Airborne radar STAP method and system based on ANM depth expansion, and storage medium

Abstract

The invention discloses an airborne radar STAP method and system based on ANM depth expansion, and a storage medium. The method comprises the following steps: constructing an airborne radar echo signal model; the method comprises the following steps: setting airborne radar system parameters and a range, performing simulation based on an airborne radar echo signal model, randomly generating an echo signal matrix of L training distance units in each simulation, solving an ANM problem to obtain label data corresponding to the echo signal matrix, and dividing a training data set and a test data set; constructing a DU-ANM network based on an alternating direction multiplier method and a deep expansion technology; the method comprises the following steps: initializing learnable parameters of a DU-ANM network, and training the DU-ANM network; and processing actual data by using the trained DU-ANM network to obtain a CNCM estimation result, and calculating a STAP filter weighting vector for suppressing clutter and noise. The clutter and noise suppression performance can be ensured, and the calculation complexity is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of radar, and in particular, to an airborne radar STAP method, system, and storage medium based on ANM depth unfolding. Background Art

[0002] Space-time adaptive processing (STAP) is one of the basic technologies for realizing multi-channel adaptive signal detection and is also an airborne radar signal processing technology for effectively suppressing strong ground / sea clutter. The clutter plus noise covariance matrix (CNCM) determines the performance of STAP. In practical applications, the CNCM of the cell under test (CUT) is a priori unknown and is usually estimated by training samples of its independent and identically distributed (IID) adjacent range cells. The Reed-Mallett-Brennan (RMB) criterion was proposed by I.S. Reed, J.D. Mallett, and L.E. Brennan, “Rapid Convergence Rate in Adaptive Arrays,” IEEE Trans. Aerosp. Electron. Syst. vol. 10, no. 6, pp. 853-863, Nov. 1974. To ensure that the signal-to-interference-plus-noise ratio (SINR) loss after STAP processing is less than 3 dB compared to the optimal case, the number of independent and identically distributed training samples needs to be at least twice the system degrees of freedom. However, in a non-uniform clutter environment, it is usually difficult for an airborne radar to obtain sufficient independent and identically distributed training samples.

[0003] To reduce the number of IID training samples, the literature S. Sen, "Low-rank matrix decomposition and spatio-temporal sparse recovery for STAP radar," IEEE J. Sel. Top. Signal Process., vol. 9, no. 8, pp. 1510-1523, Dec. 2015 proposed a sparse recovery (SR)-based STAP (SR-STAP) method. SR-STAP utilizes the sparsity of clutter in the angle-Doppler (AD) plane and can accurately estimate the CNCM with fewer training range cells. However, due to the discreteness of the predefined spatio-temporal steering dictionary, SR-STAP may encounter the off-grid problem, resulting in performance degradation. The literature W. Feng, Y. Guo, Y. Zhang, and J. Gong, "Airborne radar space time adaptive processing based on atomic norm minimization," Signal Process., vol. 148, pp. 31-40, Jul. 2018 pointed out that the STAP method based on atomic norm minimization (ANM-STAP) does not require discretization of the AD domain and can avoid the off-grid problem. The ANM-STAP method can obtain an accurate estimate of the clutter covariance matrix (CCM) with a small number of training samples in the continuous domain by solving the ANM problem and performing eigenvalue decomposition. However, the existing ANM-STAP methods are computationally complex and it is difficult to manually set their parameters (such as the regularization and penalty factors). Improper parameter setting will affect the convergence speed and accuracy of the ANM algorithm, resulting in a decline in clutter and noise suppression performance.

[0004] Therefore, it is urgent to develop an ANM-STAP method that is convenient for parameter setting to solve the problems of poor clutter and noise suppression performance and high computational complexity in the existing technology. Summary of the Invention

[0005] The object of the present invention is to provide an airborne radar STAP method, system, and storage medium based on ANM deep unfolding, which can reduce the computational complexity while maintaining good clutter and noise suppression performance, and do not require manual parameter setting.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] An airborne radar STAP method based on ANM deep unfolding includes the following steps:

[0008] S1, constructing an airborne radar echo signal model;

[0009] S2. Set the parameters and range of the airborne radar system, perform Z simulations based on the airborne radar echo signal model. In each simulation, randomly generate an echo signal matrix for L training range cells, solve the ANM problem to obtain the label data corresponding to the echo signal matrix, form a signal matrix data set and a label data set, and divide them into a training data set and a test data set;

[0010] S3. Based on the alternating direction multiplier method and the deep unfolding technique, construct a DU-ANM network with K layers;

[0011] S4. Initialize the learnable parameters of the DU-ANM network, train the DU-ANM network based on the training data set, and learn the optimal parameters;

[0012] S5. Use the trained DU-ANM network to process the actual data, obtain the CNCM estimation result, and calculate the STAP filter weighting vector for suppressing clutter and noise.

[0013] Further, in S1, constructing the airborne radar echo signal model specifically includes:

[0014] Assume that the number of array elements of the airborne radar uniform linear array is N, the element spacing is d = λ / 2, where λ is the wavelength, the radar flies at a constant speed v and altitude h, and the pulse repetition frequency is f r , and a total of M pulses are transmitted within a coherent processing period. Then, the echo signal x of the range cell to be measured containing the target and the echo signal x of the l-th training range cell near the range cell to be measured without the target received by the airborne radar l are respectively expressed as:

[0015]

[0016] where, x c represents the clutter component of the range cell to be measured, and n represents the noise component of the range cell to be measured; α T represents the complex amplitude of the target, represents the spatio-temporal steering vector of the target; i = 1, 2,..., N c , N c is the number of clutter blocks evenly distributed in each range cell; α i represents the complex amplitude of the i-th clutter block in the range cell to be measured; represents the spatio-temporal steering vector of the i-th clutter block in the range cell to be measured; represents the clutter component of the l-th training range cell, and n l represents the noise component of the l-th training range cell; l = 1, 2,..., L, and L represents the number of training range cells; Denote the complex amplitude of the \(i\)-th clutter patch in the \(l\)-th training range cell; Denote the spatio-temporal steering vector of the \(i\)-th clutter patch in the \(l\)-th training range cell, denoted as Where:

[0017]

[0018] Among them, Denote the temporal steering vector of the \(i\)-th clutter patch in the \(l\)-th training range cell; Denote the spatial steering vector of the \(i\)-th clutter patch in the \(l\)-th training range cell; Denote the Kronecker product, [·] T Denote the matrix transpose; And Respectively denote the normalized Doppler frequency and spatial frequency of the \(i\)-th clutter patch in the \(l\)-th training range cell; And Are respectively the azimuth angle and elevation angle of the \(i\)-th clutter patch in the \(l\)-th training range cell.

[0019] Furthermore, for the above-mentioned S2, set the parameters and range of the airborne radar system, conduct \(Z\) simulations based on the airborne radar echo signal model. Each simulation randomly generates an echo signal matrix of \(L\) training range cells, and solves the ANM problem to obtain the label data corresponding to the echo signal matrix, forming a signal matrix data set and a label data set, and dividing them into a training data set and a test data set, which specifically includes the following steps:

[0020] S2.1, Set the parameters and range of the airborne radar system, including the number of array elements \(N\) of the airborne radar, the element spacing \(d\), the signal wavelength \(\lambda\), the flight speed \(v\), the altitude \(h\), the pulse repetition frequency \(f\) r , The number of coherent pulses \(M\), the number of clutter patches \(N\) c , The distance range of the range cells to be measured, the clutter-to-noise ratio range;

[0021] S2.2, Randomly generate an echo signal matrix \(X = [x_1, x_2, \cdots, x\) of \(L\) training range cells based on the airborne radar echo signal model L ;

[0022] S2.3, Solve the ANM problem to obtain the clutter signal matrix corresponding to the signal matrix \(X\) Hermitian matrix \(\varPsi\) A And complex matrix \(U\) A :

[0023]

[0024] Among them, \(X\) C And respectively represent the clutter signal matrices of the unknown and obtained L training range cells, Ψ and Ψ A respectively represent the Hermitian matrices of size L×L that are unknown and obtained, U and U A respectively represent the complex matrices of size (2N - 1)×(2M - 1) that are unknown and obtained, denotes the Toeplitz matrix formed by U, Tr(·) represents the trace of a matrix, ε n denotes the noise energy, ||·|| F represents the F-norm of a matrix;

[0025] S2.4. For the Toeplitz matrix formed by U A formed perform eigenvalue decomposition to obtain Based on Γ C , obtain the estimate of the clutter covariance matrix is expressed as:

[0026]

[0027] where, Γ C represents the eigenvector matrix of, Σ C represents the diagonal matrix formed by the eigenvalues of S(U), represents the l-th column of X C , diag(·) represents converting a vector into a diagonal matrix;

[0028] Based on estimate to obtain the CNCM of the range cell to be measured, which is expressed as:

[0029]

[0030] where, represents the noise power, I NM represents the identity matrix of size NM×NM;

[0031] S2.5. Perform eigenvalue decomposition on , and use the vector composed of the eigenvalues as the label data E corresponding to the echo signal matrix X A ;

[0032] S2.6. Repeat steps S2.2 to S2.5 a total of Z times to obtain the signal matrix dataset and the label dataset where, X z represents the echo signal matrix of the L training range cells obtained in the z-th simulation, represents the label data obtained in the z-th simulation, z = 1, 2,..., Z;

[0033] S2.7. Group the signal matrix dataset and the label dataset, and divide them into a training dataset and a test dataset according to a ratio of 4:1 and a test dataset where Q is the size of the training data, and O = Z - Q is the size of the test data

[0034] Further, in S3, based on the alternating direction multiplier method and the deep unfolding technique, construct a DU-ANM network with K layers, specifically including:

[0035] Based on the deep unfolding technique, unfold the ADMM algorithm with K iterations into a DU-ANM network with K layers. Among them, the non-linear function corresponding to the (k + 1)-th layer in the DU-ANM network is:

[0036]

[0037] where X is the echo signal matrix, used as the network input; ρ k+1 and τ k+1 are the learnable penalty factor and regularization factor of the (k + 1)-th layer of the network respectively; Λ k is the Lagrange multiplier of the k-th layer of the network; Θ k is the auxiliary variable of the k-th layer of the network; and respectively represent the matrices composed of the elements corresponding to X k , Ψ, and S(U) in Λ C ; and respectively represent the matrices composed of the elements corresponding to X k , Ψ, and S(U) in Θ C ; represents the mapping from an MN×MN matrix to a 2N - 1×2M - 1 matrix; E M,N represents a matrix of size 2N - 1×2M - 1, whose (M, N)-th element is 1 and the rest of the elements are 0; G and δ g are respectively 's eigenvector matrix and eigenvalue vector; diag({δ g}) is a diagonal matrix whose diagonal elements are δ g ; {δ g} + means setting all negative eigenvalues to zero, g = 1, 2, ···, MN + L; η k+1 is the learnable iteration step size of the (k + 1)-th layer of the network;

[0038] The input of the DU-ANM network is X, and the learnable parameters are and the direct output is Ψ K and UK , the indirect output is The final output is Eig K ; where represents the CNCM estimated based on U K and Eig K represents the vector composed of the eigenvalues of .

[0039] Furthermore, for the S4, initialize the learnable parameters of the DU-ANM network, and train the DU-ANM network based on the training data set to learn the optimal parameters, which specifically includes the following steps:

[0040] S4.1, initialize the learnable parameters of the DU-ANM network, denoted as where ρ0 is the initialization penalty factor, τ0 is the initialization regularization factor, and η0 is the initialization iteration step size;

[0041] S4.2, based on the training data set, train the DU-ANM network to learn the optimal parameters:

[0042] Construct the network loss function

[0043]

[0044] where div[a,b] means each element of vector a is divided by the corresponding element of vector b, and 1 represents a vector with each element being 1;

[0045] Based on the loss function Use the Adam algorithm for network training, and learn the optimal parameters through the backpropagation method denoted as:

[0046]

[0047] Furthermore, for the S5, use the trained DU-ANM network to process the actual data to obtain the CNCM estimation result, and calculate the STAP filter weighting vector for suppressing clutter and noise, which specifically includes the following steps:

[0048] S5.1, use the trained DU-ANM network to process the actual data to obtain the CNCM estimation result, denoted as:

[0049]

[0050] where Γ C,real is the eigenvector matrix of, X C,realand U real respectively represent the clutter signal matrix and the complex matrix of size (2N - 1)×(2M - 1) obtained by processing the actual data with the trained DU - ANM network, represents the l - th column of X C,real ;

[0051] S5.2. Based on the CNCM estimation result, calculate the STAP filter weight vector for suppressing clutter and noise, expressed as:

[0052]

[0053] The present invention also provides a depth - unfolded ANM - STAP system for performing the airborne radar STAP method based on ANM depth unfolding, including:

[0054] A construction module for constructing an airborne radar echo signal model;

[0055] A data set acquisition module for setting the parameters and range of the airborne radar system, performing Z simulations based on the airborne radar echo signal model, randomly generating the echo signal matrix of L training range cells each time, solving the ANM problem to obtain the label data corresponding to the echo signal matrix, forming a signal matrix data set and a label data set, and dividing them into a training data set and a test data set;

[0056] A DU - ANM network module for constructing a DU - ANM network with K layers based on the alternating direction method of multipliers and depth unfolding technology;

[0057] A training module for initializing the learnable parameters of the DU - ANM network and training the DU - ANM network based on the training data set to learn the optimal parameters;

[0058] A result module for processing the actual data with the trained DU - ANM network to obtain the CNCM estimation result and calculating the STAP filter weight vector for suppressing clutter and noise.

[0059] The present invention also provides a computer - readable storage medium storing computer instructions, which cause one or more processors to execute the steps in the method when the computer instructions are executed by the one or more processors.

[0060] According to the specific embodiments provided by the present invention, the following technical effects are disclosed: The airborne radar STAP method, system and storage medium based on the depth unfolding of ANM provided by the present invention establish an airborne radar clutter estimation model based on ANM and construct an ANM network based on depth unfolding. Then, by designing an appropriate loss function and constructing a complete data set to train the DU-ANM network. Finally, the trained DU-ANM network processes the training range cell data to obtain the clutter plus noise covariance matrix estimation and the STAP weighting vector. The simulation results show that compared with the existing ANM-STAP method, the proposed airborne radar STAP method based on the depth unfolding of ANM can achieve higher clutter and noise suppression performance at a lower computational cost, and can effectively reduce the number of iterations, the demand for training samples, reduce the computational complexity, and solve the problems of improper parameter setting and high computational complexity existing in the existing ANM-STAP method. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0062] Figure 1 It is a schematic diagram of the geometric model of the airborne radar in the embodiment of the present invention;

[0063] Figure 2 It is the structural diagram of the DU-ANM network in the embodiment of the present invention;

[0064] Figure 3 It is the CNCM estimation performance of the DU-ANM-STAP method and the optimal CVX-ANM-STAP method under different loss functions: (a)-(e) are respectively the Capon space-time spectra estimated by the DU-ANM-STAP method and the optimal CVX-ANM-STAP method trained based on formulas (12)-(15), and (f) is the corresponding signal-to-interference-noise ratio (SINR) loss;

[0065] Figure 4 It is a comparison chart of the running times of different methods: among them, (a) shows the relationship between the running times of different methods and the number of pulses under the conditions of L = 8 and N = M; (b) shows the relationship between the running times of different methods and the number of training range cells L under the conditions of N = M = 8;

[0066] Figure 5SINR losses for different methods: where, (a) shows the relationship between the SINR losses of different methods and the number of network layers and the number of iterations when fixing L = 8; (b) shows the relationship between the SINR losses of different methods and the number of training range cells when fixing the number of network layers and the number of iterations K = 25.

[0067] Figure 6 The figure is a flowchart of the airborne radar STAP method based on ANM deep unfolding according to an embodiment of the present invention. Detailed implementation manners

[0068] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0069] The purpose of the present invention is to provide an airborne radar STAP method, system and storage medium based on ANM deep unfolding, which can reduce the computational complexity while maintaining good clutter and noise suppression performance, and without the need for manual parameter setting.

[0070] To make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0071] Embodiment 1

[0072] As Figures 1 - 6 shown, an airborne radar STAP method based on ANM deep unfolding provided by an embodiment of the present invention includes the following steps:

[0073] S1, construct an airborne radar echo signal model;

[0074] S2, set the parameters and range of the airborne radar system, perform Z simulations based on the airborne radar echo signal model, randomly generate an echo signal matrix of L training range cells each time, solve the ANM problem to obtain the label data corresponding to the echo signal matrix, form a signal matrix data set and a label data set, and divide them into a training data set and a test data set;

[0075] S3, based on the alternating direction multiplier method and the deep unfolding technology, construct a DU-ANM network with K layers;

[0076] S4, initialize the learnable parameters of the DU-ANM network, train the DU-ANM network based on the training data set, and learn the optimal parameters;

[0077] S5. Use the trained DU-ANM network to process the actual data, obtain the CNCM estimation result, and calculate the STAP filter weighting vector for suppressing clutter and noise.

[0078] In this embodiment, the S1, constructing the airborne radar echo signal model, specifically includes:

[0079] As Figure 1 shown, assume that the number of array elements of the airborne radar uniform linear array is N, the element spacing is d = λ / 2, where λ is the wavelength, the radar flies at a constant speed v and altitude h, and the pulse repetition frequency is f r , and a total of M pulses are transmitted within one coherent processing period. Then, the echo signal x of the range cell under test containing the target and the echo signal x l of the l-th training range cell near the range cell under test without the target are respectively expressed as:

[0080]

[0081] Among them, x c represents the clutter component of the range cell under test, and n represents the noise component of the range cell under test; α T represents the complex amplitude of the target, represents the spatio-temporal steering vector of the target; i = 1, 2,..., N c , N c is the number of clutter blocks evenly distributed in each range cell; α i represents the complex amplitude of the i-th clutter block in the range cell under test; represents the spatio-temporal steering vector of the i-th clutter block in the range cell under test; represents the clutter component of the l-th training range cell, and n l represents the noise component of the l-th training range cell; l = 1, 2,..., L, where L represents the number of training range cells; represents the complex amplitude of the i-th clutter block in the l-th training range cell; represents the spatio-temporal steering vector of the i-th clutter block in the l-th training range cell, expressed as Among them:

[0082]

[0083] Among them, represents the temporal steering vector of the i-th clutter block in the l-th training range cell; represents the spatial steering vector of the i-th clutter block in the l-th training range cell; represents the Kronecker product, [·] T represents the matrix transpose; and represent the normalized Doppler frequency and spatial frequency of the i-th clutter patch in the l-th training range cell, respectively; and are the azimuth angle and elevation angle of the i-th clutter patch in the l-th training range cell, respectively.

[0084] Assume that each clutter patch is independent of each other and uncorrelated with the noise, and the noise follows a complex Gaussian distribution with a mean of 0 and a covariance matrix of Then, the clutter-plus-noise covariance matrix (CNCM) R of the range cell to be measured I can be expressed as:

[0085]

[0086] where, E[·] represents the expectation, (·) H represents the conjugate transpose of the matrix, represents the noise power, I NM represents the identity matrix of size NM×NM. By maximizing the SINR, the best STAP filter weight vector w for suppressing the clutter in the range cell to be measured and detecting the moving target opt is expressed as:

[0087]

[0088] where, (·) -1 represents the inverse of the matrix.

[0089] In practical applications, the CNCM of the range cell to be measured is usually unknown. Assume that the clutter signals of the training range cells and the clutter signals of the range cell to be measured are independent and identically distributed (IID). The sampling matrix inversion (SMI) method can be used to process the echo signals of L IID training range cells, and the CNCM of the range cell to be measured is estimated and expressed as However, in a non-uniform environment, it is generally difficult for the SMI-STAP method to obtain sufficient echo signals of IID training range cells. To address this problem, the SR-STAP method has been proposed. This type of method is based on the sparse characteristics of clutter in the spatio-temporal plane, and can obtain an accurate CNCM estimate using a small number of echo signals of IID training range cells. However, due to the discreteness of the pre-defined spatio-temporal steering dictionary, the SR-STAP method has an off-grid problem, which may lead to a serious degradation in the CNCM estimate and clutter suppression performance.

[0090] In this embodiment, in step S2, the parameters and range of the airborne radar system are set, and Z simulations are performed based on the airborne radar echo signal model. In each simulation, an echo signal matrix of L training range cells is randomly generated, and the label data corresponding to the echo signal matrix is obtained by solving the ANM problem, forming a signal matrix data set and a label data set, which are divided into a training data set and a test data set. The specific steps are as follows:

[0091] S2.1, set the parameters and range of the airborne radar system, including the number of array elements N of the airborne radar, the element spacing d, the signal wavelength λ, the flight speed v, the altitude h, the pulse repetition frequency f r , the number of coherent pulses M, the number of clutter blocks N c , the distance range of the range cells to be measured, the clutter-to-noise ratio range;

[0092] S2.2, based on the constructed airborne radar echo signal model, randomly generate an echo signal matrix X = [x1, x2, ···, x L of L training range cells;

[0093] S2.3, solve the ANM problem to obtain the clutter signal matrix Hermitian matrix Ψ A and complex matrix U A , specifically including:

[0094] The ANM-STAP method does not require discretization of the spatio-temporal plane and can obtain an accurate estimate of the CNCM with only a small number of training range cell echo signals, avoiding the off-grid problem of the SR-STAP method. This method directly estimates the CNCM in the continuous domain by solving the ANM problem, expressed as:

[0095]

[0096] where X C and respectively represent the unknown and obtained clutter signal matrices of L training range cells, Ψ and Ψ A respectively represent the unknown and obtained Hermitian matrices of size L×L, U and U A respectively represent the unknown and obtained complex matrices of size (2N - 1)×(2M - 1), represents the Toeplitz matrix formed by U, Tr(·) represents the trace of the matrix, ε n represents the noise energy, ||·|| F represents the Frobenius norm of the matrix;

[0097] S2.4, perform eigenvalue decomposition on the Toeplitz matrix A formed by U to obtain Based on Γ C , an estimate of the clutter covariance matrix is obtained which is expressed as:

[0098]

[0099] where Γ C denotes the eigenvector matrix of C , Σ denotes the diagonal matrix composed of the eigenvalues of , C denotes the l-th column of X

[0100] Based on the estimate, the CNCM of the distance cell to be measured is obtained, which is expressed as:

[0101]

[0102] S2.5, perform eigenvalue decomposition on , and use the vector composed of eigenvalues as the label data E corresponding to the echo signal matrix X A ;

[0103] S2.6, repeat steps S2.2 to S2.5 for a total of Z times to obtain the signal matrix data set and the label data set where X z denotes the echo signal matrix of L training distance cells obtained in the z-th simulation, denotes the label data obtained in the z-th simulation, z = 1, 2,..., Z;

[0104] S2.7, group the signal matrix data set and the label data set, and divide them into a training data set and a test data set where Q is the size of the training data and O = Z - Q is the size of the test data.

[0105] In this embodiment, in S3, based on the alternating direction multiplier method and the deep unfolding technique, a DU-ANM network with K layers is constructed, which specifically includes:

[0106] The ANM problem shown in Equation (5) can be solved by the SDPT3 solver in the convex optimization toolbox (CVX), but this method has a huge amount of computation. To improve the solution efficiency of Equation (5), the alternating direction multiplier method (ADMM) is used to rewrite Equation (5) as:

[0107]

[0108] Among them, τ > 0 represents the regularization factor.

[0109] Equation (8) can be transformed into the augmented Lagrangian form, expressed as:

[0110]

[0111] Among them, Λ is the Lagrange multiplier, <·,·> represents the inner product, and ρ > 0 is the penalty factor.

[0112] Equation (9) can be solved through the following iterative process:

[0113]

[0114] Among them, Ψ k+1 、U k+1 、Θ k+1 and Λ k+1 are the (k + 1)-th iterative estimation values of X C , Ψ, U, Θ, and Λ respectively, where k = 0, 1, …, K - 1.

[0115] The ADMM algorithm needs to perform multiple iterations to solve Equation (9), and the computational complexity is still relatively high. Moreover, it requires manual setting of algorithm parameters, which is difficult in practical applications. To solve Equation (9) quickly and accurately, in this embodiment, based on the deep unfolding technology, the ADMM algorithm with K iterations is unfolded into a DU-ANM network with K layers, as Figure 2 shown. Among them, F k+1 (·) represents the non-linear function corresponding to the (k + 1)-th layer of the DU-ANM network, expressed as:

[0116]

[0117] Among them, X is the echo signal matrix and serves as the network input; ρ k+1 and τ k+1 are the learnable penalty factor and regularization factor of the (k + 1)-th layer of the network respectively; Λ k is the Lagrange multiplier of the k-th layer of the network; Θ k is the auxiliary variable of the k-th layer of the network; and represent the matrices composed of the elements corresponding to X k , Ψ, and S(U) in Λ C respectively; and represent the matrices composed of the elements corresponding to X k , Ψ, and S(U) in Θ C respectively; represents the mapping from the MN×MN matrix to the 2N - 1×2M - 1 matrix; E M,Nrepresents a matrix of size \(2N - 1\times2M - 1\), where the \((M, N)\) - th element is 1 and the rest of the elements are 0; \(G\) and \(\delta\) g are respectively the eigen - vector matrix and the eigen - value vector of g ; \(diag(\{\delta\) g \}) is a diagonal matrix whose diagonal elements are \(\delta\) g \}; \(\{\delta\) + \} represents setting all negative eigenvalues to zero, \(g = 1,2,\cdots,MN + L\); \(\eta\) k+1 is the learnable iteration step of the \((k + 1)\) - th layer of the network;

[0118] The input of the DU - ANM network is \(X\), and the learnable parameters are The direct output is \(\varPsi\) K and \(U\) K , and the indirect output is The final output is \(Eig\) K ; where, represents the CNCM estimated based on \(U\) K and , and \(Eig\) K represents the vector composed of the eigenvalues of .

[0119] In this embodiment, in step S4, the learnable parameters of the DU - ANM network are initialized, and the DU - ANM network is trained based on the training data set to learn the optimal parameters. Specifically, it includes the following steps:

[0120] S4.1, Initialize the learnable parameters of the DU - ANM network, denoted as where \(\rho_0\) is the initialization penalty factor, \(\tau_0\) is the initialization regularization factor, and \(\eta_0\) is the initialization iteration step.

[0121] S4.2, Based on the training data set, train the DU - ANM network to learn the optimal parameters, specifically including:

[0122] Existing DU networks usually use the normalized mean - square error (NMSE) between the direct output of the network and the label data as the loss function. When applied to the DU - ANM network, it is expressed as:

[0123]

[0124] where \(Y\) K (X q ,\(\varOmega\)) represents the matrix composed of and , and are with respect to \(X\)q is the direct output of the K-layer DU-ANM network with Ω as the learnable parameter; Y A (X q ) represents the matrix composed of and , and are the clutter signal matrix, Hermitian matrix, and complex matrix obtained by solving the ANM problem based on CVX with X q as the input.

[0125] The loss function shown in Equation (12) only considers the overall approximation between the direct output and the label data, and it is often difficult to obtain an accurate estimate of the CNCM. To solve this problem, the CNCM can be used as the label, and the loss function is expressed as:

[0126]

[0127] where represents the CNCM estimated based on the direct output of the DU-ANM network with X q as the input, represents the CNCM estimated by solving the ANM problem based on CVX with X q as the input.

[0128] Using Equation (13) as the loss function, the DU-ANM network can converge quickly, but compared with the optimal case, the suppression performance of sidelobe clutter and noise may not be ideal. In practice, the larger eigenvalues of the CNCM will affect the clutter part, and the smaller eigenvalues will affect the noise part. Therefore, the CNCM can be eigen-decomposed, and the vector composed of its eigenvalues is used as the label, and the loss function is expressed as:

[0129]

[0130] where represents the vector composed of the eigenvalues of .

[0131] Simply using Equation (14) as the loss function only considers the overall approximation of the eigenvalues and may ignore the influence of small eigenvalues. Considering the influence of eigenvalues comprehensively, this embodiment proposes a new network loss function, which is expressed as:

[0132]

[0133] where div[a, b] represents each element of vector a divided by the corresponding element of vector b, and 1 represents a vector with each element being 1.

[0134] Based on the loss function The Adam algorithm is used for network training, and the optimal parameters are learned through the backpropagation method. It is expressed as:

[0135]

[0136] In this embodiment, in S5, the trained DU-ANM network is used to process the actual data to obtain the CNCM estimation result, and the STAP filter weight vector for suppressing clutter and noise is calculated:

[0137] S5.1, the trained DU-ANM network is used to process the actual data to obtain the CNCM estimation result, which is expressed as:

[0138]

[0139] Among them, Γ C,real is the eigenvector matrix of C,real and U real respectively represent the clutter signal matrix obtained by the trained DU-ANM network processing the actual data and the complex matrix of size (2N - 1)×(2M - 1), represents the l-th column of X C,real .

[0140] S5.2, based on the CNCM estimation result, calculate the STAP filter weight vector for suppressing clutter and noise, which is expressed as:

[0141]

[0142] The following is the experimental result of the present invention:

[0143] The simulation parameters are set as h = 3km, v = 100m / s, M = 8, N = 8, f r = 2kHz, λ = 0.2m, d = 0.1m, N c = 181, Z = 500, the distance range of the distance cell to be measured is [5, 15]km, and the clutter-to-noise ratio range is [30, 50]dB. The offline training of the network is implemented based on Python 3.8, the platform is Intel(R) Xeon(R) Gold 5218 2.3GHz CPU and NVIDIA GeForce RTX8000 GPU, and the online test is implemented based on MATLAB R2019a.

[0144] In this embodiment, the SINR loss is used to measure the clutter and noise suppression performance of different methods, which is expressed as:

[0145]

[0146] Among them, w is the STAP filter weighting vector.

[0147] Set the number of network layers, the number of training range cells, and the number of network training epochs to K = 15, L = 8, and 500 respectively, and set the initial iteration parameters to ρ0 = 0.1, τ0 = 0.1, and η0 = 0.1. Figure 3 Capon spectra and SINR loss curves obtained by the DU-ANM-STAP method under different loss functions are shown. The optimal Capon spectra and SINR loss curves are obtained by the CVX-ANM-STAP method. Figure 3 It can be seen that the clutter and noise suppression performance corresponding to the loss function shown in Equation (15) is better than that of the loss functions shown in Equations (12 - 14). At this time, the DU-ANM-STAP method can achieve performance close to that of the CVX-ANM-STAP method.

[0148] Taking the number of complex multiplications as an index, the computational complexities of the CVX-ANM-STAP method for solving Equation (5) and the ADMM-ANM-STAP method for solving Equation (9) are O{(L 2 +(2M - 1)(2N - 1)+MNL) 2 (L + MN) 2.5} and O{K((MN + L) 3 +(MN) 2 +6MN + L 2 +L)}, respectively. Since the DU-ANM network is based on offline training and online application, the computational complexity analysis of DU-ANM-STAP does not include network training. In addition, after obtaining the optimal parameters through training, the computational complexities of the DU-ANM-STAP method and the ADMM-ANM-STAP method are exactly the same. Let K = 15, and the running times of different methods are as Figure 4 shown. Figure 4 It can be seen that when K = 15, although the clutter and noise suppression performance of DU-ANM-STAP is slightly worse than that of ANM-CVX-STAP, its computational complexity is much lower than that of ANM-CVX-STAP. Let the number of training epochs be 500, the loss function of the DU-ANM-STAP method be (15), and the initial iteration parameters be ρ0 = 0.1, τ0 = 0.1, and η0 = 0.1. Figure 5 The SINR loss curves of DU-ANM-STAP and ADMM-ANM-STAP under different network / iteration layer numbers and training cell numbers are given.

[0149] It can be seen that when K = 25, DU-ANM-STAP can achieve clutter and noise suppression performance close to that of the optimal STAP. When K is small, the performance of ADMM-ANM-STAP is poor. Only when K = 300 can it achieve clutter and noise suppression performance comparable to that of DU-ANM-STAP. Figure 5 As shown in (b) of Figure 5 , when the number of training range cells is the same, the clutter and noise suppression performance of DU-ANM-STAP is always better than that of ADMM-ANM-STAP. At the same time, even when the number of training range cells is small, DU-ANM-STAP can still achieve good performance. Figure 5 It can also be seen that compared with ADMM-ANM-STAP, DU-ANM-STAP can reduce the number of iterations and the number of training range cells while maintaining comparable clutter and noise suppression performance, thereby further reducing the computational complexity.

[0150] Embodiment 2

[0151] An embodiment of the present invention provides an ANM-STAP system based on deep unfolding for performing the airborne radar STAP method based on ANM deep unfolding described in Embodiment 1. The system includes:

[0152] A construction module for constructing an airborne radar echo signal model;

[0153] A dataset acquisition module for setting the parameters and range of the airborne radar system, performing Z simulations based on the airborne radar echo signal model, randomly generating an echo signal matrix of L training range cells each time, solving the ANM problem to obtain the label data corresponding to the echo signal matrix, forming a signal matrix dataset and a label dataset, and dividing them into a training dataset and a test dataset;

[0154] A DU-ANM network module for constructing a DU-ANM network with K layers based on the alternating direction method of multipliers and deep unfolding technology;

[0155] A training module for initializing the learnable parameters of the DU-ANM network, training the DU-ANM network based on the training dataset, and learning the optimal parameters;

[0156] A result module for processing the actual data using the trained DU-ANM network to obtain the CNCM estimation result and calculating the STAP filter weighting vector for suppressing clutter and noise.

[0157] Embodiment 3

[0158] An embodiment of the present invention provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed by one or more processors, the one or more processors are caused to execute the steps in the method described in Embodiment 1.

[0159] In summary, for the STAP method, system, and storage medium based on ANM deep unfolding provided by the present invention, after proposing an appropriate loss function and constructing a complete data set, a DU-ANM network model is designed and offline trained, and a DU-ANM-STAP method is proposed to solve the problems of improper parameter setting and high computational complexity existing in the existing ANM-STAP method. The simulation results show that DU-ANM-STAP can effectively utilize data to obtain optimal parameters and solve the problem of difficult parameter setting in the existing ANM-STAP method. At the same time, on the premise of ensuring good clutter and noise suppression performance, DU-ANM-STAP can effectively reduce the number of iterations and the requirement for the number of training range cells, and reduce the computational complexity.

[0160] For the remaining technical features in this embodiment, those skilled in the art can flexibly select them according to the actual situation to meet different specific actual needs. However, it is obvious to those of ordinary skill in the art that these specific details do not have to be adopted to implement the present invention. In other instances, well-known components, structures, or parts are not specifically described to avoid obscuring the present invention, and all are within the scope of the technical solutions claimed in the claims of the present invention.

[0161] Modifications and changes made by those skilled in the art without departing from the spirit and scope of the present invention shall fall within the protection scope of the appended claims of the present invention. In the above description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not have to be adopted to implement the present invention. In other instances, well-known technologies, such as specific construction details, working conditions, and other technical conditions, are not specifically described to avoid obscuring the present invention.

[0162] Specific examples are used in this article to illustrate the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. An airborne radar STAP method based on ANM depth unfolding, characterized in that, It includes the following steps: S1. Construct an airborne radar echo signal model; S2. Set the parameters and range of the airborne radar system, conduct Z simulations based on the airborne radar echo signal model. In each simulation, randomly generate an echo signal matrix of L training range cells, solve the ANM problem to obtain the label data corresponding to the echo signal matrix, form a signal matrix data set and a label data set, and divide them into a training data set and a test data set; S3. Based on the alternating direction multiplier method and the deep unfolding technique, construct a DU-ANM network with K layers; S4. Initialize the learnable parameters of the DU-ANM network, and train the DU-ANM network based on the training data set to learn the optimal parameters; S5. Use the trained DU-ANM network to process the actual data, obtain the CNCM estimation result, and calculate the STAP filter weighting vector for suppressing clutter and noise.

2. The airborne radar STAP method based on ANM depth unfolding according to claim 1, characterized in that, In S1, constructing an airborne radar echo signal model specifically includes: Assume that the number of array elements of the airborne radar's uniform linear array is N, the element spacing is d = λ / 2, where λ is the wavelength, the radar flies at a constant speed v and altitude h, and the pulse repetition frequency is f r , and a total of M pulses are transmitted within a coherent processing period. Then, the echo signal x of the range cell under test containing the target and the echo signal x of the l-th training range cell near the range cell under test without the target received by the airborne radar l are respectively expressed as: where x c represents the clutter component of the range cell under test, and n represents the noise component of the range cell under test; α T represents the complex amplitude of the target, represents the spatio-temporal steering vector of the target; i = 1, 2,..., N c , N c is the number of clutter patches uniformly distributed in each range cell; α i represents the complex amplitude of the i-th clutter patch in the range cell under test; represents the spatio-temporal steering vector of the i-th clutter patch in the range cell under test; represents the clutter component of the l-th training range cell, and n l represents the noise component of the l-th training range cell; l = 1, 2,..., L, where L represents the number of training range cells; represents the complex amplitude of the i-th clutter patch in the l-th training range cell; represents the spatio-temporal steering vector of the i-th clutter patch in the l-th training range cell, denoted as where: Among them, represents the time-domain steering vector of the i-th clutter patch in the l-th training range cell; represents the spatial-domain steering vector of the i-th clutter patch in the l-th training range cell; represents the Kronecker product, [·] T represents the matrix transpose; and respectively represent the normalized Doppler frequency and spatial frequency of the i-th clutter patch in the l-th training range cell; and are respectively the azimuth angle and elevation angle of the i-th clutter patch in the l-th training range cell.

3. The airborne radar STAP method based on ANM depth unfolding according to claim 1, wherein In S2, setting the parameters and range of the airborne radar system, conducting Z simulations based on the airborne radar echo signal model. In each simulation, randomly generate an echo signal matrix of L training range cells, solve the ANM problem to obtain the label data corresponding to the echo signal matrix, form a signal matrix data set and a label data set, and divide them into a training data set and a test data set, specifically including the following steps: S2.1, Set the parameters and range of the airborne radar system, including the number of array elements N of the airborne radar, the element spacing d, the signal wavelength λ, the flight speed v, the altitude h, the pulse repetition frequency f r , the number of coherent pulses M, the number of clutter blocks N c , the distance range of the distance unit to be measured, the clutter-to-noise ratio range; S2.2, randomly generate an echo signal matrix X = [x1, x2, ···, x L of L training range cells based on the airborne radar echo signal model; S2.3, Solve the ANM problem to obtain the clutter signal matrix corresponding to the signal matrix X Hermitian matrix Ψ A and complex matrix U A : Among them, X C and respectively represent the clutter signal matrices of the unknown and obtained L training range cells, Ψ and Ψ A respectively represent the unknown and obtained Hermitian matrices of size L×L, U and U A respectively represent the unknown and obtained complex matrices of size (2N - 1)×(2M - 1), S(U) represents the Toeplitz matrix formed by U, Tr(·) represents the trace of the matrix, ε n represents the noise energy, ||·|| F represents the Frobenius norm of the matrix; S2.4, for U A The Toeplitz matrix S(U A ) is eigen - value decomposed to obtain Based on Γ C , an estimate of the clutter covariance matrix is obtained Expressed as: Among them, Γ C represents the eigenvector matrix of S(U A ), Σ C represents the diagonal matrix composed of the eigenvalues of S(U), represents the l-th column of X C , and diag(·) represents converting a vector into a diagonal matrix; Based on the CNCM of the distance unit to be measured is estimated and expressed as: Among them, represents the noise power, and I NM represents an identity matrix of size NM×NM; S2.5, for perform eigenvalue decomposition, and use the vector composed of eigenvalues as the label data E corresponding to the echo signal matrix X A ; S2.

6. Repeat steps S2.2 to S2.5 for a total of Z times to obtain a signal matrix data set and a label data set wherein, X z represents the echo signal matrix of L training range cells obtained during the z-th simulation, represents the label data obtained during the z-th simulation, where z = 1, 2,..., Z; S2.7, group the signal matrix data set and the label data set, and divide them into a training data set and a test data set according to a ratio of 4:1 where Q is the size of the training data, and O = Z - Q is the size of the test data where Q is the size of the training data, and O = Z - Q is the size of the test data.

4. The airborne radar STAP method based on ANM depth unfolding according to claim 1, characterized in that In S3, based on the alternating direction multiplier method and the deep unfolding technique, constructing a DU-ANM network with K layers specifically includes: Based on the deep unfolding technique, expand the ADMM algorithm with K iterations into a DU-ANM network with K layers. Among them, the non-linear function corresponding to the (k + 1)-th layer in the DU-ANM network is: Among them, X is the echo signal matrix, serving as the network input; ρ k+1 and τ k+1 are respectively the learnable penalty factor and the regularization factor of the (k + 1)-th layer of the network; Λ k is the Lagrange multiplier of the k-th layer of the network; Θ k is the auxiliary variable of the k-th layer of the network; and respectively represent the matrices composed of the elements corresponding to X k , Ψ, and S(U) in Λ C ; and respectively represent the matrices composed of the elements corresponding to X k , Ψ, and S(U) in Θ C ; S * (·) represents the mapping from the MN×MN matrix to the 2N - 1×2M - 1 matrix; E M,N represents a matrix of size 2N - 1×2M - 1, whose (M, N)-th element is 1 and the rest of the elements are 0; G and δ g are respectively 's eigenvector matrix and eigenvalue vector; diag({δ g}) is a diagonal matrix whose diagonal elements are δ g ; {δ g} + means setting all negative eigenvalues to zero, g = 1, 2, ···, MN + L; η k+1 is the learnable iteration step size of the (k + 1)-th layer of the network; The input of the DU-ANM network is X, and the learnable parameters are The direct output is Ψ K and U K The indirect output is The final output is Eig K ; where represents the estimated CNCM based on U K and Eig K represents the vector composed of the eigenvalues of .

5. The airborne radar STAP method based on ANM depth unfolding according to claim 1, characterized in that, In S4, initializing the learnable parameters of the DU-ANM network, and training the DU-ANM network based on the training data set to learn the optimal parameters, specifically including the following steps: S4.1, Initialize the learnable parameters of the DU-ANM network, denoted as where ρ0 is the initialization penalty factor, τ0 is the initialization regularization factor, and η0 is the initialization iteration step size; S4.

2. Based on the training data set, train the DU-ANM network to learn the optimal parameters: Construct the network loss function L div (Eig): Where div[a, b] represents dividing each element of vector a by the corresponding element of vector b, and 1 represents a vector with each element being 1; Based on the loss function L div (Eig), the Adam algorithm is used for network training, and the optimal parameters are learned through the backpropagation method It is expressed as:

6. The airborne radar STAP method based on ANM depth unfolding according to claim 1, wherein In S5, using the trained DU-ANM network to process the actual data, obtain the CNCM estimation result, and calculate the STAP filter weighting vector for suppressing clutter and noise, specifically including the following steps: S5.

1. Use the trained DU-ANM network to process the actual data to obtain the CNCM estimation result, expressed as: Among them, Γ C,real is the eigenvector matrix of S(U real ), X C,real and U real respectively represent the clutter signal matrix obtained by processing the actual data by the trained DU-ANM network and the complex matrix of size (2N - 1)×(2M - 1), represents the l-th column of X C,real ; S5.

2. Based on the CNCM estimation result, calculate the STAP filter weighting vector for suppressing clutter and noise, expressed as:

7. A depth-unrolled ANM-STAP system for performing the airborne radar STAP method based on ANM depth unrolling according to any one of claims 1-6, characterized in that, It includes: A construction module for constructing an airborne radar echo signal model; The dataset acquisition module is used to set the parameters and range of the airborne radar system, perform Z simulations based on the airborne radar echo signal model. In each simulation, L echo signal matrices of training range cells are randomly generated, and the label data corresponding to the echo signal matrix is obtained by solving the ANM problem, forming a signal matrix dataset and a label dataset, and dividing them into a training dataset and a test dataset; The DU-ANM network module is used to construct a DU-ANM network with K layers based on the alternating direction multiplier method and the deep unfolding technique; The training module is used to initialize the learnable parameters of the DU-ANM network, and train the DU-ANM network based on the training dataset to learn the optimal parameters; The result module is used to process the actual data using the trained DU-ANM network to obtain the CNCM estimation result, and calculate the STAP filter weighting vector for suppressing clutter and noise.

8. A computer-readable storage medium storing computer instructions, characterized in that, When the computer instructions are executed by one or more processors, the one or more processors are caused to execute the steps in the method according to any one of claims 1-6.

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