A batch processing super-resolution method for sparse targets in scanning radar

Abstract

The present invention discloses a scanning radar sparse target batch processing super-resolution method, which performs distance dimension processing by acquiring and preprocessing echo data, realizes decoupling of echo distance dimension and angle dimension, constructs matrix form objective function, transforms super-resolution problem into matrix form optimization problem under regularization framework, and finally realizes super-resolution operation directly on two-dimensional echo matrix by adopting alternating direction multiplier method in matrix form. Compared with traditional sparse super-resolution algorithm, the method of the present invention can directly process two-dimensional echo data, does not need to process echo data row by row or column vectorization, and greatly saves space and time complexity required for super-resolution processing.

Description

Technical field:

[0001] The present invention is applied to the field of radar imaging, and in particular relates to a scanning radar sparse target batch processing super-resolution method. Background technology:

[0002] Scanning radar uses beam scanning to obtain detailed information of the observation area, and does not rely on Doppler information, so it has a wide range of imaging capabilities. However, in practical applications, due to the limited azimuth resolution of scanning radar, it is urgent to use super-resolution technology to improve the azimuth resolution.

[0003] The deconvolution method can restore the target scattering coefficient distribution and obtain a resolution beyond the real beam result. Therefore, it is widely used in the field of scanning radar azimuth super-resolution imaging. The paper "Y. Kang, Y. Zhang, D. Mao, X. Tuo, Y. Zhang and Y. Huang, Super-resolution Doppler Beam Sharpening based on Online Tikhonov Regularization. 2019 6th Asia-Pacific Conference on Synthetic Aperture Radar (pp. 1-4). IEEE" proposed an improved Tikhonov regularization (REGU) method, which has limited improvement on resolution. In the literature "Q. Zhang, Y. Zhang, Y. Zhang, Y. Huang, W. Li and J. Yang, Majorize-Minimization Based Super-Resolution Method for Radar Forward-Looking Imaging. 2020 IEEE International Geoscience and Remote Sensing Symposium, pp. 3188-3191. IEEE, 2020." Based on the regularization framework, a sparse regularization method is proposed, and the maximization-minimization (MM) strategy is used to improve the azimuth super-resolution performance. In the literature "Chen H, Li Y, Gao W, et al. Bayesian Forward-Looking Superresolution Imaging Using Doppler Deconvolution in Expanded Beam Space for High-Speed ​​Platform. IEEE Transactions on Geoscience and Remote Sensing, 2021, 60: 1-13." Based on the Bayesian framework, a Bayesian method is proposed, which uses Laplace distribution to describe the characteristics of sparse targets and realizes target azimuth super-resolution imaging.The paper "Yardibi T, Li J, Stoica P, et al. Source localization and sensing: A nonparametric iterative adaptive approach based on weighted least squares. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(1): 425-443." proposes an iterative adaptive (IAA) azimuth super-resolution method based on the array signal processing framework, which realizes super-resolution imaging of sparse targets. The above sparse super-resolution methods all require the echo data to be processed line by line, which has high computational complexity. Summary of the invention:

[0004] In order to solve the above technical problems, the present invention proposes a scanning radar sparse target batch processing super-resolution method.

[0005] The technical solution of the present invention is: a scanning radar sparse target batch processing super-resolution method, the specific steps are as follows:

[0006] Step 1: Scanning radar echo modeling,

[0007] According to the motion geometry model of the scanning radar, the radar transmits a linear frequency modulation signal, and the received echo signal is compressed and compensated in the range dimension, which can be expressed as follows:

[0008]

[0009] Among them, R represents the distance information, θ represents the target space azimuth, A is a constant related to the radar system, g(R,θ) represents the echo signal received by the radar, f(R,θ) represents the target scattering coefficient, and h(θ) represents the antenna pattern function. represents the pulse compression response function, represents the convolution operation, and c represents the propagation speed of electromagnetic waves.

[0010] Considering the echo signal within a range unit, the azimuth echo expression can be rewritten in matrix form:

[0011] g=Hf+n (2)

[0012] Wherein, g represents the received azimuth echo vector, f represents the target scattering coefficient vector, n represents the noise vector satisfying the Gaussian distribution, and H represents the convolution measurement matrix composed of the antenna pattern function.

[0013] Step 2: Construction of batch processing objective function.

[0014] Assuming that the target of interest is sparse compared to the entire observation scene, under the regularization framework, the following sparse target reconstruction function is constructed:

[0015]

[0016] in, represents an estimate of the target scattering coefficient vector; represents the square of the vector 2 norm, represents the data fidelity term; ||·||1 represents the vector 1-norm, ||f||1 represents the regularization term; λ represents the regularization parameter.

[0017] Since the acquired echo is usually in the form of a two-dimensional matrix, its dimension is M×N, M represents the number of distance sampling points, and N represents the number of azimuth sampling points. Formula (3) can be rewritten into a batch processing objective function in matrix form as follows:

[0018]

[0019] in, is the estimate of the transposed target scattering coefficient matrix, whose dimension is N×M; represents the Frobenius norm of the matrix; G represents the transposed echo matrix, whose dimension is N×M; H represents the convolution measurement matrix composed of antenna pattern functions, whose dimension is N×N; F represents the transposed target scattering coefficient matrix, whose dimension is N×M.

[0020] Step 3: Transformation of objective function

[0021] Based on the batch processing objective function of formula (4) in step 2, the alternating direction multiplication method in matrix form is used to solve the objective function. By introducing an additional variable Z, the objective function is transformed into the following form:

[0022]

[0023] Where Z represents an additional matrix, whose dimension is N×M; represents the estimate of the additional matrix Z, whose dimension is N×M.

[0024] Secondly, the augmented Lagrangian strategy is adopted and the variable W is introduced. For p>0, the objective function in equation (5) can be rewritten as:

[0025]

[0026] Where W represents the Lagrange multiplier matrix with dimension N×M; p represents the augmented Lagrangian parameter.

[0027] Step 4: Batch update of target scattering coefficient matrix F.

[0028] For the batch update of the target scattering coefficient matrix F, the solution expression is:

[0029] F=(H T H+pI) -1 (H T G+p(ZW)) (7)

[0030] Where I represents the identity matrix and T represents the transpose of the matrix.

[0031] Step 5: Additional variable Z is updated.

[0032] For the update problem of the additional variable Z, the solution is explicitly given by the soft threshold function, expressed as:

[0033]

[0034] in, Indicates an element-by-element operation. Specifically, soft(A,δ) means that the following operation is performed on all elements of the i×j matrix A:

[0035] soft(A,δ)=sgn(A ij )·max(|A ij |-δ,0) (9)

[0036] Among them, sgn represents the sign function, δ represents the threshold, and A ij Represents each element of the matrix A.

[0037] Step 6: Update variable W.

[0038] For the update problem of variable W, its solution can be updated using F and Z:

[0039] W=W+(FZ) (10)

[0040] Step 7: Sparse target batch super-resolution,

[0041] Repeat steps 4, 5, and 6 until the optimal target scattering coefficient matrix is ​​obtained. The iterative process is as follows:

[0042]

[0043] Where k represents the number of iterations. k and W k represents the Z matrix and W matrix after the kth iteration; similarly, F k+1 , Z k+1 With W k+1 They represent the F matrix, Z matrix and W matrix after the k+1th iteration respectively.

[0044] Beneficial effects of the present invention: The method of the present invention performs distance dimension processing by acquiring and preprocessing echo data, realizes decoupling of echo distance dimension and angle dimension, constructs a matrix form objective function, and transforms the super-resolution problem into a matrix form optimization problem under the regularization framework. Finally, by adopting the alternating direction multiplier method in matrix form, super-resolution operation of two-dimensional echo matrix is ​​realized directly. Compared with the traditional sparse super-resolution algorithm, the method of the present invention can directly process two-dimensional echo data, does not need to process the echo data row by row or column vectorization, and greatly saves the space and time complexity required for super-resolution processing. Description of the drawings:

[0045] Figure 1 The present invention is a flow chart of a scanning radar sparse target batch processing super-resolution method.

[0046] Figure 2 This is the motion model of the airborne scanning radar in an embodiment of the present invention.

[0047] Figure 3 The following is a comparison of imaging effects in sparse scenes according to an embodiment of the present invention. Specific implementation method:

[0048] The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0049] The present invention adopts simulation experiments to demonstrate the effectiveness of the proposed method. All the steps and conclusions of the present invention are verified on the Matlab2021 simulation platform. Figure 1 As shown, a flow chart of a scanning radar sparse target batch processing super-resolution method of the present invention, the specific steps are as follows:

[0050] Step 1: Echo data acquisition and preprocessing,

[0051] The present invention adopts the airborne scanning radar motion model, such as Figure 2 The specific parameter values ​​of the airborne platform system are shown in Table 1. In order to simulate the low signal-to-noise ratio environment of the real environment, the noise added to the simulation in this embodiment is 25dB.

[0052] Table 1

[0053] Simulation parameters Numeric Carrier frequency 35GHz Time Width 2us bandwidth 40MHz Antenna beam width 3° Pulse repetition frequency 1000Hz Scan speed 60° / s Scan range ±10°

[0054] The radar transmits a linear frequency modulated pulse signal with a fixed pulse repetition frequency (PRF).

[0055]

[0056] Where g(τ) represents the transmitted linear frequency modulation signal, τ is the distance dimension time; Tp =2us is the pulse width of the transmitted signal; carrier frequency f c =35GHz; K is the linear modulation frequency, K = B / T p , signal bandwidth B = 40MHz, rect is the rectangular window function.

[0057] Real simulation scenes such as Figure 3 (a) The original simulation scene results are shown. The scanning detection area of ​​this embodiment is set to Ω = -10° ~ 10°, the antenna beam width is 3°, and the scanning speed is 60° / s. The acquired radar original echo signal is subjected to range-dimensional pulse pressure and motion compensation, and the phase term is removed by modulo, and its expression is as follows:

[0058]

[0059] Wherein, R represents distance information, θ represents the target spatial azimuth; g(R,θ) represents the echo signal received by the radar, f(R,θ) represents the target scattering coefficient, h(θ) represents the antenna pattern function, θ0 is the starting azimuth, which is θ0=-10° in this embodiment, R0 represents the initial distance, which is R0=3000m in this embodiment, and n(R,θ) is additive noise; sinc(·) represents the pulse response function, and c represents the electromagnetic wave propagation speed.

[0060] Considering the echo signal within a range unit, the azimuth echo in equation (13) can be converted into a matrix form:

[0061] g=Hf+n (14)

[0062] Among them, g=[g(θ1),g(θ2),L,g(θ N )] T represents the received azimuth echo vector, g(θ1) represents the first element of vector g, and similarly g(θ N ) represents the Nth element of the vector g; f=[f(θ1),f(θ2),…,f(θ N )] T represents the target scattering coefficient vector, f(θ1) represents the first element of the vector f, and similarly f(θ N ) represents the Nth element of the vector f; n=[n(θ1),n(θ2),…,n(θ N )] T represents a noise vector that satisfies the Gaussian distribution, n(θ1) represents the first element of vector n, and similarly n(θ N ) represents the Nth element of vector n; H represents the convolution measurement matrix composed of N×N antenna pattern functions.

[0063] Step 2: Construct the objective function in matrix form.

[0064] Assuming that the target of interest is sparse compared to the entire observation scene, the following objective function is constructed:

[0065]

[0066] in, represents an estimate of the target scattering coefficient vector; represents the square of the vector 2 norm, represents the data fidelity term; ||·||1 represents the vector 1-norm, ||f||1 represents the regularization term; λ represents the regularization parameter.

[0067] Since the acquired echo is a two-dimensional matrix of size M×N, in this embodiment, the optimization problem of formula (15) is expanded into an optimization problem in matrix form:

[0068]

[0069] in, is the estimate of the transposed target scattering coefficient matrix, whose dimension is N×M; represents the Frobenius norm of the matrix; G represents the transposed echo matrix, whose dimension is N×M; H represents the convolution measurement matrix composed of antenna pattern functions, whose dimension is N×N; F represents the transposed target scattering coefficient matrix, whose dimension is N×M; λ represents the regularization parameter; M represents the number of range sampling points, and N represents the number of azimuth sampling points.

[0070] Step 3: Conversion of objective function

[0071] By introducing an additional variable Z, the alternating direction multiplier method is used to solve equation (16):

[0072]

[0073] Using the augmented Lagrangian strategy, the variable W is introduced to transform the objective function of equation (17) into the following expression:

[0074]

[0075] Among them, Z is an N×M additional matrix, is an estimate of the N×M additional matrix Z, W represents the N×M size Lagrangian multiplier matrix, and p (p>0) is the augmented Lagrangian parameter.

[0076] Step 4: Update the target scattering coefficient matrix F.

[0077] The target scattering coefficient matrix F is solved by an iterative method. The specific iterative expression is:

[0078] Fk+1 =(H T H+pI) -1 (H T G+p(Z k -W k )) (19)

[0079] Wherein, k represents the number of iterations, I represents the identity matrix, T represents the transpose of the matrix, and p represents the augmented Lagrangian parameter, which is generally adjusted between 1 and 10. In this embodiment, p is set to 1. k and W k represents the Z matrix and W matrix after the kth iteration, F k+1 represents the F matrix after the k+1th iteration.

[0080] Step 5: Update Z.

[0081] The solution of the additional matrix Z can be achieved through the soft threshold function:

[0082]

[0083] Wherein, λ represents a regularization parameter, and in this embodiment, λ=2 is set. k+1 represents the Z matrix after the k+1th iteration. Indicates an element-by-element operation. Specifically, soft(A,δ) means that the following operation is performed on all elements of the i×j matrix A:

[0084] soft(A,δ)=sgn(A ij )·max(|A ij |-δ,0) (21)

[0085] Among them, sgn represents the sign function, δ represents the threshold, and A ij Represents each element of the matrix A.

[0086] Step 6: Update W.

[0087] For the Lagrange multiplier matrix W, its iterative expression is:

[0088] W k+1 =W k +(F k+1 -Z k+1 ) (twenty two)

[0089] Among them, W k+1 represents the W matrix after the k+1th iteration.

[0090] Step 7: Solve the super-resolution imaging results.

[0091] Repeat steps 4, 5, and 6 until the error between two adjacent super-resolution results is less than the set error ε, and then end the loop to output the super-resolution imaging result. The detailed expression is:

[0092]

[0093] The super-resolution imaging results are as follows Figure 3 As shown, Figure 3 (b) is the real beam result after pulse compression and motion compensation. Due to the modulation of the antenna pattern function in the azimuth dimension, its azimuth resolution is low and the target echo aliasing cannot be distinguished. Figure 3 (c) shows the imaging result of the sparse regularization method. Figure 3 (d) shows the imaging result of the Bayesian method. Figure 3 (e) shows the imaging result of IAA method. Figure 3 (f) represents the imaging result of the method of the present invention. The simulation conditions of the simulation in this embodiment are shown in Table 2.

[0094] Table 2

[0095] Hardware or software parameter CPU Intel(R)Core(TM)i5-9500 RAM 8GB Simulation Platform Matlab2021

[0096] It can be seen that the above methods all achieve the improvement of azimuth resolution, and the method of the present invention has comparable performance to the traditional sparse method, which can also be proved by the structural similarity (SSIM) comparison in Table 3. Combined with the operation time in Table 3, it can be concluded that compared with other sparse super-resolution imaging methods, the method of the present invention greatly saves the time and space complexity required for super-resolution processing while ensuring the resolution performance.

[0097] Table 3

[0098] method Regularization methods Bayesian Methods IAA method Method of the present invention SSIM 0.9821 0.9802 0.9736 0.9925 Run time(s) 18.149 18.907 21.550 0.090

[0099] From the above, it can be seen that the method of the present invention can directly perform super-resolution batch processing on M×N two-dimensional echo data without processing the echo data line by line. Compared with the traditional sparse method, the computational complexity is MN 3 Reduced to max{N 3 ,MN 2}.

[0100] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, relevant modifications or applications can be made based on the super-resolution imaging method proposed in this invention, but the relevant knowledge is still within the scope of protection of this invention.

Claims

1. A scanning radar sparse target batch processing super-resolution method, the specific steps are as follows: Step 1: Scanning radar echo modeling, The radar transmits a linear frequency modulation signal, and the received echo signal is expressed as follows after range-dimensional pulse compression and compensation: in, R represents the distance information, θ represents the target spatial azimuth, A is a constant related to the radar system, g(R,θ) represents the echo signal received by the radar, f(R,θ) represents the target scattering coefficient, and h(θ) represents the antenna pattern function. represents the pulse compression response function, represents the convolution operation, c represents the propagation speed of electromagnetic waves; The azimuth echo expression is rewritten in matrix form: g=Hf+n (2) Wherein, g represents the received azimuth echo vector, f represents the target scattering coefficient vector, n represents the noise vector satisfying the Gaussian distribution, and H represents the convolution measurement matrix composed of the antenna pattern function; Step 2: Construction of batch processing objective function. Under the regularization framework, the following sparse target reconstruction function is constructed: in, represents an estimate of the target scattering coefficient vector; represents the square of the vector 2 norm, represents the data fidelity term; ||·||1 represents the vector 1 norm, ||f||1 represents the regularization term; λ represents the regularization parameter; The acquired echo is in the form of a two-dimensional matrix with a dimension of M×N, where M represents the number of distance sampling points and N represents the number of azimuth sampling points. The batch processing objective function of formula (3) is rewritten into a matrix form as follows: in, is the estimate of the transposed target scattering coefficient matrix, whose dimension is N×M; represents the Frobenius norm of the matrix; G represents the transposed echo matrix, whose dimension is N×M; H represents the convolution measurement matrix composed of antenna pattern functions, whose dimension is N×N; F represents the transposed target scattering coefficient matrix, whose dimension is N×M; Step 3: Transformation of objective function Based on the batch processing objective function of formula (4) in step 2, the alternating direction multiplication method in matrix form is used to solve the objective function. By introducing an additional variable Z, the objective function is transformed into the following form: Where Z represents an additional matrix, whose dimension is N×M; represents the estimate of the additional matrix Z, whose dimension is N×M; Secondly, the augmented Lagrangian strategy is adopted, and the variable W is introduced. For p>0, the objective function in equation (5) is rewritten as: Where W represents the Lagrange multiplier matrix with dimension N×M; p represents the augmented Lagrangian parameter; Step 4: Batch update of target scattering coefficient matrix F. For the batch update of the target scattering coefficient matrix F, the solution expression is: F=(H T H+pI) -1 (H T G+p(ZW)) (7) Among them, I represents the identity matrix, and T represents the transpose of the matrix; Step 5: Additional variable Z is updated. For the update problem of the additional variable Z, the solution is explicitly given by the soft threshold function, expressed as: in, Indicates an element-by-element operation. Specifically, soft(A,δ) means that the following operation is performed on all elements of the i×j matrix A: soft(A,δ)=sgn(A ij )·max(|A ij |-δ,0) (9) Among them, sgn represents the sign function, δ represents the threshold, and A ij Represents each element of matrix A; Step 6: Update variable W. For the update problem of variable W, its solution can be updated using F and Z: W=W+(FZ) (10) Step 7: Sparse target batch super-resolution, Repeat steps 4, 5, and 6 until the optimal target scattering coefficient matrix is ​​obtained. The iterative process is as follows: Where k represents the number of iterations; Z k and W k represents the Z matrix and W matrix after the kth iteration; similarly, F k+1 , Z k+1 With W k+1 They represent the F matrix, Z matrix and W matrix after the k+1th iteration respectively.

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