Airborne radar clutter suppression method based on autoencoder under insufficient sample conditions

Abstract

The invention discloses an airborne radar clutter suppression method based on an autoencoder under the condition of insufficient samples. The radar transmits a signal and obtains received data after matched filtering and pulse stacking. A real-domain matrix to be reconstructed is designed, whose dimension is less than half of the system's degree of freedom and which has been processed by matrix transformation. The structural characteristics of the real-domain matrix to be reconstructed and the characteristics of the autoencoder are then used to design encoding and decoding activation functions and a network loss function to construct an autoencoder neural network. The total loss function is then reduced through gradient descent iteration to achieve training of the autoencoder. Finally, the real-domain matrix to be reconstructed and the decoder output are used to design an inverse processing process for the matrix transformation data, reconstruct the clutter plus noise covariance, and utilize space-time adaptive processing to suppress clutter and detect targets. The invention reduces the clutter spectrum broadening phenomenon caused by insufficient training samples, improves the radar clutter suppression performance, and adapts to non-ideal sample conditions faced by real applications such as non-uniform clutter environments and insufficient training samples.

Description

Technical Field

[0001] The present invention relates to the technical field of airborne radar systems, and in particular to an airborne radar clutter suppression method based on an autoencoder under conditions of insufficient samples. Background Art

[0002] Airborne radars offer significant advantages in long-range vision and flexibility, but their core challenge is that strong clutter can drown targets within a broadened clutter spectrum. Space-time adaptive processing (STAP) for airborne radars has become a core technology for clutter suppression and target detection. Accurately estimating the clutter-plus-noise covariance matrix (CNCM) is crucial for STAP, requiring the number of independent and identically distributed (IID) training samples to be greater than twice the system's degrees of freedom (DOF) to achieve an output signal-to-clutter-noise ratio (SCNR) loss of less than 3dB. However, due to the array configuration and complex clutter environment, the non-uniform, time-varying environment in practical applications makes it difficult to obtain sufficient IID training samples for STAP, resulting in a significant degradation in STAP performance. In particular, as a form of clutter inhomogeneity, clutter range dependence occurs when the array antenna is configured as a non-side-looking array, which directly prevents the training samples from meeting the IID condition.

[0003] The above problems are usually solved by reducing the system DOF and selecting some samples to estimate the CNCM of the unit to be detected. A local joint processing (JDL) method (Electronics Letters, 1996, 32(3): 258) was proposed to reduce the dimension of adaptive processing to the product of the length and width of the selected processing local area. It uses two-dimensional Fourier transform and simultaneously processes beamforming and Doppler frequency, selecting a rectangular joint processing local area. Another auxiliary channel processing (ACP) method (Journal of Circuits and Systems, 2004, 9(6): 100-104) sets the two-dimensional beam near the clutter ridge as an auxiliary beam to reduce the DOF. However, the existing dimensionality reduction and rank reduction methods have the following problems: 1) the reduced system degrees of freedom and the reduced sample data directly lead to a decrease in STAP performance; 2) they do not directly solve the sample inhomogeneity problem caused by distance dependence, and the selected samples are still inhomogeneous.

[0004] In order to avoid the problem of sample non-uniformity caused by the distance dependence of clutter, it can also be solved by distance compensation and scale conversion. The clutter spectrum of adjacent training units is compensated so that the space-time distribution of the compensated clutter is as consistent as possible with the unit to be detected. A Doppler shift compensation (DW) algorithm based on a non-side-looking array (IEE proceedings. Radar, sonar and navigation, 2001, 148 (5), 390: 253-258) uses the inertial navigation parameters of the radar system to obtain the Doppler frequency of the unit to be detected and compensated, and performs a one-dimensional translation on the two-dimensional clutter spectrum so that it coincides with the clutter spectrum of the unit to be detected in the Doppler frequency direction, thereby eliminating the clutter distance correlation. Another angle-Doppler compensation (ADC) method (Proceedings of IEEE Radar Conference, Long Beach, CA, 2002, 311-317) was proposed. By calculating the inertial navigation parameters and performing linear transformation, the center of the clutter spectrum of each range unit is translated to improve the clutter diffusion degree in the Doppler domain and beam domain. In addition, high-order Doppler shift compensation (HODW) methods have been proposed (Adaptive Sensor Array Processing Workshop, MIT Lincoln Laboratory, Lexington, 2001: 13-14), which compensate for adjacent range cells from multiple spatial angles. However, existing range compensation methods have the following shortcomings: 1) they rely heavily on the given and estimated parameters of the inertial navigation system, making them non-adaptive algorithms; and 2) they struggle to simultaneously account for insufficient training samples, as well as sample non-uniformity caused by non-front-view array configurations and complex time-varying clutter environments. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides an airborne radar clutter suppression method based on an autoencoder under sample-sufficient conditions. This method provides a significantly superior improvement factor and a narrower and deeper improvement factor notch for both side-viewing and non-side-viewing radars. This method significantly reduces the clutter spectrum broadening caused by insufficient IID training samples, significantly improves radar clutter suppression performance, and enhances adaptability without reducing the system's degrees of freedom. The method can better adapt to non-ideal sample conditions encountered in real-world applications, such as non-uniform clutter environments and insufficient training samples.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] An airborne radar clutter suppression method based on an autoencoder under insufficient sample conditions comprises the following steps:

[0008] 1) The radar transmits a signal and obtains received data after matched filtering and pulse stacking. Based on the space-time multidimensional structure of the received data and the covariance properties of clutter plus noise, a real-domain matrix to be reconstructed with a dimension less than half the system's degrees of freedom and processed by matrix transformation is designed;

[0009] 2) Using the structural characteristics of the real-domain matrix to be reconstructed and the characteristics of the autoencoder, we design encoding and decoding activation functions and network loss functions for the real-domain matrix to be reconstructed, and construct an autoencoder neural network with l2 regularization and sparse regularization;

[0010] 3) Through gradient descent iteration, the total loss function is reduced to train the constructed autoencoder;

[0011] 4) Using the designed special structure of the real-domain matrix to be reconstructed and the decoder output, the inverse processing process of the matrix transformation data is designed to reconstruct the covariance of the clutter plus noise, and space-time adaptive processing is used to suppress the clutter and detect the target.

[0012] The step 1) is specifically as follows:

[0013] 1.1) Each column of N×K dimensional echo data collected by K pulses of a CPI is stacked into an NK×1 dimensional vector x cn,l ,as follows:

[0014]

[0015] where N c is the total number of clutter blocks in the clutter unit, ξ i (l) is the complex amplitude of the i-th clutter block, l represents the l-th range unit, n(l) is the zero-mean noise vector, a st (f s,i ,f d,i ) is the space-time two-dimensional vector of the i-th clutter block, specifically expressed as:

[0016]

[0017] The time-domain steering vector a of the i-th clutter block t (f d,i ) is:

[0018]

[0019] where f d,i and f PRF is its Doppler frequency and pulse repetition frequency, K is the number of pulses; in addition, the spatial steering vector a of the i-th clutter block s (f s,i ) is:

[0020]

[0021] where f s,i is its spatial frequency, N is the number of uniform linear array elements; according to the spatial geometric relationship, the Doppler frequency f of the i-th clutter scatterer d,i for:

[0022]

[0023] where v a is the speed of the moving platform, λ is the wavelength, θ i and are the pitch angle and azimuth angle of the scatterer relative to the platform velocity vector, β i is the spatial cone angle; the spatial frequency of the clutter scatterer is:

[0024]

[0025] Where d is the array element spacing, is the angle between the array and the motion platform velocity direction, α i is the angle formed by the i-th clutter scatterer and the antenna array, and the rest of the meanings are the same as in equation (5);

[0026] 1.2) For the clutter plus noise covariance matrix, its matrix elements Calculated as:

[0027]

[0028] in(·) H is the conjugate transpose, (·) * is conjugated, X cn =[x cn,1 ,...,x cn,L ] is composed of x cn,l The receiving data matrix composed of x cn,l Given by formula (1), X cn (i,:) and X cn (j,:) are X cn The i-th and j-th rows, X cn (i,l) and X cn (j,l) is X cn The (i, l)th and (j, l)th elements; L is the total number of nearby range rings excluding the unit where the target to be detected is located, and N and K are the number of array elements and the number of pulses;

[0029] 1.3) Design a special matrix to be encoded and decoded, the matrix dimension, and its original data matrix as follows:

[0030]

[0031] Where p represents the dimension of the special real-domain matrix to be reconstructed, l = 1, 2, ... L represents the lth distance ring, and the rest of the meanings are given by formula (7); the original data matrix The number of rows and columns p of the system is designed to satisfy p<NK / 2, that is, p is a positive integer less than half of the system's degree of freedom, and based on the calculation form of formula (7) Contains the selected clutter plus noise covariance features;

[0032] 1.4) Construct the following matrix transformation:

[0033]

[0034] Among them C re is the new data obtained after the above conversion, To sum, the original data matrix The number of rows and columns p is given by formula (8), is a p×1 dimensional vector with 1 as its element, is a matrix abbreviation, [·](i,p) represents the (i,p)th element of the matrix [·], and the p×p dimensional matrix Specifically:

[0035]

[0036] in The original data matrix is ​​given by formula (8), represents the (i,p)th element, and the rest of the meanings are given by formula (9);

[0037] The final matrix to be reconstructed is proposed as follows:

[0038]

[0039] where real{·} is the real part of {·}.

[0040] The step 2) is specifically as follows:

[0041] 2.1) Design After that, we construct an automatic encoding network for it. First, we define:

[0042]

[0043] Where H represents the encoder output, F(·) is the encoder activation function, W and b are the weight matrix and bias vector of the encoding network layer respectively; Representatives Column p2 is the overall function of the input encoder; the encoding layer is connected to the decoding layer, and the output H of the encoder is also the input of the decoder. The decoder is expressed as:

[0044]

[0045] in is the decoder output, H(:,p2) is the p2th column of the encoder output H obtained by equation (12), γ(·) is the decoder activation function different from F(·), U and f are the weight matrix and bias vector of the decoder network layer, respectively, and g(H(:,p2)) represents the overall decoder function with H(:,p2) as input. The encoder activation function to be reconstructed is selected as follows:

[0046]

[0047] Where 1≤p2≤p and p is the dimension defined by Equation (8), H(i,p2) is the (i,p2)th element, W(i,:) is the i-th row, is the p2th column, b(i) and is the i-th element of the vector;

[0048] 2.2) Based on the nonlinear function characteristics, the decoder activation function of the real domain matrix to be reconstructed is set to:

[0049]

[0050] in Represents the original input, that is, the special real-domain matrix to be reconstructed The estimate is also the decoder output, [·](:,p2) represents the p2th column of the matrix [·], e -[·] is an exponential function with the natural constant e as the base, U and f are the decoder weights and biases, W and b are the encoder weights and biases, H(:,p2) is the encoder output column p2, F(·) is the encoder activation function; let I np and O up Denote the encoder input and decoder output respectively, then the autoencoder loss function criterion is:

[0051] Θ loss (I np ,O up )=Δ(I np ,O up )≈0 (16)

[0052] 2.3) is the autoencoder neural network of the real domain matrix to be reconstructed, and the network output is made as close as possible to its input through encoding and decoding Therefore, its output is regarded as Reconstruction of each element; network training is regarded as the following optimization problem:

[0053]

[0054] in is the special real-domain matrix to be reconstructed, for is an estimate of and is also the decoder output, is the actual encoder weight and bias, and decoder weight and bias obtained after network training, that is, the estimate of the theoretical value of the corresponding weight and bias (W, b, U, f), Indicates the value of (W, b, U, f) when <·> reaches the minimum value;

[0055] The entire loss function is divided into three parts. The first part of the loss function E0 is directly obtained by the autoencoder criterion, which is:

[0056]

[0057] Where 1≤p1,p2≤p, p is the special real domain matrix to be reconstructed The dimension of for The estimate of is also the decoder output, [·](p1,p2) represents the (p1,p2)th element of the matrix [·], are the subparts of E0 corresponding to 1≤p1, p2≤p respectively; at the same time, the l2 weight regularization term E1 is introduced as follows:

[0058]

[0059] The number of neurons in the hidden layer is set to h n , p is the dimension of the special real-domain matrix to be reconstructed, W(i,j) and U(i,j) are the (i,j)th elements of the encoder and decoder weight matrices W and U respectively; in addition, the sparse regularization term E2 is introduced as follows:

[0060]

[0061] where h n is the number of neurons in the hidden layer, is the Kullback-Leiber divergence equation, which measures and β distribution difference; when KL(·) takes the value of 0, otherwise the value becomes larger; and Indicated by Column p2 is the overall encoder function of the input, that is, the encoder output, yes The i-th element of , β is Finally, based on E0, E1 and E2, the total loss function L oss Expressed as:

[0062]

[0063] Where η and λ are the coefficients of the l2 weight regularization term and the sparse regularization term, respectively. The rest of the meanings are given in Equations (18), (19), and (20).

[0064] The step 3) is specifically as follows:

[0065] 3.1) Use gradient descent to iteratively update W(i,j) and U(i,j) as follows:

[0066]

[0067] in and ε represent the derivative and learning rate respectively, W(i,j) and U(i,j) are the (i,j)th element of the weight matrix of the encoder and decoder respectively, L oss is the total loss function;

[0068] At the same time, each iteration, update b(i) and f(i) as:

[0069]

[0070] in and ε are the derivative and learning rate; b(i) and f(i) are the i-th element of the bias vector of the encoder and decoder respectively, L oss is the total loss function;

[0071] 3.2) For the weight matrix, derive as follows:

[0072]

[0073] The abbreviation and Respectively and η and λ are the weight regularization term and sparse regularization term coefficients, p is the dimension of the special matrix to be reconstructed, h n is the number of hidden neurons, and the rest of the meanings are shown in formulas (18)-(21); the abbreviations in formula (24) are obtained specifically as follows:

[0074]

[0075] where \(F(\cdot)\) and \(\gamma(\cdot)\) are the encoder and decoder activation functions respectively, \(F'(Z(i, p2))\) represents the derivative of the function \(F(Z(i, p2))\) with respect to \(Z(i, p2)\), and \(\{W, U; b, f\}\) are the weight matrices and bias vectors. is the special real domain matrix to be reconstructed in the design. is The estimate of is also the output of the decoder network. is in abbreviated form; in addition, in Equation (25) and we get Also, in Equation (24) is the average activation value which can be obtained from and the detailed derivation of the abbreviation in Equation (24) is:

[0076]

[0077] where \(F'[Z(i, p2)]\) is the derivative corresponding to \(Z(i, p2)\), and for \(0 < Z(i, p2) \lt 1\), \(F'[Z(i, p2)] = 1\), otherwise \(F'[Z(i, p2)] = 0\); for the bias vector, the derivation of its derivative is:

[0078]

[0079] where the abbreviation is obtained from Equation (25). and represents the average activation value of the encoder output input by the \(p2\) - th column is is the \(i\) - th element, \(\beta\) is the expected value of; in addition, in Equation (27) specifically

[0080]

[0081] While updating the weights \(W\) and the bias \(b\), based on the total loss function and the weights \(U\) and the bias \(f\) in the decoding layer, by the same token as the steps in formulas (22) - (28), we get and which are:

[0082]

[0083] where is defined in Equation (25), \(L\) ossis the total loss function, H(j,p2) is the (j,p2)th element of the encoder output H obtained by Equation (12), η is the l2 weight regularization term coefficient, p is the dimension of the special matrix to be reconstructed, U(i,j) is the (i,j)th element of U, and f(i) is the i-th element of f.

[0084] The step 4 is specifically as follows:

[0085] 4.1) After encoding and decoding, based on the constructed covariance feature Dimensional Matrix The structure of the matrix is ​​transformed by the following inverse processing:

[0086]

[0087] in is the new data matrix after inverse transformation, The special real domain matrix to be reconstructed is designed The estimate of is also the decoder output, p is The dimension of is the original data matrix obtained by formula (8) The (i,p)th element of The matrix obtained by formula (10) is The (i,p)th element of is a p×1-dimensional vector with all elements set to 1.

[0088] 4.2) The final reconstruction form of the extracted clutter plus noise covariance is designed as:

[0089]

[0090] Where imag{·} represents the imaginary part, and the clutter plus noise covariance matrix CNCM is reconstructed as follows:

[0091]

[0092] in is the reconstructed CNCM, N and K are the number of array elements and pulses, and p is the dimension of the special real-domain matrix to be reconstructed; and They are the clutter plus noise covariance matrices before reconstruction The corresponding sub-matrices are the upper left corner p×(NK-p) dimension, the lower left corner (NK-p)×(NK-p) dimension, and the lower right corner (NK-p)×p dimension, and Obtained from formula (7);

[0093] 4.3) Using the reconstructed clutter plus noise covariance and space-time adaptive processing technology, the airborne radar clutter suppression is realized; according to the linear constrained minimum variance (LCMV) criterion, the adaptive optimal weight vector w opt It is derived from the following formula:

[0094]

[0095] where f d0 and f s0 is the temporal frequency and spatial frequency of the target, a st (f s0 ,f d0 ) is the NK×1-dimensional target space-time steering vector; According to the Lagrange multiplier method, the optimal weight vector w opt for:

[0096]

[0097] in(·) -1 To invert the matrix, is the reconstructed clutter plus noise covariance matrix obtained by equation (32), a st (f s0 ,f d0 ) is the target space-time steering vector, f d0 and f s0 are the target temporal and spatial frequencies.

[0098] So, the weight vector w of STAP is opt Acting on the received data in equation (1), the clutter suppression of the airborne radar under the condition of insufficient samples is realized; the target detection process is:

[0099]

[0100] Where H1 and H0 are hypothesis tests with and without targets, respectively, and η0 is the detection threshold.

[0101] Compared with the prior art, the present invention has the following characteristics:

[0102] 1. The present invention takes into account the properties of space-time multidimensional covariance, designs matrix transformation processing and real-domain matrices to be encoded and decoded, constructs an autoencoder neural network for it, and fully utilizes the network's nonlinear advantages, discarding the covariance deviation caused by sample non-uniformity and insufficient number, thereby significantly improving the clutter suppression performance. Under the conditions of sample non-uniformity and insufficient number, the present invention has better clutter suppression performance than the DW algorithm, ADC algorithm, JDL algorithm, and STAP algorithm.

[0103] 2. The present invention designs a special real-domain matrix structure to be reconstructed with a dimension less than half the system's degrees of freedom, and designs matrix transformation and inverse transformation processing for it. This dimension more effectively compresses and preserves the clutter-plus-noise characteristics during the encoding and decoding process. The present invention has significantly superior clutter suppression performance compared to the DW, ADC, JDL, and STAP algorithms in both side-viewing and non-side-viewing radars.

[0104] 3. Due to the application of the above-mentioned technologies, the present invention can better adapt to non-ideal sample conditions faced by real applications such as non-uniform clutter environments and insufficient training samples. The clutter suppression performance of the present invention is better than that of traditional methods.

[0105] 4. This invention addresses the shortcomings of traditional dimensionality reduction and rank reduction and distance compensation methods, which attempt to adapt to non-ideal samples at the expense of reducing system degrees of freedom, abandoning some sample data, and relying heavily on inertial navigation system parameters. This results in suboptimal clutter suppression and target detection performance, as well as low adaptability. This invention improves adaptability without reducing system degrees of freedom, and provides superior clutter suppression performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 It is the overall framework diagram of the present invention.

[0107] Figure 2 This is a comparison of the spatial and temporal distribution of clutter spectra using different methods.

[0108] Figure 3 This is a comparison chart of the space-time two-dimensional frequency responses of different methods.

[0109] Figure 4 This is the relationship between the improvement factor of different algorithms and the normalized Doppler frequency under non-side-looking array radar.

[0110] Figure 5 It is the relationship between the improvement factor and normalized Doppler frequency of different methods under different airborne platform parameters.

[0111] Figure 6 This is the relationship between the improvement factor and normalized Doppler frequency of different methods under the positive side-looking array radar.

[0112] Figure 7 This is the relationship between the improvement factor and normalized Doppler frequency of different methods under forward-looking array radar.

[0113] Figure 8 It is the relationship between the input and output root mean square error of the automatic encoder of the present invention and the number of training rounds.

[0114] Figure 9 The relationship between the network root mean square error and the number of training rounds under different hidden layer sizes and sparsity. DETAILED DESCRIPTION

[0115] The present invention will be described in more detail below with reference to the embodiments and accompanying drawings.

[0116] Reference Figure 1 , an airborne radar clutter suppression method based on an autoencoder under insufficient sample conditions, comprising the following steps:

[0117] 1) The radar transmits a signal and obtains received data after matched filtering and pulse stacking. Based on the space-time multidimensional structure of the received data and the covariance properties of clutter plus noise, a real-domain matrix to be reconstructed with a dimension less than half the system's degrees of freedom and processed by matrix transformation is designed;

[0118] The received data after matched filtering and pulse stacking is obtained as follows:

[0119] Consider an airborne monostatic radar system with a uniform linear array (ULA) of N receiving elements, where the receiving element spacing d is half a wavelength d = λ / 2; within a coherent processing interval (CPI), the pulse repetition frequency (PRF) f PRF K pulses are transmitted; a range unit is composed of all statistically independent clutter scattering units with the same slant range from the antenna array; for the antenna array and clutter scatterers, it is assumed that the moving platform moves at a uniform speed v a The non-positive side view angles of motion, ULA and motion platform velocity directions are The angle between the clutter scatterer and the antenna array is α, and the angle between the clutter scatterer and the platform velocity direction is β. In addition, the pitch angle and azimuth angle of the clutter scatterer relative to the velocity vector of the moving platform are θ and Therefore, each column of N×K dimensional echo data collected by K pulses of a CPI is stacked into an NK×1 dimensional vector x cn,l ,as follows:

[0120]

[0121] where N c is the total number of clutter blocks in the clutter unit, ξ i (l) is the complex amplitude of the i-th clutter block, l represents the l-th range unit, n(l) is the zero-mean noise vector, a st (f s,i ,f d,i ) is the space-time two-dimensional vector of the i-th clutter block, specifically expressed as:

[0122]

[0123] The time-domain steering vector a of the i-th clutter block t (f d,i ) is:

[0124]

[0125] where f d,i and f PRF is its Doppler frequency and pulse repetition frequency, K is the number of pulses; in addition, the spatial steering vector a of the i-th clutter block s (f s,i ) is:

[0126]

[0127] where f s,i is its spatial frequency, N is the number of uniform linear array elements; according to the spatial geometric relationship, the Doppler frequency f of the i-th clutter scatterer d,i for:

[0128]

[0129] where v a is the speed of the moving platform, λ is the wavelength, θ i and are the pitch angle and azimuth angle of the scatterer relative to the platform velocity vector, β i is the spatial cone angle. The spatial frequency of the clutter scatterer is:

[0130]

[0131] Where d is the array element spacing, is the angle between the array and the motion platform velocity direction, α i is the angle formed by the i-th clutter scatterer and the antenna array, and the rest of the meanings are the same as in equation (5);

[0132] According to the space-time multidimensional structure of the received data and the covariance properties of clutter plus noise, the real-domain matrix to be reconstructed with a dimension less than half of the system's degree of freedom and processed by matrix transformation is designed as follows:

[0133] For the clutter plus noise covariance matrix, its matrix elements The calculation method is:

[0134]

[0135] in(·) H is the conjugate transpose, (·) * is conjugated, X cn =[x cn,1 ,...,x cn,L ] is composed of x cn,l The receiving data matrix composed of x cn,l Given by formula (1), X cn (i,:) and X cn(j,:) are X cn The i-th and j-th rows, X cn (i,l) and X cn (j,l) is X cn The (i, l)th and (j, l)th elements. L is the total number of nearby range rings excluding the unit where the target to be detected is located, and N and K are the number of array elements and pulses. The present invention designs a special matrix to be encoded and decoded for clutter suppression of airborne radar under insufficient sample conditions. First, the matrix dimension and its original data matrix are designed as follows:

[0136]

[0137] Where p is the dimension of the special real domain matrix to be reconstructed, l = 1, 2, ... L is the lth distance ring, and the rest of the meanings are shown in formula (7); the original data matrix is ​​designed The number of rows and columns is p<NK / 2, that is, p is a positive integer less than half of the system's degree of freedom, and the calculation form based on formula (7) is Contains the clutter plus noise covariance characteristics; then, in order to improve the estimation accuracy of the airborne radar clutter plus noise covariance matrix, before finally proposing the real domain matrix to be reconstructed, a matrix transformation is constructed:

[0138]

[0139] Among them C re is the new data obtained after the above conversion, To sum, the original data matrix The number of rows and columns p is given by formula (8), is a p×1 dimensional vector with 1 as its element, is a matrix abbreviation, [·](i,p) represents the (i,p)th element of the matrix [·], and the p×p dimensional matrix Specifically:

[0140]

[0141] in The original data matrix is ​​given by formula (8), represents the (i,p)th element, and the rest of the meanings are given by formula (9);

[0142] Finally, in order to achieve clutter suppression under the condition of insufficient samples, after the design of the number of matrix rows and columns and matrix conversion processing of equations (9)-(10), the final matrix to be reconstructed is proposed as follows:

[0143]

[0144] where real{·} is the real part of {·}; the dimension of the real-domain matrix to be reconstructed for the clutter plus noise covariance is less than half the system's degrees of freedom and is processed by matrix transformation. This matrix can better adapt to the subsequent training of the autoencoder neural network and overcome the problem of large covariance estimation bias caused by sample unevenness and insufficient number of IID samples through encoding and decoding.

[0145] 2) Using the structural characteristics of the real-domain matrix to be reconstructed and the characteristics of the autoencoder, we design encoding and decoding activation functions and network loss functions for the real-domain matrix to be reconstructed, and construct an autoencoder neural network with l2 regularization and sparse regularization;

[0146] design After that, we construct an automatic encoding network for it. First, we define:

[0147]

[0148] Where H represents the output of the encoder, F(·) is the encoder activation function, W and b are the weight matrix and bias vector of the encoder network layer respectively, Representatives Column p2 is the overall function of the input encoder; the encoding layer is connected to the decoding layer, and the output H of the encoder is also the input of the decoder. The decoder can be expressed as:

[0149]

[0150] in is the decoder output, H(:, p2) is the p2th column of the encoder output H obtained by equation (12), γ(·) is the decoder activation function different from F(·), U and f are the weight matrix and bias vector of the decoder network layer, respectively, and g(H(:, p2)) represents the overall decoder function with H(:, p2) as input; the designed real-domain matrix to be reconstructed selects the following encoder activation function:

[0151]

[0152] Where 1≤p2≤p and p is the dimension defined by Equation (8), H(i,p2) is the (i,p2)th element, W(i,:) is the i-th row, is the p2th column, b(i) and is the i-th element of the vector; in addition, based on the characteristics of nonlinear functions, the decoder activation function of the real domain matrix to be reconstructed is set to:

[0153]

[0154] in Represents the original input, that is, the special real-domain matrix to be reconstructed The estimate is also the decoder output, [·](:,p2) represents the p2th column of the matrix [·], e -[·] is an exponential function with the natural constant e as the base, U and f are the decoder weights and biases, W and b are the encoder weights and biases, H(:,p2) is the encoder output column p2, F(·) is the encoder activation function; let I np and O up Denote the encoder input and decoder output respectively, then the autoencoder loss function criterion is:

[0155] Θ loss (I np ,O up )=Δ(I np ,O up )≈0 (16)

[0156] The proposed autoencoder neural network for the real-domain matrix to be reconstructed makes the network output as close as possible to its input through encoding and decoding Therefore, its output can be regarded as Reconstruction of each element; network training is regarded as the following optimization problem:

[0157]

[0158] in is the special real-domain matrix to be reconstructed, for is an estimate of and is also the decoder output, is the actual encoder weight and bias, and decoder weight and bias obtained after network training, that is, the estimate of the theoretical value of the corresponding weight and bias (W, b, U, f), Indicates the value of (W, b, U, f) when <·> reaches the minimum value.

[0159] In order to further solve Equation (17), the loss function is deduced and analyzed in detail. The entire loss function is divided into three parts. The first part is directly obtained by the autoencoder criterion, which is:

[0160]

[0161] Where 1≤p1,p2≤p, p is the special real domain matrix to be reconstructed The dimension of for The estimate of is also the decoder output, is the subpart of E0 corresponding to 1≤p1,p2≤p, and [·](p1,p2) is the (p1,p2)th element. At the same time, to avoid overfitting and improve the generalization ability of the network, the l2 weight regularization term is introduced as follows:

[0162]

[0163] The number of neurons in the hidden layer is set to h n , p is the dimension of the special real-domain matrix to be reconstructed, W(i,j) and U(i,j) are the (i,j)th elements of the encoder and decoder weight matrices W and U respectively; In addition, to constrain the sparsity of the hidden layer output and promote the network to obtain the real-domain matrix to be reconstructed A more useful structural feature in , introducing a sparse regularization term, is:

[0164]

[0165] where h n is the number of neurons in the hidden layer, is the Kullback-Leiber divergence equation, which measures and β distribution difference; when KL(·) takes the value of 0, otherwise the value becomes larger; and Indicated by Column p2 is the overall encoder function of the input, that is, the encoder output, yes The i-th element of , β is Finally, based on E0, E1 and E2, the total loss function is expressed as:

[0166]

[0167] Where η and λ are the coefficients of the l2 weight regularization term and the sparse regularization term, respectively. The rest of their meanings are given in Equations (18), (19), and (20).

[0168] 3) Through gradient descent iteration, the total loss function is reduced to train the constructed autoencoder;

[0169] To train the autoencoder, we need to obtain the required network weights and biases to reconstruct Using the gradient descent method to iteratively update W(i,j) and b(i), the weight matrices of the encoder and decoder are updated as follows:

[0170]

[0171] in and ε represent the derivative and learning rate respectively, W(i,j) and U(i,j) are the (i,j)th element of the weight matrix of the encoder and decoder respectively, L oss is the total loss function;

[0172] The bias matrices of the encoder and decoder are updated for each iteration as follows:

[0173]

[0174] where and ε are the derivative and learning rate; b(i) and f(i) are the i-th elements of the bias vectors of the encoder and decoder, and L oss is the total loss function; further derivation is as follows:

[0175]

[0176] where the abbreviations and represent and respectively. η and λ are the coefficients of the weight regularization term and the sparse regularization term, p is the dimension of the special matrix to be reconstructed, h n is the number of hidden neurons, and the other meanings are shown in Eqs. (18)-(21); to continue obtaining the above formula, specifically obtaining the abbreviations in Eq. (24) is as follows:

[0177] <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0182] The abbreviation From formula (25), and Indicated by Column p2 The encoder outputs the average activation value for the input, yes The i-th element, β is The expected value of Specifically:

[0183]

[0184] At this time, using formulas (22)-(28), update the weight W and bias b. Based on the total loss function and the weight U and bias f in the decoding layer, the steps of formulas (22)-(28) can be similarly obtained. and for:

[0185]

[0186] in Defined in formula (25), L oss is the total loss function, H(j,p2) is the (j,p2)th element of the encoder output H obtained by equation (12), η is the coefficient of the l2 weight regularization term, p is the dimension of the special matrix to be reconstructed, U(i,j) is the (i,j)th element of U, and f(i) is the i-th element of f; therefore, by iteratively using the gradient descent method, the total loss function is gradually reduced, and the proposed method for airborne radar clutter suppression under insufficient sample conditions has a dimension less than half of the system's degree of freedom and is processed by matrix transformation to be reconstructed in the real domain. The reconstruction can be obtained by the autoencoder neural network constructed by equations (12)-(29) and its training;

[0187] 4) Using the designed special structure of the real-domain matrix to be reconstructed and the decoder output, design the inverse processing process of the matrix transformation data, reconstruct the clutter plus noise covariance, and use space-time adaptive processing to suppress clutter and detect targets;

[0188] Using the real-domain matrix to be reconstructed and the decoder output, we design the inverse processing of the matrix transformation data to reconstruct the clutter plus noise covariance as shown below:

[0189] After encoding and decoding, based on the constructed covariance feature Dimensional Matrix The structure of the matrix is ​​transformed by the following inverse processing:

[0190]

[0191] in is the new data matrix after inverse transformation, The special real domain matrix to be reconstructed is designed The estimate of is also the decoder output, p is The dimension of is the original data matrix obtained by formula (8) The (i,p)th element of The matrix obtained by formula (10) is The (i,p)th element of is a p×1-dimensional vector with 1 as its element; then, the final reconstruction form of the extracted clutter plus noise covariance is designed as:

[0192]

[0193] Where imag{·} is the imaginary part, so the reconstructed clutter plus noise covariance matrix CNCM is as follows:

[0194]

[0195] in is the reconstructed CNCM, N and K are the number of array elements and pulses, and p is the dimension of the special real-domain matrix to be reconstructed; and They are the clutter plus noise covariance matrices before reconstruction The corresponding sub-matrices are the upper left corner p×(NK-p) dimension, the lower left corner (NK-p)×(NK-p) dimension, and the lower right corner (NK-p)×p dimension, and Obtained from formula (7); reconstructed While retaining the main characteristics of covariance, the covariance estimation bias caused by sample unevenness and insufficient number of IID samples is discarded.

[0196] Airborne radar clutter suppression is achieved by using reconstructed clutter plus noise covariance and space-time adaptive processing technology, as shown below:

[0197] The goal of STAP technology is to suppress clutter as much as possible and keep the output target gain unchanged; according to the linear constrained minimum variance criterion, the adaptive optimal weight vector w opt It is derived from the following formula:

[0198]

[0199] where f d0 and f s0 is the target temporal and spatial frequency, a st (f s0 ,f d0) is the NK×1-dimensional target space-time steering vector, obtained by equations (2)-(4); according to the Lagrange multiplier method, the optimal weight vector is:

[0200]

[0201] in(·) -1 To invert the matrix, is the reconstructed clutter plus noise covariance matrix obtained by equation (32), a st (f s0 ,f d0 ) is the target space-time steering vector, f d0 and f s0 are the target temporal and spatial frequencies.

[0202] So, the STAP weight vector w opt Acting on the received data of formula (1), the subsequent signal processing process can achieve airborne radar clutter suppression under the condition of insufficient samples; for example, target detection is

[0203]

[0204] Where H1 and H0 are hypothesis tests with and without targets, respectively, and η0 is the detection threshold.

[0205] The effect of the present invention can be illustrated by the following simulation:

[0206] (I) Simulation conditions and contents: To verify the effectiveness and advantages of the method of the present invention. Assuming that the number of receiving antenna elements, the number of pulses in one CPI, the height of the airborne platform, the pulse repetition frequency, the element spacing and the wavelength are N=8, K=9, f=1, and f=2, respectively. PRF =6000m, d=0.3m and λ=0.15m. In addition, the encoder and decoder activation functions of the present invention are respectively expressed as Equation (14) and Equation (15), the l2 weight regularization term coefficient is η=0.01, the sparse regularization term coefficient is λ=15, and the maximum number of training rounds is 300. The noise power is fixed, and the amplitude of the clutter block scattering coefficient that obeys the complex Gaussian distribution is determined by the clutter-to-noise ratio (CNR); the improvement factor is defined as The clutter suppression performance of the present invention is compared with that of different representative methods, and other related parameters will be given in detail in the following simulation.

[0207] (2) Simulation results:

[0208] 1. Comparison of spatial and temporal distribution of clutter spectrum using different methods: Figure 2 The left and right columns are the space-time distribution of the clutter spectrum of the original sample and the sample processed by the present invention, respectively. The speed of the front-side array platform is 70m / s, and the angle between the antenna axis and the airborne platform is In addition, the number of training samples L = 40, and the noise-to-noise ratio CNR = 50dB. The number of hidden neurons in the present invention is h n =10, and the sparsity ratio is 0.01. Simulations verify that the present invention effectively obtains a better clutter spectrum estimate and overcomes the disadvantage of the original STAP data, which is that the clutter spectrum estimate is not ideal due to the range-dependent clutter range broadening.

[0209] 2. Comparison of space-time two-dimensional frequency responses of different methods: Figure 3 The left and right columns are the space-time frequency responses of the original STAP and the present invention respectively. Figure 2 same. Figure 3 In the figure, the upper left sub-graph and the lower left sub-graph are the frequency responses of the original STAP when CNR=50dB and CNR=60dB. In addition, for comparison, the upper right sub-graph and the lower right sub-graph are the frequency responses of the present invention when CNR=50dB and CNR=60dB respectively. Figure 3 It can be seen that in the corresponding clutter region, the present invention achieves a deep notch in the space-time two-dimensional frequency response along the clutter ridge. However, due to the insufficient number of samples, the performance of the original STAP is severely degraded. This means that the present invention can effectively suppress clutter and greatly improve the suppression performance.

[0210] 3. Relationship between the improvement factor and normalized Doppler frequency of different methods under non-side-looking array radar: Figure 4 It shows that the angle between the antenna axis and the platform velocity is The relationship between the improvement factor and the normalized Doppler frequency under the non-side-looking radar is: Figure 4 Other simulation conditions and Figure 2 The same. For non-side-view array conditions with clutter range dependence, averaging samples from adjacent range units will lead to severe broadening of the clutter spectrum due to the different spatial and temporal distributions of the clutter spectrum in each range unit, especially in the main lobe STAP, where clutter suppression performance is severely degraded. After distance compensation using the DW and ADC methods, the clutter non-uniformity is improved. Overall, the improvement factor curve of the present invention maintains both a deeper and narrower notch compared to the STAP, JDL, DW, and ADC methods, meaning that the present invention achieves better clutter suppression performance than other methods.

[0211] 4. Relationship between the improvement factor and normalized Doppler frequency of different methods under different airborne platform parameters: Figure 5 The effects of different platform parameters on the improvement factor were evaluated. The airborne platform speed was 170 m / s. Other conditions and Figure 4 same. Figure 5In the CNN, distance dependence and insufficient training samples lead to relatively shallow notches in the improvement factor curves of the DW and ADC methods. In contrast, the present invention maintains a deep and narrow improvement factor notch. Furthermore, the present invention achieves an average improvement factor improvement of 10 dB over the other methods. Figure 4 and Figure 5 It shows that under the conditions of non-uniform clutter distribution and insufficient training samples, the present invention has better suppression performance for strong clutter.

[0212] 5. Relationship between the improvement factor and normalized Doppler frequency of different methods under the positive side-looking array radar: Figure 6 The relationship between the improvement factor IF and the normalized Doppler frequency under different methods was verified. Assuming For a side-viewing array radar, consider different cases where the noise ratio is CNR = 40dB and CNR = 60dB. Figure 6 As shown, for all methods, the clutter suppression performance shown by the improvement factor increases with increasing CNR. For different CNRs, the present invention provides narrower and deeper improvement factor notches compared to other methods. The present invention compresses the characteristics of the clutter-plus-noise covariance matrix and discards characteristic deviations caused by sample heterogeneity and insufficient number.

[0213] 6. Relationship between the improvement factor and normalized Doppler frequency of different methods under forward-looking array radar: Figure 7 To improve the relationship between the factor IF and the normalized Doppler frequency, assume that and v a =150m / s forward-looking radar, the noise-to-noise ratio is CNR=50dB. For the present invention, the proposed special matrix to be encoded and decoded is also compared The impact of different row and column numbers p = 25, p = 31 and p = 35. The number of training samples corresponding to the distance unit, Figure 7 In (a), L=50, Figure 7 In (b), L=60. Figure 7 It is verified that the present invention maintains superior performance under different numbers of training samples. In addition, the simulation shows The size of the matrix has an impact on the clutter suppression performance. The reason is that the matrix with low number of rows and columns This results in insufficient reconstruction of the clutter plus noise covariance matrix and a decrease in clutter suppression performance. This results in excessive deviation and too many features in the uneven samples, making it impossible for the network to obtain a good reconstruction of the covariance matrix.

[0214] 7. Figure 8The seventh simulation considers the relationship between the root mean square error (RMSE) between the input and output of the autoencoder network and the number of training rounds. Specifically, the input is the designed p×p dimensional special matrix The output is the reconstructed data A large RMSE means and It can be seen that the root mean square error is larger in the number of rounds n. ep =100 to n ep = 250, and the root mean square error remains unchanged as the number of training rounds increases. For different noise-to-noise ratios (CNR), the present invention has good convergence.

[0215] 8. The relationship between the network root mean square error and the number of training rounds under the same hidden layer size and sparsity: Figure 9 The effects of different numbers of hidden layer neurons and sparsity on the root mean square error and number of training rounds of the present invention are analyzed and compared. Under different parameter settings, the present invention can converge at a certain number of hidden layer neurons. Figure 9 As we can see, in round number n ep =5 to n ep The condition with sparsity sp = 0.0001 between ∑ Hiddensize = 30 and ∑ Hiddensize = 30 exhibits the lowest RMS error and the fastest convergence rate. Furthermore, at the same sparsity, the condition with Hiddensize = 30 hidden neurons exhibits a higher RMS error than the condition with Hiddensize = 10. This is because low sparsity sp leads to high sparsity. Within appropriate values, higher sparsity and a smaller number of hidden neurons allow the proposed network to capture more prominent features and be less sensitive to inaccurate sample bias.

Claims

1. A method for suppressing clutter in airborne radar based on an autoencoder under insufficient sample conditions, characterized in that: It includes the following steps: 1) The radar transmits signals and obtains the received data after matched filtering processing and pulse stacking. According to the spatio-temporal multi-dimensional structure of the received data and the properties of clutter plus noise covariance, a to-be-reconstructed real-domain matrix with a dimension less than half of the system freedom degree and processed by matrix transformation is designed; 2) Utilizing the structural characteristics of the to-be-reconstructed real-domain matrix and the characteristics of the autoencoder, encoding, decoding activation functions and network loss functions are designed for the to-be-reconstructed real-domain matrix, and an autoencoder neural network with l2 regularization and sparse regularization is constructed; 3) Through gradient descent iteration, the total loss function is reduced to realize the training of the constructed autoencoder; 4) Utilizing the special structure of the designed to-be-reconstructed real-domain matrix and the decoder output, a matrix transformation data inverse processing process is designed to reconstruct the clutter plus noise covariance, and space-time adaptive processing is used to suppress clutter and detect targets.

2. The method according to claim 1, characterized in that The specific content of step 1) is as follows: 1.1) Each column of N×K dimensional echo data collected by K pulses of a CPI is stacked into an NK×1 dimensional vector x cn,l ,as follows: where N c is the total number of clutter blocks in the clutter unit, ξ i (l) is the complex amplitude of the i-th clutter block, l represents the l-th range unit, and n(l) is the zero-mean noise vector; is the space-time two-dimensional vector of the i-th clutter block, and its time domain and space domain steering vectors are and , for a t (f d,i ), and f PRF are the Doppler frequency and pulse repetition frequency, K is the number of pulses, and v a is the speed of the moving platform, λ is the wavelength, β i is the space cone angle; for a s (f s,i ), is the spatial frequency of the clutter scatterer, N is the number of uniform linear array elements, d is the element spacing, α i is the angle formed by the i-th clutter scatterer and the antenna array; 1.2) The clutter plus noise covariance feature is included in the following form of covariance middle: in(·) H is the conjugate transpose, (·) * is conjugated, X cn =[x cn,1 ,...,x cn,L ] is composed of x cn,l The receiving data matrix composed of x cn,l Given by formula (1), X cn (i,:) and X cn (j,:) are X cn The i-th and j-th rows, X cn (i,l) and X cn (j,l) is X cn The (i, l)th and (j, l)th elements; L is the total number of nearby range rings excluding the unit where the target to be detected is located, and N and K are the number of array elements and the number of pulses; 1.3) Design a special matrix to be encoded and decoded. First, design the dimension of this matrix and its original data matrix as follows: Where p represents the dimension of the special real-domain matrix to be reconstructed, l = 1, 2, ... L represents the lth distance ring, and the rest of the meanings are given by formula (2); the original data matrix The number of rows and columns p is designed to satisfy p<NK / 2, that is, p is a positive integer less than half of the system's degree of freedom, and based on the calculation form of formula (2) Contains the selected clutter plus noise covariance features; 1.4) Design the following matrix transformation: Among them C re is the new data obtained after the above conversion, To sum, the original data matrix The number of rows and columns p is given by formula (3), is a p×1 dimensional vector with 1 as its element, is a matrix abbreviation, [·](i,p) represents the (i,p)th element of the matrix [·], and the p×p dimensional matrix Specifically: in The original data matrix is ​​given by formula (3), represents the (i,p)th element, and the rest of the meanings are as in formula (3); Furthermore, the final to-be-reconstructed real-domain matrix is proposed as follows: where real{·} is the real part of {·}.

3. The method according to claim 2, characterized in that The specific content of step 2) is as follows: 2.1) Design After that, we construct an automatic encoding network for it. First, we define: Where H is the encoder output, F(·) is the encoder activation function, W and b are the encoder network layer weight matrix and bias vector respectively, Representatives Column p2 is the overall encoder function of the input; the encoding layer is connected to the decoding layer, and the decoder is expressed as: in is the decoder output, H(:,p2) is the p2th column of the encoder output H, Υ(·) is the decoder activation function, U and f are the decoder weights and biases, and g(H(:,p2)) represents the overall function; for Equation (7), is the real-domain matrix to be reconstructed Select the following encoder activation function: Where 1≤p2≤p and p is the dimension defined by Equation (3), H(i,p2) is the (i,p2)th element, W(i,:) is the i-th row, is the p2th column, b(i) and is the i-th element of the vector, and the rest of the meanings are the same as those in formula (7); 2.2) Based on the non-linear characteristics, the decoder activation function of the to-be-reconstructed real-domain matrix is set as: in Represents the original input, that is, the special real-domain matrix to be reconstructed The estimate is also the decoder output, [·](:,p2) represents the p2th column of the matrix [·], e -[·] is an exponential function with the natural constant e as the base, U and f are the decoder weights and biases, W and b are the encoder weights and biases, and F(·) is the encoder activation function; Order I np and O up Denote the encoder input and decoder output respectively, then the autoencoder loss function criterion is Θ loss (I np ,O up )=Δ(I np ,O up )≈0; 2.3) The proposed autoencoder network for the real-domain matrix to be reconstructed makes the output as close as possible to the input through encoding and decoding Therefore, its output is regarded as Reconstruction; network training is regarded as an optimization problem is the special real-domain matrix to be reconstructed, for is an estimate of and is also the decoder output, is the actual encoder weight and bias, decoder weight and bias obtained after network training, that is, the estimate of the corresponding theoretical value (W, b, U, f), The value of (W, b, U, f) when <·> obtains the minimum value; For the entire loss function involved in the above optimization, it is divided into three parts. The first part is: Where 1≤p1,p2≤p, p is the special real domain matrix to be reconstructed The dimension of for The estimate of is also the decoder output, [·](p1,p2) represents the (p1,p2)th element of the matrix [·], are the subparts of E0 corresponding to 1≤p1, p2≤p respectively; at the same time, the second part introduces the l2 weight regularization term as follows: The number of neurons in the hidden layer is set to h n , p is the dimension of the special real-domain matrix to be reconstructed, W(i,j) and U(i,j) are the (i,j)th elements of the encoder and decoder weight matrices W and U respectively; In addition, the third part introduces the sparse regularization term, which is: where h n is the number of neurons in the hidden layer, is the Kullback-Leiber divergence equation, which measures and β distribution difference; when KL(·) takes the value of 0, otherwise the value becomes larger; is Column p2 is the overall encoder function of the input, that is, the encoder output, yes The i-th element of , β is expected value; Finally, based on E0, E1 and E2, the total loss function is expressed as: where η and λ are the coefficients of the l2 weight regularization term and the sparse regularization term respectively, and the other meanings are shown in equations (11), (12) and (13).

4. The method according to claim 3, characterized in that The specific content of step 3) is as follows: 3.1) Use the gradient descent method to iteratively update W(i,j) and b(i), and the weight matrices of the encoder and decoder are updated as: in and ε represent the derivative and learning rate respectively, W(i,j) and U(i,j) are the (i,j)th elements of the encoder and decoder weight matrices respectively, and L oss is the total loss function; In each iteration, the bias matrices of the encoder and decoder are updated as: in and ε are the derivative and learning rate; b(i) and f(i) are the i-th element of the encoder and decoder bias vectors, respectively, and L oss is the total loss function; 3.2) To obtain the equations (15) and (16), first, derive as follows: The abbreviation and Respectively and η and λ are weight and sparse regularization coefficients, p is the dimension of the special matrix to be reconstructed, and the rest are shown in Equations (11)-(14); the abbreviations in Equation (17) are obtained specifically as follows: where F(·) and Υ(·) are the encoder and decoder activation functions, respectively. F′(Z(i,p2)) represents the derivative of the function F(Z(i,p2) with respect to Z(i,p2). {W,U;b,f} are the weight matrix and bias vector. is the special real-domain matrix to be reconstructed, for The estimate of is also the decoder network output, is an abbreviation; and, in formula (18) And get In addition, the average activation value in formula (17) with abbreviations for: where F′[Z(i,p2)] is the derivative corresponding to Z(i,p2). For 0 < Z(i,p2) < 1, F′[Z(i,p2)] = 1, otherwise F′[Z(i,p2)] = 0; In addition, for the bias vector in equation (16), its derivative is derived as: The abbreviation From formula (18), and Indicated by Column p2 The encoder outputs the average activation value for the input, yes The i-th element, β is The expected value of ; and, in formula (20) Specifically: While updating the weight W and bias b, based on the total loss function and the weight U and bias f in the decoding layer, we can get and for: in After being defined in formula (18), L oss is the total loss function, H(j,p2) is the (j,p2)th element of the encoder output H obtained by Equation (9), η is the l2 weight regularization term coefficient, p is the dimension of the special matrix to be reconstructed, U(i,j) is the (i,j)th element of U, and f(i) is the i-th element of f.

5. The method according to claim 4, characterized in that The specific content of step 4 is as follows: 4.1) After encoding and decoding, based on the constructed covariance feature Dimensional Matrix The structure of the matrix is ​​transformed by the following inverse processing: in is the new data matrix after inverse transformation, The special real domain matrix to be reconstructed is designed The estimate of is also the decoder output, p is The dimension of is the original data matrix obtained by formula (3) The (i,p)th element of The matrix obtained by formula (5) is The (i,p)th element of is a p×1-dimensional vector with 1 as its element; 4.2) The final reconstructed form of the extracted clutter plus noise covariance is designed as: where imag{·} represents the imaginary part, and the clutter plus noise covariance matrix CNCM is reconstructed as follows: in is the reconstructed CNCM, N and K are the number of array elements and pulses, and p is the dimension of the special real-domain matrix to be reconstructed; and They are the clutter plus noise covariance matrices before reconstruction The corresponding sub-matrices are the upper left corner p×(NK-p) dimension, the lower left corner (NK-p)×(NK-p) dimension, and the lower right corner (NK-p)×p dimension, and See formula (2) and then X cn Definition of; 4.3) Using the reconstructed clutter plus noise covariance and space-time adaptive processing (STAP) technology, the airborne radar clutter suppression is realized; according to the linear constrained minimum variance criterion, the adaptive optimal weight vector w opt It is derived from the following formula: where f d0 and f s0 is the temporal frequency and spatial frequency of the target, a st (f s0 ,f d0 ) is the NK×1-dimensional target space-time steering vector; according to the Lagrange multiplier method, the STAP optimal weight vector is: in(·) -1 To invert the matrix, is the reconstructed clutter plus noise covariance matrix obtained by formula (25), a st (f s0 ,f d0 ) is the target space-time steering vector, f d0 and f s0 are the target temporal and spatial frequencies; So, the weight vector w of STAP is opt Acting on the received data in equation (1), the clutter suppression of the airborne radar under the condition of insufficient samples is realized; the target detection process is: where H1 and H0 are the hypothesis tests with and without targets respectively, and η0 is the detection threshold.

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