An Online Super-Resolution Imaging Method for Scanning Radar Based on Minimization Criterion

Abstract

This invention discloses an online super-resolution imaging method for scanning radar based on the minimization criterion. By establishing an azimuth echo convolution model and discretizing it, the super-resolution problem is transformed. Under a regularization framework, the minimization criterion is used to construct an analytically optimizeable cost function containing sparse prior information, transforming the forward-looking imaging resolution improvement problem into an optimization estimation problem. By dividing the antenna measurement matrix into rows and blocks, matrix operations are degraded into the continuous accumulation of vector operations, enabling real-time online updates of targets in the forward-looking region. Finally, the conjugate gradient method is used to degrade and invert the matrix, outputting the super-resolution result. This method can achieve rapid imaging with limited system memory through an online conjugate gradient super-resolution algorithm based on the minimization criterion. Compared with existing batch processing regularization methods, it eliminates false targets, significantly reduces computational complexity, and is beneficial for rapid imaging of scanning radar.

Description

Technical Field

[0001] This invention belongs to the field of radar detection and imaging technology, specifically relating to an online super-resolution imaging method for scanning radar based on the minimization criterion. Background Technology

[0002] Forward-looking radar imaging has important applications in autonomous landing and autonomous navigation. However, existing single static SAR systems suffer from forward-looking imaging blind zones due to Doppler symmetry ambiguity. While real-aperture radar can achieve forward-looking imaging, its azimuth resolution is limited by the antenna aperture. Therefore, in the past few decades, many researchers have focused on improving azimuth resolution through signal processing methods.

[0003] In recent years, several sparse regularization methods have been proposed to address this problem. These methods typically improve the azimuth resolution of scanning radar by introducing prior target information, constructing a sparse regularization objective function, and solving it. The paper "Jianchao Yang, John Wright, Thomas S Huang, and Yi Ma, “Image super-resolution via sparse representation,” IEEE transactions on image processing, vol. 19, no. 11, pp. 2861-2873, 2010,” proposes a sparse regularization method based on the L1 norm, which can effectively improve radar forward-looking resolution. However, the L1 norm is non-differentiable, making it difficult to directly obtain an analytical solution in practical processing. The paper "Qiping Zhang, Yin Zhang, Yongchao Zhang, Yulin Huang, Wenchao Li, and Jianyu Yang, Majorize-minimization (MM) based super-resolution method for radar forward-looking imaging, in IGARSS2020-2020 IEEE International Geoscience and Remote Sensing Conference,” proposes a sparse regularization method based on the L1 norm, which can effectively improve radar forward-looking resolution. "Sensing Symposium. IEEE, 2020, pp. 3188-3191" proposes a Modigliani-Manufacturer (MM) method that approximates the complex L1 norm with a simpler L2 norm, effectively solving the non-differentiability problem of the L1 norm. However, the MM algorithm also has its limitations. It typically requires hundreds of iterations to converge, resulting in slow speed in practical applications. Furthermore, the large condition number for the inverse term in the MM iterative formula leads to significant perturbations in the inverse matrix, further contributing to its tendency to amplify noise. In addition, the MM algorithm can only be used in batch processing and cannot update images online in real time. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes an online super-resolution imaging method for scanning radar based on the minimization criterion, thereby solving the real-time problem of existing batch processing MM methods.

[0005] The technical solution adopted in this invention is: an online super-resolution imaging method for scanning radar based on the minimization criterion, the specific steps of which are as follows:

[0006] Step 1: Establishing the azimuth echo convolution model;

[0007] Echo data is acquired and preprocessed. Assume the airborne radar platform flies at a constant speed v along the y-axis, and the radar antenna scans the oblique forward-looking region at an angular velocity ω. The platform's flight altitude is H0, and the initial slant range between the platform and the target P is R0. At time t, the distance history R(t) between the platform and the target is expressed as:

[0008]

[0009] Where θ and β represent the azimuth and elevation angles, respectively.

[0010] The radar transmits a linear frequency modulated (LFM) signal to acquire the raw echo from the target. The acquired raw echo undergoes range pulse compression and range travel correction, and the echo signal is represented as follows:

[0011]

[0012] Where τ and t represent the range and azimuth time variables, respectively; σ(x,y) and h(·) represent the target backscattering coefficient and antenna pattern response function, respectively; sinc(·) represents the pulse compression response function; Φ represents the observation region of interest; B represents the bandwidth; λ represents the wavelength; ω represents the beam scanning speed; c represents the electromagnetic wave propagation speed; R0 represents the initial slant range between the radar platform and the target; and R(t) represents the range history between the radar platform and the target.

[0013] Step 2: Super-resolution problem transformation, i.e., discretization of the azimuth echo convolution model;

[0014] As shown in step one, based on the scanning imaging process, the azimuth echo signal is constructed as the convolution of the antenna function and the target scattering coefficient. Considering additive white Gaussian noise, after discretizing the azimuth signal, the azimuth signal model is expressed as:

[0015] y=Aσ+n (3)

[0016] Where y = [y1 y2 … y N ] T This represents the received echo signal matrix, with dimensions N×1; σ=[σ1 σ2 …σ N ] T This represents the target scattering coefficient matrix, with dimensions N×1; n=[n1,n2,…,n N ] T The noise matrix follows a Gaussian distribution and has a dimension of N×1. T represents the transpose of the matrix, and N represents the number of azimuth sampling points. A represents the antenna measurement matrix composed of antenna pattern samplings and has a dimension of N×N, as shown below:

[0017]

[0018] Among them, [a-l …a0…a l [] indicates antenna pattern sampling, l indicates the number of antenna pattern sampling points, and N indicates the number of azimuth sampling points. Ω represents the azimuth imaging range, ω represents the beam scanning speed, and PRF represents the pulse repetition frequency.

[0019] Step 3: Construction and transformation of the objective function;

[0020] For solving the target backscattering coefficient in the discrete echo model (3) The problem, within the framework of sparse regularization, is to transform the convolutional model into a mathematically convex optimization problem:

[0021]

[0022] Where μ represents the regularization parameter that balances sparsity and noise.

[0023] Step 4: Update the objective function online;

[0024] If the antenna measurement matrix is ​​divided into rows, then A = [a1 a2 … a n ] T .

[0025] in, Let A be the row vector of the nth row. Therefore, the first term in equation (5) can be equivalently expressed as:

[0026]

[0027] in, The dimension symbol is y. j Let represent the j-th element of the echo signal matrix y, i.e., the j-th echo value received in the azimuth direction. The second term in equation (5), the L1 norm, can be equivalently expressed by the minimization criterion as:

[0028] μ||σ||1=μσ T W n σ (7)

[0029] Among them, W n =diag(1 / |σ n |) represents the diagonal loading matrix, then the model in equation (5) can be equivalently represented as:

[0030]

[0031] Where, σ n This represents the real-time target scattering coefficient value obtained when the nth echo arrives. This represents the instantaneous target scattering coefficient estimate when the (n+1)th echo arrives. The closed-form solution of equation (8) can be given by the following formula:

[0032]

[0033] Step 5: Degradation and inversion using the conjugate gradient method;

[0034] make Then equation (9) can be written as:

[0035] A n σ=b n (10)

[0036] According to the conjugate gradient method, when A n When the matrix is ​​positive definite, solving this system of linear equations is equivalent to finding the minimum value of the function:

[0037]

[0038] in, R represents the defined cost function. n The solution set is the set of real numbers, σ * This represents the solution to the equation.

[0039] For the above minimization problem, an iterative solution is adopted, and the iterative calculation process is as follows:

[0040] First, initialize the solution σ of the equation. * The iterative value is chosen by selecting σ0∈R. n Let r0 = b n -A n σ0, the iterative steps are as follows:

[0041]

[0042] Where σ0 represents the initial iteration value of the independent variable in equation (11), k represents the number of iterations, H represents the conjugate transpose of the matrix, and ε represents an infinite decimal.

[0043] When ||σ k+1 -σ k When || < ε, the loop iteration ends, and the solution to the equation σ = σ k .

[0044] Based on the above derivation, an online update based on the conjugate gradient method for degradation and inversion can be performed when each echo arrives. When n=1, the initialization is set as follows:

[0045]

[0046] Where, when n≥2, let Then An =μW n +Q n The calculation is performed recursively using the following formula:

[0047]

[0048] The beneficial effects of this invention are as follows: The method of this invention establishes an azimuth echo convolution model, performs discretization processing, and completes the transformation of the super-resolution problem. Under the regularization framework, it constructs an analytically optimizeable cost function containing sparse prior information using the minimization criterion, transforming the forward-looking imaging resolution improvement problem into an optimization estimation problem. By performing row-block processing on the antenna measurement matrix, matrix operations are degraded into the continuous accumulation of vector operations, achieving real-time online updates of targets in the forward-looking region. Finally, the conjugate gradient method is used to degrade and invert the matrix, outputting the super-resolution result. This invention's method can achieve rapid imaging with limited system memory through an online conjugate gradient super-resolution algorithm based on the minimization criterion. Compared with existing batch processing regularization methods, it eliminates false targets, significantly reduces computational complexity, and is beneficial for rapid imaging in scanning radar. Attached Figure Description

[0049] Figure 1 This is a flowchart of an online super-resolution imaging method for scanning radar based on the minimization criterion of the present invention.

[0050] Figure 2 This is a geometric model diagram of the forward-looking imaging of airborne radar in an embodiment of the present invention.

[0051] Figure 3 This is a comparison chart of simulation results in the embodiments of the present invention. Detailed Implementation

[0052] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] This invention is mainly verified by simulation experiments, and all steps and conclusions have been verified to be correct on Matlab2019.

[0054] like Figure 1 The flowchart of an online super-resolution imaging method for scanning radar based on the minimization criterion of the present invention is shown below. The specific steps are as follows:

[0055] Table 1. System parameters of the radar platform

[0056] Table 2. Comparison of convergence speed between the method of this invention and the traditional method

[0057] Step 1: Establishing the azimuth echo convolution model;

[0058] Adopting such Figure 2The airborne radar forward-looking imaging geometric model shown is used, and the radar simulation system parameters are selected as shown in Table 1.

[0059] Table 1

[0060] parameter numerical values Operating frequency band 30.75GHz bandwidth 40MHz Time width 2μs Scanning area -10°～10° Scan speed 30° / s beamwidth 3° Pulse repetition frequency 1KHz Initial slope distance 3000m Airborne platform flight speed 20m / s

[0061] The signal-to-noise ratio (SNR) is set to SNR = 20 dB. Assume the airborne radar platform flies at a constant speed v = 20 m / s along the y-axis, and the radar antenna scans the forward-looking area at ω = 30° / s. The platform's flight altitude is H0 = 1000 m, and the initial slant range between the platform and the target P is R0 = 3000 m. At time t, the distance history R(t) between the platform and the target is expressed as:

[0062]

[0063] Where θ and β represent the azimuth and elevation angles, respectively.

[0064] Radar acquires raw echo data by transmitting a linear frequency modulated signal with a large time-bandwidth product. After range pulse compression and range travel correction, the raw echo signal can be represented as follows:

[0065]

[0066] Where τ and t represent the range and azimuth time variables, respectively; σ(x,y) and h(·) represent the target backscattering coefficient and antenna pattern response function, respectively; sinc(·) represents the pulse compression response function; Φ represents the region of interest; B = 40MHz represents the bandwidth; λ = 0.01m represents the wavelength; ω = 30° / s represents the beam scanning speed; and c = 3 × 10⁻⁶. 8 m / s represents the propagation speed of electromagnetic waves, R0 = 3000m represents the initial slant range between the platform and the target, and R(t) represents the distance history between the radar platform and the target.

[0067] Step 2: Super-resolution problem transformation, i.e., discretization of the azimuth echo convolution model;

[0068] As shown in step one, based on the scanning imaging process, the azimuth echo signal can be constructed as the convolution of the antenna function and the target scattering coefficient, considering additive white Gaussian noise. After discretizing the azimuth signal, the azimuth signal model is expressed as:

[0069] y=Aσ+n (17)

[0070] Where y = [y1 y2 … y N ] T This represents the received echo signal matrix, with dimensions N×1; σ=[σ1 σ2 …σ N ] TThis represents the target scattering coefficient matrix, with dimensions N×1; n=[n1,n2,…,n N ] T The noise matrix follows a Gaussian distribution and has a dimension of N×1. T represents the transpose of the matrix, and N represents the number of azimuth sampling points. A represents the antenna measurement matrix composed of antenna pattern samplings and has a dimension of N×N, as shown below:

[0071]

[0072] Among them, [a -l …a0…a l [] indicates antenna pattern sampling, l indicates the number of antenna pattern sampling points, and N indicates the number of azimuth sampling points. Ω represents the azimuth imaging range, ω represents the beam scanning speed, and PRF represents the pulse repetition frequency.

[0073] Step 3: Construction and transformation of the objective function;

[0074] For solving the target backscattering coefficient in the discrete echo model (17) The problem, within the framework of sparse regularization, is to transform the convolutional model into a mathematically convex optimization problem:

[0075]

[0076] Where μ = 225 represents the regularization parameter that balances sparsity and noise.

[0077] Step 4: Update the objective function online;

[0078] Equation (19) in step three cannot be solved directly due to its L1 norm. Therefore, the antenna measurement matrix in equation (18) of step three is divided into row blocks, resulting in A = [a1 a2 … a n ] T .

[0079] in, Let A be the nth row vector. Therefore, the first term in equation (19) can be equivalently expressed as:

[0080]

[0081] in, The dimension symbol is y. j Let represent the j-th element of the echo signal matrix y, i.e., the j-th echo value received in the azimuth direction. The second term in equation (19), the L1 norm, can be equivalently expressed by the minimization criterion as:

[0082] μ||σ||1=μσ T W n σ (21)

[0083] Among them, W n =diag(1 / |σ n |) represents the diagonal loading matrix, therefore, the model in equation (19) can be equivalently represented as:

[0084]

[0085] Where, σ n This represents the real-time target scattering coefficient value obtained when the nth echo arrives. This represents the instantaneous target scattering coefficient estimate when the (n+1)th echo arrives. The closed-form solution of equation (22) can be given by the following formula:

[0086]

[0087] Step 5: Degradation and inversion using the conjugate gradient method;

[0088] Step four, equation (23), provides the online update iterative formula for the target scattering coefficient, which recovers a real-time estimate of the target scattering coefficient with each echo signal arrival. However, due to the inversion term in equation (23), this computational complexity is unacceptable for an online method. To address this problem, let... Then equation (23) can be written as:

[0089] A n σ=b n (twenty four)

[0090] For this system of linear equations, the conjugate gradient algorithm is used to solve it, thus avoiding the inversion operation required for each online update of the target scattering coefficients. As can be seen from the conjugate gradient method, when A... n When the matrix is ​​positive definite, solving this system of linear equations is equivalent to finding the minimum value of the function:

[0091]

[0092] in, R represents the defined cost function. n The solution set is the set of real numbers, σ * This represents the solution to the equation.

[0093] The above minimization problem can usually be solved iteratively. The iterative calculation process is as follows:

[0094] First, initialize the solution σ of the equation. * The iterative value is chosen by selecting σ0∈R. n Let r0 = b n -A n σ0. Then, iterate in a loop following these steps:

[0095]

[0096] Where σ0 represents the initial iteration value of the independent variable in equation (11), k represents the number of iterations, H represents the conjugate transpose of the matrix, and ε represents an infinite decimal.

[0097] When ||σ k+1 -σ k When || < ε, the loop iteration ends, and the solution to the equation σ = σ k .

[0098] Therefore, based on the above derivation, an online update based on the conjugate gradient method for degradation and inversion can be performed upon the arrival of each echo. When n=1, the initialization can be set to...

[0099]

[0100] Where, when n≥2, let Then A n =μW n +Q n The calculation is performed recursively using the following formula:

[0101]

[0102] Compared with the existing MM method, the method of the present invention makes full use of the similarity between adjacent echo signals. The initial value of the iteration at time n+1 is the estimated value at time n. Since adjacent echo signals are often quite similar, the method of the present invention only requires 1-2 iterations to obtain a better recovered image as the echo data increases.

[0103] Simulation results are as follows Figure 3 As shown, where Figure 3 (a) and (b) are real target scenes and their cross-sectional views, with a signal-to-noise ratio (SNR) of 20dB. Figure 3 (c) shows the real beam echo result. Figure 3 (d) shows the real beam echo profile. These two figures demonstrate that the target cannot be distinguished. Figure 3 (e) and Figure 3 (f) shows the super-resolution results and their profiles processed by the existing minimization algorithm. Figure 3 (g) and Figure 3(h) shows the super-resolution results and their cross-sectional images processed by the method of this invention. It can be seen that the existing minimax algorithm produces false targets in its super-resolution results, while the method of this invention effectively suppresses noise amplification and eliminates false targets under conditions of almost identical resolution. Furthermore, to evaluate the convergence speed of the proposed algorithm, the simulation computation time was compared with that of the existing batch minimax algorithm, and the comparison results are shown in Table 2. It can be seen that the computation time of the method proposed in this invention is significantly reduced.

[0104] Table 2

[0105] method Runtime Existing Max-Min 1.61s Method of the present invention 0.78s

[0106] In summary, the method of this invention can achieve rapid imaging with limited system memory by using an online conjugate gradient super-resolution algorithm based on the minimization criterion. Compared with existing batch processing regularization methods, it eliminates false targets, significantly reduces computational complexity, and is beneficial for rapid imaging of scanning radar.

[0107] 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. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. An online super-resolution imaging method for scanning radar based on the minimization criterion, the specific steps of which are as follows: Step 1: Establishing the azimuth echo convolution model; Echo data is acquired and preprocessed. Assume the airborne radar platform flies at a constant speed v along the y-axis, and the radar antenna scans the oblique forward-looking region at an angular velocity ω. The platform's flight altitude is H0, and the initial slant range between the platform and the target P is R0. At time t, the distance history R(t) between the platform and the target is expressed as: in, θ and β represent the azimuth and elevation angles, respectively; The radar transmits a linear frequency modulated (LFM) signal to acquire the raw echo from the target. The acquired raw echo undergoes range pulse compression and range travel correction, and the echo signal is represented as follows: Where τ and t represent the range and azimuth time variables, respectively; σ(x,y) and h(·) represent the target backscattering coefficient and antenna pattern response function, respectively; sinc(·) represents the pulse compression response function; Φ represents the observation area of ​​interest; B represents the bandwidth; λ represents the wavelength; ω represents the beam scanning speed; c represents the electromagnetic wave propagation speed; R0 represents the initial slant range between the radar platform and the target; and R(t) represents the range history between the radar platform and the target. Step 2: Super-resolution problem transformation, i.e., discretization of the azimuth echo convolution model; As shown in step one, based on the scanning imaging process, the azimuth echo signal is constructed as the convolution of the antenna function and the target scattering coefficient. Considering additive white Gaussian noise, after discretizing the azimuth signal, the azimuth signal model is expressed as: y=Aσ+n (3) Where y = [y1 y2 … y N ] T This represents the received echo signal matrix, with dimensions N×1; σ=[σ1 σ2 … σ N ] T This represents the target scattering coefficient matrix, with dimensions N×1; n=[n1,n2,…,n N ] T The noise matrix follows a Gaussian distribution and has a dimension of N×1. T represents the transpose of the matrix, and N represents the number of azimuth sampling points. A represents the antenna measurement matrix composed of antenna pattern samplings and has a dimension of N×N, as shown below: Among them, [a -l …a0…a l [] indicates antenna pattern sampling, l indicates the number of antenna pattern sampling points, and N indicates the number of azimuth sampling points. Ω represents the azimuth imaging range, ω represents the beam scanning speed, and PRF represents the pulse repetition frequency; Step 3: Construction and transformation of the objective function; For solving the target backscattering coefficient in the discrete echo model (3) The problem, within the framework of sparse regularization, is to transform the convolutional model into a mathematically convex optimization problem: Where μ represents the regularization parameter that balances sparsity and noise; Step 4: Update the objective function online; If the antenna measurement matrix is ​​divided into rows, then A = [a1 a2 … a n ] T ; in, Let A be the row vector of the nth row. Therefore, the first term in equation (5) can be equivalently expressed as: in, The dimension symbol is y. j Let represent the j-th element of the echo signal matrix y, i.e., the j-th echo value received in the azimuth direction; and the second term L1 norm in equation (5) can be equivalently expressed by the minimization criterion as: μ||σ||1=μσ T W n p (7) Among them, W n =diag(1 / |σ n |) represents the diagonal loading matrix, then the model in equation (5) can be equivalently represented as: Where, σ n This represents the real-time target scattering coefficient value obtained when the nth echo arrives. This represents the instantaneous target scattering coefficient estimate when the (n+1)th echo arrives; and the closed-form solution of equation (8) can be given by the following formula: Step 5: Degradation and inversion using the conjugate gradient method; make Then equation (9) can be written as: A n σ=b n (10) As can be seen from the conjugate gradient method, when A n When the matrix is ​​positive definite, solving this system of linear equations is equivalent to finding the minimum value of the function: in, R represents the defined cost function. n The solution set is the set of real numbers, σ * Represents the solution to the equation; For the above minimization problem, an iterative solution is adopted, and the iterative calculation process is as follows: First, initialize the solution σ of the equation. * The iterative value is chosen by selecting σ0∈R. n Let r0 = b n -A n σ0, the iterative steps are as follows: Where σ0 represents the initial iteration value of the independent variable in equation (11), k represents the number of iterations, H represents the conjugate transpose of the matrix, and ε represents an infinite decimal. When ||σ k+1 -σ k When || < ε, the loop iteration ends, and the solution to the equation σ = σ k ; Based on the above derivation, an online update based on the conjugate gradient method for degradation and inversion can be performed when each echo arrives. When n=1, the initialization is set as follows: Where, when n≥2, let Then A n =μW n +Q n The calculation is performed recursively using the following formula: W n =diag(1 / |σ n |) (14).

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