Phased array radar sparse super-resolution imaging method based on antenna pattern correction

Abstract

The invention discloses a phased array radar sparse super-resolution imaging method based on antenna pattern correction, which comprises the following steps of: firstly, combining Doppler phase information under a motion platform to construct a reconvolution model of a phased array radar, then dynamically adjusting the number of sampling points of an antenna pattern according to a scanning angle, and correcting an antenna pattern matrix; and finally, based on a covariance criterion, proposing a weighted sparse iteration solution framework, and realizing sparse target reconstruction. According to the method, the scanning process of the phased array radar is accurately represented by correcting an antenna pattern matrix, and a weighted sparse iteration solving framework based on a covariance fitting criterion is provided to realize sparse target reconstruction under the condition of low signal-to-noise ratio. The problems of model mismatch caused by broadening of an antenna pattern along with a scanning angle in the electronic scanning process of the phased array radar and imaging distortion caused by Doppler phase errors of a high-speed motion platform are solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a phased array radar sparse super-resolution imaging method based on antenna pattern correction. BACKGROUND

[0002] Phased array radars are widely used in marine monitoring, target tracking, aircraft autonomous landing, weather forecasting and other fields due to their efficient electronic scanning capability. However, due to the limitation of the physical aperture of the antenna, the azimuth resolution is low, and it is difficult to meet the demand of high-resolution imaging. In terms of signal processing, the azimuth echo signal can be modeled as the convolution of the antenna pattern and the target scattering coefficient, and the azimuth resolution can be improved through convolution inversion.

[0003] Currently, researchers have proposed various deconvolution methods based on different criteria. The literature “J. Yang, Y. Kang, Y. Zhang, Y. Huang, and Y. Zhang, ‘A Bayesian angular super resolution method with lognormal constraint for sea surface target’, IEEE Access, vol. 8, pp. 13419-13428, 2020” proposes a deconvolution method based on the maximum a posteriori (MAP) criterion, which combines the prior constraints of Rayleigh distribution and lognormal distribution to achieve super-resolution imaging of sea surface targets, but its performance depends on the prior assumption of the statistical characteristics of background noise. The literature “A. Gambardella and M. Migliaccio, ‘On the superresolution of microwave scanning radiometer measurements’, IEEE Geoscience and Remote Sensing Letters, vol. 5, no. 4, pp. 796-800, 2008” proposes a Tikhonov regularization method based on convex optimization theory, but the excessive smoothness of the L2 norm limits the resolution improvement of this method. The literature “X. Tuo, Y. Zhang, Y. Huang, and J. Yang, ‘Fast sparse-tsvd super resolution method of real aperture radar forward-looking imaging’, IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 8, pp. 6609-6620, 2020” proposes a super-resolution imaging method combining sparse L1 regularization and truncated singular value decomposition (TSVD), which effectively suppresses noise while improving resolution.

[0004] Although the above super-resolution imaging methods improve the azimuth resolution to some extent, existing methods generally assume that the antenna pattern remains unchanged throughout the scanning process, ignoring the spatial variation of the electronic scanning radar antenna pattern. In addition, most super-resolution methods only use the amplitude information of the echo signal, without fully considering the Doppler phase information, resulting in imaging distortion under high-speed moving platforms. SUMMARY

[0005] To solve the above technical problems, the application provides a phased array radar sparse super-resolution imaging method based on antenna pattern correction, which corrects an antenna pattern matrix to accurately represent a scanning process of the phased array radar, and proposes a weighted sparse iterative solving framework based on a covariance fitting criterion to realize sparse target reconstruction under a low signal-to-noise ratio condition.

[0006] The technical scheme adopted by the application is as follows: a phased array radar sparse super-resolution imaging method based on antenna pattern correction, and the specific steps are as follows:

[0007] S1, obtaining echo data for pretreatment and phased array radar echo modeling;

[0008] The phased array radar transmits a linear frequency modulation (LFM) pulse signal at a fixed frequency and scans a target region, and the radar platform moves along a straight line at a speed V; at time t, the slant range R(t) between the target imaging point and the radar platform is expressed as follows:

[0009]

[0010] Wherein, R0 represents the initial slant range between the radar and the target at time 0, θ represents the azimuth angle of the target relative to the radar at time t, represents the pitch angle of the target relative to the radar at time t.

[0011] Then, Taylor series expansion is performed, and the approximate expression of R(t) is as follows:

[0012]

[0013] The expression of the linear frequency modulation signal y(τ) transmitted by the radar is as follows:

[0014]

[0015] Wherein, rect(·) represents a rectangular window function, τ represents a distance time vector, T p represents a pulse width, f c represents a carrier frequency, K c represents a linear frequency modulation slope.

[0016] The expression of the target echo signal y P (τ,t) is as follows:

[0017]

[0018] Wherein, s P represents a target scattering coefficient, h(t) represents a phased array radar two-way antenna pattern function, τ d =2R(t) / c represents echo delay, and c represents light speed.

[0019] Then the target echo signal is pulse compressed and motion compensated, and the echo signal y(R, θ) can be expressed as follows:

[0020]

[0021] Wherein, R represents the distance between the radar and the target line-of-sight direction, s(R, θ) represents the backscattering coefficient of the target, h(θ-θ0) represents the two-way antenna pattern function, θ0 represents the pointing azimuth angle of the center of the radar beam, B represents the bandwidth of the signal, ω represents the angular velocity of the radar beam scanning, and λ represents the wavelength of the signal. represents the Doppler phase.

[0022] The Doppler phase influence is then summarized in the form of a matrix D, and the expression is as follows:

[0023]

[0024] Wherein, N represents the number of azimuth antenna pattern sampling points, [t1, t2, … t N ] represents the azimuth sampling time, [θ1, θ2, … θ N ] represents the azimuth sampling angle, R(t n , θ n ) represents the discrete sampling points of the distance history, and n = 1, 2, …, N.

[0025] In radar imaging, the azimuth echo signal is modeled as the convolution of the target scattering coefficient and the antenna pattern, and the matrix expression is as follows:

[0026] y = Hs + n (7)

[0027] Wherein, y represents the echo signal received by the radar, H represents the antenna pattern convolution matrix, s represents the target scattering coefficient vector, and n represents the noise.

[0028] Then, after introducing the Doppler phase matrix, the modified expression of formula (7) is as follows:

[0029] y = (H⊙D)s + n (8)

[0030] Wherein, ⊙ represents the matrix point multiplication operation.

[0031] S2, based on step S1, correcting the antenna pattern distortion;

[0032] Without considering the spatial variation of the antenna pattern, the ideal antenna pattern convolution matrix expression is as follows:

[0033]

[0034] Wherein, K represents the number of azimuth sampling points, [h1, h2, …, hL ] represents the sampling vector of the antenna pattern, L represents the number of antenna pattern sampling points, and the calculation expression is as follows:

[0035]

[0036] where θ B represents the main lobe beam width of the antenna, ω represents the equivalent scanning speed of the array antenna, and PRF represents the pulse repetition frequency.

[0037] Actual antenna beam width Affected by the scanning angle θ i , resulting in changes in the number of pattern sampling points L(θ i ), and the expression is as follows:

[0038]

[0039] where θ i ∈ [θ1, θ2, … θ N ], θ1, θ2, … θ N represent the discrete angle sampling of the scanning scene.

[0040] Then the expression of the corrected antenna pattern matrix is as follows:

[0041]

[0042] where h i,j represents the jth element value of the antenna pattern sampling vector in the ith scanning.

[0043] Considering the spatial variation of the antenna pattern and the influence of the Doppler phase, the expression of the echo signal model of the phased array radar is as follows:

[0044]

[0045] Finally, let simplify the echo signal model to the following expression:

[0046] y = As + n (14)

[0047] S3, define the objective function, construct a sparse iterative solution framework to obtain the optimal solution of the objective function;

[0048] First, define the objective function as follows:

[0049]

[0050] where s represents the target scattering coefficient vector, represents the reconstructed target scattering coefficient vector, s nThe nth element of s, and δ represents the noise power, which is subject to uniform distribution, and 0≤δ<∞, represents the estimated value of the noise power, q represents the target sparsity control parameter, and 0<q<1.

[0051] The target sparsity prior probability density function expression is as follows:

[0052]

[0053] Wherein, f(s) represents the sparsity prior probability density function.

[0054] Based on the Bayesian criterion and variable separation principle, the sparse iterative solution framework can be decomposed into two sub-problems of s and δ for iterative solution. Assuming that the initial estimates of s and δ are known, 0 is taken, and then the optimal solution of the objective function is obtained by solving the s and δ problems through cyclic iteration, and the specific steps are as follows:

[0055] 1) Fixing δ, solving s:

[0056] Assuming that the result of the kth iteration has been obtained s k , δ k . The objective function expression is as follows:

[0057]

[0058] Solving the partial derivative of the cost function with respect to s, the k+1th iteration result of s is obtained, and the expression is as follows:

[0059]

[0060] Wherein, () H represents the conjugate transpose operation, P=diag(p), p=[p1,p2,p3,...,p N ] T , () T represents the transpose operation, and p n The expression is as follows:

[0061] p n =|s n | 2-q (19)

[0062] Let P=P k , then P k The specific expression is as follows:

[0063]

[0064] Then equation (18) can be converted into the following expression:

[0065] [A H A+δk (P k ) -1 ]s-A H y = 0 (21)

[0066] The k+1th iteration result s of s is obtained, and the expression is as follows k+1

[0067]

[0068] 2) Fix s, solve δ:

[0069] Similarly, the k+1th iteration result is obtained by taking the first-order partial derivative of the cost function with respect to δ, and the expression is as follows:

[0070]

[0071] The k+1th iteration result δ of δ is obtained, and the expression is as follows:

[0072]

[0073] S4, based on step S3, introduce a weighting strategy and construct a sparse iterative solution framework, complete the iterative update and output the super-resolution result;

[0074] The weighting strategy is introduced to improve the target reconstruction quality, and the autocorrelation matrix R of the radar echo matrix is defined as follows:

[0075]

[0076] Where, () H represents the conjugate transpose operation, A H represents the conjugate transpose of the antenna pattern matrix A, y H represents the conjugate transpose of the echo signal y, P = diag(p) represents the signal power matrix, and the expression is as follows:

[0077]

[0078] Where, represents the signal power estimation value of the k+1th iteration, represents the signal power estimation value of the kth iteration, represents the conjugate transpose of the nth column of matrix A, represents the signal power estimation value of the kth iteration The autocorrelation matrix constructed, represents the weight vector.

[0079] The weighting strategy is combined with the sparse iterative solution framework, and the weight vector is defined as follows:

[0080] ​ω n = (1 / p n ) q (28)

[0081] where ω n represents a weight vector.

[0082] Combining formula (20), formula (27) and formula (28), the iterative updating expression of the target signal power is as follows:

[0083]

[0084] After the iteration is terminated, the output of the last iteration result s k+1 is taken as the super-resolution output result.

[0085] Advantages of the present application: the method of the present application firstly constructs a complex convolution model of a phased array radar in combination with Doppler phase information under a motion platform, then dynamically adjusts the sampling point number of an antenna pattern according to a scanning angle, corrects an antenna pattern matrix, so as to accurately represent the scanning process of the phased array radar, finally proposes a weighted sparse iterative solving framework based on a covariance criterion, so as to realize sparse target reconstruction. The method of the present application corrects the antenna pattern matrix, so as to accurately represent the scanning process of the phased array radar, and proposes a weighted sparse iterative solving framework based on a covariance fitting criterion, so as to realize sparse target reconstruction under a low signal-to-noise ratio condition, and solves the problems of model mismatch caused by the antenna pattern expansion with the scanning angle in the electronic scanning process of the phased array radar, and imaging distortion caused by the Doppler phase error of the high-speed motion platform. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 A flow chart of a phased array radar sparse super-resolution imaging method based on antenna pattern correction according to the present application.

[0087] Figure 2 A schematic diagram of a phased array radar motion model in an embodiment of the present application.

[0088] Figure 3 A schematic diagram of an ideal antenna pattern matrix in an embodiment of the present application.

[0089] Figure 4 A schematic diagram of an improved antenna pattern convolution process in an embodiment of the present application.

[0090] Figure 5 A point target simulation original scene diagram in an embodiment of the present application.

[0091] Figure 6 A schematic diagram of a phased array radar antenna pattern matrix in an embodiment of the present application.

[0092] Figure 7 Schematic diagram of point target reconstruction results when the signal-to-noise ratio is 5dB in an embodiment of the present invention. DETAILED DESCRIPTION

[0093] The method of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0094] like Figure 1 As shown in FIG, a flow chart of a phased array radar sparse super-resolution imaging method based on antenna pattern correction of the present invention is shown, and the specific steps are as follows:

[0095] S1. Acquire echo data for preprocessing and perform phased array radar echo modeling;

[0096] Phased array radar transmits linear frequency modulation (LFM) pulse signals at a fixed frequency and scans the target area. Its motion model is as follows: Figure 2 As shown, assume that the radar platform moves along a straight line at a speed V. At time 0, the radar platform is located at point A. At this time, the slant distance between the radar and the target imaging point P is R0, and the spatial azimuth is The horizontal azimuth angle is θ0. At time t, the radar platform arrives at point B and is aligned with the target imaging point P. K The slope distance becomes R(t), the point target P K The slant range R(t) from the radar platform is expressed as follows:

[0097]

[0098] Where R0 represents the initial slant range between the radar and the target at time 0, θ represents the azimuth of the target relative to the radar at time t, It represents the pitch angle of the target relative to the radar at time t.

[0099] Then perform Taylor series expansion, and the approximate expression of R(t) is as follows:

[0100]

[0101] Then the linear frequency modulation signal y(τ) emitted by the radar is expressed as follows:

[0102]

[0103] Where rect(·) represents the rectangular window function, τ represents the distance time vector, and T p Indicates the pulse width, f c Indicates the carrier frequency, K c Indicates the linear frequency modulation slope.

[0104] Then the target echo signal y P The expression of (τ,t) is as follows:

[0105]

[0106] where s P represents the target scattering coefficient, h(t) represents the phased array radar two-way antenna pattern function, τ d = 2R(t) / c represents the echo delay, and c represents the speed of light.

[0107] Then the target echo signal is pulse compressed and motion compensated, and the echo signal y(R, θ) can be represented as follows:

[0108]

[0109] where R represents the distance between the radar and the target line-of-sight direction, s(R, θ) represents the target backscattering coefficient, h(θ-θ0) represents the two-way antenna pattern function, θ0 represents the pointing azimuth angle of the radar beam center, B represents the signal bandwidth, ω represents the angular velocity of the radar beam scanning, and λ represents the signal wavelength. represents the Doppler phase, and under the condition of a stationary or slow-moving platform, the Doppler phase can be ignored, and when the radar platform moves at a high speed and the scanning range is large, the term cannot be ignored.

[0110] In order to accurately describe the phase modulation effect of the high-speed moving platform, the Doppler phase influence is summarized in the form of a matrix D, and the expression is as follows:

[0111]

[0112] where N represents the number of azimuth antenna pattern sampling points, [t1, t2, … t N ] represents the azimuth sampling time, [θ1, θ2, … θ N ] represents the azimuth sampling angle, R(t n , θ n ) represents the discrete sampling points of the distance history, and n = 1, 2, …, N.

[0113] In radar imaging, the azimuth echo signal is modeled as the convolution of the target scattering coefficient and the antenna pattern, and the matrix expression is as follows:

[0114] y = Hs + n (7)

[0115] where y represents the echo signal received by the radar, H represents the antenna pattern convolution matrix, s represents the target scattering coefficient vector, and n represents the noise.

[0116] Since the existing amplitude convolution model does not consider the Doppler phase information, after introducing the Doppler phase matrix, the modified expression of formula (7) is as follows:

[0117] y = (H⊙D)s + n (8)

[0118] where, ⊙ represents the matrix point multiplication operation.

[0119] S2, based on step S1, correcting the antenna pattern distortion;

[0120] Without considering the spatial variation of the antenna pattern, the ideal antenna pattern convolution matrix expression is as follows:

[0121]

[0122] where, K represents the number of azimuth sampling points, [h1, h2, …, h L ] represents the sampling vector of the antenna pattern, L represents the number of antenna pattern sampling points, the value of which is determined by the beam width, the pulse repetition frequency and the antenna scanning speed, and the calculation expression is as follows:

[0123]

[0124] where, θ B represents the main lobe beam width of the antenna, ω represents the equivalent scanning speed of the array antenna, and PRF represents the pulse repetition frequency.

[0125] The matrix H has N rows, and the i-th row represents the sampling of the antenna pattern at the i-th scan. Since the ideal antenna pattern matrix ignores the spatial variability of the antenna pattern, the model sets L as a fixed value within the scanning range. The ideal antenna pattern matrix is as shown in Figure 3 .

[0126] In practice, the antenna beam width is affected by the scanning angle θ i , resulting in a change in the number of pattern sampling points L(θ i ), and the expression is as follows:

[0127]

[0128] where, θ i ∈ [θ1, θ2, … θ N ], θ1, θ2, … θ N represent the discrete angle sampling of the scanning scene.

[0129] Then the modified antenna pattern matrix expression is as follows:

[0130]

[0131] where, h i,j represents the j-th element value of the antenna pattern sampling vector at the i-th scan. The improved antenna pattern matrix is as shown in Figure 4 .

[0132] Taking into account the spatial variation of the antenna pattern and the influence of Doppler phase, the echo signal model of the phased array radar is expressed as follows:

[0133]

[0134] Final Order The echo signal model is simplified into the following expression:

[0135] y=As+n (14)

[0136] S3. Define the objective function and build a sparse iterative solution framework to obtain the optimal solution of the objective function;

[0137] First, define the objective function expression as follows:

[0138]

[0139] Where s represents the target scattering coefficient vector, Represents the reconstructed target scattering coefficient vector, s n represents the nth element of s, δ represents the noise power, which obeys the uniform distribution and 0≤δ<∞, Represents the estimated value of noise power, q represents the target sparsity control parameter, 0<q<1.

[0140] The sparse prior probability density function of the target is expressed as follows:

[0141]

[0142] Where f(s) represents the sparse prior probability density function.

[0143] Based on the Bayesian criterion and the principle of variable separation, the sparse iterative solution framework can be decomposed into two sub-problems, s and δ, for iterative solution. Assume that the initial estimates of s and δ are known and set to 0. Then, the optimal solution of the objective function is obtained by iteratively solving the s and δ problems. The specific steps are as follows:

[0144] 1) Fix δ and solve for s:

[0145] Assume that the result s of the kth iteration has been obtained k , δ k The objective function expression is established as follows:

[0146]

[0147] Then solve the partial derivative of the cost function with respect to s, and we can get the k+1th iteration result of s, which is expressed as follows:

[0148]

[0149] where, H denotes the conjugate transpose operation, P = diag(p), p = [p1, p2, p3,..., pN]T, and N ] T , () T denotes the transpose operation, and p n The expression is as follows:

[0150] p n = |s n | 2-q (19)

[0151] For the P -1 term contained in formula (18) and s, it is not a linear mapping function relationship, and it is difficult to directly solve the value of s k+1 . Let P = P k , then P k The specific expression is as follows:

[0152]

[0153] Then formula (18) can be converted into the following expression:

[0154] [A H A+δ k (P k ) -1 ]s-A H y = 0 (21)

[0155] The k+1th iteration result s k+1 of s is obtained, and the expression is as follows

[0156]

[0157] 2) Fix s, solve δ:

[0158] By the same reasoning as step 1), the k+1th iteration result is obtained by taking the first-order partial derivative of the cost function with respect to δ, and the expression is as follows:

[0159]

[0160] The k+1th iteration result of δ is obtained, and the expression is as follows:

[0161]

[0162] S4, based on step S3, introduce a weighting strategy and construct a sparse iteration solving framework, complete iteration update and output super-resolution results;

[0163] The weighting strategy is introduced to improve the target reconstruction quality, and the autocorrelation matrix R of the radar echo matrix is defined as follows:

[0164]

[0165] wherein, H denotes the conjugate transpose operation, A H denotes the conjugate transpose of the antenna pattern matrix A, y H denotes the conjugate transpose of the echo signal y, P = diag(p) denotes the signal power matrix, and the expression is as follows:

[0166]

[0167] wherein, denotes the signal power estimation value of the k+1th iteration, denotes the signal power estimation value of the kth iteration, denotes the conjugate transpose of the nth column of the matrix A, denotes the signal power estimation according to the kth iteration the autocorrelation matrix constructed, denotes the weight vector.

[0168] As can be seen from equations (26)-(27), the calculation method of the signal power is affected by the weight vector , which determines the power intensity and helps to improve the signal-to-noise ratio and sparsity.

[0169] In order to further optimize the estimation accuracy, the above weighting strategy method is combined with the sparse iterative solution framework, and the weight vector is defined as follows:

[0170] ω n = (1 / p n ) q (28)

[0171] wherein, ω n denotes the weight vector.

[0172] Combining equations (20), (27) and (28), the iterative update expression of the target signal power is as follows:

[0173]

[0174] After the iteration is terminated, the output of the last iteration result s k+1 is combined with equation (22) as the super-resolution output result.

[0175] This embodiment further carries out simulation verification, and the effectiveness of the method of the present application is verified through simulation experiments. All steps and conclusions of the method of the present application are verified on the Matlab2022b simulation platform.

[0176] Considering the low signal-to-noise ratio condition in actual radar application, 5dB additive white Gaussian noise is added in the echo signal in the simulation to evaluate the imaging performance of different methods in the low signal-to-noise ratio environment. The simulation of one-dimensional point target is shown in FIG. 8, and the equivalent target scattering coefficient is set to 1, and the positions are ±1.2°, ±55.5° and ±52.5°, respectively. The related simulation parameters are shown in Table 1, and the simulation environment and platform are shown in Table 2. Figure 5

[0177] Table 1 Simulation parameters

[0178] Simulation parameters Numerical values Carrier frequency 30.75 GHz Bandwidth 60 MHz Signal pulse width 2 μs Pulse repetition frequency 1200 Hz Antenna scan speed 80° / s° Beam width 4° Scan range ±40° Platform speed 340 m / s

[0179] Table 2 Simulation environment

[0180] Hardware / software Parameter values CPU Inter(R) Core(TM) i7-9700K RAM 64 GB Simulation software Matlab 2022a

[0181] Figure 6 The matrix represents the antenna pattern matrix, where Figure 6 (a) represents the ideal antenna pattern matrix, Figure 6 (b) represents the distorted antenna pattern matrix.

[0182] Figure 7 The point target reconstruction results of seven different super-resolution methods under SNR=5dB are shown in FIG. 7. Figure 7 (a) is the imaging result of the real beam echo, and due to the influence of low signal-to-noise ratio, the target signal is seriously polluted by noise, and aliasing and artifacts are obvious. Figure 7 (b) and 7(c) represent the processing results of the TSVD regularization method and the Tikhonov regularization method, and under the low signal-to-noise ratio, the two methods are difficult to effectively reconstruct and distinguish the targets in the imaging scene. Figure 7 (d) and 7(e) respectively represent the processing results of the sparse L1 regularization method and the L1-L2 mixed regularization method, and under the low signal-to-noise ratio condition, the two methods fail to effectively recover the target information, resulting in a sharp deterioration of the imaging result. Figure 7 (f) and Figure 7 (g) are respectively the processing results of the IAA method and the SPICE method, and more false targets appear on the edge of the imaging area. Figure 7 (h) is the processing result of the method of the present application, and under the low signal-to-noise ratio condition, the six point targets can still be effectively reconstructed, and the noise in the imaging scene can be effectively suppressed. The above results prove the effectiveness and stability of the method of the present application.

[0183] ​In summary, the method of the present application accurately characterizes the scanning process of phased array radar by modifying the antenna pattern matrix, and proposes a weighted sparse iterative solving framework based on the covariance fitting criterion to realize sparse target reconstruction under low signal-to-noise ratio conditions, solving the model mismatch caused by the antenna pattern widening with the scanning angle during the electronic scanning process of the phased array radar, and the imaging distortion problem caused by the Doppler phase error of the high-speed motion platform.

[0184] Those skilled in the art will appreciate that the embodiments described herein are presented for the purpose of aiding the reader in understanding the principles of the present application, and should be understood as not limiting the scope of protection of the present application to such specific recitations and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspiration disclosed by 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 phased array radar sparse super-resolution imaging method based on antenna pattern correction, the specific steps are as follows: S1. Acquire echo data for preprocessing and perform phased array radar echo modeling; The phased array radar transmits linear frequency modulation (LFM) pulse signals at a fixed frequency and scans the target area. Assuming that the radar platform moves along a straight line at a speed V, the slant range R(t) between the target imaging point and the radar platform at time t is expressed as follows: in, R0 represents the initial slant range between the radar and the target at time 0, θ represents the azimuth of the target relative to the radar at time t, represents the pitch angle of the target relative to the radar at time t; Then perform Taylor series expansion, and the approximate expression of R(t) is as follows: Then the linear frequency modulation signal y(τ) emitted by the radar is expressed as follows: Where rect(·) represents the rectangular window function, τ represents the distance time vector, and T p Indicates the pulse width, f c Indicates the carrier frequency, K c represents the linear frequency modulation slope; Then the target echo signal y P The expression of (τ,t) is as follows: Among them, s P represents the target scattering coefficient, h(t) represents the two-way antenna pattern function of the phased array radar, τ d =2R(t) / c represents the echo delay, c represents the speed of light; Then, pulse compression and motion compensation are performed on the target echo signal, and the echo signal y(R,θ) can be expressed as follows: Where R is the distance between the radar and the target in the line of sight, s(R,θ) is the backscatter coefficient of the target, h(θ-θ0) is the two-way antenna pattern function, θ0 is the pointing azimuth of the radar beam center, B is the bandwidth of the signal, ω is the angular velocity of the radar beam scanning, and λ is the wavelength of the signal. represents the Doppler phase; The Doppler phase effect is then summarized into a matrix form D, which is expressed as follows: Where N represents the number of sampling points of the azimuth antenna pattern, [t1, t2, ... t N ] represents the azimuth sampling time, [θ1,θ2,…θ N ] represents the sampling angle in the azimuth direction, R(t n ,θ n ) represents the discrete sampling points of the distance history, n = 1, 2, ..., N; In radar imaging, the azimuth echo signal is modeled as the convolution of the target scattering coefficient and the antenna pattern. The matrix expression is as follows: y=Hs+n (7) Where y represents the echo signal received by the radar, H represents the antenna pattern convolution matrix, s represents the target scattering coefficient vector, and n represents noise; After introducing the Doppler phase matrix, the corrected expression of equation (7) is as follows: y=(H⊙D)s+n (8) Among them, ⊙ represents the matrix dot multiplication operation; S2. Based on step S1, correct the antenna pattern distortion; Without considering the spatial variation of the antenna pattern, the ideal antenna pattern convolution matrix expression is as follows: Among them, K represents the number of azimuth sampling points, [h1,h2,…,h L ] represents the sampling vector of the antenna pattern, L represents the number of sampling points of the antenna pattern, and the calculation expression is as follows: Among them, θ B represents the antenna main lobe beamwidth, ω represents the equivalent scanning speed of the array antenna, and PRF represents the pulse repetition frequency; Actual antenna beamwidth Scanning angle θ i Influence, resulting in the number of pattern sampling points L(θ i ) changes, and its expression is as follows: Among them, θ i ∈[θ1,θ2,…θ N ],θ1,θ2,…θ N Represents discrete angular sampling of the scanned scene; The corrected antenna pattern matrix expression is as follows: Among them, h i,j Represents the j-th element value of the antenna pattern sampling vector during the i-th scan; Taking into account the spatial variation of the antenna pattern and the influence of Doppler phase, the echo signal model of the phased array radar is expressed as follows: Final Order The echo signal model is simplified into the following expression: y=As+n (14) S3. Define the objective function and build a sparse iterative solution framework to obtain the optimal solution of the objective function; First, define the objective function expression as follows: Where s represents the target scattering coefficient vector, Represents the reconstructed target scattering coefficient vector, s n represents the nth element of s, δ represents the noise power, which obeys the uniform distribution and 0≤δ<∞, represents the estimated value of noise power, q represents the target sparsity control parameter, 0<q<1; The sparse prior probability density function of the target is expressed as follows: Where f(s) represents the sparse prior probability density function; Based on the Bayesian criterion and the principle of variable separation, the sparse iterative solution framework can be decomposed into two sub-problems, s and δ, for iterative solution. The initial estimated values ​​of s and δ are set to 0, and then the optimal solution of the objective function is obtained by iteratively solving the s and δ problems. The specific steps are as follows: 1) Fix δ and solve for s: Assume that the result s of the kth iteration has been obtained k , δ k ; The objective function expression is as follows: Then solve the partial derivative of the cost function with respect to s, and we can get the k+1th iteration result of s, which is expressed as follows: in,() H represents the conjugate transpose operation, P = diag(p), p = [p1, p2, p3, ..., p N ] T ,() T represents the transpose operation, and p n The specific expression is as follows: p n =|s n | 2-q (19) Let P = P k , then P k The specific expression is as follows: Then formula (18) can be transformed into the following expression: [A H A+δ k (P k ) -1 ]s-A H y=0 (21) Get the k+1th iteration result s of s k+1 , the expression is as follows 2) Fix s and solve for δ: Similar to step 1), the k+1th iteration result is obtained by taking the first-order partial derivative of the cost function with respect to δ, and the expression is as follows: The k+1th iteration result of δ is obtained as follows: S4: Based on step S3, a weighted strategy is introduced and a sparse iterative solution framework is constructed to complete the iterative update and output the super-resolution result; The weighted strategy is introduced to improve the target reconstruction quality, and the autocorrelation matrix R of the radar echo matrix is ​​defined as follows: in,() H represents the conjugate transpose operation, A H represents the conjugate transpose of the antenna pattern matrix A, y H represents the conjugate transpose of the echo signal y, P = diag(p) ​​represents the signal power matrix, and the expression is as follows: in, represents the signal power estimate at the k+1th iteration, represents the signal power estimate at the kth iteration, represents the conjugate transpose of the nth column of matrix A, Denotes the signal power estimate based on the kth iteration The constructed autocorrelation matrix is represents the weight vector; Combining the weighted strategy with the sparse iterative solution framework, the weight vector expression is defined as follows: oh n =(1 / p n ) q (28) Among them, ω n represents the weight vector; Combining equations (20), (27), and (28), the iterative update expression of the target signal power is obtained as follows: After the iteration is terminated, combined with formula (22), the last iteration result s k+1 The output is taken as the super-resolution output result.

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