mutual coupling channels; From the mathematical model of equation (4), according to the above assumptions, the covariance matrix of the array snapshot data can be obtained as follows: R=E{XX H } =AE{SS H }A H +E{NN H } =ON S A H +R N (8) Where RS and RN are the covariance matrices of the signal and noise respectively. 2 The ideal white noise sequence is R=AR S A H +R N =AR s A H +σ 2 I (9)。 4. The low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network according to claim 3, characterized in that: Establish multiple signal classification algorithms and rotation-invariant subspace algorithms; The multiple signal classification algorithm is to decompose the array output covariance matrix eigenvalues ​​to obtain the signal subspace formed by the signal components and the noise subspace orthogonal to the signal components, and then use the orthogonality of the subspaces to estimate the signal parameters (incident direction, signal strength and polarization information, etc.); First, perform eigendecomposition on the covariance matrix R of the array data in equation (9): Where Us is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues, and Un is the noise subspace spanned by the eigenvectors corresponding to the small eigenvalues; Under ideal conditions, the signal subspace and the noise subspace are orthogonal to each other, that is, the steering vector of the signal subspace is also orthogonal to the noise subspace, then a H (i)U N =0 (11) Formula (11) is also the core solution idea of ​​the MUSIC algorithm. Considering that the actual array output matrix is ​​of finite length, the maximum likelihood estimate of R is Where L is the number of sampling points for received data; right Performing eigendecomposition can obtain the noise subspace eigenvector matrix Due to the presence of noise, a H (θ) and If they are not completely orthogonal, the estimated arrival angle in actual engineering is obtained by minimum optimization search, that is, Then the spatial spectrum estimation formula of the MUSIC algorithm is: The rotation invariant subspace algorithm is based on the rotation invariance of the signal subspace of the array received data covariance matrix. When estimating signal parameters, it requires that the geometric structure of the array is rotation invariant, that is, the array itself has two or more identical subarrays, or the same subarray can be obtained through some transformation. For the same signal, since the two subarrays are exactly the same, their outputs differ by only φ i , assuming that the outputs of the two sub-arrays are X1 and X2 respectively, according to the array model of formula (4), we have X1=[a(θ1)…a(θ N )]S+N1 =AS+N1 (15) In the formula, the steering vector matrix of subarray 1 is A, the steering vector matrix of subarray 2 is, and there is The direction information of the signal is contained in A and Φ, and Φ is a diagonal matrix, so we can get f k =(2π|Δ|sinθ k ) / l (18) Where Δ is the spacing between two sub-arrays; Therefore, as long as the relationship Φ between the two sub-arrays is obtained and then substituted into equation (18) to solve, the angle estimation value can be obtained. First, the two sub-array models are merged, that is, The covariance matrix under ideal conditions is The characteristic decomposition can be obtained Where US is the signal subspace spanned by the eigenvectors corresponding to large eigenvalues, and UN is the noise subspace spanned by the eigenvectors corresponding to small eigenvalues. Considering the actual snapshot data, equation (21) is modified to The signal subspace spanned by the eigenvectors corresponding to the large eigenvalues ​​and the signal subspace spanned by the steering vectors should be equal, then there exists a non-singular matrix T such that And it holds true for both of the above sub-matrices, that is Bringing in the relationship between the two arrays, we get U S2 =U S1 T -1 ΦT=U S1 Ψ (25) Formula (25) reflects the rotation invariance between the signal subspaces of the two subarrays receiving data. If the received signals are incoherent, that is, the steering vector array A is a full-rank matrix, then Φ=TΨT -1 (26) After obtaining the above rotation invariant relationship matrix Ψ, we can substitute it into equation (18) to get the signal angle; The Capon algorithm is also a spectrum peak search algorithm. The DOA estimation value is determined by the angle at which equation (27) reaches its minimum value. Where θ is the angle estimate, Receives the covariance matrix of the data as an array.

5. The low signal-to-noise ratio DOA estimation method based on autoencoder and deep neural network according to claim 1, characterized in that: Establishing the DAE network structure: DAE is a variation of the autoencoder (AE). The difference is that DAE learns features by training the corrupted data with added noise, and uses the input original data and the output denoised data to calculate the loss function and perform error back propagation. The input data of the DAE network structure is the real and imaginary parts of the array received signal covariance matrix. A data set is created in the interval of [-60°, 60°] with an interval of 1°. The size is 2×M×M, where M is the number of array elements. The encoding layer is composed of 4 layers of two-dimensional convolutional layers, nonlinear activation layers, and pooling layers. The loss function uses the mean square error function (MSE). After denoising, the mean square error function is used again to examine the denoising effect. The network can be divided into the encoding part and the decoding part. The encoding part has 4 convolutional layers. The convolution kernel size of each convolutional layer is 4×4, the step size is 2 for downsampling, the edge padding is set to 1, and each convolutional layer is connected to a batch normalization layer and a Tanh nonlinear activation layer. Therefore, the size of the data matrix is ​​reduced to half of its original size after a convolution operation.

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