A scanning radar fast batch processing iterative super-resolution imaging method

Abstract

The application discloses a kind of scanning radar fast batch processing iterative adaptive super-resolution imaging method, first single distance unit echo model is extended to full distance unit scanning radar echo model, then it is proposed based on batch processing iterative adaptive method to multiple distance units in echo matrix synchronous parallel super-resolution processing, the target scattering iteration formula is solved, and two-dimensional conjugate gradient algorithm is used to solve target scattering and accelerate iteration process, output target scattering and noise power, realize scanning radar fast batch processing iterative adaptive super-resolution imaging.The method of the application overcomes the calculation redundancy problem introduced by the existing iterative adaptive method row by row processing, and uses the conjugate gradient algorithm to avoid matrix inversion operation to reduce the computational complexity, while ensuring the imaging resolution, with lower computational complexity, reduce hardware computing burden.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a scanning radar fast batch processing iterative adaptive super-resolution imaging method. BACKGROUND

[0002] The scanning radar is widely applied to important applications such as air target detection, tracking and early warning due to its wide detection range and high revisit rate. However, the azimuth resolution of the scanning radar is limited by the size of the antenna aperture. Large-scale antennas have technical bottlenecks in hardware implementation and signal processing complexity. Therefore, it is necessary to seek some new technical means to break through the limitation of the antenna parameters on the imaging resolution of the scanning radar.

[0003] In order to improve the imaging resolution of the scanning radar, the document "Tarik Yardibi, Jian Li, Petre Stoica, Ming Xue, and Arthur B. Baggeroer, "Source localization and sensing: An nonparametric iterative adaptive approach based on weighted least squares" IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 1, pp. 425-443, 2010" proposes a super-resolution method based on an iterative adaptive method, which is based on a weighted least squares method and further improves the angle resolution, but faces the problem of high computational complexity. The document "P. Stoica, P. Babu and J. Li, "New Method of Sparse Parameter Estimation in Separable Models and Its Use for Spectral Analysis of Irregularly Sampled Data" in IEEE Transactions on Signal Processing, vol. 59, no. 1, pp. 35-47, Jan. 2011." proposes a sparse covariance fitting estimation method based on a covariance fitting criterion, which solves the problem of super parameter selection and further improves the imaging resolution. However, the existing super-resolution methods are each distance unit by row iteration, which has high iterative calculation complexity and is difficult to implement in hardware. SUMMARY

[0004] To solve the above technical problems, the application provides a scanning radar fast batch processing iterative adaptive super-resolution imaging method to solve the problems of high calculation complexity and difficult hardware implementation of existing super-resolution methods.

[0005] The technical scheme adopted by the application is as follows: a scanning radar fast batch processing iterative adaptive super-resolution imaging method, and the specific steps are as follows:

[0006] Step 1: Construct a full-range unit scanning radar echo signal model;

[0007] Suppose that after distance compression, the scanning radar echo model expression in the mth distance unit is as follows:

[0008]

[0009] wherein, S represents an echo vector, N represents a number of echo signal azimuth sampling points, represents a complex domain, [·] T represents a transposition operation of a matrix; represents a target scattering vector, θ i i=1,…,K1 represents an azimuth angle at the ith sampling point, and K1 represents a number of target scattering signal azimuth sampling points; represents an additive Gaussian white noise vector; represents an antenna pattern vector, and L represents a number of antenna pattern sampling points; represents a vector convolution operation; the antenna pattern vector is converted into a matrix form, and then the expression of formula (1) is rewritten as follows:

[0010] s m =Hx m +e m (2)

[0011] wherein, represents a steering matrix;

[0012] The mth distance unit in formula (2) is expanded into a full-range unit, and then the full-range unit scanning radar echo signal model expression is as follows:

[0013] S=HX+E (3)

[0014] wherein, represents a target scattering matrix, K1 and M respectively represent a number of azimuth and range sampling points of target scattering signals; represents a steering matrix, and N represents a number of echo signal azimuth sampling points; represents an echo matrix; represents an additive Gaussian white noise matrix;

[0015] Step 2: Based on the full-range cell scanning radar echo signal model from Step S1, the target scattering iterative formula is obtained using a batch-processing-based iterative adaptive method.

[0016] First, based on the iterative adaptive method under a single distance cell, the cost function J of weighted least squares and the noise covariance matrix Q are given respectively. k The expression is as follows:

[0017] J = (s - Hx) H W(s-Hx) (4)

[0018] Q k =Rp k h k h k H (5)

[0019] Where s represents the single-range echo vector, x represents the single-range target scattering vector, [·] H p represents the conjugate transpose operation. k =|s k | 2 h represents the scattered energy of a target in each direction. k Let H represent the k-th column of the steering matrix H, and R represent the echo covariance matrix; according to the weighted least squares method, If W is chosen as the weighting matrix, then minimizing the cost function yields the target scattering iterative formula. The expression is as follows:

[0020]

[0021] According to the Capon filtering rule, equation (6) is approximately: Then, based on the full-range intra-cell scanning radar echo signal model and the properties of the Kronecker product, The expression for this transforms into an iterative adaptive method based on batch processing is as follows:

[0022] X (q+1) =Σ (q) ⊙(H H U (q) (8)

[0023] in, x K1M express The K1M-th element; q represents the number of iterations of the iterative adaptive method. This represents the result of the (q+1)th iteration of target scattering across the entire range. Let Σ represent the target scattering matrix, and Σ ij =|X ij |l represents the i-th row and j-th column element of (q) , l represents a pre-set artificial parameter used to control the sparsity of the result, and represents Hadamard product;

[0024] Set u = vec(U), represents the intermediate formula, and a two-dimensional conjugate gradient algorithm is used for solving;

[0025] wherein, is used to correct the ill-conditioned inverse of the matrix R, I represents the unit matrix, and λ represents the correction parameter;

[0026] Step three, using a two-dimensional conjugate gradient algorithm to solve the target scattering and accelerate the iteration process, and output the target scattering and noise power;

[0027] According to the two-dimensional conjugate gradient algorithm, the iteration process expression for solving the target scattering is as follows:

[0028] U t+1 = U t + α t D t (9)

[0029]

[0030] W t = H(Σ⊙(H H D t+1 ))+ λD t+1 (11)

[0031] D t+1 = G t + β t D t (12)

[0032] G t+1 = G t - α t W t (13)

[0033] wherein, t and q respectively represent the iteration number in the conjugate gradient algorithm and the iteration number of the iteration adaptive method; d t = vec(D t ) represents the conjugate direction of the matrix ; w t = vec(W t ) represents an intermediate variable; β t+1 = ρ t+1 / ρ t ; g t = vec(Gt represents the gradient; ||·|| represents the Frobenius norm; F represents the Frobenius norm;

[0034] The parameters in the iteration process are initialized as follows: The initialization value is substituted into the iteration process of formula (14), the outer loop is the iteration loop of the iterative adaptive method, and the iteration is performed Q times; the outer loop starts, and the parameters U0=0, G0=S, D0=0, and β0=0 are initialized, Then the inner loop starts, the inner loop is the iteration loop of the conjugate gradient algorithm, and the iteration is performed T times; the parameters initialized by the outer loop are substituted into the iteration to obtain:

[0035]

[0036] After the inner loop ends, the assignment is performed as follows:

[0037]

[0038] Finally, the iteration ends to derive the full-range unit cell scattering estimation of the target, and the fast batch processing iterative adaptive super-resolution imaging of the scanning radar is realized.

[0039] The method of the present application firstly expands the single-range unit echo model to the full-range unit scanning radar echo model, then proposes a batch processing-based iterative adaptive method to synchronously and in parallel super-resolution process multiple range units in the echo matrix, solves the target scattering iteration formula, and then uses a two-dimensional conjugate gradient algorithm to solve the target scattering and accelerate the iteration process, and outputs the target scattering and noise power, thereby realizing the fast batch processing iterative adaptive super-resolution imaging of the scanning radar. The method of the present application solves the problem of single-range unit row-by-row iteration and high computational complexity in the prior art, compared with the existing super-resolution method, the method overcomes the calculation redundancy problem introduced by the row-by-row processing of the existing iterative adaptive method, and uses the conjugate gradient algorithm to avoid matrix inversion operation, thereby reducing the computational complexity, ensuring the imaging resolution, and reducing the hardware calculation burden. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The flowchart of the scanning radar fast batch processing iterative adaptive super-resolution imaging method of the present application.

[0041] Figure 2 The original scene diagram of the two-dimensional scanning radar in the embodiment of the present application.

[0042] Figure 3 The real beam two-dimensional imaging result diagram under SNR=20dB in the embodiment of the present application.

[0043] Figure 4This is an image of the IAA imaging result in an embodiment of the present invention.

[0044] Figure 5 The image shows the imaging results of the FBB-IAA method in this embodiment of the invention at l=1.2 and λ=20.

[0045] Figure 6 This is a comparison diagram of the imaging results of the IAA and FBB-IAA methods and the real beam echo profile in the embodiments of the present invention. Detailed Implementation

[0046] This invention is primarily verified using simulation experiments, and all steps and conclusions have been verified correctly using Matlab 2018. The method of this invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] like Figure 1 The flowchart of a fast batch processing iterative adaptive super-resolution imaging method for scanning radar according to the present invention is shown below, and the specific steps are as follows:

[0048] Step 1: Construct a full-range cell scanning radar echo signal model;

[0049] In this embodiment, the original scene of the two-dimensional scanning radar is as follows: Figure 2 As shown. Figure 2 The range-azimuth target scene is displayed, including 7 independent targets. In the scanning radar echo signal model, the azimuth angle θ ranges from -10° to 10°, the initial azimuth scanning speed is 60° / s, the azimuth beamwidth is 3°, and the PRF is 1000Hz.

[0050] After range compression, the scanning radar echo model expression within the m-th range cell is as follows:

[0051]

[0052] in, This represents the echo vector, and N represents the number of azimuth sampling points of the echo signal. To represent the field of complex numbers, [·] T This represents the matrix transpose operation; θ represents the target scattering vector. i ,i=1,...,K1 represents the azimuth angle of the i-th sampling point, and K1 represents the number of azimuth sampling points of the target scattered signal; This represents an additive white Gaussian noise vector. represents the antenna pattern vector, and L represents the number of antenna pattern sampling points; Let (1) represent the vector convolution operation; after converting the antenna pattern vector into matrix form, equation (1) can be rewritten as follows:

[0053] sm =Hx m +e m (2)

[0054] in, Represents the steering matrix;

[0055] Expanding the m-th range cell in equation (2) into a full-range cell, we can obtain the following expression for the full-range cell scanning radar echo signal model:

[0056] S=HX+E (3)

[0057] in, Let K1 and M represent the target scattering matrix, and K1 and M represent the number of sampling points in the azimuth and range directions of the target scattering signal, respectively. This represents the steering matrix, and N represents the number of azimuth sampling points of the echo signal. Represents the echo matrix; This represents the additive white Gaussian noise matrix;

[0058] Step 2: Based on the full-range cell scanning radar echo signal model from Step S1, the target scattering iterative formula is obtained using a batch-processing-based iterative adaptive method.

[0059] First, based on the iterative adaptive method under a single distance cell, the cost function J of weighted least squares and the noise covariance matrix Q are given respectively. k The expression is as follows:

[0060] J = (s - Hx) H W(s-Hx) (4)

[0061] Q k =Rp k h k h k H (5)

[0062] Where s represents the single-range echo vector, x represents the single-range target scattering vector, [·] H p represents the conjugate transpose operation. k =|s k | 2 h represents the scattered energy of a target in each direction. k Let H represent the k-th column of the steering matrix H, and R represent the echo covariance matrix; according to the weighted least squares method, If W is chosen as the weighting matrix, then minimizing the cost function yields the target scattering iterative formula. The expression is as follows:

[0063]

[0064] According to the Capon filtering rule, equation (6) is approximately: Then, based on the full-range intra-cell scanning radar echo signal model and the properties of the Kronecker product, The expression for this transforms into an iterative adaptive method based on batch processing is as follows:

[0065] X (q+1) =Σ (q) ⊙(H H U (q) (8)

[0066] in, express The K1M-th element; q represents the number of iterations of the iterative adaptive method. This represents the result of the (q+1)th iteration of target scattering across the entire range. Let Σ represent the target scattering matrix, and Σ ij =|X ij | l Represents Σ (q) The element in the i-th row and j-th column represents the pre-set artificial parameter used to control the sparsity of the result, and ⊙ represents the Hadamard product.

[0067] set up u = vec(U), The intermediate expression is solved using the two-dimensional conjugate gradient algorithm.

[0068] in, Used to correct the ill-conditioned nature of matrix inversion R, where I represents the identity matrix and λ represents the correction parameter;

[0069] Step 3: Use the two-dimensional conjugate gradient algorithm to solve for target scattering and accelerate the iterative process, and output the target scattering and noise power;

[0070] The iterative process for solving the target scattering problem using the two-dimensional conjugate gradient algorithm is expressed as follows:

[0071] U t+1 =U t +α t D t (9)

[0072]

[0073] W t =H(Σ⊙(H) H D t+1 ))+λD t+1 (11)

[0074] D t+1 =Gt +β t D t (12)

[0075] G t+1 =G t -α t W t (13)

[0076] where t and q represent the iteration number of the conjugate gradient algorithm and the iteration adaptive method respectively; d t = vec(D t ) represents the conjugate direction of matrix D ; w t = vec(W t ) represents an intermediate variable; β t+1 = ρ t+1 / ρ t ; g t = vec(G t ) represents the gradient; ‖·‖ F represents the Frobenius norm;

[0077] The parameters in the iteration process are initialized as follows: The initialization value is substituted into the iteration process of formula (14), the outer loop is the iteration loop of the iteration adaptive method, and the iteration number is Q times; the outer loop starts, and the parameters U0=0, G0=S, D0=0, β0=0, Then the inner loop starts, the inner loop is the iteration loop of the conjugate gradient algorithm, and the iteration number is T times; the parameters initialized by the outer loop are substituted into the iteration to obtain:

[0078]

[0079] After the inner loop ends, the assignment is performed:

[0080]

[0081] Finally, the iteration ends to derive the full-range unit scattering estimation of the target, and the fast batch processing iteration adaptive super-resolution imaging of the scanning radar is realized.

[0082] In the embodiment, it can be seen from the simulation results that in the two-dimensional imaging results of the real beam of Figure 3 , the adjacent targets in the scene are blurred due to the wide main lobe in the azimuth direction, which leads to difficulty in distinguishing. Figure 4 The imaging result of the iteration adaptive method (IAA) is Figure 5 The imaging result of the method (FBB-IAA) of the application is shown. Figure 6The imaging results of the two methods and the profile of the real beam echo are compared. From the results, FBB-IAA obtains higher imaging resolution than IAA. In addition, since IAA is iterated by each distance unit, and FBB-IAA is iterated by full distance unit, the calculation complexity is significantly reduced. In terms of algorithm complexity, the algorithm complexity of each iteration of each distance unit of IAA is N 3 +2N 2 K1+NK1, so the total algorithm complexity is MQ(N 3 +2N 2 K1+NK1). The total algorithm complexity of FBB-IAA of the method of the present application is Q(K1M((2N+1+M)T+N+2)+NTM). The calculation complexity is reduced from O(MQN 3 ) to O(2K1MNQT), wherein O represents the order of magnitude. In the case of Q=12, T=20, echo signal sampling points M=248, and N=334, IAA needs 33.7s for each run. FBB-IAA of the method of the present application needs 0.6s for each run, and the iteration time of the method of the present application is only 1.8% of that of the existing IAA. This shows that, compared with IAA, the method of the present application not only obtains good azimuth resolution, but also greatly reduces the time and space complexity.

[0083] In summary, the method of the present application first extends the single distance unit echo model to the full distance unit echo model to realize parallel processing of multiple distance unit echo data, then based on the full distance unit echo model, proposes a batch-based iterative adaptive method for synchronous and parallel super-resolution processing of multiple distance units in the echo matrix, and finally uses the conjugate gradient algorithm and the property of Kronecker product to speed up the iterative estimation of target scattering, realizes fast sparse super-resolution imaging of scanning radar. The method of the present application overcomes the calculation redundancy problem introduced by the row-by-row processing of the existing iterative adaptive method, and uses the conjugate gradient algorithm to avoid matrix inversion operation to reduce the calculation complexity. Compared with the existing super-resolution method, the method of the present application has lower calculation complexity while ensuring imaging resolution, and reduces the hardware calculation burden.

[0084] Those skilled in the art will realize that the embodiments described herein are for the purpose of helping the reader understand the principles of the present application, and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspiration disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.

Claims

1. A scanning radar fast batch processing iterative adaptive super-resolution imaging method, the specific steps are as follows: Step 1, construct a full range cell scanning radar echo signal model; After distance compression, the scanning radar echo model expression in the mth distance cell is as follows: wherein represents echo vector, N represents echo signal azimuth sampling point number, represents complex domain, [·] T represents the transpose operation of a matrix; represents target scattering vector, θ i , i = 1, …, K1 represents azimuth angle at the i th sampling point, K1 represents target scattering signal azimuth sampling point number; represents additive white Gaussian noise vector; represents antenna pattern vector, L represents antenna pattern sampling point number; represents vector convolution operation; the antenna pattern vector is converted into matrix form, then formula (1) is rewritten as follows: s m = Hx m + e m (2) wherein denotes a steering matrix; The mth distance cell in formula (2) is extended to the full distance cell, and the full distance cell scanning radar echo signal model expression is as follows: S=HX+E (3) wherein, denotes a target scattering matrix, K1 and M denote the number of azimuth and range sampling points of the target scattering signal, respectively; denotes a steering matrix, and N denotes the number of azimuth sampling points of the echo signal; denotes an echo matrix; denotes an additive white Gaussian noise matrix; Step 2, based on the full distance cell scanning radar echo signal model of step S1, the target scattering iterative formula is solved by using the batch-based iterative adaptive method; Firstly, based on the single-distance unit under the iterative adaptive method, the cost function J and the noise covariance matrix Q of weighted least squares are given respectively k The expression is as follows: J = (s - Hx) H W(s - Hx) (4) Q k = R-p k h k h k H (5) where s represents a single range echo vector, x represents a single range target scattering vector, [·] H denotes a conjugate transpose operation, p k = |s k | 2 denotes each azimuth target scattering energy, h k denotes the kth column of the steering matrix H, and R denotes the echo covariance matrix; according to the weighted least squares method, is selected as the weighting matrix W, then the cost function is minimized to obtain the target scattering iteration formula The expression is as follows: According to Capon filtering rule, formula (6) is approximated as: Then according to the full-range cell-in-scan radar echo signal model and the properties of Kronecker product, the formula (7) is transformed into the iteration formula of the batch-based iterative adaptive method, which is expressed as follows: Then according to the full-range cell-in-scan radar echo signal model and the properties of Kronecker product, the formula (7) is transformed into the iteration formula of the batch-based iterative adaptive method, which is expressed as follows: X (q+1) =∑ (q) ⊙(H H U (q) ) (8) wherein, x K1M denotes the K1Mth element of the matrix X denotes the q+1th iteration result of the full-distance unit target scatter iteration, denotes the target scatter matrix, and Σ ij = |X ij | l denotes the element in the i-th row and j-th column of the matrix X (q) , l denotes a pre-set artificial parameter used to control the sparsity of the result, and ⊙ denotes Hadamard product. Setting u = vec(U), in the intermediate representation, is solved using a two-dimensional conjugate gradient algorithm; wherein for correcting the ill-conditioning of the inverse of the matrix R, I denotes the identity matrix and λ denotes a correction parameter; Step 3, the two-dimensional conjugate gradient algorithm is used to solve the target scattering and accelerate the iteration process, and the target scattering and noise power are output; The iteration process expression for solving the target scattering according to the two-dimensional conjugate gradient algorithm is as follows: U t+1 = U t + α t D t (9) W t = H(∑⊙(H H D t+1 ))+ λD t+1 (11) D t+1 = G t + β t D t (12) G t+1 = G t - a t W t (13) where t and q denote the iteration number in the conjugate gradient algorithm and the iterative adaptive method, respectively; d t = vec(D t ) denotes the conjugate direction of the matrix w t = vec(W t ) denotes an intermediate variable; β t+1 = p t+1 / p t ; g t = vec(G t ) denotes the gradient; || · || F denotes the Frobenius norm;​ The parameters in the iteration process are initialized as follows: The initialization values are substituted into the iteration process of formula (14), the outer loop is the iteration loop of the iteration adaptive method, and the iteration is performed Q times; the outer loop starts, and the parameters U0=0, G0=S, D0=0, and β0=0 are initialized, Then the inner loop starts, the inner loop is the iteration loop of the conjugate gradient algorithm, and the iteration is performed T times; the parameters initialized by the outer loop are substituted into the iteration to obtain: After the inner loop is finished, the assignment is performed: Finally, the iteration is finished to derive the full distance cell scattering estimation of the target, and the scanning radar fast batch processing iterative adaptive super-resolution imaging is realized.

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