A super-resolution method for scanning radar under unknown broadening of antenna pattern

Abstract

The present invention discloses a scanning radar super-resolution method under unknown broadening of the antenna pattern. First, through echo modeling, the azimuth echo is constructed as the convolution of the target scattering coefficient and the antenna pattern. Then, a broadening correction matrix is introduced into the echo convolution model to characterize the error of the antenna pattern function. Finally, an alternating iteration strategy is adopted to update the broadening correction matrix and the target scattering coefficient until convergence. All range cells in the echo are traversed, and the azimuth super-resolution imaging result is output. The method of the present invention introduces a broadening correction error matrix into the azimuth echo convolution model and continuously updates the target and the error matrix by means of alternating iteration, so as to achieve robust imaging under error conditions. Compared with the existing super-resolution methods, it can achieve robust super-resolution imaging when there is unknown broadening in the antenna pattern function, has stronger applicability, and solves the problem of super-resolution imaging when the antenna pattern function undergoes unknown broadening.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar imaging, and particularly relates to a scanning radar super-resolution method under unknown broadening of an antenna pattern. Background Art

[0002] The scanning radar super-resolution technology uses signal processing means to break through the inherent limitations of the antenna aperture and obtain an azimuth resolution better than that of a real beam. This technology has important research significance and application value in applications such as sea surface search and earth observation.

[0003] The super-resolution technology mainly utilizes the convolution relationship between the target scattering coefficient and the antenna function, and uses deconvolution to achieve super-resolution imaging. The literature "Huang Y, Zha Y, Wang Y, et al. Forward looking radar imaging by truncated singular value decomposition and its application for adverse weather aircraft landing. Sensors, 2015, 15(6): 14397-14414." proposed a truncated singular value decomposition super-resolution method to improve the azimuth resolution. The literature "Zhang Q, Zhang, Huang Y, et al. Sparse with fast MM superresolution algorithm for radar forward-looking imaging. IEEE Access, 2019, 7: 105247-105257." proposed a fast MM sparse super-resolution imaging method based on the convolution model and obtained a higher resolution improvement. The literature "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." utilized the mathematical similarity between the convolution model and the array processing model to propose an iterative adaptive super-resolution method and obtained nonparametric iterative adaptive super-resolution imaging.

[0004] However, in practical applications, due to motion errors such as pitch, yaw, and roll of the radar platform, there will be an unknown beam broadening error between the actual antenna pattern of the radar and the ideal measurement antenna pattern. The super-resolution imaging performance of existing super-resolution methods will drop sharply or even become ineffective. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a super-resolution method for a scanning radar with unknown beam broadening of the antenna pattern. A broadening correction error matrix is introduced into the azimuth echo convolution model, and the target and the error matrix are continuously updated in an alternating iteration manner, so as to achieve robust imaging under error conditions.

[0006] The technical solution adopted by the present invention is as follows: a super-resolution method for a scanning radar with unknown beam broadening of the antenna pattern, and the specific steps are as follows:

[0007] Step 1: Model the azimuth convolution model;

[0008] The scanning radar radiates a linear frequency modulation (LFM) signal at a set fixed pulse repetition frequency (PRF), and at the same time uses the antenna to scan and detect the observation area. Based on the process of scanning imaging, the echo signal in a range cell of the observation area is constructed as the convolution of the antenna function and the target scattering coefficient, and considering additive white Gaussian noise, the azimuth signal model is expressed as:

[0009] y = Hx + n (1)

[0010] Wherein, represents the received echo vector, with a dimension of N×1, represents the i-th (1≤i≤N) element of the echo vector; represents the target scattering coefficient vector, with a dimension of N×1, x (θi) represents the i-th (1≤i≤N) element of the target scattering coefficient vector; represents the noise vector that satisfies the Gaussian distribution, with a dimension of N×1, represents the i-th (1≤i≤N) element of the noise vector; T represents the transpose operation of the vector, N represents the number of azimuth sampling points, [θ1, θ2, …, θ N ] represents the azimuth sampling of the imaging scene; H represents the antenna pattern matrix composed of the antenna pattern sampling, with a dimension of N×N, and the expression is as follows:

[0011]

[0012] Wherein, represents the antenna pattern sampling vector, represents the sampling value of the antenna pattern. N represents the number of azimuth sampling points, and Ω represents the imaging area, ω represents the scanning speed, and PRF represents the pulse repetition frequency.

[0013] Step 2: Convolution model correction;

[0014] Considering the case where there is an unknown beam broadening error in the antenna pattern, a broadening correction error matrix is introduced, and the convolution model in Equation (1) is corrected to:

[0015] y = (H + E)x + n (3)

[0016] where E represents the broadening correction error matrix of dimension N×N.

[0017] Step 3: Construction of the objective function;

[0018] Based on the sparsity of the target, on the basis of the least squares, the objective function J(x, E) is constructed as follows:

[0019]

[0020] where, represents the data fidelity term, represents the square of the vector 2-norm; α||x||1 represents the target constraint term, α represents the parameter for adjusting the strength of the target constraint term, and ||·||1 represents the vector L1-norm; represents the broadening correction error matrix constraint term, β represents the parameter for adjusting the strength of the broadening correction error matrix constraint term, represents the square of the matrix Frobenius norm.

[0021] Step 4: Solve the E problem;

[0022] Adopt an alternating iteration strategy to solve the objective function.

[0023] First, fix the variable x, and the objective function is transformed into:

[0024]

[0025] Adopt a derivative strategy to obtain the update expression of the variable E:

[0026]

[0027] where the superscript H represents the conjugate transpose operation.

[0028] Step 5: Solve the x problem;

[0029] Fix the variable E, let Then the objective function is transformed into:

[0030]

[0031] Since the problem in Equation (7) contains a non-differentiable L1 norm constraint term, an iterative reweighting method is used to solve it. The specific update steps are as follows:

[0032]

[0033] for j = 1, 2, …, J

[0034] W j = diag(|x j-1 | -1 )

[0035]

[0036] end (8)

[0037] where the subscript j represents the iteration order, J represents the number of iterations required for the problem in Equation (7) to converge, x0 represents the initialized target scattering coefficient, and x j represents the target scattering coefficient after the j-th iteration, W j represents the weighted matrix after the j-th iteration, and diag(·) represents a diagonal matrix.

[0038] Step Six: Obtain the imaging result;

[0039] After updating the target scattering coefficient to x = x J , repeat Step Four and Step Five until both the target scattering coefficient and the error matrix converge. Output the result of this range cell, and traverse all range cells within the echo to obtain the azimuth super-resolution imaging result of the entire observation area.

[0040] Advantages of the present invention: The method of the present invention first constructs the azimuth echo as the convolution of the target scattering coefficient and the antenna pattern through echo modeling, then introduces a broadening correction matrix into the echo convolution model to characterize the error of the antenna pattern function, and finally adopts an alternating iteration strategy to update the broadening correction matrix and the target scattering coefficient until convergence, traversing all range cells within the echo and outputting the azimuth super-resolution imaging result. The method of the present invention introduces a broadening correction error matrix into the azimuth echo convolution model and continuously updates the target and error matrices by means of alternating iteration, thereby achieving robust imaging under error conditions. Compared with existing super-resolution methods, it can achieve robust super-resolution imaging when there is an unknown broadening in the antenna pattern function, has a stronger applicability, and solves the problem of super-resolution imaging when the antenna pattern function undergoes unknown broadening. Description of the Drawings

[0041] Figure 1 is a flowchart of a scanning radar super-resolution method with unknown broadening of the antenna pattern according to the present invention.

[0042] Figure 2 This is the geometric schematic diagram of the real aperture scanning radar in the embodiment of the present invention.

[0043] Figure 3 This is the graph of the ideal antenna pattern function and the antenna pattern function with broadening error in the embodiment of the present invention.

[0044] Figure 4 This is the simulation result graph in the embodiment of the present invention. Detailed implementation manners

[0045] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0046] As Figure 1 shown, the flowchart of the super-resolution method for a scanning radar with unknown broadening of the antenna pattern according to the present invention is as follows:

[0047] Step 1: Build an azimuth convolution model;

[0048] As Figure 2 shown, in this embodiment, a real aperture radar scanning model is adopted, and the specific system parameters of the radar system are shown in Table 1. The scanning radar radiates a linear frequency modulation (LFM) signal at a set fixed pulse repetition frequency PRF = 2000 Hz.

[0049] Table 1

[0050] Simulation parameters Numerical value Carrier frequency 10.75 GHz Pulse width 2 μs Bandwidth 40 MHz Antenna beam width 2.5° Pulse repetition frequency 2000 Hz Scanning speed 60° / s Scanning range ±10° Initial slant range 3 km Platform speed 30 m / s

[0051] In this embodiment, the simulated scanning detection area is set to Ω = -10° to 10°, the antenna beam width is 2.5°, and the scanning speed is 60° / s.

[0052] Then the radar transmitted linear frequency modulation pulse is expressed as:

[0053]

[0054] where τ represents the time in the range dimension; the carrier frequency f c = 10.75 GHz; the pulse width T p = 2 us; K represents the frequency modulation rate, and the signal bandwidth B = 40 MHz, and rect(·) represents the rectangular window function.

[0055] Perform range dimension matched filtering and scaling processing on the demodulated original echo in the frequency domain at the same time, and the echo expression can be transformed into:

[0056]

[0057] where \(t\) represents the azimuth - dimensional time; \(\sigma\) represents the target scattering back - coefficient; \(h(t)\) represents the antenna pattern modulation function; \(\text{sinc}(\cdot)\) represents the pulse compression response function; \(R_0\) represents the initial slant range between the radar and the target, with a value of \(R_0 = 3\mathrm{km}\); represents the range history, \(V = 30\mathrm{m / s}\) is the platform moving speed, \(\theta_0\) represents the azimuth angle, and its value range is the scanning range \(\Omega=-10^{\circ}\sim10^{\circ}\) in Table 1; \(c = 3\times10\) 8 represents the electromagnetic wave propagation speed, \(\lambda\) represents the transmitted signal wavelength; \(n(\tau,t)\) represents additive white Gaussian noise.

[0058] After pulse compression and motion compensation processing, the echo can be transformed into the following form:

[0059] \(y = Hx + n\quad(11)\)

[0060] where, represents the received echo vector, with a dimension of \(N\times1\), represents the \(i\) - th (\(1\leq i\leq N\)) element of the echo vector; represents the target scattering coefficient vector, with a dimension of \(N\times1\), represents the \(i\) - th (\(1\leq i\leq N\)) element of the target scattering coefficient vector; represents the noise vector that satisfies the Gaussian distribution, with a dimension of \(N\times1\), represents the \(i\) - th (\(1\leq i\leq N\)) element of the noise vector; \(T\) represents the transpose operation of the vector, \(N\) represents the number of azimuth sampling points, \([\theta_1,\theta_2,\cdots,\theta\) N represents the azimuth sampling of the imaging scene; \(H\) represents the antenna pattern matrix composed of antenna pattern sampling, with a dimension of \(N\times N\), and the expression is as follows:

[0061]

[0062] where, represents the antenna pattern sampling, represents the sampling value of the antenna pattern, \(N\) represents the number of azimuth sampling points, and \(\Omega=-10^{\circ}\sim10^{\circ}\) represents the imaging area, \(\omega = 60^{\circ} / \mathrm{s}\) represents the scanning speed, \(PRF = 2000\mathrm{Hz}\) represents the pulse repetition frequency.

[0063] Step 2: Convolution model correction;

[0064] In this embodiment, considering the case where there is a broadening error in the antenna pattern, a broadening correction error matrix is introduced, and the convolution model in Equation (11) is corrected to:

[0065] \(y=(H + E)x + n\quad(13)\)

[0066] Among them, E represents the extended correction error matrix with dimensions N×N.

[0067] Step 3: Construction of the objective function;

[0068] Based on the sparsity of the target, on the basis of least squares, the objective function is constructed as follows:

[0069]

[0070] Among them, represents the data fidelity term, represents the square of the vector 2-norm; α||x||1 represents the target constraint term, α represents the parameter for adjusting the strength of the target constraint term, and ||·||1 represents the vector L1-norm; represents the extended correction error matrix constraint term, β represents the parameter for adjusting the strength of the extended correction error matrix constraint term, represents the square of the matrix Frobenius norm. α and β are both set to 1 in the simulation of this embodiment.

[0071] Step 4: Solve the E problem;

[0072] In this embodiment, an alternating iteration strategy is adopted to solve the objective function.

[0073] First, fix the variable x, and the objective function is transformed into:

[0074]

[0075] By adopting a derivative strategy, the updated expression of the variable E can be obtained:

[0076]

[0077] Among them, the superscript H represents the conjugate transpose operation.

[0078] Step 5: Solve the x problem;

[0079] Fix the variable E, and let Then the objective function is transformed into:

[0080]

[0081] The problem in Equation (17) contains a non-differentiable L1-norm constraint term. Therefore, an iteratively reweighted method is adopted to solve it. The specific update steps are as follows:

[0082]

[0083] for j = 1, 2, …, J

[0084] W j = diag(|xj-1 | -1 )

[0085]

[0086] end (18)

[0087] Among them, the subscript j represents the iteration order, J represents the number of iterations required for the problem in Equation (17) to converge, x0 represents the initialized target scattering coefficient, and x j represents the target scattering coefficient after the j-th iteration, and W j represents the weighted matrix after the j-th iteration, and diag(·) represents the diagonal matrix.

[0088] Step Six: Obtain the imaging result;

[0089] Update the target scattering coefficient to x = x J After that, repeat Step Four and Step Five until both the target scattering coefficient and the error matrix converge, that is

[0090] where k represents the outer loop iteration order, j represents the inner loop iteration order, and η represents the convergence threshold.

[0091] Then traverse all range cells in the echo, and finally output the azimuth super-resolution imaging result.

[0092] The simulation parameters of this embodiment are shown in Table 1. Figure 3 represents the ideal antenna pattern function and the antenna pattern function with broadening error. Figure 4 is the simulation result diagram in the embodiment of the present invention. Figure 4 (a) represents the original distribution of the target. Figure 4 (b) represents the original echo. Figure 4 (c) represents the reconstruction result of the conventional sparse method. Figure 4 (d) represents the reconstruction result of the method of the present invention. It can be seen from Figure 4 that when there is a broadening error in the antenna pattern, the reconstruction result of the traditional sparse method has a large error, while the method proposed by the present invention still realizes the effective reconstruction of the target when there is a broadening error in the antenna pattern.

[0093] In summary, the method of the present invention introduces a broadening correction error matrix into the azimuth echo convolution model, and uses the method of alternating iteration to continuously update the target and the error matrix, so as to achieve robust imaging under error conditions. Compared with the existing super-resolution methods, it can achieve robust super-resolution imaging when there is an unknown broadening in the antenna pattern function, has stronger applicability, and solves the super-resolution imaging problem when there is an unknown broadening in the antenna pattern function.

[0094] Those of ordinary skill in the art will realize that the embodiments described herein are to assist the reader in understanding the principles of the present invention and 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, various modifications and variations can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A super-resolution method for a scanning radar under unknown beamwidth broadening of the antenna pattern, the specific steps are as follows: Step 1: Modeling of the azimuth convolution model; The scanning radar radiates a linear frequency modulation (LFM) signal at a set fixed pulse repetition frequency (PRF), and at the same time uses antenna scanning to detect the observation area; based on the process of scanning imaging, the echo signal in a range cell of the observation area is constructed as the convolution of the antenna function and the target scattering coefficient, and considering additive white Gaussian noise, the azimuth signal model is expressed as: y = Hx + n (1) Among them, denotes the received echo vector, with a dimension of N×1, denotes the i-th element of the echo vector, where 1≤i≤N; denotes the target scattering coefficient vector, with a dimension of N×1, denotes the i-th element of the target scattering coefficient vector, where 1≤i≤N; denotes the noise vector that follows a Gaussian distribution, with a dimension of N×1, denotes the i-th element of the noise vector, where 1≤i≤N; T represents the transpose operation of the vector, N represents the number of azimuth sampling points, [θ1,θ2,…,θ N represents the azimuth sampling of the imaging scene; H represents the antenna pattern matrix composed of antenna pattern sampling, with a dimension of N×N, and the expression is as follows: Among them, represents the antenna pattern sampling vector, represents the sampling value of the antenna pattern; N represents the number of azimuth sampling points, and Ω represents the imaging area, ω represents the scanning speed, and PRF represents the pulse repetition frequency; Step 2: Correction of the convolution model; Considering the case where there is an unknown beamwidth broadening error in the antenna pattern, a broadening correction error matrix is introduced, and the convolution model in Equation (1) is corrected to: y = (H + E)x + n (3) where E represents a broadening correction error matrix of dimension N×N; Step 3: Construction of the objective function; Based on the sparsity of the target, on the basis of the least squares, the objective function J(x, E) is constructed as follows: Among them, represents the data fidelity term, represents the square of the vector 2-norm; α||x||1 represents the objective constraint term, α represents the parameter for adjusting the strength of the objective constraint term, and ||·||1 represents the vector L1-norm; represents the broadening correction error matrix constraint term, β represents the parameter for adjusting the strength of the broadening correction error matrix constraint term, represents the square of the matrix Frobenius norm; Step 4: Solving the E problem; An alternating iteration strategy is adopted to solve the objective function; First, fix the variable x, and the objective function is transformed into: By using the derivative strategy, the update expression of the variable E is obtained: where the superscript H represents the conjugate transpose operation; Step 5: Solving the x problem; Fix the variable E and let Then the objective function is transformed into: In the problem of Equation (7), there is a non-differentiable L1 norm constraint term, so an iterative reweighting method is used to solve it, and the specific update steps are as follows: Among them, the subscript j represents the iteration order, J represents the number of iterations required for the problem in Equation (7) to converge, x0 represents the initialized target scattering coefficient, and x j represents the target scattering coefficient after the j-th iteration, and W j represents the weighted matrix after the j-th iteration, and diag(·) represents the diagonal matrix; Step 6: Obtaining the imaging result; Update the target scattering coefficient to x = x J After that, repeat Step 4 and Step 5 until both the target scattering coefficient and the error matrix converge. Output the result of this range cell, traverse all range cells within the echo, and obtain the azimuth super-resolution imaging result of the entire observation area.

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