A high-speed moving platform radar vector non-uniform modulation angular super-resolution method

Abstract

The present invention discloses a high-speed moving platform radar vector non-uniform modulation angular super-resolution method. First, echo data is acquired and pre-processed along the distance dimension to achieve echo distance dimension high-resolution imaging. Then, based on the relative position relationship between the platform and the target, a non-uniform antenna pattern matrix and a Doppler phase matrix are constructed, and a vector non-uniform convolution model is established. Finally, a parameter-free iterative reweighted norm is used to solve the sparse constraint optimization problem, and a super-resolution result is output to achieve reconstruction of the sparse target of the high-speed moving platform. In the echo modeling, the method of the present invention constructs a non-uniform antenna pattern matrix and a Doppler phase matrix, improves the adaptability of the angular super-resolution method to the high-speed moving platform, solves the problem of large imaging error of the existing convolution approximation model under high-speed motion, and can better guarantee the performance of high-speed moving platform radar angular super-resolution imaging compared to the imaging results of the existing convolution approximation model super-resolution method.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar imaging, and in particular relates to a high-speed motion platform radar vector non-uniform modulation angle super-resolution method. Background Art

[0002] Radar can acquire target information within a wide observation area through beam scanning. However, in practical applications, its angular resolution is low due to the limitations of the antenna aperture. To improve angular resolution through signal processing, we continue to explore angular super-resolution technology to meet the application requirements of various high-speed platforms.

[0003] Deconvolution is a super-resolution technique that can achieve angular resolution beyond the actual aperture through convolution inversion and is widely used in the field of scanning radar angular super-resolution imaging. -Pérez, Stewart JMarshall, and Keith Gregson, 'Resolution improvement of ers scatterometer data over land by wiener filtering,' Remote sensing of environment, vol. 71, no. 3, pp. 261–271, 2000. A deconvolution method based on Wiener filtering was proposed to improve angular resolution. References: "Q. Zhang, Y. Zhang, Y. Zhang, Y. Huang, W. Li and J. Yang, Majorize-Minimization Based Super-Resolution Method for Radar Forward-Looking Imaging. 2020 IEEE International Geoscience and Remote Sensing Symposium, pp. 3188–3191. IEEE, 2020." A maximum-minimum sparse regularized angular super-resolution method was proposed to improve the angular resolution performance of sparse targets. References: "Yuebo Zha, Yulin Huang, Zhichao Sun, Yue Wang, and Jianyu Yang, 'Bayesian deconvolution for angular super-resolution in forward-looking scanning radar,'Sensors, vol.15, no.3, pp.6924–6946, 2015." A Bayesian inversion angular super-resolution method is proposed, which improves the angular resolution by assuming the statistical distribution of the target and noise.

[0004] However, the above-mentioned super-resolution methods all use convolutional approximation models, which will cause obvious reconstruction errors when performing super-resolution imaging processing on a high-speed moving platform. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a vector non-uniform modulation angular super-resolution method for high-speed moving platform radar. Aiming at the angular super-resolution imaging problem of high-speed moving platform radar, a vector non-uniform modulation echo model is established, and a parameter-free iterative reweighted norm solution sparse constraint optimization method is adopted to achieve accurate reconstruction of target information under high-speed moving platform.

[0006] The technical solution of the present invention is: a high-speed moving platform radar vector non-uniform modulation angle super-resolution method, the specific steps are as follows:

[0007] Step 1: Acquisition of echo data and preprocessing of distance dimension;

[0008] Airborne scanning radar detects target scenes by transmitting linear frequency modulation signals at a set fixed pulse repetition frequency. The target scene echo expression is as follows:

[0009]

[0010] Where τ represents the time sampling vector in the range direction, t represents the time sampling vector in the azimuth direction; x0 represents the scattering coefficient of the point target in the imaging scene; h(t) represents the time domain antenna pattern function; rect(·) represents the rectangular window function; represents the round-trip echo delay, r(t) represents the distance history of the target, and c represents the electromagnetic wave propagation speed; T r Indicates the pulse width of the transmitted signal; Kr indicates the linear modulation frequency; represents the carrier frequency of the transmitted signal, and λ represents the wavelength of the electromagnetic wave.

[0011] The original echo obtained after the range-dimension pulse pressure is expressed as follows:

[0012]

[0013] Where B represents the bandwidth of the transmitted signal.

[0014] Target's distance history When scanning at long distance and small sector, it can be approximately expressed as:

[0015] r(t)≈r0-vtcosθ0 (3)

[0016] Where r0 represents the initial slant distance of the platform, v represents the platform movement speed, and θ0 represents the initial azimuth angle.

[0017] The echo is scaled using the target distance history approximation in formula (3), and the echo expression after range movement correction is obtained as follows:

[0018]

[0019] in, represents the Doppler phase term.

[0020] Step 2: Establish a vector non-uniform convolution model;

[0021] Replace the time variable in formula (4) with the space variable, that is, and

[0022] Where r represents the range sampling of the imaging scene, θ represents the azimuth sampling of the imaging scene, and ω represents the beam scanning speed. The expression for the azimuth echo of the imaging scene is as follows:

[0023]

[0024] Among them, s(θ) represents the target azimuth echo, x(θ) represents the target azimuth scattering distribution, and h(θ) represents the spatial antenna pattern function. Represents the convolution operation.

[0025] After discretizing the azimuth echo data and considering additive Gaussian white noise, equation (5) is transformed into the following matrix-vector form:

[0026]

[0027] in, Represents matrix dot multiplication operation; Represents the received azimuth echo matrix, with dimension N×1, s(θ i )(1≤i≤N) represents the position in θ i The echo amplitude value at θ i represents the i-th azimuth; Represents the target azimuth scattering distribution matrix, with a dimension of N×1, x(θ i )(1≤i≤N) represents the position in θ i The target scattering amplitude value at ; Represents a noise matrix that satisfies Gaussian distribution, with dimensions of N×1, n(θ i )(1≤i≤N) represents the position in θ i The noise amplitude value at ; T represents the transpose of the matrix, N represents the number of azimuth sampling points, and Ω represents the imaging scene range, PRF represents the pulse repetition frequency; (θ1,θ2,…,θ N ) represents the discrete vector of the imaging scene orientation; represents the non-uniform antenna measurement matrix; P represents the Doppler phase matrix.

[0028] The specific expression is as follows:

[0029]

[0030] Among them, h i,j represents the jth element sampled by the i-th (1≤i≤N) antenna sampling pattern; L (θi) (1≤i≤N) represents the total number of points sampled by the i-th (1≤i≤N) antenna sampling pattern, and the expression is as follows:

[0031]

[0032] Among them, θ beta represents the beam width; ω represents the beam scanning speed, PRF represents the pulse repetition frequency; θ i ∈(θ1,θ2,…,θ N )(1≤i≤N) represents the discrete vector of the imaging scene orientation.

[0033] The specific expression of P is as follows:

[0034]

[0035] Step 3: Construct regularized objective function;

[0036] Based on the vector non-uniform convolution model of formula (6) in step 2, considering the target sparse prior, the objective function expression of the regularization constraint is constructed as follows:

[0037]

[0038] in, represents the target scattering distribution to be solved; represents the data fidelity term, represents the square of the vector 2-norm; u||x||1 represents the regularization term, u represents the regularization parameter, and ||·||1 represents the vector 1-norm.

[0039] Step 4: Construct a regularized weighted objective function;

[0040] Based on the covariance fitting criterion, the regularized weighted matrix is introduced, and the objective function in formula (10) can be equivalent to:

[0041]

[0042] Where D represents the regularization weight matrix, which is expressed as follows:

[0043]

[0044] Among them, d i represents the main diagonal elements of the regularized weight matrix, a i Representation matrix The i-th column data.

[0045] Step 5: Iterative reconstruction of target scattering coefficient;

[0046] Use the parameterless iterative reweighted algorithm to solve and set the initial value of the iterative solution algorithm for:

[0047]

[0048] The result of the weighted diagonal matrix is based on the previous estimation result of the target scattering coefficient, and its expression is:

[0049] W k =diag(|Dx k-1 | -1 ) (14)

[0050] Among them, W k represents the weighted diagonal matrix at the kth iteration, x k-1 It represents the k-1th estimation result, and k represents the number of iterations.

[0051] Using the diagonal weighted matrix in equation (14), the objective function is updated as:

[0052]

[0053] Combine steps 4 and 5 until the relative error between two adjacent super-resolution results is less than the set error threshold ε, the algorithm converges, ends the loop, and outputs the super-resolution imaging result. This is the target scattering distribution to be solved.

[0054] Beneficial effects of the present invention: The method of the present invention first acquires echo data and pre-processes it along the distance dimension to achieve high-resolution imaging of the echo distance dimension. Then, based on the relative position relationship between the platform and the target, a non-uniform antenna pattern matrix and a Doppler phase matrix are constructed, and a vector non-uniform convolution model is established. Finally, a parameter-free iterative reweighted norm is used to solve the sparse constrained optimization problem, and a super-resolution result is output to achieve reconstruction of sparse targets of a high-speed moving platform. In the echo modeling, the method of the present invention constructs a non-uniform antenna pattern matrix and a Doppler phase matrix, which improves the adaptability of the angular super-resolution method to high-speed moving platforms, solves the problem of large errors in the imaging results of the existing convolution approximation model under high-speed motion, and is more capable of guaranteeing the performance of radar angular super-resolution imaging of high-speed moving platforms than the imaging results of the existing convolution approximation model super-resolution method. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The present invention provides a flow chart of a high-speed moving platform radar vector non-uniform modulation angle super-resolution method.

[0056] Figure 2 This is a motion geometry model diagram of an airborne scanning radar in an embodiment of the present invention.

[0057] Figure 3 This is a comparison diagram of imaging effects under a high-speed motion platform in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The method of the present invention will be further described below with reference to the accompanying drawings and examples.

[0059] The present invention uses simulation experiments to demonstrate the effectiveness of the proposed method, and all the steps and conclusions of the present invention are verified on the Matlab2021 simulation platform.

[0060] like Figure 1 As shown in FIG, a flow chart of a high-speed moving platform radar vector non-uniform modulation angle super-resolution method of the present invention is shown, and the specific steps are as follows:

[0061] Step 1: Acquisition of echo data and preprocessing of distance dimension;

[0062] like Figure 2 As shown, this embodiment uses an airborne scanning radar motion geometry model. The specific parameter values of the airborne platform system are shown in Table 1, and the simulation environment and hardware platform are shown in Table 2. To simulate a real noisy environment, this embodiment adds Gaussian white noise to the simulation to achieve a signal-to-noise ratio of 25dB.

[0063] Table 1

[0064] Simulation parameters Numerical carrier frequency 10.75GHz Time width 2us bandwidth 40MHz Antenna beamwidth 3° Pulse repetition frequency 2000Hz Scan speed 40° / s Scan range ±15° Initial slope distance 3km Platform speed 400m / s

[0065] Table 2

[0066] Hardware or software parameter CPU Intel(R)Core(TM)i5-9500 RAM 8GB Simulation Platform Matlab2021

[0067] Airborne scanning radar detects target scenes by transmitting linear frequency modulation signals at a set fixed pulse repetition frequency. The expression of the transmitted linear frequency modulation signal is:

[0068]

[0069] Where τ represents the distance time sampling vector; T r =2us represents the pulse width of the transmitted signal; the carrier frequency of the transmitted signal f c =10.75GHz; K r represents the linear modulation frequency, and rect(·) represents the rectangular window function.

[0070] like Figure 3 As shown in the figure, the imaging effect comparison under the high-speed motion platform, the real simulation original scene is as follows Figure 3 (a) In this embodiment, the simulated scanning detection area is set to Ω = -15° to 15°. The expression of the acquired radar original echo signal is as follows:

[0071]

[0072] Where t represents the azimuth time sampling vector; x0 represents the scattering coefficient of the point target in the imaging scene; h(t) represents the time domain antenna pattern function; represents the round-trip echo delay, r(t) represents the distance history of the target, and c represents the electromagnetic wave propagation speed.

[0073] The original echo obtained after the range-dimension pulse pressure is expressed as follows:

[0074]

[0075] Wherein, B=40MHz represents the transmission signal bandwidth.

[0076] Target's distance history When scanning at long distance and small sector, it can be approximately expressed as:

[0077] r(t)≈r0-vtcosθ0 (19)

[0078] Where r0 = 3 km represents the initial slant range of the platform, v = 400 m / s represents the platform movement speed, and θ0 represents the initial azimuth angle.

[0079] The target distance history approximation in formula (19) can be used to scale the echo, and the echo expression after range movement correction is obtained as follows:

[0080]

[0081] in, represents the Doppler phase term.

[0082] Step 2: Establish a vector non-uniform convolution model;

[0083] Replace the time variable in Equation (20) with the space variable, that is, and

[0084] Where r represents the imaging scene distance sampling, θ represents the imaging scene azimuth sampling, and ω = 40° / s represents the beam scanning speed. The expression for the imaging scene azimuth echo is as follows:

[0085]

[0086] Among them, s(θ) represents the target azimuth echo, x(θ) represents the target azimuth scattering distribution, and h(θ) represents the spatial antenna pattern function. Represents the convolution operation.

[0087] After discretizing the azimuth echo data and considering additive white Gaussian noise, Equation (21) is transformed into the following matrix-vector form:

[0088]

[0089] in, Represents matrix dot multiplication operation; Represents the received azimuth echo matrix, with dimension N×1, s(θ i )(1≤i≤N) represents the position in θ i The echo amplitude value at θ i represents the i-th azimuth; Represents the target azimuth scattering distribution matrix, with a dimension of N×1, x(θ i )(1≤i≤N) represents the position in θ i The target scattering amplitude value at ; Represents a noise matrix that satisfies Gaussian distribution, with dimensions of N×1, n(θ i )(1≤i≤N) represents the position in θ i The noise amplitude value at ; T represents the transpose of the matrix, N represents the number of azimuth sampling points, after calculation Ω=30° represents the imaging scene range, PRF=2000 represents the pulse repetition frequency; (θ1,θ2,…,θ N ) represents the discrete vector of the imaging scene orientation; represents the non-uniform antenna measurement matrix; P represents the Doppler phase matrix.

[0090] The specific expression is as follows:

[0091]

[0092] Among them, h i,j represents the jth element sampled by the i-th (1≤i≤N) antenna sampling pattern; L (θi) (1≤i≤N) represents the total number of points sampled by the i-th (1≤i≤N) antenna sampling pattern, and the expression is as follows:

[0093]

[0094] Among them, θ beta =3° represents the beam width; θ i ∈(θ1,θ2,…,θ N )(1≤i≤N) represents the discrete vector of the imaging scene orientation.

[0095] The specific expression of P is as follows:

[0096]

[0097] Step 3: Construct regularized objective function;

[0098] Based on the vector non-uniform convolution model of formula (22) in step 2, considering the target sparse prior, the objective function expression of the regularization constraint is constructed as follows:

[0099]

[0100] in, represents the target scattering distribution to be solved; represents the data fidelity term, represents the square of the vector 2-norm; u||x||1 represents the regularization term, u represents the regularization parameter, and ||·||1 represents the vector 1-norm.

[0101] Step 4: Construct a regularized weighted objective function;

[0102] The selection of regularization parameters will affect the final imaging results. In order to remove the influence of regularization parameters on the algorithm, a parameter-free iterative reweighting algorithm is used to solve the problem. Based on the covariance fitting criterion, the regularization weighting matrix is introduced, and the objective function in formula (26) can be equivalent to:

[0103]

[0104] Where D represents the regularization weight matrix, which is expressed as follows:

[0105]

[0106] Among them, d i represents the main diagonal elements of the regularized weight matrix, a i Representation matrix The i-th column data.

[0107] Step 5: Iterative reconstruction of target scattering coefficient;

[0108] This embodiment uses a parameterless iterative reweighted algorithm to solve the problem, and sets the initial value of the iterative solution algorithm to for:

[0109]

[0110] The result of the weighted diagonal matrix is based on the previous estimation result of the target scattering coefficient, and its expression is:

[0111] W k =diag(|Dx k-1 | -1 ) (30)

[0112] Among them, W k represents the weighted diagonal matrix at the kth iteration, x k-1 It represents the k-1th estimation result, and k represents the number of iterations.

[0113] Using the diagonal weighted matrix in equation (30), the objective function is updated as:

[0114]

[0115] Combine steps 4 and 5 until the relative error between two adjacent super-resolution results is less than the set error threshold ε = 0.001, the algorithm converges, ends the loop, and outputs the super-resolution imaging result. This is the target scattering distribution to be solved.

[0116] The super-resolution imaging results are as follows Figure 3 As shown, Figure 3 (b) shows the azimuth echo after pulse compression. The high-speed motion of the platform causes nonuniform antenna modulation and Doppler phase. The nonuniform antenna modulation results in a "high on the left and low on the right" echo amplitude, while the Doppler phase causes a distinct "alternating strong and weak" echo distribution. Figure 3 (c) shows the super-resolution imaging results of the traditional convolutional approximation model, where false targets and high side lobes appear under high-speed platforms; Figure 3 (d) shows the results of the method of the present invention, which effectively reconstructs the target under high-speed motion. The above simulation results show that the method of the present invention can overcome the large imaging errors of traditional methods under high-speed platforms, and broaden the speed range of super-resolution methods.

[0117] In summary, the method of the present invention constructs a non-uniform antenna pattern matrix and a Doppler phase matrix in echo modeling, improves the adaptability of the angular super-resolution method to high-speed moving platforms, and solves the problem of large errors in the imaging results of the existing convolution approximation model under high-speed motion conditions. Compared with the imaging results of the existing convolution approximation model super-resolution method, it can better guarantee the performance of radar angular super-resolution imaging of high-speed moving platforms.

[0118] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art may make relevant modifications or applications based on the super-resolution imaging method proposed in this invention, while remaining within the scope of protection of this invention.

Claims

1. A high-speed moving platform radar vector non-uniform modulation angle super-resolution method, the specific steps are as follows: Step 1: Acquisition of echo data and preprocessing of distance dimension; Airborne scanning radar detects target scenes by transmitting linear frequency modulation signals at a set fixed pulse repetition frequency. The target scene echo expression is as follows: in, τ represents the time sampling vector in the range direction, t represents the time sampling vector in the azimuth direction; x0 represents the scattering coefficient of the point target in the imaging scene; h(t) represents the time domain antenna pattern function; rect(·) represents the rectangular window function; represents the round-trip echo delay, r(t) represents the distance history of the target, and c represents the electromagnetic wave propagation speed; T r Indicates the pulse width of the transmitted signal; Kr indicates the linear modulation frequency; represents the carrier frequency of the transmitted signal, and λ represents the wavelength of the electromagnetic wave; The original echo obtained after the range-dimension pulse pressure is expressed as follows: Where B represents the bandwidth of the transmitted signal; Target's distance history When scanning at long distance and small sector, it can be approximately expressed as: r(t)≈r0-vtcosθ0 (3) Where r0 represents the initial slant distance of the platform, v represents the platform movement speed, and θ0 represents the initial azimuth angle; The echo is scaled using the target distance history approximation in formula (3), and the echo expression after range movement correction is obtained as follows: in, represents the Doppler phase term; Step 2: Establish a vector non-uniform convolution model; Replace the time variable in formula (4) with the space variable, that is, and Where r represents the range sampling of the imaging scene, θ represents the azimuth sampling of the imaging scene, and ω represents the beam scanning speed. The expression for the azimuth echo of the imaging scene is as follows: Among them, s(θ) represents the target azimuth echo, x(θ) represents the target azimuth scattering distribution, and h(θ) represents the spatial antenna pattern function. Represents the convolution operation; After discretizing the azimuth echo data and considering additive Gaussian white noise, equation (5) is transformed into the following matrix-vector form: Among them, ⊙ represents the matrix dot multiplication operation; Represents the received azimuth echo matrix, with dimension N×1, s(θ i )(1≤i≤N) represents the position in θ i The echo amplitude value at θ i represents the i-th azimuth; Represents the target azimuth scattering distribution matrix, with a dimension of N×1, x(θ i )(1≤i≤N) represents the position in θ i The target scattering amplitude value at ; Represents a noise matrix that satisfies Gaussian distribution, with dimensions of N×1, n(θ i )(1≤i≤N) represents the position in θ i The noise amplitude value at ; T represents the transpose of the matrix, N represents the number of azimuth sampling points, and Ω represents the imaging scene range, PRF represents the pulse repetition frequency; (θ1,θ2,…,θ N ) represents the discrete vector of the imaging scene orientation; represents the non-uniform antenna measurement matrix; P represents the Doppler phase matrix; The specific expression is as follows: Among them, h i,j represents the jth element sampled by the i-th (1≤i≤N) antenna sampling pattern; L (θi) (1≤i≤N) represents the total number of points sampled by the i-th (1≤i≤N) antenna sampling pattern, and the expression is as follows: Among them, θ beta represents the beam width; ω represents the beam scanning speed, PRF represents the pulse repetition frequency; θ i ∈(θ1,θ2,…,θ N )(1≤i≤N) represents the discrete vector of the imaging scene orientation; The specific expression of P is as follows: Step 3: Construct regularized objective function; Based on the vector non-uniform convolution model of formula (6) in step 2, considering the target sparse prior, the objective function expression of the regularization constraint is constructed as follows: in, represents the target scattering distribution to be solved; represents the data fidelity term, represents the square of the vector 2-norm; u||x||1 represents the regularization term, u represents the regularization parameter, and ||·||1 represents the 1-norm of the vector; Step 4: Construct a regularized weighted objective function; Based on the covariance fitting criterion, the regularized weighted matrix is introduced, and the objective function in formula (10) can be equivalent to: Where D represents the regularization weight matrix, which is expressed as follows: Among them, d i represents the main diagonal elements of the regularized weight matrix, a i Representation matrix The i-th column data; Step 5: Iterative reconstruction of target scattering coefficient; Use the parameterless iterative reweighted algorithm to solve and set the initial value of the iterative solution algorithm for: The result of the weighted diagonal matrix is based on the previous estimation result of the target scattering coefficient, and its expression is: W k =diag(|Dx k-1 | -1 ) (14) Among them, W k represents the weighted diagonal matrix at the kth iteration, x k-1 Represents the k-1th estimation result, where k represents the number of iterations; Using the diagonal weighted matrix in equation (14), the objective function is updated as: Combine steps 4 and 5 until the relative error between two adjacent super-resolution results is less than the set error threshold ε, the algorithm converges, ends the loop, and outputs the super-resolution imaging result. This is the target scattering distribution to be solved.

Images