A passive radar coherent integration method based on sparse representation

Abstract

The present application belongs to the technical field of passive radar signal processing, and relates to a passive radar coherent accumulation method based on sparse representation, comprising: receiving passive radar signals, segmenting echo signals and reference signals; performing Fourier transform in the fast time direction; intercepting the effective bandwidth part to randomly extract the range frequency unit; randomly extracting the slow time segment, constructing a Doppler dictionary matrix with a range migration correction factor, solving the Doppler sparse coefficient by using a multi-observation vector orthogonal matching pursuit (MMV-OMP) method; in the range direction, estimating the continuous domain time delay support set by using the atom norm minimization and ESPRIT method, constructing a range dictionary matrix according to the estimation, calculating the corresponding coefficient by using the least square method, obtaining the range Doppler (RD) map of the target, and realizing long-time coherent accumulation of passive radar signals.

Description

Technical Field

[0001] This invention belongs to the field of passive radar signal processing technology, specifically relating to a passive radar coherent accumulation method based on sparse representation. Background Technology

[0002] In the study of range-Doppler (RD) signals from passive radar, traditional methods are based on matched filtering (MF) theory, utilizing the cross ambiguity function (CAF) and the Fast Fourier Transform (FFT) to calculate the RD response. However, these traditional methods face several challenges. Firstly, the resolution of the RD map is limited by the signal bandwidth of passive radar. Secondly, high sidelobes can affect the detection of small targets, leading to a decrease in the accuracy of the RD map.

[0003] Resolution is a crucial indicator for radar systems, and improving resolution has consistently been a mainstream direction in radar development. To enhance the range resolution of passive radar, multiple broadcast channels from a single transmitter can be used for multi-band joint processing. Furthermore, long-term accumulation can improve Doppler resolution, but this may cause migration, requiring complex compensation operations. In recent years, compressed sensing (CS) has been considered for application in passive radar. CS is a sparse signal processing technique that can reduce the amount of sampled data and achieve excellent signal reconstruction using a small amount of measurement data, showing great potential for improving resolution. With increasing attention in the field of passive radar, acquiring the target's RD map can be described as a sparse problem, and corresponding results have been achieved. Subsequently, a CS-based passive radar signal processing method emerged, achieving better range and Doppler resolution. However, because the dictionary consists of reference signals with different discrete time delays and Doppler frequency shifts, it requires a large amount of storage space and high computational complexity. Using one-dimensional cross-correlation to obtain the range-compressed envelope, the Extended Orthogonal Matching Pursuit (EOMP) algorithm was proposed to estimate Doppler frequencies. Compared with traditional algorithms, this algorithm can improve Doppler resolution and reduce sidelobe levels, but the resolution in the range dimension still needs improvement. Since the parameter space of a signal is continuous, many studies have discretized this continuous parameter space to apply compressed sensing theory, dividing it into a finite number of grids and assuming that the signal parameters are represented by certain grid points. This discretization modeling method is relatively simple and easy to analyze, but it inevitably brings some drawbacks: 1) Overly dense grids can cause excessively strong correlations between adjacent atoms in the basis dictionary, thus reducing CS reconstruction performance. 2) In reality, no matter how finely the grid is divided, the actual parameter values ​​of the signal may not fall on the discrete grids, i.e., basis mismatch. In recent years, researchers have introduced the concept of atomic norm to characterize signal features in continuous parameter space and applied it to radar signal processing. Summary of the Invention

[0004] The purpose of this invention is to propose a passive radar coherent accumulation method based on sparse representation to ensure long-term coherent accumulation of signals. This method constructs a Doppler dictionary matrix with a range migration correction factor and uses the Multiple Measurement Vector-Orthogonal Matching Pursuit (MMV-OMP) method to solve for the Doppler-dimensional sparse coefficients. In the range direction, the atomic norm minimization and rotational invariance subspace (ESPRIT) method is used to estimate the continuous domain time delay support set, based on which a range dictionary matrix is ​​constructed. The corresponding coefficients are calculated using the least squares method to achieve high-resolution sparse reconstruction of the range dimension, obtaining the target's RD map, correcting range migration while improving range dimension resolution.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] The passive radar coherent accumulation method based on sparse representation includes:

[0007] S1: Receive the reference signal and echo signal from the passive radar and segment them to obtain the reference matrix and echo matrix representing the segmented reference signal and echo signal;

[0008] S2: Perform Fast Fourier Transform on the reference matrix and echo matrix in the fast time domain and calculate the number of points within the effective bandwidth. Then, truncate the Fast Fourier Transform results of the reference matrix and echo matrix to obtain the two-dimensional reference matrix and two-dimensional echo matrix in the slow time domain-distance frequency domain.

[0009] S3: Use the first random identity matrix to perform range-direction random sampling on the two-dimensional reference matrix and the two-dimensional echo matrix respectively to achieve downsampling and obtain the range-direction downsampled reference matrix and echo matrix;

[0010] S4: The echo matrix downsampled in the range direction is randomly sampled in the slow time direction using the second random identity matrix to achieve downsampling and obtain the downsampled echo matrix;

[0011] S5: Calculate the transformation factor. Based on the reference matrix of range descent sampling, construct a Doppler sub-dictionary containing the range migration correction factor for each single observation vector. After downsampling the Doppler sub-dictionary in the slow time direction, combine them into a Doppler dictionary containing the range migration correction factor for multiple observation vectors.

[0012] The single observation vector refers to each echo distance frequency unit, which is a column of the downsampled echo matrix; the multi-observation vector refers to all echo distance frequency units.

[0013] S6: Based on the Doppler dictionary, the Doppler matrix is ​​obtained by performing Doppler-dimensional sparse reconstruction of the downsampled echo matrix using the multi-observation vector orthogonal matching pursuit method.

[0014] S7: Based on the first random identity matrix and the Doppler matrix obtained after Doppler dimension sparse reconstruction, solve the atomic norm minimization problem, calculate the normalized time delay using the rotation invariant subspace method, construct a distance dictionary, calculate the sparse coefficients using the least squares method, perform distance dimension sparse reconstruction, and obtain the RD graph.

[0015] Specifically, S5 is:

[0016] S51: Add the distance frequency of each echo distance frequency unit to the signal center frequency to get the sum of the two, and then divide the sum of the two by the center frequency to get the transformation factor.

[0017] S52: Set the number of Doppler grids, construct a range migration correction factor based on the transformation factor for each single observation vector, and add the range migration correction factor to the reference matrix of range descent sampling to construct a Doppler sub-dictionary;

[0018] S53: Slow-time downsampling is performed on the Doppler sub-dictionary using the second random identity matrix to obtain the Doppler sub-dictionary after slow-time downsampling;

[0019] S54: Arrange the Doppler sub-dictionaries after slow-time downsampling in ascending order of distance frequency index, and combine them into a Doppler dictionary for the multi-observation vector.

[0020] S52 describes constructing a distance migration correction factor based on a transformation factor, that is, through... In this implementation, l represents the distance-frequency index and the value of l ranges from [-N]. sub / 2,…,0,…,N sub / 2],N sub S is the row number of the first random identity matrix; f (l) M represents the transformation factor corresponding to the distance-frequency index l, exp() represents the exponential operation with the natural constant as the base, j represents the imaginary unit, and π represents pi; grid q represents the number of Doppler grids; m represents the column number of the Doppler sub-dictionary and the row number of the Doppler sub-dictionary, with a value range of [0, M-1]. M is the number of segments of the reference signal and is the same as the number of segments of the echo signal.

[0021] The Doppler sub-dictionary is denoted as Specifically, this is achieved through (1):

[0022]

[0023] in,

[0024] The Doppler sub-dictionary represents the single observation vector corresponding to the distance frequency index l, with a dimension of M×M. grid M is the number of segments in the reference signal, which is the same as the number of segments in the echo signal. The subscript q represents the column number of the Doppler sub-dictionary, and its value ranges from [0, M]. grid -1];

[0025] The q on the right side of the equation has the same meaning as the subscript q, both representing the column index of the Doppler sub-dictionary, with a value range of [0, M]. grid -1],M grid F is the number of Doppler grids; xn_sub (m,l) represents the data in the m-th row and l-th column of the reference matrix for range descent sampling, where l is the range frequency index.

[0026] The echo matrix of the segmented echo signal described in S1 is obtained by setting the segment length, performing overlapping segmentation of the echo signal according to the segment length and the maximum time delay, and then generating and expressing the segmented echo signal.

[0027] The reference matrix of the segmented reference signal described in S1 is generated by segmenting and zero-padding the reference signal according to the segment length to obtain a segmented reference signal with the same dimension as the segmented echo signal.

[0028] In S1, the maximum time delay is the overlap length during the overlapping segmentation process of the echo signal; the dimension of the echo matrix is ​​M×N, where M is the number of segments of the echo signal and N represents the number of sampling points in each segment; the dimension of the reference matrix is ​​M×N, where M is the number of segments of the reference signal and is the same as the number of segments of the echo signal; N represents the number of sampling points in each segment and is the same as the number of sampling points in each segment of the echo signal.

[0029] In S2, the number of points within the effective bandwidth is denoted as N. B The dimensions of both the two-dimensional reference matrix and the two-dimensional echo matrix in the slow time-range frequency domain are M×N. B And N B Less than N; in S3, the dimension of the first random identity matrix is ​​N. sub ×N B And N sub Less than N B The reference matrix for range descent sampling has dimensions M×N. sub The echo matrix of range descent sampling has dimensions M×N. subThe dimension of the second random identity matrix in S4 is M. sub ×M, and M sub Less than M; downsampling echo matrix, denoted as F y_sub The dimension is M sub ×N sub .

[0030] S6 specifically includes the following sub-steps:

[0031] S61: Set sparsity K and residual threshold Th;

[0032] S62: Initialize the number of iterations k=1, estimate the support set Let the sparse coefficient matrix F ym_sub Let the zero matrix be the residual R, and let it be equal to the downsampled echo matrix F. y_sub ;

[0033] Here, the estimated support set is the set of column indices from the k iterations, Λ0 is the estimated support set obtained from the 0th iteration, and the sparse coefficient matrix F ym_sub The desired Doppler matrix has a dimension of M. grid ×N sub ;

[0034] S63: Find the atom with the largest absolute value of the inner product with the residual from the Doppler dictionary, and record the column number of that atom in the Doppler dictionary, i.e., calculate...

[0035] Here, the atom is the column vector of the Doppler dictionary, v k is the column index of the atom obtained in the k-th iteration; For the l-th Doppler sub-dictionary The conjugate transpose of; Let l be the l-th column of the residual from the k-th iteration;

[0036] S64: Add the column number to the estimated support set, Λ k =Λ k-1 ∪v k ;

[0037] Among them, Λ k-1 Let Λ be the estimated support set obtained in the (k-1)th iteration. k This is the estimated support set obtained in the k-th iteration;

[0038] S65: Using the least squares method, calculate the sparse coefficients of the estimated Doppler units corresponding to the support set in the sparse coefficient matrix, specifically:

[0039] The Doppler unit is a row of the sparse coefficient matrix;

[0040] S65A: Let i = 1, where i represents the column number of the sparse coefficient matrix being calculated;

[0041] S65B: Select the corresponding atoms from the Doppler dictionary based on the estimated support set, and estimate the sparsity coefficients using the least squares method.

[0042] in, F represents the sparse coefficient matrix ym_sub Λ k The sparsity coefficient of the i-th row and column; [Λ k ] indicates that the estimated support set Λ k The set of atoms selected from the i-th Doppler sub-dictionary is simply called the atom set matrix; Represents the pseudo-inverse of a matrix; Represents the i-th column of the echo matrix;

[0043] S65C: Update the sparse coefficient matrix

[0044] S65D: Subtract the inner product of the current atom set matrix and the sparse coefficients from the i-th column of the echo matrix to update the residual, i.e.

[0045] S65E: Determine if i equals N sub If not, then i = i + 1, jump to S65B; if yes, then jump to S66.

[0046] S66: Determine if the iteration number k is equal to the sparsity K or ||R|| k If ||2>Th, then k = k+1, and jump to S63; if k = K or ||R k If ||2≤Th, then the sparse coefficient matrix F ym_sub The result is used as the reconstructed Doppler matrix;

[0047] Thus, from S61 to S66, the multi-observation vector orthogonal matching tracking method was completed.

[0048] S7, the specific steps are as follows:

[0049] S71: Let ii = 1, where ii represents the index of the element in the estimated support set; initialize the sparse coefficient matrix α as a zero matrix;

[0050] Wherein, the sparse coefficient matrix α is the distance-Doppler matrix to be sought;

[0051] S72: Solving the positive semidefinite problem of equation (2):

[0052]

[0053]

[0054] Where, N B The number of points within the effective bandwidth; tr() represents the operation of finding the trace of a matrix; Toep is the Hermitian-Tpritz operation factor, Toep(u) represents the Hermitian-Tpritz matrix with the elements of vector u as the first row of the matrix, where u is an unknown vector; w is an unknown constant; ε is the relevant parameter of noise or other factors causing model bias; Y is the signal to be recovered; Y H It is the conjugate transpose of the signal to be recovered; Φ n It is the first random identity matrix; The Doppler matrix F ym_sub The p-th Doppler unit, where p is the ii-th element of the estimated support set Λ;

[0055] S73: The normalized time delay is calculated using the rotation-invariant subspace method. The specific steps are as follows:

[0056] S73A: Perform eigenvalue decomposition on the Hermitian Toplitz matrix Toep(u), where Toep(u) = UλU -1 ;

[0057] Where U is a square matrix composed of the eigenvectors of the eigenvector Toep(u) matrix, and λ is a diagonal matrix whose diagonal elements are the corresponding eigenvalues;

[0058] S73B: Construct a subspace Z = U by selecting the diagonal matrices and corresponding eigenvectors corresponding to the P largest eigenvalues ​​of the Hermitian Toeptz matrix Toep(u). P λ P ;

[0059] Where, λ P It is a diagonal matrix corresponding to P large eigenvalues, U P Z is a matrix consisting of the eigenvectors corresponding to the P large eigenvalues, and Z is the constructed subspace matrix;

[0060] S73C: Remove the first row of the subspace matrix and find its inverse matrix, multiply it with the matrix obtained by removing the last row of the subspace matrix, and calculate the eigenvalues ​​of the new matrix.

[0061] Here, removing the first row of matrix Z yields matrix Zi. -1 Removing the last row of matrix Z yields matrix Z. calculate eigenvalues ​​ξ;

[0062] S73D: Calculate the phase of the eigenvalue and divide by 2π to obtain the normalized time delay, x' k = angle(ξ) / 2π;

[0063] Where angle() is the phase function, x'k For normalized delay;

[0064] S74: with Construct a distance dictionary matrix D for the elements;

[0065] Where, x p =x' k N B N B x' is the number of points within the effective bandwidth. k For normalized delay, x p For the distance unit corresponding to the normalized delay, B represents the frequency of each sampling point within the effective bandwidth, and B represents the signal bandwidth.

[0066] S75: Calculate sparse coefficients using the least squares method based on the distance dictionary matrix and the Doppler matrix.

[0067] Where D is the distance dictionary, D H For the conjugate transpose of the distance dictionary; (D H D) -1 D represents H The inverse of matrix D, The Doppler matrix F ym_sub The p-th Doppler unit, where p is the ii-th element of the estimated support set Λ; α p Let be the sparse coefficients of the p-th Doppler unit of the sparse coefficient matrix α;

[0068] S76: Determine if ii is equal to k. If not, then ii = ii + 1 and jump to S71. If yes, then use the sparse coefficient matrix α result as the distance dimension sparse reconstruction result.

[0069] Thus, the sparse reconstruction of the distance dimension from S71 to S76 is completed, and a high-resolution RD map of the distance dimension is obtained.

[0070] Beneficial effects

[0071] This invention proposes a passive radar coherent accumulation method based on sparse representation, which has the following advantages compared with existing passive radar coherent accumulation methods:

[0072] 1. The passive radar coherent accumulation method utilizes the sparsity of the passive radar observation scene to construct a Doppler sparse dictionary containing range migration correction factors, and uses the MMV-OMP method to complete the Doppler sparse reconstruction, which can correct the range migration of the target and has the advantages of low sidelobes and high resolution.

[0073] 2. The passive radar coherent accumulation method described above performs sparse modeling in the continuous domain when processing the range dimension, which solves the basis mismatch problem and improves the range resolution. Attached Figure Description

[0074] Figure 1 This is a flowchart illustrating a sparse representation passive radar coherent accumulation method according to the present invention.

[0075] Figure 2 This is a schematic diagram of the segmentation of the reference signal and the echo signal in the passive radar coherent accumulation method of sparse representation according to the present invention.

[0076] Figure 3 The RD diagram is obtained by processing the echo signal using the mutual ambiguity function method.

[0077] Figure 4 It is an RD diagram obtained by processing the signal using the existing CS-PR method;

[0078] Figure 5 These are the distance-frequency-Doppler plots after echo Doppler reconstruction using different methods;

[0079] Figure 6 The RD map is obtained using the sparse representation passive radar coherent accumulation method described in this invention. Detailed Implementation

[0080] The following description, in conjunction with the accompanying drawings and embodiments, further illustrates a passive radar coherent accumulation method based on sparse representation according to the present invention.

[0081] Example 1

[0082] This embodiment illustrates a specific implementation of the passive radar coherent accumulation method based on sparse representation described in this invention, such as... Figure 1 As shown, it includes the following steps:

[0083] S1: Receives the reference signal and echo signal from the passive radar, and expresses the reference signal and echo signal as a matrix, specifically:

[0084] S11: Set the segment length, and process the echo signal based on the segment length and the maximum time delay. Figure 2 The diagram shows overlapping segments, and the segmented echo signals are obtained and expressed as an echo matrix.

[0085] Wherein, the segment length is denoted as T; and the maximum time delay is denoted as τ. max The overlap length of overlapping segments is the maximum time delay; the echo matrix, denoted as y, has a dimension of M×N, where M represents the number of segments of the echo signal and N represents the number of sampling points in each segment;

[0086] S12: Perform the reference signal according to the segment length. Figure 2 The segmentation and zero-padding shown yields a reference matrix with the same dimension as the echo matrix.

[0087] The reference matrix, denoted as x, has a dimension of M×N, where M represents the number of segments of the reference signal and N represents the number of sampling points in each segment.

[0088] S2: Perform Fast Fourier Transform on the reference matrix and echo matrix in the fast time domain, calculate the number of points in the effective part corresponding to the signal bandwidth, and then truncate the Fast Fourier Transform results of the reference matrix and echo matrix to obtain the reference matrix and echo matrix in the slow time domain-distance frequency domain.

[0089] The number of points in the effective portion corresponding to the signal bandwidth is denoted as N. B And N B Less than N; the reference matrix in the slow time domain-range frequency domain, denoted as F. xn The dimension is M×N B The slow time-range frequency domain echo matrix, denoted as F yn The dimension is M×N B ;

[0090] S3: Obtain the reference matrix F in the slow time domain-range frequency domain. xn and echo matrix F yn Random sampling in the range direction is performed using the first random identity matrix to achieve downsampling, thereby obtaining the reference matrix and the echo matrix of the range downsampling.

[0091] The first random identity matrix is ​​denoted as Φ. n The dimension is N sub ×N B And N sub Less than N B The reference matrix for range descent sampling is denoted as F. xn_sub The dimension is M×N sub The echo matrix of range descent sampling is denoted as F. yn_sub The dimension is M×N sub ;

[0092] S4: The echo matrix downsampled in the range direction is randomly sampled in the slow time direction using the second random identity matrix to achieve downsampling and obtain a two-dimensional downsampled echo matrix.

[0093] The second random identity matrix is ​​denoted as Φ. m The dimension is M sub ×M, and M sub Less than M; the echo matrix of two-dimensional downsampling, simply called the echo matrix, denoted as F. y_sub The dimension is Msub ×N sub ;

[0094] S5: Calculate the transformation factor. Based on the reference matrix of range descent sampling, construct a Doppler sub-dictionary containing the range migration correction factor for each single observation vector. After downsampling the Doppler sub-dictionary in the slow time direction, combine them into a Doppler dictionary containing the range migration correction factor for multiple observation vectors.

[0095] The single observation vector refers to each echo range frequency unit, and the echo range frequency unit is a column of the echo matrix; the multi-observation vector refers to all echo range frequency units.

[0096] S5, specifically:

[0097] S51: Add the distance frequency of each echo distance frequency unit to the signal center frequency to get the sum of the two, and then divide the sum of the two by the center frequency to get the transformation factor.

[0098] S52: Set the number of Doppler grids, construct a range migration correction factor based on the transformation factor for each single observation vector, and add the range migration correction factor to the reference matrix of range descent sampling to construct a Doppler sub-dictionary;

[0099] The constructed Doppler sub-dictionary is denoted as... Specifically, this is achieved through (1):

[0100]

[0101] l represents the distance-frequency index, with a value range of [-N]. sub / 2,…,0,…,N sub / 2],N sub The row number of the first random identity matrix; The Doppler sub-dictionary represents the single observation vector corresponding to the distance frequency index l, with a dimension of M×M. grid M is the number of segments in the reference signal and is the same as the number of segments in the echo signal. grid The value is the Doppler raster number; the subscript q represents the column number of the Doppler sub-dictionary, with a value range of [0, M]. grid -1];

[0102] in,

[0103] The q on the right side of the equation has the same meaning as the subscript q, both representing the column index of the Doppler sub-dictionary, with a value range of [0, M]. grid -1],M grid F is the number of Doppler grids; xn_sub(m,l) represents the data in the m-th row and l-th column of the reference matrix for range descent sampling, where l is the range frequency index, m represents the row number of the Doppler sub-dictionary, and the value range is [0,M-1]. M is the number of segments of the reference signal and is the same as the number of segments of the echo signal. S represents the distance migration correction factor constructed based on the transformation factor. f (l) The transform factor corresponding to the distance frequency index l is exp(), which represents the exponential operation with the natural constant as the base, j represents the imaginary unit, and π represents pi.

[0104] S53: Doppler sub-dictionary Using the second random unit matrix Φ m Slow-time downsampling is performed to obtain the Doppler sub-dictionary after slow-time downsampling;

[0105] Among them, the Doppler sub-dictionary after slow-time downsampling is denoted as... Dimension M sub ×M grid ;

[0106] S54: Arrange the Doppler sub-dictionaries after slow time downsampling in ascending order of distance frequency index, and combine them into a Doppler dictionary for the multi-observation vector;

[0107] Among them, the Doppler dictionary of the multi-observation vectors, or simply the Doppler dictionary, is denoted as Ψ. f_MC_sub .

[0108] S6: Based on Doppler dictionary Ψ f_MC_sub The MMV-OMP method was used to analyze the echo matrix F. y_sub To perform Doppler sparse reconstruction and obtain the Doppler matrix, the specific steps are as follows:

[0109] S61: Set sparsity K and residual threshold Th;

[0110] S62: Initialize the number of iterations k=1, estimate the support set Let the sparse coefficient matrix F ym_sub Let F be the zero matrix, and let the residual R be the echo matrix. y_sub ;

[0111] Here, the estimated support set is the set of column indices from the k iterations, Λ0 is the estimated support set obtained from the 0th iteration, and the sparse coefficient matrix F ym_sub The desired Doppler matrix has a dimension of M. grid ×N sub ;

[0112] S63: From the Doppler dictionary Ψ f_MC_sub Find the atom with the largest absolute value of its inner product with the residual, and record its column number in the Doppler dictionary; that is, calculate...

[0113] Here, the atom is the column vector of the Doppler dictionary, v k is the column index of the atom obtained in the k-th iteration; For the l-th Doppler sub-dictionary The conjugate transpose of; Let l be the l-th column of the residual from the k-th iteration;

[0114] S64: Column number v k Add to the estimated support set Λ k Λ k =Λ k-1 ∪v k ;

[0115] Among them, Λ k-1 Let Λ be the estimated support set obtained in the (k-1)th iteration. k This is the estimated support set obtained in the k-th iteration;

[0116] S65: Calculate the sparse coefficient matrix F using the least squares method. ym_sub Middle estimate support set Λ k The sparsity coefficients corresponding to the Doppler elements are as follows:

[0117] The Doppler unit is the sparse coefficient matrix F. ym_sub a line of;

[0118] S65A: Let i = 1, where i represents the sparse coefficient matrix F being calculated. ym_sub Column number;

[0119] S65B: Select the corresponding atoms from the Doppler dictionary based on the estimated support set, and estimate the sparsity coefficients using the least squares method.

[0120] in, F represents the sparse coefficient matrix ym_sub Λ k The sparsity coefficient of the i-th row and column; [Λ k ] indicates that the estimated support set Λ k The set of atoms selected from the i-th Doppler sub-dictionary is simply called the atom set matrix; Represents the pseudo-inverse of a matrix; Represents the i-th column of the echo matrix;

[0121] S65C: Update the sparse coefficient matrix

[0122] S65D: Subtract the inner product of the current atom set matrix and the sparse coefficients from the i-th column of the echo matrix to update the residual, i.e.

[0123] S65E: Determine if i equals N sub If not, then i = i + 1, jump to S65B; if yes, then jump to S66.

[0124] S66: Determine if the iteration number k is equal to the sparsity K or ||R|| k If ||2>Th, then k = k+1, and jump to S63; if k = K or ||R k If ||2≤Th, then the sparse coefficient matrix F ym_sub The result is used as the reconstructed Doppler matrix;

[0125] Thus, from S61 to S66, the MMV-OMP method was completed.

[0126] S7: Based on the first random identity matrix Φ n The Doppler matrix F obtained after Doppler sparse reconstruction ym_sub To solve the atomic norm minimization problem, the ESPRIT method is used to calculate the normalized time delay. Then, a distance dictionary is constructed, and the sparse coefficients are calculated using the least squares method. Distance-dimensional sparse reconstruction is then performed to obtain the RD graph. The specific steps are as follows:

[0127] S71: Let ii = 1, where ii represents the index of the element in the estimated support set; initialize the sparse coefficient matrix α as a zero matrix;

[0128] Wherein, the sparse coefficient matrix α is the distance-Doppler matrix to be sought;

[0129] S72: Solving the positive semidefinite problem of equation (2):

[0130]

[0131]

[0132] Where, N B The number of points within the effective bandwidth; tr() represents the operation of finding the trace of a matrix; Toep is the Hermitian-Tpritz operation factor, Toep(u) represents the Hermitian-Tpritz matrix with the elements of vector u as the first row of the matrix, where u is an unknown vector; w is an unknown constant; ε is the relevant parameter of noise or other factors causing model bias; Y is the signal to be recovered; Y H It is the conjugate transpose of the signal to be recovered; Φ n It is the first random identity matrix; The Doppler matrix F ym_sub The p-th Doppler unit, where p is the ii-th element of the estimated support set Λ;

[0133] S73: The normalized delay is calculated using the ESPRIT method. The specific steps are as follows:

[0134] S73A: Perform eigenvalue decomposition on the Hermitian Toplitz matrix Toep(u), where Toep(u) = UλU -1 ;

[0135] Where U is a square matrix composed of the eigenvectors of the eigenvector Toep(u) matrix, and λ is a diagonal matrix whose diagonal elements are the corresponding eigenvalues;

[0136] S73B: Construct a subspace Z = U by selecting the diagonal matrices and corresponding eigenvectors corresponding to the P largest eigenvalues ​​of the Hermitian Toeptz matrix Toep(u). P λ P ;

[0137] Where, λ P It is a diagonal matrix corresponding to P large eigenvalues, U P Z is a matrix consisting of the eigenvectors corresponding to the P large eigenvalues, and Z is the constructed subspace matrix;

[0138] S73C: Removing the first row of the subspace matrix Z yields Z. -1 And find its inverse matrix (Z) -1 )-1, and the matrix obtained by removing the last row of the subspace matrix. Multiply, and the resulting new matrix Calculate its eigenvalue ξ;

[0139] S73D: Calculate the phase of the eigenvalue ξ and divide by 2π to obtain the normalized time delay x'. k , x' k = angle(ξ) / 2π;

[0140] Where angle(·) is the phase function, x' k For normalized delay;

[0141] S74: with Construct a distance dictionary matrix D for the elements;

[0142] Where, x p =x' k N B N B x' is the number of points within the effective bandwidth. k For normalized delay, x p For the distance unit corresponding to the normalized delay, B represents the frequency of each sampling point within the effective bandwidth, and B represents the signal bandwidth.

[0143] S75: Based on the distance dictionary matrix D and the Doppler matrix F ym_sub The sparsity coefficient α is calculated using the least squares method. p ,

[0144] Where D is the distance dictionary, D H For the conjugate transpose of the distance dictionary; (D H D) -1 D represents H The inverse of matrix D, The Doppler matrix F ym_sub The p-th Doppler unit, where p is the ii-th element of the estimated support set Λ; α p Let be the sparse coefficients of the p-th Doppler unit of the sparse coefficient matrix α;

[0145] S76: Determine if ii is equal to k. If not, then ii = ii + 1 and jump to S71. If yes, then use the sparse coefficient matrix α result as the distance dimension sparse reconstruction result.

[0146] Thus, the sparse reconstruction in the distance dimension is completed from S71 to S76, resulting in a high-resolution RD map in the distance dimension. The beneficial effects of the method described in this invention are further illustrated by the following simulations:

[0147] 1. Simulation conditions and parameters.

[0148] Table 1 Simulation Experiment Parameters

[0149] carrier frequency <![CDATA[f c ]]> 674MHz bandwidth B 7.56MHz sampling frequency <![CDATA[f s ]]> 10MHz Number of segmented sampling points N 256 Number of segments M 512

[0150] Table 2 Target Scenarios

[0151]

[0152] The simulation experiments of this invention were compiled using Matlab R2019a. DTTB signals were used as the simulation signals, and the experimental parameters used in the simulation are shown in Table 1. In the simulation scenario, the target was placed in two clusters, and the target information is shown in Table 2.

[0153] 2. Simulation content.

[0154] Simulation Experiment 1: The echo signal is processed using the mutual ambiguity function method to obtain the target's RD pattern, as shown below. Figure 3 As shown in a-3c.

[0155] Simulation Experiment 2: Signal processing using the existing CS-PR method. A. Constructing a dictionary using different time delays and Doppler frequency shifts of the reference signal, flattening the two-dimensional echo matrix as atoms and performing 1 / 4 downsampling, then using the OMP algorithm to achieve sparse reconstruction, where the number of time delay grids is set to 50 and the number of Doppler grids is set to 40, the results are as follows. Figure 4 As shown in a-4b; B. After downsampling the echo signal by 1 / 4, range-dimensional pulse compression is performed, and the Doppler dimension is reconstructed using the EOMP algorithm, where the Doppler grid number is still set to 40, and the target's RD map is obtained as shown. Figure 4 As shown in c-4d.

[0156] Simulation Experiment 3: To demonstrate the advantages of the MMV-OMP algorithm using a Doppler dictionary with a migration correction factor, we compared the range-frequency-Doppler maps after echo Doppler reconstruction using different methods. In the following methods, the echo signals were all downsampled by 1 / 4. First, the results of Doppler reconstruction using the OMP method with the original dictionary are shown below. Figure 5 As shown in figure a; a Doppler dictionary with a distance migration correction factor is used to correct distance migration, and sparse reconstruction is performed using the OMP method, with the results as shown in figure a. Figure 5 As shown in b; a Doppler dictionary with a distance migration correction factor is used to correct distance migration, and sparse reconstruction is performed using the MMV-OMP method. The results are as follows. Figure 5 As shown in c.

[0157] Simulation Experiment 4: Using the passive radar coherent accumulation method based on sparse representation proposed in this invention, the echo signal is still downsampled by 1 / 4. In the Doppler dimension, a Doppler dictionary with migration correction is used, and the MMV-OMP algorithm is used for sparse reconstruction; in the range dimension, the atomic norm minimization and ESPRIT method are used to estimate the continuous domain time delay support set, and the range dictionary is constructed accordingly. Then, the corresponding coefficients are calculated using the least squares method to achieve high-resolution sparse reconstruction in the range dimension, obtaining the target's RD map as shown below. Figure 6 As shown.

[0158] Figure 3 a-3c is the target RD map obtained by processing the echo signal using the mutual ambiguity function method. Figure 3 b-3c is Figure 3 A magnified view of the area within the rectangle, where... Figure 3 b is the RD map of the low Doppler region. Figure 3 c is the high Doppler region RD map, where the asterisks represent the real targets. Analysis Figure 3 As shown in b, due to the excessively high side lobes of the image, the mutual blurring function method cannot clearly distinguish between multiple adjacent scattering points, such as scattering point 2 and scattering point 3; analysis Figure 3As shown in b, the scattering points in the high Doppler region with higher velocities changed from point-like to block-like, such as scattering point 4, scattering point 5 and scattering point 6, indicating that energy accumulation has been dispersed.

[0159] Figure 4 a-4d is a target RD map obtained by processing the signal using the existing CS-PR method, where the asterisk positions represent the real target. Figure 4 a-4b is the result obtained by constructing a dictionary using different time delays and Doppler frequency shifts of the reference signal, flattening the two-dimensional echo matrix as atoms, and performing sparse reconstruction using the OMP algorithm. Figure 4 a is the RD map of the low Doppler region. Figure 4 b is the RD map of the high Doppler region. Figure 4 c-4d is the result obtained by reconstructing Doppler dimensions using the EOMP algorithm after pulse compression in the distance dimension. Figure 4 c is the RD map of the low Doppler region. Figure 4 d is the RD map of the high Doppler region; analysis Figure 4 It is evident that the existing CS-PR method can reduce sidelobes and achieves good energy concentration for scattering points in the low Doppler region, allowing for the differentiation of neighboring scattering points, such as scattering point 2 and scattering point 3. However, for scattering points in the high Doppler region with higher velocities, energy dispersion still exists, making it difficult to distinguish neighboring scattering points that do not fall on the grid, such as scattering point 5 and scattering point 6. Furthermore, in the presence of multiple neighboring targets, the differentiation of individual scattering points in the high Doppler region is also affected, as seen in scattering point 4.

[0160] Figure 5 a-5c are the distance-frequency-Doppler plots after echo Doppler reconstruction using different methods. Figure 5 'a' is the OMP method Doppler reconstruction result of the original dictionary; Figure 5 b is the result obtained after sparse reconstruction using the OMP method after correcting the distance migration with a dictionary with a distance migration correction factor; Figure 5 c represents the result obtained after sparse reconstruction using the MMV-OMP method, following dictionary correction for distance migration with a distance migration correction factor. Analysis Figure 5 As can be seen, in Figure 5 In region a, specifically in the high Doppler region, where the target velocity is relatively high, range migration exists, and the non-zero elements of the sparse vector corresponding to each range frequency unit are in different positions; Figure 5 In b, compared to the original dictionary-based OMP method, a dictionary with a distance migration correction factor is used to correct for distance migration, ensuring that the non-zero elements of the sparse vectors corresponding to each distance frequency unit are in the same position; Figure 5 In c, the non-zero elements of the sparse vectors corresponding to each distance frequency unit are in the same position, and the MMV model ensures the accuracy of the reconstruction.

[0161] Figure 6 a-6b is the result obtained using the passive radar coherent accumulation method based on sparse representation proposed in this invention, where the asterisk positions represent the real targets. Figure 6 a represents the result in the low Doppler region. Figure 6 b represents the high Doppler region result. Analysis Figure 6 The method of the present invention has a good energy concentration effect of scattering points while correcting range migration. It can accurately estimate and distinguish nearby targets in the low Doppler region, such as scattering points 2 and 3, as well as targets in the high Doppler region that do not fall on the range cell grid, such as scattering points 5 and 6. The range resolution is significantly improved compared with the existing methods.

[0162] The simulation results above show that, in the process of acquiring the passive radar target RD map, the RD map obtained by the passive radar coherent accumulation method based on sparse representation of the present invention corrects the target range migration, and can accurately estimate both nearby targets and targets that do not fall on the range cell grid, thus having high range resolution.

[0163] To illustrate the content and implementation method of this invention, a specific embodiment is provided in this specification. The details introduced in the embodiment are not intended to limit the scope of the claims, but rather to aid in understanding the method described in this invention. Those skilled in the art will understand that various modifications, variations, or substitutions to the steps of the preferred embodiment are possible without departing from the spirit and scope of this invention and its appended claims. Therefore, this invention should not be limited to the content disclosed in the preferred embodiment and the accompanying drawings.

Claims

1. A passive radar coherent accumulation method based on sparse representation, characterized in that, include: S1: Receive the reference signal and echo signal from the passive radar and segment them to obtain the reference matrix and echo matrix representing the segmented reference signal and echo signal; S2: Perform Fast Fourier Transform on the reference matrix and echo matrix in the fast time domain and calculate the number of points within the effective bandwidth. Then, truncate the Fast Fourier Transform results of the reference matrix and echo matrix to obtain the two-dimensional reference matrix and two-dimensional echo matrix in the slow time domain-distance frequency domain. S3: Use the first random identity matrix to perform range-direction random sampling on the two-dimensional reference matrix and the two-dimensional echo matrix respectively to achieve downsampling and obtain the range-direction downsampled reference matrix and echo matrix; S4: The echo matrix downsampled in the range direction is randomly sampled in the slow time direction using the second random identity matrix to achieve downsampling and obtain the downsampled echo matrix; S5: Calculate the transformation factor. Based on the reference matrix of range descent sampling, construct a Doppler sub-dictionary containing the range migration correction factor for each single observation vector. After downsampling the Doppler sub-dictionary in the slow time direction, combine them into a Doppler dictionary containing the range migration correction factor for multiple observation vectors. The single observation vector refers to each echo distance frequency unit, which is a column of the downsampled echo matrix; the multi-observation vector refers to all echo distance frequency units. S6: Based on the Doppler dictionary, the Doppler matrix is ​​obtained by performing Doppler-dimensional sparse reconstruction of the downsampled echo matrix using the multi-observation vector orthogonal matching pursuit method. S7: Based on the first random identity matrix and the Doppler matrix obtained after Doppler dimension sparse reconstruction, solve the atomic norm minimization problem, calculate the normalized time delay using the rotation invariant subspace method, construct a distance dictionary, calculate the sparse coefficients using the least squares method, perform distance dimension sparse reconstruction, and obtain the RD graph.

2. The passive radar coherent accumulation method according to claim 1, characterized in that, S5, specifically: S51: Add the distance frequency of each echo distance frequency unit to the signal center frequency to get the sum of the two, and then divide the sum of the two by the center frequency to get the transformation factor. S52: Set the number of Doppler grids, construct a range migration correction factor based on the transformation factor for each single observation vector, and add the range migration correction factor to the reference matrix of range descent sampling to construct a Doppler sub-dictionary; S53: Slow-time downsampling is performed on the Doppler sub-dictionary using the second random identity matrix to obtain the Doppler sub-dictionary after slow-time downsampling; S54: Arrange the Doppler sub-dictionaries after slow-time downsampling in ascending order of distance frequency index, and combine them into a Doppler dictionary for the multi-observation vector.

3. The passive radar coherent accumulation method according to claim 1 or 2, characterized in that, S52 describes constructing a distance migration correction factor based on a transformation factor, that is, through... In this implementation, l represents the distance-frequency index and the value of l ranges from [-N]. sub / 2,…,0,…,N sub / 2],N sub S is the row number of the first random identity matrix; f (l) M represents the transformation factor corresponding to the distance-frequency index l, exp() represents the exponential operation with the natural constant as the base, j represents the imaginary unit, and π represents pi; grid q represents the number of Doppler grids; m represents the column number of the Doppler sub-dictionary and the row number of the Doppler sub-dictionary, with a value range of [0, M-1]. M is the number of segments of the reference signal and is the same as the number of segments of the echo signal.

4. The passive radar coherent accumulation method according to claim 1 or 2, characterized in that, The Doppler sub-dictionary is denoted as Specifically, this is achieved through (1): in, The Doppler sub-dictionary represents the single observation vector corresponding to the distance frequency index l, with a dimension of M×M. grid M is the number of segments in the reference signal, which is the same as the number of segments in the echo signal. The subscript q represents the column number of the Doppler sub-dictionary, and its value ranges from [0, M]. grid -1]; The q on the right side of the equation has the same meaning as the subscript q, both representing the column index of the Doppler sub-dictionary, with a value range of [0, M]. grid -1],M grid F is the number of Doppler grids; xn_sub (m,l) represents the data in the m-th row and l-th column of the reference matrix for range descent sampling, where l is the range frequency index.

5. The passive radar coherent accumulation method according to claim 1, characterized in that, The echo matrix of the segmented echo signal described in S1 is obtained by setting the segment length, performing overlapping segmentation of the echo signal according to the segment length and the maximum time delay, and then generating and expressing the segmented echo signal.

6. The passive radar coherent accumulation method according to claim 1, characterized in that, The reference matrix of the segmented reference signal described in S1 is generated by segmenting and zero-padding the reference signal according to the segment length to obtain a segmented reference signal with the same dimension as the segmented echo signal.

7. The passive radar coherent accumulation method according to claim 2, characterized in that, In S1, the maximum time delay is the overlap length during the overlapping segmentation process of the echo signal; the dimension of the echo matrix is ​​M×N, where M is the number of segments of the echo signal and N represents the number of sampling points in each segment; the dimension of the reference matrix is ​​M×N, where M is the number of segments of the reference signal and is the same as the number of segments of the echo signal; N represents the number of sampling points in each segment and is the same as the number of sampling points in each segment of the echo signal.

8. The passive radar coherent accumulation method according to claim 1, characterized in that, In S2, the number of points within the effective bandwidth is denoted as N. B The dimensions of both the two-dimensional reference matrix and the two-dimensional echo matrix in the slow time-range frequency domain are M×N. B And N B Less than N.

9. The passive radar coherent accumulation method according to claim 1, characterized in that, In S3, the dimension of the first random identity matrix is ​​N. sub ×N B And N sub Less than N B The reference matrix for range descent sampling has dimensions M×N. sub The echo matrix of range descent sampling has dimensions M×N. sub .

10. The passive radar coherent accumulation method according to claim 1, characterized in that, The dimension of the second random identity matrix in S4 is M. sub ×M, and M sub Less than M; downsampling echo matrix, denoted as F y_sub The dimension is M sub ×N sub .

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