Bayesian sparse learning based two-dimensional super-resolution imaging method for scanning radar

Abstract

The application discloses a scanning radar two-dimensional super-resolution imaging method based on Bayesian sparse learning, first constructs a bearing-pitch two-dimensional scanning radar signal model, then, according to a maximum posteriori criterion under a Bayesian framework, establishes a sparse optimization target function about target scattering and environmental noise, finally, utilizes a conjugate gradient algorithm and Kronecker product properties to accelerate iterative estimation of target scattering and noise power, realizes adaptive sparse two-dimensional super-resolution imaging of the scanning radar. The method solves the problems of high complexity and poor noise robustness of prior art means, compared with prior art two-dimensional super-resolution methods, has lower calculation complexity, is more robust, has excellent noise adaptive capacity, and can realize two-dimensional scanning radar super-resolution imaging under a low signal-to-noise ratio condition.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning. Background Technology

[0002] Two-dimensional scanning radar is widely used in important applications such as airborne target detection, tracking, and early warning due to its wide detection range and high revisit rate. However, the azimuth and elevation resolution of scanning radar is limited by the size of the antenna aperture. Large-scale antennas also face technical bottlenecks in terms of hardware implementation and signal processing complexity. Therefore, it is necessary to explore new technical means to overcome the limitations imposed by antenna parameters on the imaging resolution of scanning radar.

[0003] In recent years, some new methods have been proposed for super-resolution imaging of two-dimensional scanning radar. The paper "Deqing Mao, Yongchao Zhang, Yin Zhang, Xingyu Tuo, Haiguang Yang, Yulin Huang, and Jianyu Yang, 'Super-resolution imaging for real aperture radar by two-dimensional inverse fifiltering,' in 2019 6" is relevant. thThe paper "Asia-Pacifific Conference on Synthetic Aperture Radar (APSAR). IEEE, 2019, pp. 1–4" proposes an FFT-based frequency domain inverse filtering method, which can obtain super-resolution imaging results at a low complexity cost, providing the potential for three-dimensional imaging of targets, but its improvement in two-dimensional resolution is limited. The paper "Xingyu Tuo, Yu Xia, Yin Zhang, Junyu Zhu, Yongchao Zhang, Yulin Huang, and Jianyu Yang, 'Super-resolution imaging for real aperture radar by two-dimensional deconvolution,' in 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS. IEEE, 2021, pp. 6630–6633" proposes an ADMM-based sparse method, which further improves the imaging resolution of real aperture radar in the azimuth and elevation directions, but its complexity is relatively high. The paper "Jiawei Luo, Yongchao Zhang, Yin Zhang, Yulin Huang, and Jianyu Yang, 'Two-dimensional super-resolution imaging for real aperture radar by iterative adaptive...'" The approach, 'in 2022 IEEE Radar Conference (RadarConf22). IEEE, 2022, pp.1–5,' proposes a novel two-dimensional super-resolution imaging method for scanning radar by introducing an iterative adaptive method (IAA), which has better two-dimensional angular resolution performance. However, this method has extremely high computational complexity and includes manually adjusted user parameters, resulting in poor robustness and making it unsuitable for practical engineering applications. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning, which solves the problems of high computational complexity and poor robustness of existing super-resolution methods.

[0005] The technical solution of this invention is: a two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning, the specific steps of which are as follows:

[0006] Step 1: Construct a two-dimensional scanning radar signal model with azimuth and elevation;

[0007] Construct an azimuth-elevation two-dimensional scanning radar system.

[0008] Define the region of interest as Ω. The echo of the target within Ω after pulse compression is represented as follows:

[0009]

[0010] Where θ represents the azimuth angle variable. τ represents the elevation angle variable, τ represents the range dimension time variable, and κ represents an amplitude constant related to the radar system parameters. This indicates a location located at radar coordinates. The effective scattering coefficient of the target, with an azimuth angle of θ0 and an elevation angle of θ0. The slant range is R0; a(·) represents the two-dimensional antenna pattern function. sinc(·) represents the envelope of the pulse compression response function, B represents the transmitted signal bandwidth, and c represents the electromagnetic wave propagation speed.

[0011] Considering only one distance cell and taking additive noise into account, the echo is represented as:

[0012]

[0013] Where * denotes a two-dimensional convolution operation, This indicates the antenna radiation pattern. Represents the target scattering coefficient. This represents additive Gaussian noise.

[0014] The above equation can be simplified and rewritten in discrete form as follows:

[0015] Y = AXB + N (3)

[0016] in, This represents the echo matrix, where M and N represent the number of sampling points in the azimuth and elevation dimensions of the echo, respectively. Represents the target scattering coefficient matrix; Represents the noise matrix; and These represent the azimuth and elevation pattern modulation matrices, respectively. K1 and K2 represent the number of sampling points, respectively, representing the complex number field.

[0017] A is specifically represented as:

[0018]

[0019] in, Let L1 represent the number of sampling points in the azimuth antenna pattern, and L2 represent the number of sampling points in the azimuth antenna pattern. Let L2 be the number of sampling points in the elevation antenna pattern, then B can be written as:

[0020]

[0021] in, These represent the sampling points for the elevation antenna pattern. The number of sampling points M, N, K1, K2, L1, and L2 satisfy the following relationship:

[0022]

[0023] Using the Kronecker product, the echo model is transformed into a matrix-vector form, as follows:

[0024] y = Fx + n (7)

[0025] Wherein, the vector forms y, F, x, and n of Y, F, X, and N satisfy the following relationships:

[0026]

[0027]

[0028]

[0029]

[0030] Where vec(·) denotes vectorization, This represents the Kronecker product, (·). T This represents the transpose operation of a matrix or vector.

[0031] Step 2: Establish the sparse Bayesian learning optimization objective function under the maximum a posteriori framework;

[0032] The maximum a posteriori (MAP) method constructs a cost function, which, by taking its negative logarithm, can be simply expressed as:

[0033]

[0034] Where σ represents the power of zero-mean additive Gaussian noise, q represents the sparsity parameter, and 0 < q ≤ 1, x i Let x represent the i-th element.

[0035] Step 3: Adaptive iterative estimation of target scattering;

[0036] Minimize the cost function J, and differentiate J with respect to x, and we get:

[0037]

[0038] in,(·) t Let Π represent the number of iterations, Π = diag{η}, and η i =|x i | 2-q ,i=1,…,K1K2,η i Let represent the i-th element of vector η; (·) H This represents the conjugate transpose operation of a matrix or vector; then a heuristic method is used to solve it, as shown in the following equation:

[0039]

[0040] The iterative estimates of x and σ are then obtained as follows:

[0041]

[0042]

[0043] Where I represents a unit vector.

[0044] Step 4: Two-dimensional joint iterative estimation of target scattering;

[0045] Define matrix Σ as follows:

[0046]

[0047] Where, Σ ij Let X represent the element in the i-th row and j-th column of matrix Σ. ij Let represent the element in the i-th row and j-th column of X. The relationship between Π and Σ is expressed as:

[0048]

[0049] The above relations and Substituting into the iterative estimation in step three, let u (t) =(FΠ) (t) F H +σ (t) I) -1 y, used to simplify equation (12), yields:

[0050]

[0051] Among them, vec(U (t) )=u (t) .

[0052] Using the properties of the Kronecker product, the iterative expression is equivalent to the following:

[0053]

[0054] x (t+1) =diag{vec(Σ (t) )}vec(A H U (t) B H (16)

[0055] Then, based on the properties of the Hadamard matrix, equation (16) can be rewritten as:

[0056] x (t+1) =vec(Σ (t) ⊙A H U (t) B H (17)

[0057] Let vec(X) (t+1) )=x (t+1) The super-resolution iterative equation for the scattering coefficient of the two-dimensional target is obtained as follows:

[0058]

[0059] Step 5: Introduce the conjugate gradient method to reduce computational complexity;

[0060] In the two-dimensional coefficient super-resolution iterative equation, U (t) vectorized form u (t) If the least squares form is satisfied, then the two-dimensional conjugate gradient method is used for fast iterative updates.

[0061] First, the iteration variables in the two-dimensional conjugate gradient method are initialized as follows:

[0062] U0=0, β0=0, R0=Y, P0=0, ρ0=||R0|| F 2 (19)

[0063] Where U0, β0, R0, P0, ρ0 represent the initial values ​​of the intermediate variables introduced by the conjugate gradient algorithm, ||·|| F This represents the Frobenius norm of the matrix.

[0064] Substitute the above intermediate variable initial values ​​into the following iterative process:

[0065] P l+1 =R l +β l P l

[0066] W l =A(∑⊙A) H P l+1 B H )B+σ( t)P l+1

[0067] α l =ρ l / (1 M T (P l+1 C ⊙W l )1 N )

[0068] U l+1 =U l +α l P l+1

[0069] R l+1 =R l -α l W l

[0070] ρ l+1 =||R l+1 || F 2

[0071] β l+1 =ρ l+1 / ρ l (20)

[0072] Among them, 1 M Let R represent a vector of dimension M. l Let P represent the gradient variable in the l-th iteration. l U represents the search direction in the l-th iteration. l Let β represent the vector obtained after l iterations of the conjugate gradient algorithm. l Let α represent the conjugate gradient iteration factor for the l-th iteration. l W represents the step size of the l-th iteration. l and ρ l This represents an intermediate variable introduced during the iteration process, (·). C Represents the complex conjugate operation of a matrix or vector.

[0073] When the iteration process converges, the output is as follows:

[0074] U (t) =U l+1 (twenty one)

[0075] The iterative estimation equation for the noise of the two-dimensional scanning radar is obtained as follows:

[0076]

[0077] Using X (0) =A H YBH As an initialization result.

[0078] Finally, adaptive sparse two-dimensional super-resolution imaging of scanning radar and other devices is achieved by processing the conjugate gradient algorithm and iteratively solving the two-dimensional scattering estimation of the target using the Kronecker product property.

[0079] The beneficial effects of this invention are as follows: First, the method of this invention constructs an azimuth-elevation two-dimensional scanning radar signal model. Then, based on the maximum a posteriori criterion within a Bayesian framework, a sparse optimization objective function is established regarding target scattering and environmental noise. Finally, the conjugate gradient algorithm and the Kronecker product property are used to accelerate the iterative estimation of target scattering and noise power, achieving adaptive sparse two-dimensional super-resolution imaging of the scanning radar. This invention solves the problems of high complexity and poor noise robustness of existing techniques. Compared with existing two-dimensional super-resolution methods, it not only has lower computational complexity but also stronger robustness and excellent noise adaptability, enabling adaptive two-dimensional scanning radar super-resolution imaging under low signal-to-noise ratio conditions. Attached Figure Description

[0080] Figure 1 This is a flowchart of a two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning, according to the present invention.

[0081] Figure 2 This is the original scene diagram of the two-dimensional scanning radar in an embodiment of the present invention.

[0082] Figure 3 This is a two-dimensional antenna radiation pattern in an embodiment of the present invention.

[0083] Figure 4 This is a real-beam two-dimensional imaging result diagram with SNR=20dB in an embodiment of the present invention.

[0084] Figure 5 This is a real-beam two-dimensional imaging result diagram under SNR=0dB in an embodiment of the present invention.

[0085] Figure 6 This is a two-dimensional imaging result of IAA (λ=0.1) under SNR=20dB in an embodiment of the present invention.

[0086] Figure 7 This is a two-dimensional imaging result of IAA (λ=0.1) under SNR=0dB in an embodiment of the present invention.

[0087] Figure 8 This is a two-dimensional imaging result of the method of the present invention at an SNR of 20dB in an embodiment of the present invention.

[0088] Figure 9This is a two-dimensional imaging result of the method of the present invention with SNR=0dB in an embodiment of the present invention. Detailed Implementation

[0089] 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.

[0090] like Figure 1 The flowchart of a two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning according to the present invention is shown below. The specific steps are as follows:

[0091] Step 1: Construct a two-dimensional scanning radar signal model with azimuth and elevation;

[0092] In this embodiment, the original scene of the two-dimensional scanning radar is as follows: Figure 2 As shown. In the azimuth-elevation two-dimensional scanning radar signal model, the azimuth angle θ ranges from -10° to 10°, and the elevation angle... The value range is -10° to 10°, the initial azimuth scan rate is 20° / s, the beamwidth is 2°, the PRF is 100Hz, the elevation scan rate is 20° / s, and θ0 is... R0 and R0 represent the initial values ​​of the above variables within the specified range, respectively, τ represents the distance dimension and time variable, and c represents the electromagnetic wave propagation speed.

[0093] Antenna pattern as follows Figure 3 As shown. The echo of the target in the aforementioned region after pulse compression can be expressed as:

[0094]

[0095] Wherein, κ represents an amplitude constant related to the radar system parameters; This indicates a location located at radar coordinates. The effective scattering coefficient of the target; a(·) represents the two-dimensional antenna pattern function; sinc(·) represents the envelope of the pulse compression response function; and B represents the bandwidth of the transmitted signal.

[0096] Considering only one distance cell and taking additive noise into account, the echo is represented as:

[0097]

[0098] Where * denotes a two-dimensional convolution operation, This indicates the antenna radiation pattern. Represents the target scattering coefficient. This represents additive Gaussian noise.

[0099] The above equation can be simplified and rewritten in discrete form as follows:

[0100] Y = AXB + N (3)

[0101] in, This represents the echo matrix, where M and N represent the number of sampling points in the azimuth and elevation dimensions of the echo, respectively. Represents the target scattering coefficient matrix; Represents the noise matrix; and These represent the azimuth and elevation pattern modulation matrices, respectively. K1 and K2 represent the number of sampling points, respectively, representing the complex number field.

[0102] A is specifically represented as:

[0103]

[0104] in, Let L1 represent the number of sampling points in the azimuth antenna pattern, and L2 represent the number of sampling points in the azimuth antenna pattern. Let L2 be the number of sampling points in the elevation antenna pattern, then B can be written as:

[0105]

[0106] in, These represent the sampling points for the elevation antenna pattern. The number of sampling points M, N, K1, K2, L1, and L2 satisfy the following relationship:

[0107]

[0108] Using the Kronecker product, the echo model is transformed into a matrix-vector form, as follows:

[0109] y = Fx + n (7)

[0110] Wherein, the vector forms y, F, x, and n of Y, F, X, and N satisfy the following relationships:

[0111]

[0112]

[0113]

[0114]

[0115] Where vec(·) denotes vectorization, This represents the Kronecker product, (·). T This represents the transpose operation of a matrix or vector.

[0116] Step 2: Establish the sparse Bayesian learning optimization objective function under the maximum a posteriori framework;

[0117] The maximum a posteriori (MAP) method constructs a cost function, which, by taking its negative logarithm, can be simply expressed as:

[0118]

[0119] Where σ represents the power of zero-mean additive Gaussian noise, q represents the sparsity parameter, and 0 < q ≤ 1, x i Let x represent the i-th element.

[0120] Step 3: Adaptive iterative estimation of target scattering;

[0121] Minimize the cost function J, and differentiate J with respect to x, and we get:

[0122]

[0123] in,(·) t Let Π represent the number of iterations, Π = diag{η}, and η i =|x i | 2-q ,i=1,…,K1K2,η i Let represent the i-th element of vector η; (·) H This represents the conjugate transpose operation of a matrix or vector; then a heuristic method is used to solve it, as shown in the following equation:

[0124] [F H F+σ (t) (Π( t) ) -1 ]xF H y = 0 (11)

[0125] The iterative estimates of x and σ are then obtained as follows:

[0126] x (t+1) =Π (t) F H (FΠ (t) F H +σ (t) I) -1 y

[0127]

[0128] Where I represents a unit vector.

[0129] Step 4: Two-dimensional joint iterative estimation of target scattering;

[0130] Define matrix Σ as follows:

[0131]

[0132] Where, Σ ij Let X represent the element in the i-th row and j-th column of matrix Σ. ij Let represent the element in the i-th row and j-th column of X. The relationship between Π and Σ is expressed as:

[0133]

[0134] The above relations and Substituting into the iterative estimation in step three, let u (t) =(FΠ) (t) F H +σ (t) I) -1 y, used to simplify equation (12), yields:

[0135] x (t+1) =diag{vec(Σ (t) )}vec(A H U (t) B H (15)

[0136] Among them, vec(U (t) )=u (t) .

[0137] Using the properties of the Kronecker product, the iterative expression is equivalent to the following:

[0138]

[0139] x (t+1) =diag{vec(Σ (t) )}vec(A H U (t) B H (16)

[0140] Then, based on the properties of the Hadamard matrix, equation (16) can be rewritten as:

[0141]

[0142] Let vec(X) (t+1) )=x (t+1) The super-resolution iterative equation for the scattering coefficient of the two-dimensional target is obtained as follows:

[0143]

[0144] Step 5: Introduce the conjugate gradient method to reduce computational complexity;

[0145] In the two-dimensional coefficient super-resolution iterative equation, U(t) vectorized form u (t) If the least squares form is satisfied, then the two-dimensional conjugate gradient method is used for fast iterative updates.

[0146] First, the iteration variables in the two-dimensional conjugate gradient method are initialized as follows:

[0147] U0=0, β0=0, R0=Y, P0=0, ρ0=||R0|| F 2 (19)

[0148] Where U0, β0, R0, P0, ρ0 represent the initial values ​​of the intermediate variables introduced by the conjugate gradient algorithm, ||·|| F This represents the Frobenius norm of the matrix.

[0149] Substitute the above intermediate variable initial values ​​into the following iterative process:

[0150] P l+1 =R l +β l P l

[0151] W l =A(∑⊙A) H P l+1 B H )B+σ (t) P l+1

[0152] α l =ρ l / (1 M T (P l+1 C ⊙W l )1 N )

[0153] U l+1 =U l +α l P l+1

[0154] R l+1 =R l -α l W l

[0155] ρ l+1 =||R l+1 || F 2

[0156] β l+1 =ρ l+1 / ρl (20)

[0157] Among them, 1 M Let R represent a vector of dimension M. l Let P represent the gradient variable in the l-th iteration. l U represents the search direction in the l-th iteration. l Let β represent the vector obtained after l iterations of the conjugate gradient algorithm. l Let α represent the conjugate gradient iteration factor for the l-th iteration. l W represents the step size of the l-th iteration. l and ρ l This represents an intermediate variable introduced during the iteration process, (·). C Represents the complex conjugate operation of a matrix or vector.

[0158] When the iteration process converges, the output is as follows:

[0159] U (t) =U l+1 (twenty one)

[0160] The iterative estimation equation for the noise of the two-dimensional scanning radar is obtained as follows:

[0161]

[0162] Since the azimuth and elevation pattern modulation matrices A and B in the super-resolution problem of two-dimensional scanning radar are not full rank, initializing with the minimum norm solution will cause serious noise amplification problems. Therefore, X is used instead. (0) =A H YB H As an initialization result.

[0163] Finally, through the processing of the conjugate gradient algorithm in the above steps and the iterative solution of the target's two-dimensional scattering estimation using the Kronecker product property, adaptive sparse two-dimensional super-resolution imaging of scanning radar and the like is realized.

[0164] In this embodiment, the simulation results show that, Figure 4 and Figure 7 In the real beam results shown, the energy of three points that are close to each other overlaps and is difficult to distinguish. Figure 5 and 8 As shown in the IAA imaging results, when the signal-to-noise ratio (SNR) is 20 dB, compared to Figure 4 The real-beam test showed that this method can effectively distinguish targets, but it has high computational complexity and an average runtime of 281.18 seconds. The parameter λ = 0.1 was manually adjusted after multiple tests. For the same parameters, when SNR = 0 dB, the method cannot distinguish targets, indicating poor robustness. Figure 5 and Figure 6 , Figure 8 and Figure 9 The two sets of comparisons show that the method of this invention utilizes the sparse prior features of the target, and its resolution is slightly higher than that of IAA. Furthermore, the method of this invention has low computational complexity, with an average running time of only 0.11s, and good noise adaptability; it can achieve good target resolution at SNRs of 20dB and 0dB without manual parameter adjustment. Therefore, the method of this invention possesses excellent two-dimensional resolution performance and parameter adaptive capability.

[0165] Regarding the algorithm complexity, the method of this invention requires J1 iterations, and the conjugate gradient algorithm requires J2 iterations. The initial computational complexity is MK2(K1+N)+K1K2, where K1K2 is in equation (13), MK2(K1+N)+K1K2 is in equation (18), MK2(K1+N)+MN is in equation (22), and the computational complexity of the conjugate gradient algorithm is J2[2MK2(K1+N)+8MN+K1K2]. Therefore, the total computational complexity of the method of this invention is O(J1J2MK2(K1+N)), which is far lower than the computational complexity required by existing IAA algorithms. O represents a higher-order infinitesimal, N θ , These represent the number of azimuth and elevation sampling points for the echo, respectively.

[0166] In summary, for two-dimensional scanning radar, the present invention provides a two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning, which can significantly reduce the computational complexity of existing methods and has strong robustness, enabling it to adapt to two-dimensional scanning radar super-resolution imaging under low signal-to-noise ratio conditions.

[0167] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make related modifications or applications based on the super-resolution imaging method proposed in this invention, but the relevant knowledge remains within the scope of protection of this invention.

Claims

1. A two-dimensional super-resolution imaging method for scanning radar based on Bayesian sparse learning, the specific steps of which are as follows: Step 1: Construct a two-dimensional scanning radar signal model with azimuth and elevation; Construct a two-dimensional azimuth-elevation scanning radar system; Define the region of interest as Ω. The echo of the target within Ω after pulse compression is represented as follows: in, θ represents the azimuth angle variable. τ represents the elevation angle variable, τ represents the range dimension time variable, and κ represents an amplitude constant related to the radar system parameters. This indicates a location located at radar coordinates. The effective scattering coefficient of the target, with an azimuth angle of θ0 and an elevation angle of θ0. The slant range is R0; a(·) represents the two-dimensional antenna pattern function; sinc(·) represents the envelope of the pulse compression response function; B represents the transmitted signal bandwidth; and c represents the electromagnetic wave propagation speed. Considering only one distance cell and taking additive noise into account, the echo is represented as: Where * denotes a two-dimensional convolution operation, This indicates the antenna radiation pattern. Represents the target scattering coefficient. This represents additive Gaussian noise; The above equation can be simplified and rewritten in discrete form as follows: Y = AXB + N (3) in, This represents the echo matrix, where M and N represent the number of sampling points in the azimuth and elevation dimensions of the echo, respectively. Represents the target scattering coefficient matrix; Represents the noise matrix; and These represent the azimuth and elevation pattern modulation matrices, respectively. Let K1 and K2 represent the complex number field, and K1 and K2 represent the number of sampling points; A is specifically represented as: in, Let L1 represent the number of sampling points in the azimuth antenna pattern; let L2 represent the number of sampling points in the elevation antenna pattern, then B can be written as: in, This represents the sampling points of the elevation antenna pattern; the number of sampling points M, N, K1, K2, L1, and L2 satisfy the following relationship: Using the Kronecker product, the echo model is transformed into a matrix-vector form, as follows: y = Fx + n (7) Wherein, the vector forms y, F, x, and n of Y, F, X, and N satisfy the following relationships: Where vec(·) denotes vectorization, This represents the Kronecker product, (·). T The transpose operation represents a matrix or vector; Step 2: Establish a sparse Bayesian learning optimization objective function within the maximum a posteriori framework; The maximum a posteriori (MAP) method constructs a cost function, which, by taking its negative logarithm, can be simply expressed as: Where σ represents the power of zero-mean additive Gaussian noise, q represents the sparsity parameter, and 0 < q ≤ 1, x i This represents the i-th element of x; Step 3: Adaptive iterative estimation of target scattering; Minimize the cost function J, and differentiate J with respect to x, and we get: in,(·) t Let Π represent the number of iterations, Π = diag{η}, and η i =|x i | 2-q ,i=1,…,K1K2,η i Let represent the i-th element of vector η; (·) H This represents the conjugate transpose operation of a matrix or vector; then a heuristic method is used to solve it, as shown in the following equation: [F H F+s (t) (P (t) ) -1 ]xF H y=0 (11) The iterative estimates of x and σ are then obtained as follows: x (t+1) =P (t) F H (FΠ (t) F H +s (t) I) -1 y Where I represents a unit vector; Step 4: Two-dimensional joint iterative estimation of target scattering; Define matrix Σ as follows: S ij =|X ij | 2-q i=1,…,K1,j=1…,K2 (13) Where, Σ ij Let X represent the element in the i-th row and j-th column of matrix Σ. ij Represents the element in the i-th row and j-th column of X; the relationship between Π and Σ is expressed as: Π=diag{vec(Σ)} (14) The above relations and Substituting into the iterative estimation in step three, let u (t) =(FΠ) (t) F H +σ ( t)I) -1 y, used to simplify equation (12), yields: x (t+1) =diag{vec(Σ (t ))}thing(A H U (t) B H ) (15) Among them, vec(U (t) ) = u (t) ; Using the properties of the Kronecker product, the iterative expression is equivalent to the following: x (t+1) =diag{vec(Σ (t) )}thing(A H U (t) B H ) (16) Then, based on the properties of the Hadamard matrix, equation (16) can be rewritten as: x (t+1) =vec(Σ (t) ⊙A H U (t) B H ) (17) Let vec(X) (t+1) )=x (t+1) The super-resolution iterative equation for the scattering coefficient of the two-dimensional target is obtained as follows: X (t+1) =S (t) ⊙A H U (t) B H (18) Step 5: Introduce the conjugate gradient method to reduce computational complexity; In the two-dimensional coefficient super-resolution iterative equation, U (t) vectorized form u (t) If the least squares form is satisfied, then the two-dimensional conjugate gradient method is used for fast iterative updates; First, the iteration variables in the two-dimensional conjugate gradient method are initialized as follows: U0=0,β0=0,R0=Y,P0=0,ρ0=||R0|| F 2 (19) Where U0, β0, R0, P0, ρ0 represent the initial values ​​of the intermediate variables introduced by the conjugate gradient algorithm, ||·|| F Denotes the Frobenius norm of a matrix; Substitute the above intermediate variable initial values ​​into the following iterative process: P.S l+1 ZR l +β l P.S l W l =A(∑⊙A H P l+1 B H )B+σ (t) P l+1 a l =ρ l / (1 M T (P l+1 C ⊙W l )1 N ) IN l+1 =U l +α l P l+1 R l+1 =R l -a l W l r l+1 =||R l+1 || F 2 b l+1 =ρ l+1 / r l (20) Among them, 1 M Let R represent a vector of dimension M. l Let P represent the gradient variable in the l-th iteration. l U represents the search direction in the l-th iteration. l Let β represent the vector obtained after l iterations of the conjugate gradient algorithm. l Let α represent the conjugate gradient iteration factor for the l-th iteration. l W represents the step size of the l-th iteration. l and ρ l This represents an intermediate variable introduced during the iteration process, (·). C Represents the complex conjugate operation of a matrix or vector; When the iteration process converges, the output is as follows: IN (t) =U l+1 (21) The iterative estimation equation for the noise of the two-dimensional scanning radar is obtained as follows: Using X (0) =A H YB H As an initialization result; Finally, adaptive sparse two-dimensional super-resolution imaging of scanning radar and other devices is achieved by processing the conjugate gradient algorithm and iteratively solving the two-dimensional scattering estimation of the target using the Kronecker product property.

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