Leaf cluster clutter suppression method and system based on low-rank sparse matrix constrained optimization

Abstract

The present invention discloses a foliage clutter suppression method and system based on low-rank sparse matrix constraint optimization. The method first performs a fractional Fourier transform on the radar echo and finds the maximum energy point in the plane based on the two-dimensional distribution, determines the optimal transformation order ρ, and then performs a ρ-order FRFT transform on the radar echo to maximize the energy difference between the target and the clutter in the radar received signal in the FRFT domain. Then, a low-rank sparse constraint model is constructed in the FRFT domain and the objective function is optimized. The objective function is iteratively solved by using an improved augmented Lagrange multiplier method based on simulated annealing optimization. Finally, the reconstructed signal is inversely FFT-transformed into the time domain to obtain the data after clutter suppression. The present invention addresses the difficulty of ground reconnaissance radar detecting low-speed moving targets in a foliage clutter environment by performing low-rank sparse constraint reconstruction in the frequency domain, thereby achieving foliage clutter suppression, improving the signal-to-clutter ratio of the low-speed target echo signal, and effectively improving the detection performance of low-speed targets in a forest environment.

Description

Technical Field

[0001] The present invention belongs to the field of radar signal processing, and in particular relates to a leaf cluster clutter suppression method and system based on low-rank sparse matrix constraint optimization. Background Art

[0002] Ground-based battlefield reconnaissance radars are crucial for battlefield situational awareness and intelligence acquisition in modern information warfare. However, ground clutter interference poses a significant challenge for ground-based battlefield reconnaissance radars, making low-speed targets difficult to detect. In peacetime asymmetric warfare and counterterrorism, the need to detect low-speed targets hidden by trees is common. However, since battlefield reconnaissance radars typically operate in the X-band or higher, lacking diffraction capabilities, these targets are often lost in foliage clutter, making them undetectable. Therefore, effectively suppressing foliage clutter is crucial for improving the low-speed target detection performance of ground-based battlefield reconnaissance radars. At present, in order to reduce the interference of leaf cluster clutter in ground moving target detection, a series of clutter suppression methods have been proposed. For the case where the target Doppler is outside the mainlobe clutter, the moving target indication (MTI) and moving target detection (MTD) are proposed to filter the clutter in the frequency domain by utilizing the frequency difference between the clutter and the moving target; the leaf cluster clutter is modeled using a sub-regression model, and the singular value decomposition (SVD) is used to remove the clutter and reconstruct the target signal. However, the above methods have great limitations for low-speed target monitoring scenarios.

[0003] Patent application number CN 201610060416.1 discloses a wavelet-based method for designing sea clutter suppression curves for marine radars. This method uses discrete wavelet transforms to decompose radar echo data to suppress background sea clutter. While this method has achieved some success in sea clutter suppression, it has significant limitations for ground-based battlefield reconnaissance radars in low-speed target surveillance scenarios. Summary of the Invention

[0004] The purpose of the present invention is to propose a method and system for suppressing foliage clutter in ground battlefield reconnaissance radar based on low-rank sparse matrix constraint optimization.

[0005] The technical solution to achieve the purpose of the present invention is: a leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization, the steps are as follows:

[0006] Step 1: Perform FRFT transform of different orders on the radar echo signal and find the maximum energy point in the plane according to the two-dimensional distribution;

[0007] Step 2: Determine the optimal transformation order ρ based on the maximum energy point obtained in step 1 u , and the radar echo is ρ uOrder FRFT transform;

[0008] Step 3: Sparsely decompose the radar echo matrix in the FRFT domain to establish an optimization model, and perform convex relaxation on the optimization model;

[0009] Step 4: Solve the objective function based on the improved augmented Lagrange multiplier method, initialize the relevant values ​​and iterate continuously until convergence to obtain the objective function matrix;

[0010] Step 5: Perform inverse FFT transformation of the signal reconstructed in step 4 into the time domain to obtain the data after clutter suppression.

[0011] A leaf cluster clutter suppression system based on low-rank sparse matrix constrained optimization, comprising:

[0012] The first module is used to perform FRFT transforms of different orders on the radar echo signal and find the maximum energy point in the plane according to the two-dimensional distribution;

[0013] The second module determines the optimal transformation order ρ by finding the maximum energy point in the first module. u , and the radar echo is ρ u Order FRFT transform;

[0014] In the third module, the radar echo matrix is ​​sparsely decomposed in the FRFT domain to establish an optimization model, and the optimization model is convexly relaxed;

[0015] The fourth module solves the objective function based on the improved augmented Lagrange multiplier method. After initializing the relevant values, it iterates continuously until convergence to obtain the objective function matrix.

[0016] The fifth module is used to perform an inverse FFT transformation of the signal reconstructed by the fourth module into the time domain to obtain data after clutter suppression.

[0017] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization is implemented.

[0018] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization.

[0019] Compared with the prior art, the present invention has the following significant advantages:

[0020] (1) Based on the SA algorithm, the augmented Lagrange multiplier method is improved to ensure that the optimal μ can be obtained in each round of iteration. SA , which ensures the algorithm’s adaptability and improves the integrity of target signal reconstruction.

[0021] (2) A low-rank sparse constrained reconstruction in the frequency domain is proposed to suppress leaf clutter and improve the signal-to-noise ratio of the low-speed target echo signal, effectively improving the detection performance of low-speed targets in leaf clutter. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Flowchart of the method for suppressing foliage clutter in ground battlefield reconnaissance radar based on low-rank sparse matrix constraint optimization in the present invention.

[0023] Figure 2 This is the flow chart of the algorithm of the improved augmented Lagrange multiplier method based on simulated annealing optimization (SA) proposed in the present invention.

[0024] Figure 3 Schematic diagram of radar echo power spectrum.

[0025] Figure 4 Schematic diagram of the results of leaf cluster clutter suppression using low-rank sparse joint constraints. DETAILED DESCRIPTION

[0026] The present invention proposes a foliage clutter suppression method based on low-rank sparse matrix constraint optimization. The method first performs a fractional Fourier transform on the radar echo and finds the maximum energy point in the plane according to the two-dimensional distribution, determines the optimal transformation order ρ, and then performs a ρ-order FRFT transform on the radar echo so that the energy difference between the target and the clutter in the radar received signal in the FRFT domain is maximized. Then, a low-rank sparse constraint model is constructed in the FRFT domain and the objective function is optimized. The augmented Lagrange multiplier method is improved based on simulated annealing optimization (SA) to iteratively solve the problem. Finally, the reconstructed signal is inverse FFT transformed to the time domain to obtain the data after clutter suppression. The present invention addresses the problem of ground reconnaissance radar detecting low-speed moving targets in a foliage clutter environment, performs low-rank sparse constraint reconstruction in the frequency domain, thereby achieving foliage clutter suppression, improving the signal-to-clutter ratio of the low-speed target echo signal, and effectively improving the detection performance of low-speed targets in a forest environment.

[0027] like Figure 1 As shown, the method for suppressing foliage clutter of ground battlefield reconnaissance radar based on low-rank sparse matrix constraint optimization of the present invention includes the following steps:

[0028] Step 1: Radar receiving data under different orders ρ is calculated according to the formula Perform FRFT transformation to obtain the amplitude distribution of the radar signal in the FRFT domain at all orders. And find the coordinates of the maximum energy point in the plane based on the two-dimensional distribution.

[0029] in, is the rotation angle, and ρ is the transformation order of FRFT.

[0030] Step 2: Determine the optimal transformation order ρ based on the maximum energy point obtained in step 1 u , perform ρ on the radar received echo u The FRFT transform of the order is used to maximize the energy difference between the target and the clutter in the FRFT domain.

[0031] Step 3: Based on RPCA, the radar echo matrix is ​​sparsely decomposed in the FRFT domain to establish an optimization model. The suppression of leaf clutter can be expressed as a low-rank sparse constrained optimization problem:

[0032]

[0033] Among them, Z t is the target subspace; Z f is the clutter and noise subspace; rank(·) is the rank of the matrix; ||·||0 is the zero-order norm of the matrix; λ is the regularization parameter, which is related to the decomposition accuracy. The norm relaxation is norm, and replace rank(·) with the nuclear norm to perform low-rank constraint:

[0034]

[0035] In the formula, ||·|| * is the nuclear norm of the matrix; ||·||1 is the first-order norm of the matrix; λ is the regularization parameter related to the decomposition accuracy.

[0036] Step 4: Figure 2 As shown, the augmented Lagrange multiplier method (ALM) is introduced for low-rank solution:

[0037]

[0038] Where, L(Z f ,Z t ,Y) is the augmented Lagrangian function; λ is the regularization parameter; μ>0 is the iteration coefficient, which is used to balance the number of iterations and the termination condition; Y is the Lagrangian multiplier; ||·|| F is the Frobenius norm of the matrix;

[0039] Since the adaptive ability of the iteration coefficient μ is weak, the SA algorithm is introduced to obtain the optimal μ in each round of iteration, which is expressed as μ SA , so we can get:

[0040]

[0041] Where μ SAThe optimal parameters for each round obtained by the SA algorithm are adaptively updated at each iteration of the matrix.

[0042] The specific update method is: set the value range of μ to be (where Z f k is the target matrix for the kth iteration, σ max (Z f k ) is Z f k The maximum singular value of ), the fitness function is taken as (where σ i (Z f k ) is Z f k The optimal penalty coefficient μ is obtained based on the SA algorithm. SA .

[0043] Assuming that the maximum number of iterations is k, the k-th operation process is divided into two steps: first, find the optimal parameters for this iteration Then As the parameter update for this iteration, the specific steps are:

[0044] Define the iteration operator S τ (x) = sgn(x)max(|x|-τ, 0), and substituting it into the equation, we can get:

[0045]

[0046] Where x is a complex number and τ is a real number.

[0047] Define the singular value iteration operator D again τ (Z f )=US τ (∑)V * Substituting into the above formula we can get:

[0048]

[0049] Fix Z, Z first t , Y, μ SA , then we can get Z f The iterative update formula is:

[0050]

[0051] Similar fixed Z, Z f , Y, μ SA , then we can get Z t The iterative update formula is:

[0052]

[0053] Finally, fix Z, Z f , Z t 、μ SA The iterative update formula for Y is obtained as:

[0054]

[0055] After multiple rounds of iteration, until the convergence condition is met (ε is usually taken as 10 -4 ) or the number of iterations reaches k max , the target signal matrix is ​​obtained.

[0056] Step 5: Use inverse frequency FFT to transform the signal reconstructed in step 4 into the time domain to obtain the required clutter suppression data.

[0057] The present invention also provides a leaf cluster clutter suppression system based on low-rank sparse matrix constraint optimization, comprising:

[0058] The first module is used to perform FRFT transforms of different orders on the radar echo signal and find the maximum energy point in the plane according to the two-dimensional distribution;

[0059] The second module determines the optimal transformation order ρ by finding the maximum energy point in the first module. u , and the radar echo is ρ u Order FRFT transform;

[0060] In the third module, the radar echo matrix is ​​sparsely decomposed in the FRFT domain to establish an optimization model, and the optimization model is convexly relaxed;

[0061] The fourth module solves the objective function based on the improved augmented Lagrange multiplier method. After initializing the relevant values, it iterates continuously until convergence to obtain the objective function matrix.

[0062] The fifth module is used to perform an inverse FFT transformation of the signal reconstructed by the fourth module into the time domain to obtain data after clutter suppression.

[0063] The specific implementation methods of the first to fifth modules are the same as the specific methods of each step of the aforementioned leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization, and will not be repeated here.

[0064] The following simulation verifies the clutter suppression algorithm of the present invention

[0065] The radar simulation parameters are set as follows: operating frequency of 10 GHz, linear frequency modulation (LFM) signal waveform, 30 MHz bandwidth, 0.5 µs duration, 25 µs repetition period, and 240 MHz sampling frequency. The target is located at the 200th range gate and approaches the radar at a constant speed of 0.5 m / s. The echo signal accumulation period is 512 seconds. The clutter signal is simulated using a single pendulum multipath clutter model.

[0066] The results of suppressing the leaf cluster clutter using the basic low-rank sparse joint constraint method of the present invention are as follows: Figure 3 and Figure 4 As shown. Figure 4 It can be seen that after being processed by the clutter suppression method based on low-rank sparse matrix constraint optimization of the present invention, the target signal can be well reconstructed, and the maximum clutter power spectrum is attenuated by about 15dB relative to the target spectrum, which can effectively improve the detection performance of low-speed targets in the foliage cluster environment of battlefield reconnaissance radar.

[0067] The above embodiments are only for illustrating the technical ideas of the present invention and cannot be used to limit the scope of protection of the present invention. Any changes made on the basis of the technical solutions in accordance with the technical ideas proposed by the present invention fall within the scope of protection of the present invention; any technologies not involved in the present invention can be implemented by existing technologies.

Claims

1. A leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization, characterized in that: The steps include: Step 1: Perform FRFT transform of different orders on the radar echo signal and find the maximum energy point in the plane according to the two-dimensional distribution; Step 2: Determine the optimal transformation order ρ based on the maximum energy point obtained in step 1 u , and the radar echo is ρ u Order FRFT transform; Step 3: Sparsely decompose the radar echo matrix in the FRFT domain to establish an optimization model, and perform convex relaxation on the optimization model; The radar echo matrix is ​​sparsely decomposed to establish an optimization model to obtain: Where Z t is the target subspace; Z f is the clutter and noise subspace; rank(·) is the rank of the matrix; ||·||0 is the zero-order norm of the matrix; λ is the regularization parameter; Perform convex relaxation on the above formula, relax the l0 norm to the l1 norm, and replace rank(·) with the nuclear norm to perform low-rank constraint: In the formula, ||·|| * is the nuclear norm of the matrix; ||·||1 is the first-order norm of the matrix, and λ is the regularization parameter; Step 4: Solve the objective function based on the improved augmented Lagrange multiplier method, initialize the relevant values, and iterate continuously until convergence to obtain the objective function matrix; the improved augmented Lagrange multiplier method is used to obtain the low-rank optimization solution: Where, L(Z f ,Z t ,Y) is the augmented Lagrangian function; μ>0 is the iteration coefficient, which is used to balance the number of iterations and the termination condition; Y is the Lagrangian multiplier; ||·|| F is the Frobenius norm of the matrix; The SA algorithm is introduced to obtain the optimal μ in each round of iteration, which is expressed as μ SA , so we can get: Where μ SA The optimal parameters of each round obtained by the SA algorithm are adaptively updated at each iteration of the matrix; And define the iteration operator S τ (x) = sgn(x)max(|x|-τ, 0), and the singular value iteration operator D τ (Z f )=US τ (∑)V * Substituting into the above formula we can get: Where: x is a complex number; τ is a real number; Z f =UΛV * is the matrix Z f Singular value decomposition of; U, V are matrices Z f Two orthogonal matrices obtained by singular value decomposition; S τ Is a diagonal matrix, the diagonal elements are matrix Z f After initializing the relevant values, iterate continuously until convergence to obtain the objective function matrix; Step 5: Perform inverse FFT transformation of the signal reconstructed in step 4 into the time domain to obtain the data after clutter suppression.

2. The leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization according to claim 1 is characterized in that: In step 1, the radar receiving data under different orders ρ is calculated according to the formula Perform FRFT transformation to obtain the amplitude distribution of the radar signal in the FRFT domain at all orders; and find the coordinates of the maximum energy point in the plane based on the two-dimensional distribution; where, is the rotation angle.

3. The leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization according to claim 1, characterized in that: μ SA The optimal parameters of each round obtained by the SA algorithm are updated adaptively at each iteration of the matrix. The update method is: set the value range of μ to be where Z f k is the target matrix for the kth iteration, σ max (Z f k ) is Z f k The maximum singular value of , the fitness function is taken as σ i (Z f k ) is Z f k The i-th singular value of , based on the SA algorithm, obtains the optimal penalty coefficient μ SA .

4. The leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization according to claim 3 is characterized in that: Fixed Z, Z t , Y, μ SA , then we can get Z f The iterative update formula is: Fixed Z, Z f , Y, μ SA , then we can get Z t The iterative update formula is: Fixed Z, Z f 、Z t 、μ SA The iterative update formula for Y is obtained as: After multiple rounds of iteration, until the convergence condition is met Or the number of iterations reaches k max , the target signal matrix is ​​obtained.

5. The leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization according to claim 4, characterized in that: ε is 10 -4 .

6. A leaf cluster clutter suppression system based on low-rank sparse matrix constrained optimization, characterized in that: include: The first module is used to perform FRFT transforms of different orders on the radar echo signal and find the maximum energy point in the plane according to the two-dimensional distribution; The second module determines the optimal transformation order ρ by finding the maximum energy point in the first module. u , and the radar echo is ρ u Order FRFT transform; In the third module, the radar echo matrix is ​​sparsely decomposed in the FRFT domain to establish an optimization model, and the optimization model is convexly relaxed; The fourth module solves the objective function based on the improved augmented Lagrange multiplier method. After initializing the relevant values, it iterates continuously until convergence to obtain the objective function matrix. The fifth module is used to perform an inverse FFT transformation of the signal reconstructed by the fourth module into the time domain to obtain data after clutter suppression.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization as described in any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the leaf cluster clutter suppression method based on low-rank sparse matrix constraint optimization as described in any one of claims 1 to 5 is implemented.

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