Signal direction of arrival estimation method and system based on machine learning

Abstract

The embodiment of the invention provides a signal direction-of-arrival estimation method based on machine learning, and the method comprises the steps: constructing a sparse uniform linear array, enabling a signal to enter the sparse uniform linear array, and carrying out the marking; taking the marked sparse signals as a training set and a test set, and obtaining a signal direction-of-arrival estimation model through neural network training; and estimating the signal direction of arrival through the signal direction of arrival estimation model. According to the method, the sparse uniform linear array is constructed and input to the neural network for training to obtain the signal direction-of-arrival estimation model, and then the signal direction-of-arrival is estimated through the model, so that the direction-of-arrival estimation accuracy is improved to a great extent.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a signal direction of arrival estimation method based on machine learning; in addition, the present invention also relates to a signal direction of arrival estimation system based on machine learning. Background Art

[0002] Direction of arrival refers to the direction of arrival of a spatial signal, that is, the directional angle of each signal arriving at the reference element of the array. It is an important concept in the theory of spatial spectrum estimation. Spatial spectrum estimation mainly studies the ability of spatial multi-sensor arrays to accurately estimate multiple parameters of spatial signals. The main purpose is to estimate the spatial parameters of the signal or the source position. Direction of arrival estimation is one of the two major research directions of array signal processing and is of great significance for improving the performance of communication systems.

[0003] The premise of solving the traditional DOA estimation is to select an appropriate regularization parameter, but the error vector is unknown. Since the size of the error vector is negatively correlated with the signal-to-noise ratio, in reality, the noise or signal is unknown, so the selection of the regularization parameter is an open problem, which leads to poor accuracy of DOA estimation. Summary of the invention

[0004] In order to solve the problems existing in the prior art, at least one embodiment of the present invention provides a signal direction of arrival estimation method based on machine learning, which greatly improves the accuracy of the direction of arrival estimation. To this end, at least one embodiment of the present invention also provides a signal direction of arrival estimation system based on machine learning.

[0005] In a first aspect, an embodiment of the present invention provides a signal direction of arrival estimation method based on machine learning, comprising:

[0006] Construct a sparse uniform linear array, inject the signal into the sparse uniform linear array and mark it;

[0007] The labeled sparse signals are used as training sets and test sets, and the signal direction of arrival estimation model is obtained through neural network training;

[0008] The signal direction of arrival is estimated through a signal direction of arrival estimation model.

[0009] In some embodiments, the present invention provides a signal direction of arrival estimation, and constructing a sparse uniform linear array includes:

[0010] Define a uniform linear array with M array elements and an equidistant half-wavelength spacing between array elements. Suppose K signals are incident from the far field and the sampling interval is Δθ. The angle space is uniformly sampled into a discrete grid of length N, which can be expressed as The array observation data is expressed by the following equations 1 and 2:

[0011]

[0012] Among them, x is the array observation data, is the array manifold matrix, is a sparse vector in the spatial domain, is the mth element of the steering vector; the sparse spectrum estimation is expressed by the following equation 4:

[0013]

[0014] Where η is a regularization parameter related to the noise power; the eigenvector is expressed by the following equation 5:

[0015]

[0016] in, represents a sparse vector with sparsity K, Δ is the error vector of eigenvector estimation; the sparse spectrum estimation based on the eigenvector is expressed by the following formula 6:

[0017]

[0018] Where ηΔ is a regularization parameter related to the error vector Δ.

[0019] In some embodiments, the present invention provides a signal direction of arrival estimation, wherein the signal is incident on a sparse uniform linear array and marked, including:

[0020] The label of the training network is expressed by the following formula 7:

[0021]

[0022] Among them, round(θ k ) represents the k The rounding operation of k represents the amplitude of the kth signal, θ k is the signal source angle of the kth unknown direction, is the nth discrete grid angle.

[0023] In some embodiments, the present invention provides a signal direction of arrival estimation, and a signal direction of arrival estimation model is obtained by neural network training, including:

[0024] The neural network is a deep feedforward network, which includes six network layers. ReLU activation function is added to the first five network layers of the deep feedforward network, and softmax activation function is added to the output layer of the deep feedforward network. The softmax activation function is expressed by the following formula 8:

[0025]

[0026] Among them, Zi is the output of the i-th neuron in the output layer.

[0027] In some embodiments, the present invention provides a signal direction of arrival estimation, and the loss function of the deep feedforward network is expressed by the following equations 9 and 10:

[0028]

[0029] θ={C (p) ,b (p)} p＝1,2,...,6 Formula 10;

[0030] Among them, C (p) is the weight of the pth layer, n (p) is the bias vector of the pth layer, α(n) is the element in the label vector, are the elements in the output vector.

[0031] In some embodiments, the present invention provides a signal direction of arrival estimation, which calculates a sampling covariance matrix through array observation data, inputs the sampling covariance matrix as a training set into multiple deep convolutional neural networks with different output dimensions for training, outputs multiple reduced sparse spectra, and combines the multiple sparse spectra with different output dimensions.

[0032] In a second aspect, an embodiment of the present invention further provides a signal direction of arrival estimation system based on machine learning, comprising:

[0033] Building blocks for constructing sparse uniform linear arrays;

[0034] A marking module, used for injecting a signal into a sparse uniform linear array and marking the signal;

[0035] The training module is used to use the labeled sparse signals as training sets and test sets, and obtain the signal direction of arrival estimation model through neural network training;

[0036] The estimation module is used to estimate the signal arrival direction through a signal arrival direction estimation model.

[0037] In a third aspect, an embodiment of the present invention further provides a signal arrival direction estimation device based on machine learning, comprising at least one processor; a memory coupled to the at least one processor, the memory storing executable instructions, which when executed by the at least one processor implement the steps of any one of the methods of the first aspect above.

[0038] In a fourth aspect, an embodiment of the present invention further provides a chip for executing the steps of the method in the first aspect. Specifically, the chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip is used to execute the steps of the method in the first aspect.

[0039] In a fifth aspect, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of any one of the methods in the first aspect above are implemented.

[0040] It can be seen that the signal arrival direction estimation method and system based on machine learning in the embodiment of the present invention constructs a sparse uniform linear array and inputs it into a neural network for training to obtain a signal arrival direction estimation model, and then estimates the signal arrival direction through the model, thereby greatly improving the accuracy of the arrival direction estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0042] Figure 1 Shown is a schematic diagram of an array signal processing system according to an embodiment of the present invention;

[0043] Figure 2 Shown is a flow chart of a signal direction of arrival estimation method based on machine learning in an embodiment of the present invention;

[0044] Figure 3 Shown is a structural diagram of a deep feedforward network in an embodiment of the present invention;

[0045] Figure 4 Shown is a schematic diagram of the structure of DCNN1 in an embodiment of the present invention;

[0046] Figure 5 Shown is a schematic diagram of the framework of unsupervised learning in an embodiment of the present invention;

[0047] Figure 6 Shown is a schematic diagram of a sparse power spectrum in an embodiment of the present invention;

[0048] Figure 7 Shown is a schematic diagram of the framework of a signal direction of arrival estimation system based on machine learning in an embodiment of the present invention. Specific implementation plan

[0049] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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.

[0050] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. In this article, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0051] [Example 1]

[0052] The inventor of this solution found that in the prior art, the premise of solving the traditional DOA estimation is to select an appropriate regularization parameter, but the error vector is unknown. Since the size of the error vector is negatively correlated with the signal-to-noise ratio, in actual situations, the noise or signal is unknown, so the selection of the regularization parameter is an open problem, which leads to poor accuracy of DOA estimation.

[0053] like Figure 1 As shown, the array signal processing system consists of three parts: target signal space, array observation space and parameter estimation space.

[0054] Signal space refers to the space spanned by radiation source signals and complex environmental parameters.

[0055] The array observation space refers to the space where multiple antenna units form an array in a certain geometric shape to receive and sample the signals of spatial radiation sources. Due to the uncertainty and complexity of the signal space, the array observation data not only contains the characteristics of the relevant signals (such as the incident angle, power, polarization mode, etc. of the signal), but also contains the characteristics that are not related to the signal (such as noise, interference, clutter, etc.). In addition, since the antenna units and receiving channels cannot be completely consistent and there are interactions between antenna units, the observation data will also contain the characteristics of the observation space (such as inconsistent frequency bands of antenna units, inconsistent amplitudes and phases between channels, and mutual coupling between antenna units, etc.).

[0056] The parameter estimation space is to extract useful signal feature parameters from the observed data by means of feature extraction, suppress useless features or correct the influence of useless features on the estimation of signal feature parameters through certain algorithms.

[0057] Embodiment 1 of the present invention provides the following solution:

[0058] like Figure 2 As shown, this embodiment provides a signal direction of arrival estimation method based on machine learning, and the method includes the following steps:

[0059] Step 101, construct a sparse uniform linear array, inject a signal into the sparse uniform linear array and perform marking.

[0060] In some embodiments, a uniform linear array with M array elements and an equidistant half-wavelength spacing between array elements is defined. Assume that K signals are incident from the far field and the sampling interval is Δθ. The angle space is uniformly sampled into a discrete grid of length N, which is represented as: The array observation data is expressed by the following equations 1 and 2:

[0061]

[0062] Among them, x is the array observation data, is the array manifold matrix, is a sparse vector in the spatial domain, is the mth element of the steering vector; the sparse spectrum estimation is expressed by the following equation 4:

[0063]

[0064] Where η is a regularization parameter related to the noise power; the eigenvector is expressed by the following equation 5:

[0065]

[0066] in, represents a sparse vector with sparsity K, Δ is the error vector of eigenvector estimation; the sparse spectrum estimation based on the eigenvector is expressed by the following formula 6:

[0067]

[0068] Where ηΔ is a regularization parameter related to the error vector Δ.

[0069] In some embodiments, the above formula is organized into an objective function and expressed by the following formula 11:

[0070]

[0071] Selecting the initial sparse vector is an all-zero vector. For the i-th (i=0, 1, 2, ..., T) iteration, the calculation formula of ISTA is as follows:

[0072]

[0073] Where μ is the step size; k st is the soft threshold function. For any vector υ, the definition of the soft threshold function is expressed by the following formula 14:

[0074] k st (v,ε)=sgn(v)·max(|v|-ε,0) Equation 14;

[0075] Where sgn represents the sign function, ε is the threshold related to the regularization parameter λ, and · represents the element-by-element product. The sparse spectrum is obtained by iterative solution After that, the estimated value of the signal arrival direction is the position corresponding to its spectrum peak.

[0076] In some embodiments, the label of the training network is expressed by the following formula 7:

[0077]

[0078] Among them, round(θ k ) represents the k The rounding operation of k represents the amplitude of the kth signal, θ k is the signal source angle of the kth unknown direction, is the nth discrete grid angle.

[0079] Step 102: Using the labeled sparse signals as training sets and test sets, a signal direction of arrival estimation model is obtained through neural network training.

[0080] In some embodiments, the neural network is a deep feedforward network, which includes six network layers. A ReLU activation function is added to the first five network layers of the deep feedforward network, and a softmax activation function is added to the output layer of the deep feedforward network.

[0081] It should be noted that if Figure 3 As shown in the figure, the neural network is a feedforward deep network with 6 network layers, and each layer of the network is designed as a fully connected / dense layer. The first layer is the input layer of the network, and the number of its neurons is consistent with the dimension of the feature vector ω1. The last layer is the output layer, and the number of its neurons is consistent with the number of spatial grids N; the middle 4 layers are hidden layers. Since N>M, the dimension of the hidden layer increases from M to N in sequence, so the dimension of the hidden layer can be expressed by the following formula 15:

[0082] n p =γ p N type 15;

[0083] where p = 2, ..., 6, n p represents the dimension of the pth network layer of the neural network, γ p is a scaling factor, which represents the ratio of the dimension of the pth network layer of the neural network to the dimension of the output layer, and γ6=1.

[0084] A nonlinear activation function is added to the output of neurons in each network layer of the neural network, so that the neural network can fit complex nonlinear functions. The ReLU activation function is added to the first 5 network layers (dense layers), which can effectively avoid the problem of gradient vanishing during gradient back propagation. Although there may be angle information of multiple different signals in multiple snapshot array data, the vector output by the DNN is a sparse spectrum, so it is necessary to add sparse constraints to the output of the output layer of the DNN. The nonlinear activation function softmax constrains the sum of all output units to 1, so adding a softmax activation function to the output layer of the neural network can constrain the spectrum output by the DNN to be a sparse spectrum. The softmax activation function is expressed by the following formula 8:

[0085]

[0086] Among them, Zi is the output of the i-th neuron in the output layer. After the softmax function, the output of the output layer is restricted to [0,1] and the sum of all units is 1. The output of the neural network is is a normalized sparse spectrum.

[0087] Since the parameters of the neural network are real numbers, and the network input w1 is a complex vector, we consider using the real and imaginary parts of w1 to concatenate to get a new input vector v, and the input vector v is expressed by the following formula 16:

[0088]

[0089] Among them, χ(w1) and δ(w1) are the real part and imaginary part operations respectively. The output of the network can be regarded as the prediction of the normalized sparse spectrum. Taking v as the input of the network, the output of the pth layer of the network is expressed by the following equations 17 and 18:

[0090] h (p) =g (p) (C (p)T h (p-1) +b (p) ) Formula 17;

[0091]

[0092] Where p = 1, 2, ..., 6, C (p)T and b (p) Represent the weight calculation matrix and bias vector of the pth layer, n p-1 is the number of neural units in the p-1th layer, np is the number of neural units in the pth layer; h (p-1) is the output of the p-1th layer; g (p) (·) represents the activation function of the p-th layer.

[0093] In the feedforward process, each layer of the network is equivalent to a nonlinear function, which performs a nonlinear transformation on the input of this layer before inputting it to the next layer. For the entire neural network, the set of all its parameters is expressed by the following formula 10:

[0094] θ={C (p) ,b (p)} p＝1,2,...,6 Formula 10;

[0095] The cross entropy loss function between the distribution expressed by the network parameter model and the generated data distribution is defined by the following equations 9 and 10:

[0096]

[0097] Among them, C (p) is the weight of the pth layer, b (p) is the bias vector of the pth layer, α(n) is the element in the label vector, are the elements in the output vector.

[0098] It can be understood that the training of the above neural network is to first calculate the gradient of the loss function with respect to the parameters, and then perform reverse gradient propagation in the opposite direction of the feedforward network calculation to update the parameters.

[0099] In some embodiments, a sampling covariance matrix is ​​calculated through array observation data, and the sampling covariance matrix is ​​input as a training set into multiple deep convolutional neural networks with different output dimensions for training, and multiple reduced sparse spectra are output, and the multiple sparse spectra with different output dimensions are combined.

[0100] It should be noted that when N>M, the number of parameters of the neural network mainly depends on the dimension N of the network output layer, that is, the density of the grid. As N increases, the number of parameters of the neural network increases with N. 2 As a result, the size of the parameters in the DNN becomes larger and more difficult to train. In addition, for larger N, the label storage of the dataset also requires a huge amount of memory.

[0101] The model's complex related signals are directly input into the deep convolutional neural network through the covariance matrix, allowing the network to learn and automatically extract the complex feature information in the covariance matrix. In order to reduce the quantization error of the sparse reconstruction model without increasing the complexity of the network, the large-dimensional sparse spectrum is modulo different prime numbers to obtain several sparse spectra of smaller dimensions. By training multiple small-scale deep convolutional neural networks to output multiple reduced-dimensional sparse spectra, the parameter scale of the deep convolutional neural network and the storage volume of the data set labels are greatly reduced. Finally, the original sparse spectrum is reconstructed by combining multiple reduced-dimensional sparse spectra to achieve the purpose of reducing the quantization error.

[0102] Specifically, a uniform linear array with M array elements and a spacing of half a wavelength d between array elements is defined. Assume that K far-field narrowband signals are incident on the array, and the incident directions are [θ1,...,θ2] T Taking the center of the array as the reference point, the output of the mth array element is expressed by the following equation 19:

[0103]

[0104] Where m = -m c ,...,m c , s k (t) is the transmitted signal, e m (t) is additive white Gaussian noise, a m (θ k ) is the normalized steering vector The mth element of k is the angle of the signal source in the unknown direction. Convert equation 19 into a vector form and express it through the following equation 20:

[0105] x(t)=As(t)+e(t) Formula 20;

[0106] Where s(t)=[s1(t),s1(t),...,s k(t)] T , s(t) represents the signal at time t, and e(t) is additive Gaussian white noise.

[0107] Assume that the array sampling output data within a period of time has L sampling snapshots, and the array sampling output within a period of time is:

[0108] X=AS+E

[0109] The spatial sampling covariance matrix of the array sampling data is expressed by the following equation 21:

[0110]

[0111] Where R SS is a diagonal matrix, representing the signal covariance matrix; σ 2 The table is the noise power of white noise, and I is the unit matrix.

[0112] The sampling covariance matrix is ​​calculated, and the real part real(R) and imaginary part imag(R) of the sampling covariance matrix are input into the deep convolutional neural network respectively. The output of the deep convolutional neural network is still a sparse amplitude spectrum. In order to reduce the quantization error, three deep convolutional neural networks are set in the algorithm framework, namely DCNN1, DCNN2 and DCNN3. The structures of the three deep convolutional neural networks are exactly the same. The only difference is that the dimensions of their output layers are N, P, and Q, respectively, where P is the largest prime number less than N, and Q is the smallest prime number greater than N.

[0113] In [-θ0,θ0], The sampling interval Δθ is uniformly sampled into a discrete grid of length N. For any angle θ k ∈[-θ0,θ0], can be approximately quantified by the following formula 22:

[0114]

[0115] The normalized sparse spectrum output by DCNN1 is α N , where the value of each element is shown in formula 23:

[0116]

[0117] Among them, σ k is the amplitude of the kth signal.

[0118] Select two mutually prime positive integers P and Q as the dimensions of the folded spectra of the outputs of DCNN2 and DCNN3, respectively, where P is the largest prime number less than N and Q is the smallest prime number greater than N. Sparse spectrum α P and α QThe values ​​of the elements in are defined by the following equations 24 and 25:

[0119]

[0120] Where p=1,2,...,P;q=1,2,...,Q;a=b mod c means a is the remainder of b divided by c. k When modP=0, let p=P; when n′ k When mod Q = 0, let q = Q. The sparse spectrum is reconstructed by combining the output results of the three DCNNs to obtain more accurate angle information.

[0121] like Figure 4 As shown in the figure, DCNN1 is a deep network with 8 network layers. The first 4 network layers are convolutional network layers, and the last 4 network layers are Dense layers, i.e. fully connected layers. Since the inputs of the two networks are divided into real and imaginary parts, the network contains two channels corresponding to the real and imaginary parts respectively. The convolution kernel size in each convolution layer Conv is 3×3, and the number of convolution kernels in the 1st to 4th layers is 32, 32, 64, and 64 respectively. The number of units in the first 3 Dense layers is 512, and the number of units in the final output layer corresponds to the dimension of the sparse spectrum. The nonlinear activation function used in all layers is the ReLU function.

[0122] Step 103, the signal arrival direction is estimated by the signal arrival direction estimation model. It can be understood that after the training is completed, given any unknown signal, the signal arrival direction estimation model can reconstruct its corresponding normalized sparse amplitude spectrum, and the incident angle of the signal can be obtained by searching for the peak of the sparse amplitude spectrum and locating the peak position in the spatial discrete grid.

[0123] In some other embodiments, the signal arrival direction is estimated using an unsupervised learning model. Specifically, the original sparse spectrum model takes a uniform circular array as an example. Consider a uniform circular array containing M isotropic array elements, the array radius is r, and it is assumed that there is a virtual reference array element at the origin. The array model of the uniform circular array can be modeled to know that the time delay of the signal reaching other array elements compared to the virtual reference array element can be obtained by the following

[0124] Formula 26 represents:

[0125]

[0126] Where c = 3 × 10 8 represents the propagation speed of electromagnetic waves in space. Assume that there are K far-field narrowband signals from The data observed by the array at time t is expressed by the following equation 27:

[0127]

[0128] Where x(t) and e(t) represent the array data and the amount of additive Gaussian white noise, respectively; represents the array flow matrix, whose k-th column is a column vector, represents the steering vector of the kth signal; represents the mth element of the steering vector, w0 is the frequency of the incident signal; s(t) represents the complex signal vector.

[0129] vector It has strong sparsity, so the following sparse spectrum reconstruction can be constructed, which is expressed by the following formula 28:

[0130]

[0131] Using multiple snapshots of array observation data for denoising, the overcomplete expression of L snapshots of circular array observation data is expressed by the following equation 29:

[0132]

[0133] Where X = [x(t1), x(t2), ···, x(t L )] represents the array observation data of L sampling snapshots; L sparse vectors with sparsity K; E = [e(t1), e(t2), ···, e(t L )] represents the complex valued additive Gaussian white noise matrix superimposed on the L snapshot array sampling outputs. The sparse matrix Sˉ is reconstructed by the following equation 30:

[0134]

[0135] The unsupervised training loss function is based on the unsupervised uniform circular array signal direction of arrival estimation algorithm framework. Figure 5 As shown. First, the real and imaginary parts of the covariance matrix are extracted as the input of the deep convolutional neural network. In the algorithm framework, three deep convolutional neural networks are set, namely DCNN1, DCNN2 and DCNN3. The three networks output sparse vectors of dimensions P1, P2 and P3 respectively, where P1, P2 and P3 are three mutually prime integers. The root-folded sparse spectra ρ1, ρ2 and ρ3 contain independent angle information. The reconstruction of the sparse power spectrum is expressed by the following formula 31:

[0136] p=I1p1+I2p2+I3p3 Equation 31; The pseudo power spectrum is defined by the following equation 32:

[0137]

[0138] Where V represents an overcomplete measurement matrix under a two-dimensional discrete grid, that is, the measurement matrix V is a known complex matrix. In addition, the pseudo spectrum is the result of beamforming the covariance observation vector y^.

[0139] The objective function is expressed as a loss function by the following equation 33:

[0140]

[0141] The loss function contains two terms. The first term is the mean square error term between the sparse power spectrum reconstructed by the deep convolutional neural network output and the pseudo power spectrum. The second term is the sparsity constraint term for the sparse power spectrum. Since the calculation of the loss function only requires the output and covariance matrix of the network but does not require the label corresponding to the covariance matrix, the proposed algorithm realizes unsupervised training of the network. Finally, the three networks are trained independently and in parallel under the same loss function.

[0142] The three deep convolutional neural networks have the same network structure except for the number of neurons in the output layer. DCNN1 is a deep network with 8 network layers, the first 4 network layers are convolutional network layers, and the last 4 network layers are dense layers. Since the input of the two networks is divided into real and imaginary parts, the network contains two channels corresponding to the real and imaginary parts respectively. The size of the convolution kernel in each convolutional layer is 3×3, and the number of convolution kernels in the 1st to 4th layers is 32, 32, 64, and 64 respectively. The number of units in the first 3 dense layers is 512, and the number of units in the final output layer corresponds to the dimension of the folded spectrum. The nonlinear activation function used in all layers is the ReLU function.

[0143] When the network training is completed, the sampling covariance matrix calculated by inputting the array observation data can get the folding spectrum predicted by the network. Consider two equal amplitude signals incident on the array from (30 degrees, 180 degrees) and (60 degrees, 120 degrees). The signal-to-noise ratio of the two signals is 10dB. Use 200 snapshot array observation data to calculate the covariance matrix to test the network.

[0144] like Figure 6 As shown, the sparse power spectrum produces multiple spectral lines near the true angle, but these spectral lines do not have obvious spectral peaks. It can be seen that in the airspace without angle incidence, the corresponding value of the sparse power spectrum is 0. In addition, although there is no obvious peak at the true angle, the distribution of the spectral lines is obviously clustered. Therefore, in order to obtain the signal arrival direction estimation of the true angle, the clustered sparse power spectrum is analyzed. It can be seen that the sparse power spectrum is clustered near the true angle, which means that multiple signal arrival direction estimates are clustered near the true angle. Assume that the angle of the K signals is For the kth signal, the sparse power spectrum is at the angle The set of signal direction of arrival estimates is

[0145] Since the set Θ^ k The elements in are distributed in clusters, so the center of the cluster with respect to the pitch angle θ˙ can be calculated separately k and the center of the azimuth Then the final estimated values ​​of the elevation angle and azimuth angle of the kth signal can be expressed by the estimated values ​​of the elevation angle and azimuth angle closest to the center of the set through the following equation 34:

[0146]

[0147] For all K signals, according to the criteria, the signal arrival direction estimation values ​​need to be divided into K sets first, then the elevation and azimuth centers of the K sets are calculated, and finally the signal arrival direction estimation value closest to each center is found as the final signal arrival direction estimation value. The K-means clustering algorithm is used to calculate the center of the spectral line cluster to obtain the final signal arrival direction estimation value.

[0148] The K-means algorithm includes the following steps:

[0149] Step 1: extract the elevation angle and azimuth angle of the sparse power spectrum lines to construct a signal arrival direction estimation set, where the number of spectral lines in the sparse power spectrum that are not zero is obtained.

[0150] Step 2: Assume that the number of signals K is known, and randomly select K elements from the set as the elevation angle cluster center and the azimuth angle cluster center respectively;

[0151] Step 3: For each θ^i in the set, calculate its absolute distance to the K pitch angle cluster centers and select the class with the smallest distance to mark it and divide it into the corresponding class; similarly, for each φ^i in the set, calculate its distance to the K azimuth angle cluster centers and divide it into the class corresponding to the cluster center with the closest distance;

[0152] Step 4: Use the sample mean of each category to update the cluster center of each class of pitch angle and azimuth angle respectively, and repeat steps 3 and 4 until the cluster center no longer changes;

[0153] Step 5: Calculate the final DOA estimate of the kth signal based on the kth signal direction of arrival estimate and the cluster centers of the elevation angle and azimuth angle;

[0154] Step 6: Repeat step 5 until the final signal direction of arrival estimate of all K signals is obtained.

[0155] [Example 2]

[0156] like Figure 7 As shown, this embodiment provides a signal direction of arrival estimation system based on machine learning, including

[0157] The construction module 201 is used to construct a sparse uniform linear array.

[0158] In some embodiments, a uniform linear array with M array elements and an equidistant half-wavelength spacing between array elements is defined. Assume that K signals are incident from the far field and the sampling interval is Δθ. The angle space is uniformly sampled into a discrete grid of length N, which is represented as: The array observation data is expressed by the following equations 1 and 2:

[0159]

[0160] Among them, x is the array observation data, is the array manifold matrix, is a sparse vector in the spatial domain, is the mth element of the steering vector; the sparse spectrum estimation is expressed by the following equation 4:

[0161]

[0162] Where η is a regularization parameter related to the noise power; the eigenvector is expressed by the following equation 5:

[0163]

[0164] in, represents a sparse vector with sparsity K, Δ is the error vector of eigenvector estimation; the sparse spectrum estimation based on the eigenvector is expressed by the following formula 6:

[0165]

[0166] Where ηΔ is a regularization parameter related to the error vector Δ.

[0167] In some embodiments, the above formula is organized into an objective function and expressed by the following formula 11:

[0168]

[0169] Selecting the initial sparse vector is an all-zero vector. For the i-th (i=0, 1, 2, ..., T) iteration, the calculation formula of ISTA is as follows:

[0170]

[0171] Where μ is the step size; k stis the soft threshold function. For any vector υ, the definition of the soft threshold function is expressed by the following formula 14:

[0172] k st (ν,ε)=sgn(v)·max(|v|-ε,0) Equation 14;

[0173] Where sgn represents the sign function, ε is the threshold related to the regularization parameter λ, and · represents the element-by-element product. The sparse spectrum is obtained by iterative solution After that, the estimated value of the signal arrival direction is the position corresponding to its spectrum peak.

[0174] The marking module 202 is used to inject the signal into the sparse uniform linear array and perform marking.

[0175] In some embodiments, the label of the training network is expressed by the following formula 7:

[0176]

[0177] Among them, round(θ k ) represents the k The rounding operation of k represents the amplitude of the kth signal, θ k is the signal source angle of the kth unknown direction, is the nth discrete grid angle.

[0178] The training module 203 is used to use the marked sparse signals as training sets and test sets, and obtain a signal direction of arrival estimation model through neural network training.

[0179] In some embodiments, the neural network is a deep feedforward network, which includes six network layers. A ReLU activation function is added to the first five network layers of the deep feedforward network, and a softmax activation function is added to the output layer of the deep feedforward network.

[0180] It should be noted that if Figure 3 As shown in the figure, the neural network is a feedforward deep network with 6 network layers, and each layer of the network is designed as a fully connected / dense layer. The first layer is the input layer of the network, and the number of its neurons is consistent with the dimension of the feature vector ω1. The last layer is the output layer, and the number of its neurons is consistent with the number of spatial grids N; the middle 4 layers are hidden layers. Since N>M, the dimension of the hidden layer increases from M to N in sequence, so the dimension of the hidden layer can be expressed by the following formula 15:

[0181] n p =γ p N type 15;

[0182] where p = 2, ..., 6, np represents the dimension of the pth network layer of the neural network, γ p is a scaling factor, which represents the ratio of the dimension of the pth network layer of the neural network to the dimension of the output layer, and γ6=1.

[0183] A nonlinear activation function is added to the output of neurons in each network layer of the neural network, so that the neural network can fit complex nonlinear functions. The ReLU activation function is added to the first 5 network layers (dense layers), which can effectively avoid the problem of gradient vanishing during gradient back propagation. Although there may be angle information of multiple different signals in multiple snapshot array data, the vector output by the DNN is a sparse spectrum, so it is necessary to add sparse constraints to the output of the output layer of the DNN. The nonlinear activation function softmax constrains the sum of all output units to 1, so adding a softmax activation function to the output layer of the neural network can constrain the spectrum output by the DNN to be a sparse spectrum. The softmax activation function is expressed by the following formula 8:

[0184]

[0185] Among them, Zi is the output of the i-th neuron in the output layer. After the softmax function, the output of the output layer is restricted to [0,1] and the sum of all units is 1. The output of the neural network is is a normalized sparse spectrum.

[0186] Since the parameters of the neural network are real numbers, and the network input w1 is a complex vector, we consider using the real and imaginary parts of w1 to concatenate to get a new input vector v, and the input vector v is expressed by the following formula 16:

[0187]

[0188] Among them, χ(w1) and δ(w1) are the real part and imaginary part operations respectively. The output of the network can be regarded as the prediction of the normalized sparse spectrum. Taking v as the input of the network, the output of the pth layer of the network is expressed by the following equations 17 and 18:

[0189] h (p) =g (p) (C (p)T h (p-1) +b (p) ) Formula 17;

[0190]

[0191] Where p = 1, 2, ..., 6, C (p)T and b (p) Represent the weight calculation matrix and bias vector of the pth layer, np-1 is the number of neural units in the p-1th layer, np is the number of neural units in the pth layer; h (p-1) is the output of the p-1th layer; g (p) (·) represents the activation function of the p-th layer.

[0192] In the feedforward process, each layer of the network is equivalent to a nonlinear function, which performs a nonlinear transformation on the input of this layer before inputting it to the next layer. For the entire neural network, the set of all its parameters is expressed by the following formula 10:

[0193] θ={C (p) ,b (p)} p＝1,2,...,6 Formula 10;

[0194] The cross entropy loss function between the distribution expressed by the network parameter model and the generated data distribution is defined by the following equations 9 and 10:

[0195]

[0196] Among them, C (p) is the weight of the pth layer, b (p) is the bias vector of the pth layer, α(n) is the element in the label vector, are the elements in the output vector.

[0197] It can be understood that the training of the above neural network is to first calculate the gradient of the loss function with respect to the parameters, and then perform reverse gradient propagation in the opposite direction of the feedforward network calculation to update the parameters.

[0198] In some embodiments, a sampling covariance matrix is ​​calculated through array observation data, and the sampling covariance matrix is ​​input as a training set into multiple deep convolutional neural networks with different output dimensions for training, and multiple reduced sparse spectra are output, and the multiple sparse spectra with different output dimensions are combined.

[0199] It should be noted that when N>M, the number of parameters of the neural network mainly depends on the dimension N of the network output layer, that is, the density of the grid. As N increases, the number of parameters of the neural network increases with N. 2 As a result, the size of the parameters in the DNN becomes larger and more difficult to train. In addition, for larger N, the label storage of the dataset also requires a huge amount of memory.

[0200] The model's complex related signals are directly input into the deep convolutional neural network through the covariance matrix, allowing the network to learn and automatically extract the complex feature information in the covariance matrix. In order to reduce the quantization error of the sparse reconstruction model without increasing the complexity of the network, the large-dimensional sparse spectrum is modulo different prime numbers to obtain several sparse spectra of smaller dimensions. By training multiple small-scale deep convolutional neural networks to output multiple reduced-dimensional sparse spectra, the parameter scale of the deep convolutional neural network and the storage volume of the data set labels are greatly reduced. Finally, the original sparse spectrum is reconstructed by combining multiple reduced-dimensional sparse spectra to achieve the purpose of reducing the quantization error.

[0201] Specifically, a uniform linear array with M array elements and a spacing of half a wavelength d between array elements is defined. Assume that K far-field narrowband signals are incident on the array, and the incident directions are [θ1,...,θ2] T Taking the center of the array as the reference point, the output of the mth array element is expressed by the following equation 19:

[0202]

[0203] Where m = -m c ,...,m c , s k (t) is the transmitted signal, e m (t) is additive white Gaussian noise, a m (θ k ) is the normalized steering vector The mth element of k is the angle of the signal source in the unknown direction. Convert equation 19 into a vector form and express it through the following equation 20:

[0204] x(t)=As(t)+e(t) Formula 20;

[0205] Where s(t)=[s1(t),s1(t),...,s k (t)] T , s(t) represents the signal at time t, and e(t) is additive Gaussian white noise.

[0206] Assume that the array sampling output data within a period of time has L sampling snapshots, and the array sampling output within a period of time is:

[0207] X=AS+E

[0208] The spatial sampling covariance matrix of the array sampling data is expressed by the following equation 21:

[0209]

[0210] Where RSS is a diagonal matrix, representing the signal covariance matrix; σ 2 The table is the noise power of white noise, and I is the unit matrix.

[0211] The sampling covariance matrix is ​​calculated, and the real part real(R) and imaginary part imag(R) of the sampling covariance matrix are input into the deep convolutional neural network respectively. The output of the deep convolutional neural network is still a sparse amplitude spectrum. In order to reduce the quantization error, three deep convolutional neural networks are set in the algorithm framework, namely DCNN1, DCNN2 and DCNN3. The structures of the three deep convolutional neural networks are exactly the same. The only difference is that the dimensions of their output layers are N, P, and Q, respectively, where P is the largest prime number less than N, and Q is the smallest prime number greater than N.

[0212] In [-θ0,θ0], The sampling interval Δθ is uniformly sampled into a discrete grid of length N. For any angle θ k ∈[-θ0,θ0], can be approximately quantified by the following formula 22:

[0213]

[0214] The normalized sparse spectrum output by DCNN1 is α N , where the value of each element is shown in formula 23:

[0215]

[0216] Among them, σ k is the amplitude of the kth signal.

[0217] Select two mutually prime positive integers P and Q as the dimensions of the folded spectra of the outputs of DCNN2 and DCNN3, respectively, where P is the largest prime number less than N and Q is the smallest prime number greater than N. Sparse spectrum α P and α Q The values ​​of the elements in are defined by the following equations 24 and 25:

[0218]

[0219] Where p=1,2,...,P;q=1,2,...,Q;a=b mod c means a is the remainder of b divided by c. k When modP=0, let p=P; when n′ k When mod Q = 0, let q = Q. The sparse spectrum is reconstructed by combining the output results of the three DCNNs to obtain more accurate angle information.

[0220] like Figure 4As shown in the figure, DCNN1 is a deep network with 8 network layers. The first 4 network layers are convolutional network layers, and the last 4 network layers are Dense layers, i.e. fully connected layers. Since the inputs of the two networks are divided into real and imaginary parts, the network contains two channels corresponding to the real and imaginary parts respectively. The convolution kernel size in each convolution layer Conv is 3×3, and the number of convolution kernels in the 1st to 4th layers is 32, 32, 64, and 64 respectively. The number of units in the first 3 Dense layers is 512, and the number of units in the final output layer corresponds to the dimension of the sparse spectrum. The nonlinear activation function used in all layers is the ReLU function.

[0221] The estimation module 204 is used to estimate the signal direction of arrival by using a signal direction of arrival estimation model.

[0222] It can be understood that after the training is completed, given any unknown signal, the signal arrival direction estimation model can reconstruct its corresponding normalized sparse amplitude spectrum. The incident angle of the signal can be obtained by searching for the peak of the sparse amplitude spectrum and locating the peak in the spatial discrete grid.

[0223] [Example 3]

[0224] This embodiment provides a signal direction of arrival estimation device based on machine learning, including:

[0225] At least one processor; a memory coupled to the at least one processor, the memory storing executable instructions, wherein the executable instructions, when executed by the at least one processor, implement the method steps of embodiment 1 of the present invention.

[0226] An embodiment of the present invention provides a signal direction of arrival estimation device based on machine learning, in which the processor and the memory can be provided separately or integrated together.

[0227] For example, the memory may include a random access memory, a flash memory, a read-only memory, a programmable read-only memory, a non-volatile memory or a register, etc. The processor may be a central processing unit (CPU), etc. or a graphic processing unit (GPU). The memory may store executable instructions. The processor may execute the executable instructions stored in the memory to implement the various processes described herein.

[0228] It can be understood that the memory in this embodiment can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. Among them, the non-volatile memory can be a ROM (Read-Only Memory), a PROM (Programmable ROM), an EPROM (Erasable PROM), an EEPROM (Electrically EPROM), or a flash memory. The volatile memory can be a RAM (Random Access Memory), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as SRAM (Static RAM), DRAM (Dynamic RAM), SDRAM (Synchronous DRAM), DDR SDRAM (Double Data Rate SDRAM), ESDRAM (Enhanced SDRAM), SLDRAM (Synchlink DRAM), and DRRAM (Direct Rambus RAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memories.

[0229] In some embodiments, the memory stores the following elements, upgrade packages, executable units or data structures, or a subset thereof, or an extended set thereof: an operating system and an application program.

[0230] The operating system includes various system programs, such as a framework layer, a core library layer, a driver layer, etc., which are used to implement various basic services and process hardware-based tasks. The application program includes various application programs, which are used to implement various application services. The program for implementing the method of the embodiment of the present invention can be included in the application program.

[0231] In the embodiment of the present invention, the processor calls a program or instruction stored in the memory, specifically, a program or instruction stored in an application program, and the processor is used to execute the method steps of the embodiment 1 of the present invention.

[0232] [Example 4]

[0233] This embodiment provides a chip for executing the method of the above-mentioned embodiment 1 of the present invention. Specifically, the chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip is used to execute the method of the embodiment 1 of the present invention.

[0234] [Example 5]

[0235] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method of Embodiment 1 of the present invention are implemented.

[0236] For example, machine-readable storage media may include, but are not limited to, various known and unknown types of non-volatile memory.

[0237] In summary, embodiments 1-5 of the present invention provide a signal arrival direction estimation method and system based on machine learning, which obtains a signal arrival direction estimation model by constructing a sparse uniform linear array and inputting it into a neural network for training, and then estimates the signal arrival direction through the model, thereby greatly improving the accuracy of arrival direction estimation.

[0238] It will be appreciated by those skilled in the art that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0239] In the embodiments of the present application, the disclosed systems, devices and methods can be implemented in other ways. For example, the division of units is only a logical function division, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system. In addition, the coupling between the various units can be direct coupling or indirect coupling. In addition, the various functional units in the embodiments of the present application can be integrated into a processing unit, or can be separate physical existences, etc.

[0240] It should be understood that in the various embodiments of the present application, the size of the serial number of each process does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0241] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a machine-readable storage medium. Therefore, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a machine-readable storage medium, which can include several instructions to enable an electronic device to perform all or part of the technical solution described in the embodiments of the present application. The above-mentioned storage medium may include various media that can store program codes, such as ROM, RAM, removable disk, hard disk, magnetic disk or optical disk.

[0242] The above contents are only specific implementation methods of the present application, and the protection scope of the present application is not limited thereto. Those skilled in the art may make changes or substitutions within the technical scope disclosed in the present application, and these changes or substitutions shall be within the protection scope of the present application.

Claims

1. A signal direction of arrival estimation method based on machine learning, characterized in that: include: Constructing a sparse uniform linear array, injecting a signal into the sparse uniform linear array and marking the signal; The labeled sparse signals are used as training sets and test sets, and the signal direction of arrival estimation model is obtained through neural network training; The signal direction of arrival is estimated by the signal direction of arrival estimation model.

2. The signal direction of arrival estimation method according to claim 1, characterized in that: The constructing of a sparse uniform linear array comprises: Define a uniform linear array with M array elements and an equidistant half-wavelength spacing between array elements. Suppose K signals are incident from the far field and the sampling interval is Δθ. The angle space is uniformly sampled into a discrete grid of length N, which can be expressed as The array observation data is expressed by the following equations 1 and 2: Among them, z is the array observation data, is the array manifold matrix, is a sparse vector in the spatial domain, is the mth element of the steering vector; the sparse spectrum estimation is expressed by the following equation 4: Where η is a regularization parameter related to the noise power; the eigenvector is expressed by the following equation 5: in, represents a sparse vector with sparsity K, Δ is the error vector of eigenvector estimation; the sparse spectrum estimation based on the eigenvector is expressed by the following formula 6: Where ηΔ is a regularization parameter related to the error vector Δ.

3. The signal direction of arrival estimation method according to claim 1, characterized in that: The injecting a signal into the sparse uniform linear array and marking the array comprises: The label of the training network is expressed by the following formula 7: Among them, round(θ k ) represents the k The rounding operation of k represents the amplitude of the kth signal, θ k is the signal source angle of the kth unknown direction, is the nth discrete grid angle.

4. The signal direction of arrival estimation method according to claim 3, characterized in that: The signal direction of arrival estimation model obtained by neural network training includes: The neural network is a deep feedforward network, which includes six network layers. A ReLU activation function is added to the first five network layers of the deep feedforward network, and a softmax activation function is added to the output layer of the deep feedforward network. The softmax activation function is expressed by the following formula 8: Among them, Zi is the output of the i-th neuron in the output layer.

5. The signal direction of arrival estimation method according to claim 4, characterized in that: The loss function of the deep feedforward network is expressed by the following equations 9 and 10: θ={C (p) ,b (p) } p＝1,2,...,6 Formula 10; Among them, C (p) is the weight of the pth layer, b (p) is the bias vector of the pth layer, α(n) is the element in the label vector, are the elements in the output vector.

6. The signal direction of arrival estimation method according to claim 2, characterized in that: The sampling covariance matrix is ​​calculated through array observation data, and the sampling covariance matrix is ​​used as a training set to input into multiple deep convolutional neural networks with different output dimensions for training, and multiple reduced sparse spectra with different output dimensions are output, and the multiple sparse spectra with different output dimensions are combined.

7. A signal direction of arrival estimation system based on machine learning, characterized in that: include: Building blocks for constructing sparse uniform linear arrays; A marking module, used for injecting a signal into the sparse uniform linear array and marking the signal; The training module is used to use the labeled sparse signals as training sets and test sets, and obtain the signal direction of arrival estimation model through neural network training; The estimation module is used to estimate the signal direction of arrival by using the signal direction of arrival estimation model.

8. A signal direction of arrival estimation device based on machine learning, comprising at least one processor; a memory coupled to the at least one processor, the memory storing executable instructions, characterized in that: The executable instructions, when executed by the at least one processor, enable the steps of the method according to any one of claims 1 to 6 to be implemented.

9. A chip, characterized in that: It comprises a processor, which is used to call and run a computer program from a memory, so that a device equipped with the chip executes the steps of the method as claimed in any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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