Airborne radar STAP method and system based on deep expansion and convolutional neural network

Abstract

The invention discloses an airborne radar STAP method and system based on depth expansion and a convolutional neural network, and relates to the technical field of radars, and the method comprises the steps: S1, setting a specific parameter range of an airborne radar, and generating a plurality of radar space-time echo signals through a space-time echo signal model of the airborne radar, so as to construct an input data set; s2, taking the obtained estimation of the clutter space-time amplitude spectrum and the estimation of the high-resolution clutter space-time power spectrum as an intermediate data set, and outputting a label data set; integrating the input data set, the intermediate data set and the output label data into a DU-CNN data set; s3, a DU-CNN network is constructed; s4, performing independent pre-training on the ADMM-Net module and the CNN module respectively, and then performing end-to-end training on the DU-CNN network; and S5, combining the trained DU-CNN with an STAP method, and processing the space-time echo signal of the target to be detected to obtain the estimation of CNCM and the estimation of the adaptive weight vector of the space-time filter. The clutter suppression performance can be improved, and the operation complexity can be reduced.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to an airborne radar STAP method and system based on deep expansion and convolutional neural network. Background Art

[0002] Airborne radars usually face complex ground / sea clutter when detecting moving targets on the ground / sea surface or at low altitude. The clutter exhibits space-time coupling characteristics and has a serious power spectrum broadening. One-dimensional methods such as moving target detection or beamforming cannot effectively detect targets. The STAP (Space Time Adaptive Processing) method combines spatial and temporal two-dimensional information to adaptively suppress clutter in the space-time domain, effectively improving the detection performance of airborne radars for moving targets. However, the traditional STAP method requires a certain number of independent and identically distributed (IID) training range cell data to estimate the clutter plus noise covariance matrix (CNCM) of the range cell under test (RUT). Studies have shown that in order to ensure that the output signal to clutter plus noise ratio (SCNR) does not lose more than 3dB compared to the optimal STAP, the number of IID training range cells required by the traditional STAP method is at least twice the system's degrees of freedom. In actual environments, factors such as non-stationary land / sea environments, non-uniform clutter characteristics, and complex platform motion make this condition usually difficult to meet. Therefore, the insufficient number of independent and identically distributed training range units is one of the key factors restricting the performance of traditional airborne radar space-time adaptive processing methods.

[0003] In order to reduce the demand for IID training distance units, scholars have successively proposed the dimension reduction STAP method, the rank reduction STAP method, and the SR-based STAP method. Among them, the SR-STAP method based on the Focal Under-determined System Solver (FOCUSS), the Alternating Direction Method of Multipliers (ADMM), the Sparse Bayesian Learning (SBL) algorithm, etc. can achieve high-resolution estimation of the clutter space-time amplitude spectrum using a small number of IID training distance units, thereby calculating CNCM, suppressing clutter, and detecting targets. However, the SR algorithm used in the SR-STAP method usually has problems such as difficult parameter setting, high computational complexity, and low accuracy. In addition, the sparsity of clutter deteriorates under non-frontal side-view conditions, and the performance of the SR-STAP method is seriously degraded, which limits its application in practice.

[0004] In recent years, Duan Keqing and others have provided ideas for super-resolution image reconstruction based on deep learning, and proposed a new STAP method based on convolutional neural network (CNN). The CNN-STAP method constructs a data set that simulates a real clutter environment and trains CNN offline to enable it to have the ability to reconstruct from low-resolution images to high-resolution images. Then, CNN is applied online to reconstruct the low-resolution clutter space-time power spectrum obtained based on a small number of IID training distance units to obtain a high-resolution estimate of the clutter space-time power spectrum, thereby constructing a space-time filter for clutter suppression and target detection. CNN-STAP can achieve better clutter suppression performance, and compared with the SR-STAP method, the amount of online computation required is greatly reduced. However, due to the small size of the network, the reconstruction ability of the CNN constructed in the literature "Duan, K.; Chen, H.; Xie, W.; Wang, Y. Deep learning for high-resolution estimation of clutter angle-Doppler spectrum in STAP. IET Radar Sonar Navig. 2022, 16, 193-207" is weak, and the clutter suppression performance of the CNN-STAP method needs to be further improved. Increasing the network size can improve the reconstruction ability of CNN and the performance of CNN-STAP, but it will lead to an increase in computational complexity.

[0005] Therefore, it is urgent to design an airborne radar STAP method to solve the above problems. Summary of the invention

[0006] The purpose of the present invention is to provide an airborne radar STAP method and system based on deep expansion and convolutional neural network, which reduces the requirements for network reconstruction capability, obtains better clutter suppression performance, improves the accuracy of clutter space-time spectrum estimation, and reduces computational complexity.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A STAP method for airborne radar based on deep unfolding and convolutional neural network, comprising the following steps:

[0009] S1, setting a specific parameter range of the airborne radar, and using the space-time echo signal model of the airborne radar to generate multiple radar space-time echo signals, thereby constructing an input data set;

[0010] S2, based on the SR-STAP method and ADMM algorithm, the radar space-time echo signal is processed to obtain an estimate of the clutter space-time amplitude spectrum as an intermediate data set; and based on the theoretical value of the clutter covariance matrix and the MVDR spectrum estimation method, an estimate of the high-resolution clutter space-time power spectrum is obtained as an output label data set; the input data set, the intermediate data set, and the output label data set are integrated into a DU-CNN data set, and divided into a training data set and a validation data set according to a set ratio;

[0011] S3, constructing a DU-CNN network, wherein the DU-CNN network includes an ADMM-Net module, a squarer module, a power normalization module, a CNN module, and a power restoration module, wherein the ADMM-Net module is a network for solving the sparse recovery problem, and is used to realize the rapid acquisition of the clutter space-time amplitude spectrum; the CNN module is a space-time power spectrum reconstruction network, and is used to realize the acquisition of the normalized high-resolution clutter space-time power spectrum estimation;

[0012] S4, based on the training data sets corresponding to the input data set and the intermediate data set, and the training data sets corresponding to the intermediate data set and the output label data set, the ADMM-Net module and the CNN module are independently pre-trained, and then based on the training data sets corresponding to the input data set and the output label data set, the DU-CNN network is end-to-end trained, and the network parameters of the ADMM-Net module and the CNN module are jointly fine-tuned to obtain a trained DU-CNN network;

[0013] S5, the trained DU-CNN network is combined with the STAP method to process the space-time echo signal of the target to be detected, and the estimation of CNCM and the estimation of the space-time filter adaptive weight vector are obtained.

[0014] Furthermore, the squarer module is used to complete the conversion from the space-time amplitude spectrum to the space-time power spectrum and output the space-time power spectrum;

[0015] The power normalization module is used to normalize the space-time power spectrum to obtain input data of the CNN module;

[0016] The power restoration module is used to perform clutter power restoration on high-resolution clutter space-time power spectrum estimation.

[0017] Further, the S1 sets a specific parameter range of the airborne radar, generates multiple radar space-time echo signals using the space-time echo signal model of the airborne radar, and constructs an input data set, specifically including:

[0018] S1.1, given the aircraft height H, the number of ULA array elements M, the number of CPI pulses N, the array element spacing d and the carrier wavelength λ; assuming that the pitch angle, non-positive side view angle, clutter ridge slope and clutter-to-noise ratio corresponding to the range unit all obey uniform random distribution, that is, θ e :U(θ min ,θ max ), β=2υT r / λ:U(β min ,β max ) and CNR:U(CNR min ,CNR max );

[0019] Based on the airborne radar space-time echo signal model, generate P radar space-time echo signals As the input dataset of the DU-CNN network,

[0020] Each distance ring contains N c clutter blocks are uniformly distributed in the azimuth range [0,π], whose scattering coefficient obeys complex Gaussian distribution, and whose amplitude is determined by the clutter-to-noise ratio CNR; the clutter and noise components contained in the space-time echo signal model of the airborne radar are:

[0021]

[0022] Where: x c represents the clutter signal, x n Represents a noise signal, assuming that the mean is 0 and the variance is σ n 2 Complex Gaussian white noise signal; represents the Kronecker product; σ c；n represents the scattering coefficient of the nth clutter block; v d (f c；d,n ) and v s (f c；s,n ) are the time domain steering vector and spatial domain steering vector of the nth clutter block, respectively, expressed as:

[0023]

[0024] Where: and denote N×1 and M×1 dimensional complex vectors respectively, exp(g) denotes exponential operation with base e, [·] T represents transpose, f c；d,n and f c；s,n are the Doppler frequency and spatial frequency of the nth clutter block, respectively, expressed as:

[0025]

[0026] Where: and θ n are the elevation angle and azimuth angle of the nth clutter block, θ e It represents the angle between the antenna array and the direction of radar movement, and λ is the signal wavelength.

[0027] Further, the S2 processes the radar space-time echo signal based on the SR-STAP method and the ADMM algorithm to obtain an estimate of the clutter space-time amplitude spectrum as an intermediate data set; and according to the theoretical value of the clutter covariance matrix, based on the MVDR spectrum estimation method, obtains an estimate of the high-resolution clutter space-time power spectrum as an output label data set, specifically including:

[0028] S2.1, given the spatial frequency [f s,min ,f s,max ], Doppler frequency range [f d,min ,f d,max ], given the number of grids N s =ρ s M and N d =ρ d N, construct the space-time steering vector dictionary Φ based on formula (10):

[0029]

[0030] In the formula, f d,i is the i-th Doppler frequency, f s,j is the jth spatial frequency, v(f d,i ,f s,j ) is the space-time steering vector corresponding to the ijth grid point, Indicates the Nth d , N s The space-time steering vector corresponding to each grid point;

[0031] S2.2, according to the convergence conditions of the ADMM algorithm, different combinations of iteration parameters are set, and all space-time echo signals are calculated based on formula (12) The iterative parameters with the best estimation performance are obtained by processing, regularization factor ρ = ρ0, quadratic penalty factor β = β0, iteration step size τ = τ0, and number of iterations K = K0 as parameters of the ADMM algorithm, and the estimated set of clutter space-time amplitude spectrum is obtained. As an intermediate data set;

[0032]

[0033] Where: is the pth estimated value in the clutter space-time amplitude spectrum estimation set, ||·||0 and ||·||2 represent the L0 norm and L2 norm of the vector respectively, and ε represents the noise level;

[0034] According to the theoretical value R of the clutter covariance matrix c , based on the MVDR spectrum estimation method, the estimated set of high-resolution clutter space-time power spectrum is obtained As output label dataset;

[0035]

[0036] Where: is the pth estimated value in the high-resolution clutter space-time power spectrum estimation set.

[0037] Further, the S4, based on the training data set corresponding to the input data set and the intermediate data set, and the training data set corresponding to the intermediate data set and the output label data set, independently pre-trains the ADMM-Net module and the CNN module, and then based on the training data set corresponding to the input data set and the output label data set, performs end-to-end training on the DU-CNN network, and jointly fine-tunes the network parameters of the ADMM-Net module and the CNN module to obtain a trained DU-CNN network, specifically including:

[0038] S4.1, initialize the parameters of each layer of the ADMM-Net network according to the iterative parameter setting of the ADMM algorithm, that is, The network loss function is defined as the mean square error MSE between the ADMM-Net output and the label data, expressed as:

[0039]

[0040] Where: Indicates x p As input, Θ A The K-th layer output of ADMM-Net with parameters; the optimal parameters of ADMM-Net The network loss function is minimized by the back propagation method and is expressed as:

[0041]

[0042] S4.2, the Glorot method is used to initialize the network parameters of CNN, and the network loss function is defined as the MSE of CNN output and label data, expressed as:

[0043]

[0044] Where: Indicates As input, Θ C is the output of the CNN with parameters; similarly, the optimal parameters of CNN are obtained by solving the following formula through the back propagation method:

[0045]

[0046] S4.3, based on the independent pre-training of ADMM-Net and CNN, the DU-CNN is trained end-to-end. At this time, the initialization of DU-CNN is based on Implementation, the network loss function is:

[0047]

[0048] Where: Indicates x p As input, Θ={Θ A ,Θ C} is the output of the DU-CNN with parameters; similarly, the optimal parameters of the DU-CNN By solving the following equation:

[0049] The present invention also provides an airborne radar STAP system based on deep expansion and convolutional neural network, which is used to execute the airborne radar STAP method based on deep expansion and convolutional neural network, and is characterized by comprising:

[0050] The signal generation module is used to set the specific parameter range of the airborne radar and generate multiple radar space-time echo signals using the space-time echo signal model of the airborne radar to construct an input data set;

[0051] The data set module is used to process the radar space-time echo signal based on the SR-STAP method and the ADMM algorithm to obtain an estimate of the clutter space-time amplitude spectrum as an intermediate data set; and according to the theoretical value of the clutter covariance matrix, based on the MVDR spectrum estimation method, obtain an estimate of the high-resolution clutter space-time power spectrum as an output label data set; the input data set, the intermediate data set, and the output label data set are integrated into a DU-CNN data set, and divided into a training data set and a verification data set according to a set ratio;

[0052] A model building module is used to build a DU-CNN network, wherein the DU-CNN network includes an ADMM-Net module, a squarer module, a power normalization module, a CNN module, and a power restoration module, wherein the ADMM-Net module is a solution network for the sparse recovery problem, and is used to realize the rapid acquisition of the clutter space-time amplitude spectrum; the CNN module is a space-time power spectrum reconstruction network, and is used to realize the acquisition of the normalized high-resolution clutter space-time power spectrum estimation;

[0053] A training module is used to pre-train the ADMM-Net module and the CNN module independently based on the training data sets corresponding to the input data set and the intermediate data set, and the training data sets corresponding to the intermediate data set and the output label data set, and then perform end-to-end training on the DU-CNN network based on the training data sets corresponding to the input data set and the output label data set, and jointly fine-tune the network parameters of the ADMM-Net module and the CNN module to obtain a trained DU-CNN network;

[0054] The result output module is used to combine the trained DU-CNN network with the STAP method to process the space-time echo signal of the target to be detected, and obtain the estimation of CNCM and the estimation of the space-time filter adaptive weight vector.

[0055] The present invention also provides a computer-readable storage medium storing computer instructions, which, when executed by one or more processors, causes the one or more processors to execute the steps in the method.

[0056] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the airborne radar STAP method and system based on deep unfolding and convolutional neural network provided by the present invention uses CNN to reduce the requirements of the SR algorithm for parameter setting and number of iterations, and improves its estimation accuracy, and uses the clutter space-time spectrum obtained by SR to reduce the requirements of CNN for network scale, and proposes a DU-CNN-STAP method. Based on the idea of ​​deep unfolding (DU), the method unfolds the SR algorithm into a deep neural network, uses training data to obtain its optimal parameters, and improves its convergence performance. On this basis, the SR network and CNN are trained end-to-end to achieve rapid and accurate estimation of the clutter space-time spectrum. Simulation experiments show that compared with the SR-STAP method and the CNN-STAP method, the method proposed by the present invention can improve the clutter suppression performance and reduce the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments 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.

[0058] Figure 1 A geometric model diagram of an airborne radar according to an embodiment of the present invention;

[0059] Figure 2 It is a structural diagram of the DU-CNN-STAP framework of an embodiment of the present invention;

[0060] Figure 3 A network structure diagram of ADMM-Net according to an embodiment of the present invention;

[0061] Figure 4 It is a structural diagram of a CNN network according to an embodiment of the present invention;

[0062] Figure 5 A data set partitioning method according to an embodiment of the present invention;

[0063] Figure 6 The training convergence of different networks, where (a) is the training convergence of ADMM-Net, (b) is the training convergence of CNN, and (c) is the training convergence of DU-CNN;

[0064] Figure 7 The clutter space-time spectrum estimation results obtained by different methods, among which (a) is the theoretical value of the clutter space-time spectrum estimation result, (b), (c), and (d) are the clutter space-time spectrum estimation results obtained by using the SR-STAP method, CNN-STAP, and DU-CNN-STAP method respectively;

[0065] Figure 8 are the clutter space-time spectrum estimation results obtained by different methods, where: , β=2.49, θ e =-15.61°, CNR = 38.65dB, (a), (b), (c), (d) are the theoretical values ​​of the clutter space-time spectrum estimation results, and the clutter space-time spectrum estimation results obtained by the SR-STAP method, CNN-STAP, and DU-CNN-STAP method;

[0066] Fig. 9 SCNR loss curves of different methods, where (a) is the positive side view array and (b) is the non-positive side view array;

[0067] Fig.10 is the computational complexity of different methods under different conditions. DETAILED DESCRIPTION

[0068] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0069] The purpose of the present invention is to provide an airborne radar STAP method and system based on deep expansion and convolutional neural network, which reduces the requirements for network reconstruction capability, obtains better clutter suppression performance, improves the accuracy of clutter space-time spectrum estimation, and reduces computational complexity.

[0070] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0071] In order to reduce the requirements of the CNN-STAP method on the network reconstruction capability, the high-resolution clutter space-time spectrum obtained by the SR algorithm can be used as the input of the CNN, that is, the SR-STAP method and the CNN-STAP method are cascaded. At this time, due to the high quality of the input clutter space-time spectrum, it can be reconstructed using a smaller-scale CNN. At the same time, this method can reduce the requirements of the SR-STAP method on parameter settings and the number of iterations, and improve its estimation accuracy: based on more reasonable iteration parameters and a small number of iterations, the SR method is used to process a small amount of IID training distance unit data to obtain a high-resolution clutter space-time spectrum estimation with errors, and then CNN is used to reconstruct it, which can be estimated. The accuracy. Furthermore, based on the idea of ​​deep unrolling (DU), the SR algorithm can be expanded into a deep neural network, and the optimal parameters under a certain number of iterations can be obtained by using a learning method, which improves the accuracy of the clutter space-time spectrum estimation to a certain extent, and then CNN is used to reconstruct it to obtain the final clutter space-time spectrum estimation result.

[0072] Based on the above ideas, the embodiment of the present invention proposes the DU-CNN-STAP method. First, an airborne radar echo signal model is established, and the SR-STAP and CNN-STAP methods are briefly introduced; then, the processing framework, network structure, data set construction, and training method of the DU-CNN-STAP method are introduced in detail; finally, the performance and advantages of the DU-CNN-STAP method are verified through simulation experiments. The simulation experiment results show that compared with the SR-STAP method and the CNN-STAP method, the DU-CNN-STAP method proposed in this embodiment has lower computational complexity and better clutter suppression performance.

[0073] like Figure 1-10 As shown, the airborne radar STAP method based on deep expansion and convolutional neural network provided by an embodiment of the present invention includes the following steps:

[0074] S1, setting a specific parameter range of the airborne radar, and using the space-time echo signal model of the airborne radar to generate multiple radar space-time echo signals, thereby constructing an input data set;

[0075] S2, based on the SR-STAP method and ADMM algorithm, the radar space-time echo signal is processed to obtain an estimate of the clutter space-time amplitude spectrum as an intermediate data set; and based on the theoretical value of the clutter covariance matrix and the MVDR spectrum estimation method, an estimate of the high-resolution clutter space-time power spectrum is obtained as an output label data set; the input data set, the intermediate data set, and the output label data set are integrated into a DU-CNN data set, and divided into a training data set and a validation data set according to a set ratio;

[0076] S3, constructing a DU-CNN network, wherein the DU-CNN network includes an ADMM-Net module, a squarer module, a power normalization module, a CNN module, and a power restoration module, wherein the ADMM-Net module is a network for solving the sparse recovery problem, and is used to realize the rapid acquisition of the clutter space-time amplitude spectrum; the CNN module is a space-time power spectrum reconstruction network, and is used to realize the acquisition of the normalized high-resolution clutter space-time power spectrum estimation;

[0077] S4, based on the training data sets corresponding to the input data set and the intermediate data set, and the training data sets corresponding to the intermediate data set and the output label data set, the ADMM-Net module and the CNN module are independently pre-trained, and then based on the training data sets corresponding to the input data set and the output label data set, the DU-CNN network is end-to-end trained, and the network parameters of the ADMM-Net module and the CNN module are jointly fine-tuned to obtain a trained DU-CNN network;

[0078] S5, the trained DU-CNN network is combined with the STAP method to process the space-time echo signal of the target to be detected, and the estimation of CNCM and the estimation of the space-time filter adaptive weight vector are obtained.

[0079] like Figure 1 As shown, in this embodiment, the S1, setting a specific parameter range of the airborne radar, and using the space-time echo signal model of the airborne radar to generate multiple radar space-time echo signals, specifically includes:

[0080] S1.1, Assume that the airborne phased array radar flies at a constant speed along the y-axis at an altitude of H and a speed of v. The number of elements in the uniform linear array is M, the spacing between the elements is d, and the angle between the elements and the direction of the aircraft's speed is θe , a total of N pulses are transmitted and received in a coherent processing interval (CPI), and the pulse repetition interval is T r , carrier wavelength λ;

[0081] Without considering the influence of range ambiguity, assume that the clutter range ring corresponding to each range unit is composed of N c The clutter and noise components contained in the radar space-time echo signal x can be expressed as:

[0082]

[0083] Where: x c represents the clutter signal, x n Represents a noise signal, assuming that the mean is 0 and the variance is σ n 2 Complex Gaussian white noise signal; represents the Kronecker product; σ c；n represents the scattering coefficient of the nth clutter block; v d (f c；d,n ) and v s (f c；s,n ) are the time domain steering vector and spatial domain steering vector of the nth clutter block, respectively, expressed as:

[0084]

[0085] Where: and denote N×1 and M×1 dimensional complex vectors respectively, exp(g) denotes exponential operation with base e; [·] T represents transpose, f c；d,n and f c；s,n are the Doppler frequency and spatial frequency of the nth clutter block, respectively, expressed as:

[0086]

[0087] Where: and θ n are the elevation angle and azimuth angle of the nth clutter block, θ e It represents the angle between the antenna array and the direction of radar movement, and λ is the signal wavelength.

[0088] From the above content, we can know that the parameters such as the aircraft height H, the number of ULA array elements M, the number of CPI pulses N, the array element spacing d and the carrier wavelength λ are given; it is assumed that the pitch angle, non-positive side view angle, clutter ridge slope and clutter-to-noise ratio corresponding to the range unit all obey uniform random distribution, that is, ,θe :U(θ min ,θ max ), β=2vT r / λ:U(β min ,β max ) and CNR:U(CNR min ,CNR max );

[0089] Based on the airborne radar space-time echo signal model, generate P radar space-time echo signals As the input data set of DU-CNN, each distance ring contains N c The clutter blocks are uniformly distributed in the azimuth range [0,π], and their scattering coefficients obey the complex Gaussian distribution, and the amplitude is determined by the clutter-to-noise ratio CNR.

[0090] Furthermore, according to equation (1), assuming that clutter and noise are independent of each other, CNCM can be obtained as:

[0091]

[0092] Where: E[·] represents expectation, [·] H represents the conjugate transpose, I NM Represents the NM×NM identity matrix.

[0093] The output of STAP is the inner product of the space-time filter weight vector w and the radar space-time echo signal x, expressed as:

[0094] y=w H x (5)

[0095] In order to keep the target power after filtering unchanged and minimize the power of clutter plus noise, the optimal weight vector of the space-time filter can be calculated by the following formula:

[0096]

[0097] Where: (·) -1 Indicates the inversion of the matrix, v t is the space-time guidance vector of the target.

[0098] In fact, the CNCM of the RUT is unknown, and generally a certain number of training distance units that do not contain the target are required to estimate it. Assuming that the training distance units and the RUT are independent and identically distributed, the CNCM of the RUT can be estimated by the Sample Matrix Inversion (SMI) method, which is expressed as:

[0099]

[0100] Where: L is the number of IID training distance units, x l represents the space-time echo signal of the lth (l=1,2,...,L) training range unit. According to the RMB criterion, the ratio of the output SCNR of the SMI method and the optimal STAP method can be expressed as:

[0101] SCNR loss =(L-O+2) / (L+1) (8)

[0102] In the formula: O=MN represents the system degree of freedom.

[0103] Formula (8) shows that if the output SCNR loss is required to be less than 3 dB, the SMI method requires at least twice the system degree of freedom of the IID training distance unit, that is, L ≥ 2O, which is usually difficult to meet in actual non-uniform and non-stationary clutter environments.

[0104] 1. In order to highlight the advantages of the method described in this embodiment, the SR-STAP method and the CNN-STAP method are introduced. The specific contents are as follows:

[0105] 1) Introduction to the SR-STAP method

[0106] It can be seen from equation (1) that the clutter signal can be composed of the superposition of space-time signals corresponding to different spatial frequencies and Doppler frequencies. Therefore, under the premise of allowing a certain quantization error, the entire spatial frequency-Doppler frequency plane can be discretized into N s =ρ s M and N d =ρ d N grid points (N s N d >>NM), then the clutter component contained in the space-time echo signal can be expressed as:

[0107]

[0108] Where: f d,i is the i-th Doppler frequency, f s,j is the jth spatial frequency, v(f d,i ,f s,j ) is the space-time steering vector corresponding to the ijth grid point, γ i,j is the complex amplitude corresponding to the ijth grid point, is the complex amplitude vector corresponding to all grid points, that is, the clutter space-time amplitude spectrum, Φ is the space-time steering vector dictionary, expressed as:

[0109]

[0110] In the formula, f d,i is the i-th Doppler frequency, fs,j is the jth spatial frequency, v(f d,i ,f s,j ) is the space-time steering vector corresponding to the ijth grid point, that is, Indicates the Nth d , N s The space-time steering vector corresponding to each grid point;

[0111] Therefore, the space-time echo signal of the lth training range unit that does not contain the target can be expressed as:

[0112]

[0113] Due to the coupling of clutter space-time frequency, the clutter space-time amplitude spectrum is sparse on the entire spatial frequency-Doppler frequency plane. Based on this characteristic, the SR-STAP method can estimate the clutter space-time amplitude spectrum by solving a constrained optimization problem, which is expressed as:

[0114]

[0115] Where: ||·||0 and ||·||2 represent the L0 norm and L2 norm of the vector respectively, and ε represents the noise level.

[0116] For L training distance units, Equation (12) can be extended to a multi-observation model and expressed as:

[0117]

[0118] Where: ||·|| 2,0 It means taking the L2 norm of each row of the matrix first and then taking the L0 norm of the column, ||·|| F Represents the Frobenius norm of a matrix.

[0119] Based on solving equation (12) or (13) using algorithms such as FOCUSS, SBL or ADMM, the CNCM estimate can be obtained as:

[0120]

[0121] Where: γ l,i,j Represents the complex amplitude of the space-time echo signal of the lth training range unit at the ijth grid point.

[0122] According to the obtained CNCM estimation results, the optimal weight vector of the space-time filter can be obtained by solving the following formula:

[0123]

[0124] The SR-STAP method can obtain an accurate estimate of CNCM using IID training distance units with far fewer system degrees of freedom, that is, L = O, which has significant advantages over the SMI method. However, under the premise of constructing the clutter space-time amplitude spectrum estimation model shown in equation (12) or (13), the performance of the SR-STAP method often depends on the SR algorithm it adopts. Although scholars have proposed a series of efficient SR methods, there are generally problems such as difficulty in parameter setting, high computational complexity and low accuracy. In addition, under non-frontal side-view conditions, the reduction in clutter sparsity will seriously affect the performance of the SR-STAP method, limiting its application in practice.

[0125] 2) Introduction to the CNN-STAP method

[0126] Based on the idea of ​​deep learning image super-resolution reconstruction, the CNN-STAP method first uses a small number of IID training distance units to estimate the low-resolution clutter space-time power spectrum, and then uses CNN to reconstruct it to obtain the high-resolution clutter space-time power spectrum, thereby calculating CNCM and space-time adaptive weight vectors for clutter suppression and target detection. The details are as follows:

[0127] Assuming that there are L training range units (L = O), the corresponding space-time echo signal matrix is ​​X, then the low-resolution clutter space-time power spectrum can be obtained based on the Fourier transform method: As the input data of CNN, it is expressed as:

[0128]

[0129] Then, according to the theoretical value of the clutter covariance matrix R c Based on the minimum variance distortion less response (MVDR) spectrum estimation method, a high-resolution clutter space-time power spectrum can be obtained. As the output label data of CNN, it is expressed as:

[0130]

[0131] Using CNN to analyze the low-resolution clutter space-time power spectrum Y F The reconstruction process can be expressed as:

[0132]

[0133] Where: Represents the nonlinear transformation operation of the image, Θ C = {W1,W2,L,W E ,b1,b2,L,b E} represents the network parameters of CNN, We (e=1,2,...,E) indicates the dimension is c e ×f e ×f e ×n e Convolution kernel, b e Indicates dimension n e The bias vector of .

[0134] By constructing a data set to train CNN offline, we can get its optimal network parameters, which are expressed as:

[0135]

[0136] Where: and They represent the p-th low-resolution clutter space-time power spectrum input and the p-th high-resolution clutter space-time power spectrum output label respectively, and P is the size of the data set.

[0137] Finally, the trained CNN is used to calculate the actual space-time echo signal matrix X R Online processing can be performed to obtain the corresponding low-resolution clutter space-time power spectrum Reconstruct and obtain high-resolution clutter space-time power spectrum estimation and CNCM estimation, expressed as:

[0138]

[0139] Similar to the SR-STAP method, the CNN-STAP method can achieve better clutter suppression performance by using a small number of IID training distance units, and requires less computation. However, due to the poor quality of the clutter space-time power spectrum image generated by Fourier transform (low resolution and high sidelobe level), the CNN-STAP method has high requirements on the reconstruction ability of CNN. Although the reconstruction ability of CNN and the performance of CNN-STAP can be improved to a certain extent by increasing the network size, it will lead to an increase in computational complexity.

[0140] 3. The following is the specific content of the method described in the embodiment of the present invention:

[0141] In order to solve the problems existing in the SR-STAP method and the CNN-STAP method at the same time, the present invention proposes a DU-CNN-STAP method, whose processing framework is as follows: Figure 2 As shown, the specific operation can be expressed as follows: ① The space-time echo signal matrix Input the DU-CNN network shown in the dashed box, and after nonlinear transformation, the estimation of high-resolution clutter space-time power spectrum is obtained. ;②Based on And (20) to get the estimate of CNCM ; ③ According to formula (15), the estimation of the adaptive weight vector of the space-time filter is obtained , completing clutter suppression and target detection.

[0142] The DU-CNN-STAP method realizes the direct conversion of the space-time echo signal x to a high-resolution power spectrum. The nonlinear transformation of The method focuses on constructing a DU-CNN network, wherein the DU-CNN network specifically includes:

[0143] ①ADMM-Net module is the network for solving the sparse recovery problem (12), and its network parameters are Θ A , realize the clutter space-time amplitude spectrum Quick access to

[0144] ② Squarer module, used to complete the conversion from space-time amplitude spectrum to space-time power spectrum, transform T(·) to change the data format from N d N s ×1 to 1N d N s , output data ;

[0145] ③Power normalization module, used for air-time power Normalize (normalization is beneficial to improve the convergence of the network) to obtain the input data of CNN Where P S is the clutter power;

[0146] ④CNN module, which is a space-time power spectrum reconstruction network, and its network parameters are Θ C , to achieve normalized high-resolution clutter space-time power spectrum estimation Acquisition of

[0147] ⑤Power recovery module, used for Perform clutter power restoration and output , and finally get the network output of DN-CNN

[0148] In the DU-CNN network described in the present invention, the ADMM-Net module can obtain a high-resolution estimate of the clutter space-time spectrum based on a small number of iterations, and the CNN module can further improve the accuracy of the clutter space-time spectrum estimation. Therefore, the DU-CNN-STAP method can effectively solve the problems of difficult parameter setting, high computational complexity and low accuracy in the SR-STAP method. In addition, unlike the CNN-STAP method which uses a low-resolution clutter space-time spectrum as the input of the reconstruction network, the input of the reconstruction network in the DU-CNN-STAP method is a high-resolution clutter space-time spectrum. Therefore, the DU-CNN-STAP method can effectively reduce the requirements for the nonlinear transformation capability of the reconstruction network and reduce the network scale and computational complexity.

[0149] Below, the specific contents of the DU-CNN network in the DU-CNN-STAP method are introduced in detail, namely the network structure, data set construction and training method. It should be noted that this embodiment only considers the case of a single training distance unit, that is, L = 1. The processing of multiple training distance units can be simply expanded to implement the method in this paper. Therefore, in the subsequent derivation, the subscript l will be ignored.

[0150] (1) DU-CNN network structure

[0151] 1) ADMM-Net module

[0152] Since the L0 norm is a discontinuous function of a vector, the complexity of directly solving equation (12) is too high. Therefore, equation (12) is often converted into the following L1 convex optimization problem for solution:

[0153]

[0154] By introducing the auxiliary variable r, equation (21) can be equivalent to:

[0155]

[0156] Where: ρ>0 represents the regularization factor.

[0157] The augmented Lagrangian function of formula (22) can be expressed as:

[0158]

[0159] Where: represents the Lagrange multiplier, and β>0 represents the quadratic penalty factor.

[0160] Given the initial value {γ (0) ,r (0) ,λ (0)}, the ADMM algorithm uses K iterations to alternately solve the following three sub-problems to solve equation (23):

[0161]

[0162] Where: r (k) , γ (k) and λ (k) denote the k-th iterative estimates of r, γ and λ respectively, k = 1, 2, L, K.

[0163] The solution of formula (24) can be expressed as:

[0164]

[0165] Where: S(·) is the soft threshold operator, and τ is the iteration step size.

[0166] Given the iteration parameters ρ, β and τ, the ADMM algorithm can obtain a high-resolution estimate of the clutter space-time amplitude spectrum after K iterations. Then, according to formula (14-15), the adaptive weight vector of CNCM and space-time filter can be calculated.

[0167] However, ADMM belongs to the model-driven algorithm, and its parameters such as regularization factor ρ, quadratic penalty factor β and iteration step length τ need to be given in advance. In practical applications, parameter setting is generally difficult. Inappropriate parameter setting will affect the convergence performance of the ADMM algorithm, thereby increasing the complexity of solving equation (12) and reducing the estimation performance of the clutter space-time amplitude spectrum. Even if the parameters can be set well, using the same parameters for each iteration cannot guarantee that the ADMM algorithm will obtain the best convergence performance. In order to solve this problem, based on the idea of ​​deep expansion, the ADMM algorithm with a specific number of iterations can be expanded into a deep neural network ADMM-Net, and the different parameters for each iteration can be obtained by using data learning methods, thereby improving its convergence performance.

[0168] like Figure 3 As shown in the figure, the ADMM algorithm with the number of iterations K is expanded into a K-layer ADMM-Net, whose input is the space-time echo signal and the space-time steering vector matrix Φ, with parameters The output of each layer is a Lagrange multiplier Auxiliary variables and space-time amplitude spectrum The final output of the network is The nonlinear function is F k {·}, which can be expressed as:

[0169]

[0170] Where: r (k) =(ρ k / 1+ρ k βk )(λ (k-1) -β k Φγ (k-1) +β k x), γ (k) =S(γ (k-1) +τ k Φ H r (k) / (ρ k β k ),τ k / β k ), λ (k) =λ (k-1) -β k (Φγ (k) +r (k) -x).

[0171] ADMM-Net is driven by both training data and algorithm models, which makes it both adaptable to data and interpretable. In the data-driven network training process, the 3K network parameters of ADMM-Net It is adaptively adjusted so that under the same data environment, ADMM-Net has better convergence performance than the ADMM algorithm with the same number of iterations, thereby improving the estimation accuracy of the clutter space-time amplitude spectrum.

[0172] 2) CNN

[0173] In this embodiment, the space-time power spectrum reconstruction network in DU-CNN is a CNN with E layers of two-dimensional convolutional layers, and its network structure is as follows: Figure 4 As shown. The input of CNN is the output of ADMM-Net The normalized clutter space-time power spectrum obtained after transformation Its dimension is 1×N d ×N s , that is, the number of channels is 1, and the length × width is N d ×N s The output of CNN is the normalized high-resolution clutter space-time power spectrum , because each convolutional layer uses edge zero padding operation, only the number of channels is changed, while the length and width of the image remain unchanged, so The dimension is also 1×N d ×N s The network parameters of CNN are , where W e Indicates dimension c e ×f e ×f e ×n e The convolution kernel, c e Indicates the number of input channels f eRepresents the length and width of the convolution kernel, n e represents the number of convolution kernels (i.e. the number of output channels), b e Indicates dimension n e The bias vector of . * represents the convolution operation, and the operation of each convolution layer is:

[0174] ① The convolution layer Conv-1 is used to extract features from the input clutter space-time power spectrum. It uses the ReLU activation function. The specific operation can be expressed as:

[0175]

[0176] ② The convolutional layers Conv-2 to Conv-(E-1) realize the nonlinear mapping of features, and all use the ReLU activation function. The specific operation can be expressed as:

[0177]

[0178] ③The convolution layer Conv-E is the image reconstruction layer, and the dimension is 1×N d ×N s The high-resolution clutter space-time power spectrum output can be expressed as:

[0179]

[0180] (2) DU-CNN dataset construction

[0181] DU-CNN adopts a supervised learning method, that is, network training is performed based on data and its labels given in advance. This embodiment adopts the following steps to construct a sufficient and complete data set to ensure the clutter space-time spectrum estimation performance and network generalization ability of DU-CNN. The method for constructing the DU-CNN data set (i.e., S2) specifically includes:

[0182] ① Use the method described above to construct the input dataset of the DU-CNN network.

[0183] ② Given the spatial frequency and Doppler frequency range [f s,min ,f s,max ] and [f d,min ,f d,max ], given the number of grids N s =ρ s M and N d =ρ d N, construct the space-time steering vector dictionary Φ based on formula (10); according to the convergence condition of the ADMM algorithm, set different combinations of iteration parameters, and calculate all space-time echo signals based on formula (12) The iterative parameters with the best estimation performance are obtained by processing, regularization factor ρ = ρ0, quadratic penalty factor β = β0, iteration step size τ = τ0, and number of iterations K = K0 as parameters of the ADMM algorithm, and the estimation of the clutter space-time amplitude spectrum is obtained. As the intermediate data set of DU-CNN; according to the theoretical value of the clutter covariance matrix, the estimation of the high-resolution clutter space-time power spectrum is obtained based on formula (17): As the output label dataset of DU-CNN.

[0184] ③ Such as Figure 5 As shown, the constructed DU-CNN is input into the dataset And output label dataset And the clutter space-time amplitude spectrum dataset Divide into training data set and validation data set according to a certain ratio, the data set sizes are P train and P test Among them, the input dataset of ADMM-Net is The output label dataset is The data set can be expressed as The input data set of CNN is The output label dataset is The data set can be expressed as

[0185] (3) DU-CNN training method

[0186] In order to avoid falling into the local optimum and improve the convergence performance of the network, this embodiment adopts the method of pre-training + joint fine-tuning to train DU-CNN. Figure 5 shown and ADMM-Net and CNN are pre-trained separately, and then Figure 5 shown Perform end-to-end training on DU-CNN, that is, fine-tune the network parameters of ADMM-Net and CNN as a whole. The specific steps (i.e., step S5) are as follows:

[0187] ① Initialize the parameters of each layer of the ADMM-Net network according to the iterative parameter settings of the ADMM algorithm, that is, The network loss function is defined as the mean square error (MSE) between the ADMM-Net output and the label data, expressed as:

[0188]

[0189] Where: Indicates xp As input, Θ A The K-th layer output of ADMM-Net with parameters. The optimal parameters of ADMM-Net It can be obtained by minimizing the network loss function through the back propagation method

[19] and is expressed as:

[0190]

[0191] ② The Glorot method is used to initialize the network parameters of CNN. The network loss function is also defined as the MSE of CNN output and label data, expressed as:

[0192]

[0193] Where: Indicates As input, Θ C is the output of the CNN with parameters. Similarly, the optimal parameters of CNN can be obtained by solving the following formula using the back propagation method:

[0194]

[0195] ③ Based on the independent pre-training of ADMM-Net and CNN, DU-CNN is trained end-to-end to further improve the convergence performance of the network. Implementation, thereby avoiding the local convergence problem that may be caused by direct training of DU-CNN, the network loss function is shown as follows:

[0196]

[0197] Where: Indicates x p As input, Θ={Θ A ,Θ C} is the output of DU-CNN with parameters. Similarly, the optimal parameters of DU-CNN It can be obtained by solving the following formula:

[0198] 4. The following is a simulation analysis of the DU-CNN-STAP method described in this embodiment

[0199] This section verifies the performance of the DU-CNN-STAP method through simulation experiments, and compares and analyzes it with the CNN-STAP method and the SR-STAP method based on the ADMM algorithm. The simulation parameters are shown in Table 1. For the SR-STAP algorithm, the iteration parameters of the ADMM algorithm are set to ρ0 = 0.5, β0 = 0.01, τ0 = 0.04 and K0 = 2000; for the method described in the present invention, the number of CNN network layers in DU-CNN is set to E = 5, and the convolution kernel dimension is Set to (1×11×11×16), (16×9×9×8), (8×7×7×4), (4×5×5×2) and (2×3×3×1); for the CNN-STAP method, it uses the same number of network layers and convolution kernel dimensions as this method.

[0200] Table 1 Simulation parameters

[0201]

[0202] (1) Network convergence

[0203] This section analyzes the training convergence of ADMM-Net, CNN, and DU-CNN in this method, and compares it with the training convergence of CNN in the CNN-STAP method. Figure 6 The training convergence of ADMM-Net is given when the number of network layers K is equal to 20, 30 and 40. It can be seen that: under different network layers, the loss function of ADMM-Net gradually decreases and tends to be stable; as the number of network layers increases, the loss function of ADMM-Net decreases and the convergence performance improves. Considering the amount of computation and convergence performance, in the following simulations, the number of network layers of ADMM-Net is set to K = 20. Figure 6 (b) shows the convergence comparison of CNN in this method and CNN-STAP method. It can be seen that: under the condition that the number of network layers and convolution kernel dimensions are equal, since the input of CNN in this method is the high-resolution clutter space-time spectrum obtained by the ADMM algorithm, it has better convergence performance than the CNN-STAP method which takes Fourier low-resolution clutter space-time spectrum as input. Figure 6(c) shows the convergence of DU-CNN in this method and CNN in CNN-STAP method, where CNN-New has 7 network layers and the dimensions of convolutional layers are (1×11×11×16), (16×9×9×12), (12×9×9×10), (10×7×7×8), (8×5×5×4), (4×5×5×2) and (2×3×3×1). It can be seen that: ① Under the condition that the number of network layers and convolution kernel dimensions are equal, DU-CNN has better convergence performance than CNN in CNN-STAP method; ② Increasing the network size can improve the convergence performance of CNN in CNN-STAP method and obtain results similar to DU-CNN in this method, but it will increase the computational complexity.

[0204] (2) Clutter suppression performance

[0205] This section verifies the clutter suppression performance of the proposed method and compares it with the CNN-STAP method and the SR-STAP method. Figure 7 and Figure 8 As shown, Figure 7 Corresponding to the front and side view array, the parameters are β=1、θ e = 0° and CNR = 32.77dB, Figure 8 For the non-positive side view array, the parameters are β=2.49、θ e =-15.61° and CNR = 38.65dB. It can be seen that: under the condition of positive side view, the SR-STAP method can obtain better clutter space-time spectrum estimation performance, but there are problems of discontinuous clutter distribution and off-ridge interference; under the condition of non-positive side view, due to the deterioration of the sparsity of clutter in the space-time two-dimensional plane, the performance of the SR-STAP method is seriously degraded; under two different conditions, the CNN-STAP method can reconstruct the clutter space-time spectrum well, the clutter distribution is continuous and the off-ridge interference is less, but there is a problem of clutter ridge widening; the DU-CNN-STAP method described in the present invention can obtain better performance than the CNN-STAP method and the SR-STAP method, and the obtained clutter space-time spectrum estimation result is closer to the theoretical value.

[0206] based on Figure 7 and Figure 8 The clutter space-time spectrum shown in FIG. 1 is shown in FIG. 1 . The present invention uses SCNR loss to measure the clutter suppression performance of different methods. The results are shown in FIG. 1 . Fig. 9As shown. Among them, the spatial frequency of the target is set to 0, and the normalized Doppler frequency changes linearly in the range of [-0.5, 0.5]. It can be seen that: under the condition of positive side view, the SR-STAP method can form a deeper depression near the zero frequency, which can suppress clutter well, but the interference outside the ridge makes the notch widen, affecting its slow target detection ability; under the condition of non-positive side view, the SR-STAP method is difficult to form a deeper depression, and the clutter suppression performance is poor; under two different conditions, the CNN-STAP method can form a deeper depression near the zero frequency, but the notch width is large, and the SCNR loss outside the zero frequency is about 10dB; compared with the SR-STAP method and the CNN-STAP method, the DU-CNN-STAP method in this paper can obtain better clutter suppression performance, with a deeper depression and a smaller notch width, and the SCNR loss outside the zero frequency is about 5dB.

[0207] (3) Computational complexity

[0208] This section analyzes the computational complexity of this method and compares it with the SR-STAP method and the CNN-STAP method. Taking the number of multiplications as an indicator, the computational complexity of the Fourier spectrum estimation method (i.e., Equation 16), the ADMM algorithm (i.e., Equation 25), and the CNN method (i.e., Equations 27-29) are shown in Table 2. It should be noted that the trained ADMM-Net and the ADMM algorithm have the same operations and only differ in the iteration parameters. Therefore, under the condition of the same number of iterations (number of network layers), the computational complexity of the ADMM-Net and ADMM algorithms is equal. According to Table 2, the computational complexity of this method, the SR-STAP method, and the CNN-STAP method for clutter space-time spectrum estimation are C respectively. A (K)+C C , C A (K0) and C F +C C Based on this, the computational complexity of different methods under the condition of M = N = Nd / 5 = Ns / 5 = 4 to 16 can be obtained as follows: Fig.10 As shown. Among them, CNN-STAP-New corresponds to Figure 6 CNN-New in (c) increases the network size of CNN to improve the performance of CNN-STAP. It can be seen that the computational complexity of this method and CNN-STAP is much lower than that of SR-STAP, and the higher the dimension of the clutter space-time spectrum estimation problem, the more obvious the advantage; under the condition of a large number of array elements, the computational complexity of this method is higher than that of CNN-STAP; in order to obtain performance similar to that of this method, the computational complexity of CNN-STAP method is increased, which is significantly higher than that of this method.

[0209] Table 2 Operational complexity

[0210]

[0211] (4) Summary

[0212] In order to solve the problem of a large number of independent and identically distributed training distance units required by the airborne radar STAP method, this embodiment proposes the DU-CNN-STAP method, and introduces its processing framework, network structure, data set construction and training method in detail. The simulation experimental results under different conditions show that compared with the SR-STAP method, this method can improve the accuracy of clutter space-time spectrum estimation and reduce the computational complexity; compared with the CNN-STAP method, this method can reduce the requirements for network reconstruction capabilities and obtain better clutter suppression performance. The next step will be to conduct in-depth research on the improvement of methods under non-ideal conditions, the construction of multi-dimensional deep expansion networks, and the optimization of CNN network structures.

[0213] The remaining technical features in this embodiment can be flexibly selected by those skilled in the art according to actual conditions to meet different specific practical needs. However, it is obvious to those skilled in the art that it is not necessary to adopt these specific details to implement the present invention. In other examples, in order to avoid confusing the present invention, the well-known components, structures or parts are not specifically described, which are all within the technical protection scope defined by the technical solution claimed for protection in the claims of the present invention.

[0214] Modifications and changes made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the scope of protection of the claims attached to 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 are not necessary to practice the present invention. In other examples, in order to avoid confusing the present invention, well-known technologies, such as specific construction details, operating conditions and other technical conditions, are not specifically described.

[0215] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A STAP method for airborne radar based on deep expansion and convolutional neural network, characterized in that: The following steps are involved: S1, setting a specific parameter range of the airborne radar, and using the space-time echo signal model of the airborne radar to generate multiple radar space-time echo signals, thereby constructing an input data set; S2, based on the SR-STAP method and ADMM algorithm, the radar space-time echo signal is processed to obtain the estimation of the clutter space-time amplitude spectrum as the intermediate data set; According to the theoretical value of the clutter covariance matrix and based on the MVDR spectrum estimation method, an estimate of the high-resolution clutter space-time power spectrum is obtained as an output label data set; the input data set, the intermediate data set, and the output label data are integrated into a DU-CNN data set, and divided into a training data set and a validation data set according to a set ratio; S3, constructing a DU-CNN network, wherein the DU-CNN network includes an ADMM-Net module, a squarer module, a power normalization module, a CNN module, and a power restoration module, wherein the ADMM-Net module is a network for solving the sparse recovery problem, and is used to realize the rapid acquisition of the clutter space-time amplitude spectrum; the CNN module is a space-time power spectrum reconstruction network, and is used to realize the acquisition of the normalized high-resolution clutter space-time power spectrum estimation; S4, based on the training data sets corresponding to the input data set and the intermediate data set, and the training data sets corresponding to the intermediate data set and the output label data set, the ADMM-Net module and the CNN module are independently pre-trained, and then based on the training data sets corresponding to the input data set and the output label data set, the DU-CNN network is end-to-end trained, and the network parameters of the ADMM-Net module and the CNN module are jointly fine-tuned to obtain a trained DU-CNN network; S5, the trained DU-CNN network is combined with the STAP method to process the space-time echo signal of the target to be detected, and the estimation of CNCM and the estimation of the space-time filter adaptive weight vector are obtained.

2. The airborne radar STAP method based on deep expansion and convolutional neural network according to claim 1, characterized in that: The squarer module is used to complete the conversion from the space-time amplitude spectrum to the space-time power spectrum and output the space-time power spectrum; The power normalization module is used to normalize the space-time power spectrum to obtain input data of the CNN module; The power restoration module is used to perform clutter power restoration on high-resolution clutter space-time power spectrum estimation.

3. The airborne radar STAP method based on deep expansion and convolutional neural network according to claim 1, characterized in that: The S1, setting a specific parameter range of the airborne radar, generating multiple radar space-time echo signals using the space-time echo signal model of the airborne radar, and constructing an input data set, specifically includes: S1.1, given the aircraft height H, the number of ULA array elements M, the number of CPI pulses N, the array element spacing d and the carrier wavelength λ; assuming that the pitch angle, non-positive side view angle, clutter ridge slope and clutter-to-noise ratio corresponding to the range unit all obey uniform random distribution, that is, θ e :U(θ min ,θ max ), β=2vT r / λ:U(β min ,β max ) and CNR:U(CNR min ,CNR max ); Based on the airborne radar space-time echo signal model, generate P radar space-time echo signals As the input dataset of the DU-CNN network, Each distance ring contains N c clutter blocks are uniformly distributed in the azimuth range [0,π], whose scattering coefficient obeys complex Gaussian distribution, and whose amplitude is determined by the clutter-to-noise ratio CNR; the clutter and noise components contained in the space-time echo signal model of the airborne radar are: Where: x c represents the clutter signal, x n Represents a noise signal, assuming that the mean is 0 and the variance is σ n 2 Complex Gaussian white noise signal; represents the Kronecker product; σ c；n represents the scattering coefficient of the nth clutter block; v d (f c；d,n ) and v s (f c；s,n ) are the time domain steering vector and spatial domain steering vector of the nth clutter block, respectively, expressed as: Where: and denote N×1 and M×1 dimensional complex vectors respectively, exp(g) denotes exponential operation with base e, [·] T represents transpose, f c；d,n and f c；s,n are the Doppler frequency and spatial frequency of the nth clutter block, respectively, expressed as: Where: and θ n are the elevation angle and azimuth angle of the nth clutter block, θ e It represents the angle between the antenna array and the direction of radar movement, and λ is the signal wavelength.

4. The airborne radar STAP method based on deep expansion and convolutional neural network according to claim 1, characterized in that: S2, based on the SR-STAP method and the ADMM algorithm, processes the radar space-time echo signal to obtain an estimate of the clutter space-time amplitude spectrum as an intermediate data set; According to the theoretical value of the clutter covariance matrix and the MVDR spectrum estimation method, the high-resolution clutter space-time power spectrum is estimated as the output label data set, which specifically includes: S2.1, given the spatial frequency [f s,min ,f s,max ], Doppler frequency range [f d,min ,f d,max ], given the number of grids N s =ρ s M and N d =ρ d N, construct the space-time steering vector dictionary Φ based on formula (10): In the formula, f d,i is the i-th Doppler frequency, f s,j is the jth spatial frequency, v(f d,i ,f s,j ) is the space-time steering vector corresponding to the ijth grid point, Indicates the Nth d , N s The space-time steering vector corresponding to each grid point; S2.2, according to the convergence conditions of the ADMM algorithm, different combinations of iteration parameters are set, and all space-time echo signals are calculated based on formula (12) The iterative parameters with the best estimation performance are obtained by processing, regularization factor ρ = ρ0, quadratic penalty factor β = β0, iteration step size τ = τ0, and number of iterations K = K0 as parameters of the ADMM algorithm, and the estimated set of clutter space-time amplitude spectrum is obtained. As an intermediate data set; Where: is the pth estimated value in the clutter space-time amplitude spectrum estimation set, ||·||0 and ||·||2 represent the L0 norm and L2 norm of the vector respectively, and ε represents the noise level; According to the theoretical value R of the clutter covariance matrix c , based on the MVDR spectrum estimation method, the estimated set of high-resolution clutter space-time power spectrum is obtained As output label dataset; Where: is the pth estimated value in the high-resolution clutter space-time power spectrum estimation set.

5. The airborne radar STAP method based on deep expansion and convolutional neural network according to claim 1, characterized in that: The S4, based on the training data set corresponding to the input data set and the intermediate data set, and the training data set corresponding to the intermediate data set and the output label data set, independently pre-trains the ADMM-Net module and the CNN module, and then based on the training data set corresponding to the input data set and the output label data set, performs end-to-end training on the DU-CNN network, and jointly fine-tunes the network parameters of the ADMM-Net module and the CNN module to obtain a trained DU-CNN network, specifically including: S4.1, initialize the parameters of each layer of the ADMM-Net network according to the iterative parameter setting of the ADMM algorithm, that is, And define the network loss function as the mean square error MSE between ADMM-Net output and label data, expressed as: Where: Indicates x p As input, Θ A The K-th layer output of ADMM-Net with parameters; The optimal parameters of ADMM-Net network The network loss function is minimized by the back propagation method and is expressed as: S4.2, the Glorot method is used to initialize the network parameters of CNN, and the network loss function is defined as the MSE of CNN output and label data, expressed as: Where: Indicates As input, Θ C is the output of the CNN with parameters; similarly, the optimal parameters of CNN are obtained by solving the following formula through the back propagation method: S4.3, based on the independent pre-training of ADMM-Net and CNN, the DU-CNN is trained end-to-end. At this time, the initialization of DU-CNN is based on Implementation, the network loss function is: Where: Indicates x p As input, Θ={Θ A ,Θ C } is the output of the DU-CNN with parameters; similarly, the optimal parameters of the DU-CNN By solving the following equation:

6. An airborne radar STAP system based on deep expansion and convolutional neural network, used to execute the airborne radar STAP method based on deep expansion and convolutional neural network according to any one of claims 1 to 5, characterized in that: include: The signal generation module is used to set the specific parameter range of the airborne radar and generate multiple radar space-time echo signals using the space-time echo signal model of the airborne radar to construct an input data set; The data set module is used to process the radar space-time echo signal based on the SR-STAP method and the ADMM algorithm to obtain the estimation of the clutter space-time amplitude spectrum as the intermediate data set; According to the theoretical value of the clutter covariance matrix and based on the MVDR spectrum estimation method, an estimate of the high-resolution clutter space-time power spectrum is obtained as an output label data set; the input data set, the intermediate data set, and the output label data are integrated into a DU-CNN data set, and divided into a training data set and a validation data set according to a set ratio; A model building module is used to build a DU-CNN network, wherein the DU-CNN network includes an ADMM-Net module, a squarer module, a power normalization module, a CNN module, and a power restoration module, wherein the ADMM-Net module is a solution network for the sparse recovery problem, and is used to realize the rapid acquisition of the clutter space-time amplitude spectrum; the CNN module is a space-time power spectrum reconstruction network, and is used to realize the acquisition of the normalized high-resolution clutter space-time power spectrum estimation; A training module is used to pre-train the ADMM-Net module and the CNN module independently based on the training data sets corresponding to the input data set and the intermediate data set, and the training data sets corresponding to the intermediate data set and the output label data set, and then perform end-to-end training on the DU-CNN network based on the training data sets corresponding to the input data set and the output label data set, and jointly fine-tune the network parameters of the ADMM-Net module and the CNN module to obtain a trained DU-CNN network; The result output module is used to combine the trained DU-CNN network with the STAP method to process the space-time echo signal of the target to be detected, and obtain the estimation of CNCM and the estimation of the space-time filter adaptive weight vector.

7. 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 to 5.

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