Unmanned aerial vehicle target subject and micro-motion component echo signal separation method based on factor decomposition group sparse regularization

Abstract

The application particularly relates to a UAV target main body and micro-motion component echo signal separation method based on factor decomposition group sparse regularization, which comprises the following steps: firstly, constructing a radar echo time-frequency representation into a Hankel matrix; secondly, using the characteristic that the echo Hankel matrix of the target main body uniform motion has low rank, establishing a signal separation model containing a low rank term, a sparse term and a noise term; thirdly, using a factor decomposition group sparse regularization method to effectively relax the rank function in the model, so as to improve the robustness of the algorithm; finally, using a linearized alternating direction multiplier method to iteratively solve the optimization model, so as to realize effective separation of the target main body echo and the micro-motion component echo in the time-frequency domain. The application is particularly suitable for narrow-band radar and short coherent accumulation time detection conditions, can effectively overcome the problems of model mismatch and low calculation efficiency existing in traditional methods, and simulation and measured data verify that the method has good separation precision and robustness in a noise environment.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing, specifically to a method for separating the echo signals of a target subject and micro-moving components based on sparse regularization of factor decomposition groups, for separating the echo signals of a target subject and micro-moving components under narrowband radar detection conditions. Background Technology

[0002] When a target or certain structures of a target involve vibration or rotation in addition to translational motion, this motion modulates the radar echo signal and generates time-varying sidebands around the target's Doppler frequency. This phenomenon can be described as the micro-Doppler effect. The micro-Doppler effect is a characteristic unique to radar targets and provides valuable information for research on radar imaging, feature extraction, and target recognition. For UAV targets, the echo is a multi-component signal composed of the echoes from the main body and micro-moving parts. In the field of inverse synthetic aperture radar (ISAR), because the motion characteristics of micro-moving parts differ from those of the main body, the echoes from micro-moving parts need to be filtered to improve imaging quality. In the field of automatic target recognition (ATR), the echo from the main body can be considered as information that hinders the extraction of micro-Doppler features. Therefore, in the past decade, the separation and estimation of the echoes from the main body and micro-moving parts have been extensively studied. Existing methods for separating the echoes from the target main body and micro-moving parts mainly involve projecting the target echo signal onto a transform domain where feature differences are easily extracted, thereby achieving echo separation. The methods can be broadly categorized into three types: parameter domain processing, time domain processing, and time-frequency domain processing.

[0003] The target body and micro-motion component echo separation method based on parameter domain processing mainly relies on point-line duality. It projects the information of the micro-motion and body signals in the image domain to a parameter domain that is easier to analyze and process, thereby extracting or removing the micro-motion component echo signal. Professor Zhang Qun of the Air Force Engineering University used the standard Hough transform and the extended Hough transform to detect straight lines and sinusoidal curves on the spectrum, respectively, thus achieving echo separation between the target body and rotating components. Existing literature uses the integral of the cubic phase function to estimate the signal frequency modulation slope to extract the body echo, and then uses the extended Hough transform to estimate the parameters of the sinusoidal frequency-modulated signal, reducing the dimension of the extended Hough transform. Existing literature applies the inverse Jordan transform to the spectrum, proposing a method for extracting the parameters of the sinusoidal frequency-modulated micro-Doppler signal. Existing literature uses the inverse Jordan transform to extract the echo of the rotating component, achieving the extraction of the target body signal and the removal of the micro-motion component echo. Professor Wang Yong of Harbin Institute of Technology extended the traditional Jordan transform to a three-parameter Jordan transform and used the three-parameter Jordan transform and inverse Jordan transform to separate linear frequency modulated (LFM) signals and sinusoidal frequency modulated (SFM) signals. However, most parameter domain processing methods require pre-setting the instantaneous frequency modulation model of the micro-motion signal. When the micro-motion model is unknown, the above methods will encounter model mismatch problems.

[0004] Time-domain processing-based methods for separating target body and micro-motion component echoes typically decompose the radar time-domain signal into a combination of basis functions, and then separate the target body and micro-motion component echoes based on the differences in the representations of the basis functions. Existing literature uses Empirical Mode Decomposition (EMD) to separate the echo signals of target bodies and micro-motion components. Since most radar data are complex signals, researchers have proposed Complex-valued Empirical Mode Decomposition (CEMD). CEMD decomposes the complex signal into positive and negative frequency components using a bandpass filter, converts the real part information of the EMD decomposition into Intrinsic Mode Functions (IMFs), and finally obtains the complex IMFs through Hilbert transform, thereby improving the separation accuracy. Building on this, Bivariate Variational Mode Decomposition (BVMD) has also been used to separate the echo signals of the target's main body and micro-movement components. This method decomposes the radar echo into a series of complex IMFs, distinguishes micro-movement features based on these functions, and removes micro-movement information from the Doppler effect.

[0005] Time-frequency domain processing-based methods for separating the echoes of the target body and the micro-moving parts generally separate them based on the characteristic differences of the echoes in the time-frequency domain. Existing literature uses a sliding window time-frequency transform to process the echo signal and determines whether the echo energy belongs to the target body or the rotating part based on the obtained time-frequency characterization order statistics. Building on this, existing literature uses the L-statistic method in the time-frequency domain to remove micro-Doppler signals, which is more robust than the order statistics method. However, this method also loses some of the target body signal when removing micro-Doppler signals, so it is necessary to reconstruct the target body echo based on the remaining samples. Existing literature obtains a highly concentrated spectrum of energy by summing the short-time Fourier transform of the remaining samples along the time dimension, making the reconstructed target body echo more complete. By recording the frequency of occurrence of the frequency distribution points after the time-frequency transform of the echo signal, existing literature uses histogram statistics to preserve the signal energy of high-frequency occurrences in the frequency dimension, thereby extracting the target body signal. Existing literature combines Fourier-Bessel transform to decompose radar echoes into stationary and non-stationary components, and further employs inverse Fourier-Bessel transform to reconstruct the echo signal of the micro-moving component. The effectiveness of this method is verified using measured data from a rotating corner reflector. Other existing literature uses wavelet transform with an adjustable Q-factor to construct the dictionary matrix and solves it using a basis pursuit denoising algorithm, effectively separating the echo signals of the measured helicopter body and micro-moving components. The performance of the above methods generally depends on the degree of focusing of the micro-moving target echo signal in the time-frequency domain.

[0006] While the aforementioned methods can effectively separate the echoes of the target body and the micro-moving parts, some suffer from low computational efficiency, model mismatch, or limited resolution. With the development of low-rank learning theory, low-rank and sparse matrix decomposition (LRSD), such as iterative hard thresholding, iterative shrinking thresholding, and robust principal component analysis (RPCA), has been successfully used to remove echoes from micro-moving parts in broadband radar and to perform ISAR imaging of the target body. Inspired by LRSD, this chapter proposes a method for separating the echoes of UAV targets and micro-moving parts based on Hankel matrix low-rank sparse decomposition under narrowband radar detection conditions. When the coherence integration time (CIT) is short and the target body moves slowly, it can be approximated as a uniform motion. The Hankel matrix of the echo of a uniformly moving target body is low-rank, therefore, the problem of separating the echo signals of the target body and the micro-moving parts can be modeled as a low-rank sparse matrix decomposition model. Since radar echoes typically contain noise, auxiliary variables are added to the model to estimate the noise energy, thus extending the low-rank sparse matrix factorization problem into an optimization problem with three constraint variables. Based on this, following the idea of ​​factorization, the rank function in the model is relaxed using the Factor Group-sparse Regularization (FGSR) method, and solved using the Linearized Alternating Direction Multiplier Method (L-ADMM). Finally, the effectiveness and robustness of the method are verified based on simulation and experimental data.

[0007] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] This invention provides a method for separating the echo signals of the target subject and the micro-moving parts based on sparse regularization of factor decomposition groups. It aims to solve the technical problem that existing methods for narrowband radar under conditions of low signal-to-noise ratio, short coherence accumulation time, and low-speed movement of UAVs are difficult to separate the echo signals of the target subject and the micro-moving parts with high precision and efficiency due to the need to preset micro-movement models, sensitivity to noise, and large computational load.

[0009] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0010] According to a first aspect of the present invention, a method for separating echo signals of a target subject and a micro-moving component based on factorization group sparse regularization is provided, the method comprising: Step 1: Construct an additive model of the echo of the UAV micro-moving target, use short-time Fourier transform to perform time-frequency analysis on the non-stationary echo signal, convert the echo signal into Hankel matrix form, and use the low-rank characteristic of the Hankel matrix of the echo of the uniformly moving target body to decompose and obtain the time-frequency representation of the echo signal of the target body, the micro-moving parts, and the noise in the form of Hankel matrix. Step 2: Model the problem of separating the echo signal of the target body and the micro-movement component as a low-rank sparse matrix decomposition model, introduce noise variables to expand it into an optimization problem with three constraint variables, relax the 0 norm to the 1 norm and the rank function to the nuclear norm, and transform the optimization problem into an unconstrained optimization form; Step 3: Relax the rank function by using the factorization group sparsity regularization method. Decompose the low-rank matrix into two sub-matrices and add group sparsity constraints. Combine the Schatten-1 / 2 norm to define the relaxation rank function, and transform the optimization problem into the augmented Lagrangian function form. Step 4: The augmented Lagrangian function is solved using the linearized alternating direction multiplier method. The overall optimization problem is decomposed into multiple sub-problems. Each sub-matrix is ​​solved by near-end gradient projection, group soft thresholding operator, soft thresholding function and partial derivative calculation. The Lagrangian multipliers are updated alternately until the relative error convergence condition is met, thereby achieving the separation of the target body and the echo signal of the micro-moving parts, and simultaneously completing noise estimation and elimination.

[0011] In some exemplary implementations, step one is to construct an additive model of the UAV micro-movement target echo, perform time-frequency analysis on the non-stationary echo signal using short-time Fourier transform, convert the echo signal into Hankel matrix form, and utilize the low-rank characteristic of the Hankel matrix of the echo of the uniformly moving target body to decompose and obtain the time-frequency representation of the echo signal and noise of the target body, micro-movement component, and Hankel matrix form. Step 2: Model the problem of separating the echo signal of the target body and the micro-movement component as a low-rank sparse matrix decomposition model, introduce noise variables to expand it into an optimization problem with three constraint variables, relax the 0 norm to the 1 norm and the rank function to the nuclear norm, and transform the optimization problem into an unconstrained optimization form; Step 3: Relax the rank function by using the factorization group sparsity regularization method. Decompose the low-rank matrix into two sub-matrices and add group sparsity constraints. Combine the Schatten-1 / 2 norm to define the relaxation rank function, and transform the optimization problem into the augmented Lagrangian function form. Step 4: The augmented Lagrangian function is solved using the linearized alternating direction multiplier method. The overall optimization problem is decomposed into multiple sub-problems. Each sub-matrix is ​​solved by near-end gradient projection, group soft thresholding operator, soft thresholding function and partial derivative calculation. The Lagrangian multipliers are updated alternately until the relative error convergence condition is met, thereby achieving the separation of the target body and the echo signal of the micro-moving parts, and simultaneously completing noise estimation and elimination.

[0012] In some exemplary embodiments, the construction of the low-rank sparse matrix factorization model in step two specifically involves utilizing the low-rank nature of the time-frequency representation of the target signal to establish a convex optimization model with the kernel norm representing low rank and the 1 norm representing sparsity. A noise parameter is introduced and the Frobenius norm is used to represent the noise energy. The constrained optimization problem is transformed into an unconstrained optimization form through the penalty parameter.

[0013] In some exemplary embodiments, the factorization group sparsity regularization method described in step three relaxes the rank function by decomposing the rank function into the sum of the number of non-zero columns and non-zero rows of two sub-matrices. By adding group sparsity constraints to the sub-matrices, the non-zero rows / columns are minimized, thereby improving the robustness and convergence of the algorithm. In combination with the characteristics of the Schatten-p norm, the Schatten-1 / 2 norm is selected to relax the rank function, avoiding the high computational cost of solving the Schatten-p norm when the matrix dimension is large.

[0014] In some exemplary embodiments, the solution process of the linearized alternating direction multiplier method in step four specifically involves linearizing the augmented Lagrangian function, approximating the quadratic term of the objective function, introducing the gradient term through the proximal operator parameter, and alternately updating the decomposed submatrix, the micro-motion component signal matrix, and the noise matrix respectively. The optimization subproblem of the target principal decomposition submatrix is ​​solved by using a group soft threshold operator; The optimization subproblem of the echo signal matrix of the micro-motion component is solved by using a soft thresholding function; The optimization subproblem of the noise matrix is ​​solved by taking the partial derivatives and setting them to zero; The Lagrange multipliers are continuously updated based on the iteration results until the relative error of the iteration results is less than a preset threshold.

[0015] In some exemplary embodiments, the initialization process of the iteration in step four is as follows: the Lagrange multipliers, the noise matrix, and the time-frequency characterization matrix of the micro-motion component echo signal are initialized to zero matrices; singular value decomposition is performed on the Hankel matrix of the target echo signal, and the two decomposition sub-matrices of the target body are initialized according to the decomposition results.

[0016] In some exemplary embodiments, the method sets the regularization parameter and the penalty parameter to values ​​greater than 0 to balance the energy of the reconstructed target main signal, the micro-motion component echo signal, and noise; the relative error is set to a value less than 0.01 to avoid introducing iteration errors; wherein the regularization parameter ranges from 0.001 to 0.04, the penalty parameter representing sparsity ranges from 0.01 to 0.1, the parameter representing noise energy ranges from 1 to 4, and the penalty coefficients corresponding to the two Lagrange multipliers are equal, and the value is the reciprocal of the Frobenius norm representing the time-frequency of the echo signal.

[0017] According to a second aspect of the present invention, a radar signal processing system is provided, the system being equipped with the above-mentioned method for separating the echo signals of a UAV target body and micro-moving parts based on factorization group sparse regularization, capable of separating the echo signals of the UAV target body and micro-moving parts such as propellers and rotors under narrowband radar detection, including a signal acquisition module, a Hankel matrix construction module, a model establishment and optimization module, an iterative solution module, and a signal reconstruction module, wherein: Signal acquisition module: used to acquire echo signals from narrowband radar to UAV targets; Hankel matrix construction module: used to perform short-time Fourier transform on the echo signal and construct the Hankel matrix of the echo signal; Model building and optimization module: used to build a low-rank sparse matrix factorization model, introduce noise variables and relax the rank function using the factorization group sparse regularization method, and convert it into the augmented Lagrangian function form; Iterative solution module: Used to iteratively solve the augmented Lagrange function using the linearized alternating direction multiplier method, alternately updating each matrix and iterating the Lagrange multipliers; Signal reconstruction module: It is used to reconstruct the time-frequency characterization of the echo signals of the target body and the micro-motion component based on the matrix results after iterative convergence, so as to achieve signal separation between the two.

[0018] This invention addresses the technical challenge of separating the echo signals from the main target and micro-moving components of a UAV under narrowband radar detection conditions. It proposes a low-rank sparse decomposition method for the Hankel matrix based on sparse regularization of factor decomposition groups. Compared to existing technologies, this method offers several significant advantages, as detailed below: 1. It solves the problems of model mismatch and resolution limitation of traditional methods. It abandons the drawback of traditional parameter domain processing methods that require pre-setting the instantaneous frequency modulation model of micro-motion signal. It does not require prior assumptions about the motion model of micro-motion components, thus avoiding the problem of reduced separation accuracy caused by model mismatch. At the same time, it breaks through the limitation of time-frequency domain processing methods that depend on the time-frequency domain focusing degree of micro-motion target echo. By combining the low-rank characteristics of Hankel matrix with the sparse regularization of factor decomposition group, it improves the resolution and adaptability of signal separation.

[0019] 2. Achieving high-precision signal separation in noisy environments: A noise variable is specifically introduced as a constraint in the low-rank sparse matrix factorization model to accurately estimate and remove additive noise in radar echoes, solving the problem of sharp drop in separation performance of existing methods in noisy environments. Through simulation and measured data verification, under low signal-to-noise ratio (SNR=-10dB) conditions, the root mean square error of target signal separation is much lower than that of traditional robust principal component analysis methods, and it can still maintain high separation accuracy even in high noise environments.

[0020] 3. Improve the computational efficiency and convergence capability of the algorithm. The rank function is relaxed by using the factorization group sparsity regularization method, which decomposes the low-rank matrix into two sub-matrices and adds group sparsity constraints. This avoids the large amount of computation caused by directly solving the Schatten-p norm of the high-dimensional matrix, and significantly reduces the computational load of the algorithm. At the same time, the linearized alternating direction multiplier method is combined to decompose the overall optimization problem into multiple easily solvable sub-problems. Fast convergence is achieved through alternating updates and gradient approximation, which solves the problem of low computational efficiency of traditional low-rank decomposition methods.

[0021] 4. Enhancing the robustness and engineering practicality of the algorithm: Factorization group sparse regularization improves the algorithm's resistance to interference from changes in target scattering points and radar system errors by minimizing the number of non-zero rows / columns of the submatrix; the parameter settings of the algorithm have been verified by a large number of experiments to provide a clear range of values, the iterative initialization process is simple and the convergence conditions are clear, and stable signal separation can be achieved without complex parameter tuning; at the same time, this method is suitable for engineering detection scenarios of narrowband radar and has good adaptability to UAV detection scenarios with short coherent accumulation time and low-speed movement of the target.

[0022] 5. The separation results are more in line with actual engineering needs. The target body echo signal obtained by this method is closer to the ideal value, and the background noise of the micro-movement component echo signal is lower. It can not only provide a clean subject signal for inverse synthetic aperture radar imaging and improve imaging quality, but also extract clear micro-Doppler features for automatic target recognition. It solves the problem that existing methods are prone to losing the subject signal when removing micro-movement signals. At the same time, the effectiveness and robustness of the method are fully confirmed by experimental data in a microwave anechoic chamber and spin target experiments. It can be directly applied to the actual engineering system of UAV radar detection.

[0023] 6. Expanded the application scenarios of low-rank learning theory in radar signal processing. The factorization group sparse regularization method was applied for the first time to the field of target echo separation of narrowband radar UAVs, breaking through the application limitations of traditional low-rank sparse matrix factorization methods in radar micro-motion signal processing, and providing new ideas and methods for the application of low-rank learning theory in the field of radar signal processing.

[0024] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0025] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0026] Figure 1 shows the framework of the method of the present invention; Figure 2 shows the results of separating sinusoidal frequency modulated signals and fixed frequency signals using different methods; Figure 3 shows the RMSE of the target subject signals separated by different methods under different signal-to-noise ratio conditions; Figure 4 Results of spin target echo signals separated by different methods. Detailed Implementation

[0027] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0028] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0029] To address the shortcomings and deficiencies of existing technologies, this example implementation provides a target subject and micro-motion echo separation method based on low-rank sparse decomposition of the Hankel matrix under narrowband radar detection conditions. When the coherence integration time (CIT) is short and the target subject's motion speed is slow, the target subject can be approximated as moving at a uniform speed. The Hankel matrix of the echo from a uniformly moving target subject has low rank, thus the problem of separating the echo signal from the target subject and the micro-motion component can be modeled as a low-rank sparse matrix decomposition model. Since radar echoes usually contain noise, auxiliary variables are added to the model to estimate the noise energy, thereby extending the low-rank sparse matrix decomposition problem into an optimization problem with three constraint variables. Based on this, according to the factorization idea, the rank function in the model is relaxed by the Factor Group-sparse Regularization (FGSR) method, and the solution is obtained using the Linearized Alternating Direction Multiplier Method (L-ADMM).

[0030] refer to Figure 1 As shown, the specific steps may include: Step 1: Construct an additive model of the echo of the UAV micro-moving target, use short-time Fourier transform to perform time-frequency analysis on the non-stationary echo signal, convert the echo signal into Hankel matrix form, and use the low-rank characteristic of the Hankel matrix of the echo of the uniformly moving target body to decompose and obtain the time-frequency representation of the echo signal of the target body, the micro-moving parts, and the noise in the form of Hankel matrix. Step 2: Model the problem of separating the echo signal of the target body and the micro-movement component as a low-rank sparse matrix factorization model, introduce noise variables to expand it into an optimization problem with three constraint variables, relax the 0 norm to the 1 norm and the rank function to the kernel norm, and transform the optimization problem into an unconstrained optimization form; Step 3: Relax the rank function by using the factorization group sparsity regularization method. Decompose the low-rank matrix into two sub-matrices and add group sparsity constraints. Combine the Schatten-1 / 2 norm to define the relaxation rank function, and transform the optimization problem into the augmented Lagrangian function form. Step 4: The augmented Lagrangian function is solved using the linearized alternating direction multiplier method. The overall optimization problem is decomposed into multiple sub-problems. Each sub-matrix is ​​solved by near-end gradient projection, group soft thresholding operator, soft thresholding function and partial derivative calculation. The Lagrangian multipliers are updated alternately until the relative error convergence condition is met, thereby achieving the separation of the target body and the echo signal of the micro-moving parts, and simultaneously completing noise estimation and elimination.

[0031] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and examples.

[0032] Step 1: When the radar system operates in the high-frequency region, the UAV target can be constructed using a point scattering model, meaning the echo can be considered as the sum of echoes from isolated scattering centers on the target. Therefore, the echo of a slightly moving target can be approximated as an additive model. Assume the target is composed of... Composed of scattering points, its echo signal can be expressed as (1) in, Indicates the first Scattering rate at each scattering point , Represents the radar signal wavelength. Representing the The instantaneous frequency of the echo from each scattering point, and satisfying , and The instantaneous phase is a slowly changing function that satisfies... , For the radar to reach the first The instantaneous distance of each scattering point For the first The initial phase of the echo signal at each scattering point. This represents additive noise. The target echo signal described by equation (1) is a typical non-stationary signal. The Short-Time Fourier Transform (STFT), as a linear time-frequency analysis method without cross terms, is often used to process non-stationary signals. The expression for STFT is: (2) in, This is the time-frequency representation of the signal after passing through the short-time Fourier transform. The representative window length is The window function can be a Gaussian window or a Hamming window, etc. The maximum overlap short-time signal matrix can be considered as a Hankel matrix, where... It is the interval of the sliding window, when When the sliding window interval is the smallest, the short-time signals overlap to the maximum.

[0033] For ease of analysis, equation (2) is rewritten in matrix form. (3) in, This is a partial Fourier transform matrix. The Hankel matrix form of the target echo signal, , and Let these represent the Hankel matrix forms of the echo signals from the target body and the micro-motion components, respectively. For the time-frequency characterization of the target echo signal, , and These represent the time-frequency characterizations of the echo signals from the target body and the micro-moving components, respectively. Represents the diagonal window matrix. , Represents the diagonalization operation. The Hankel matrix is ​​in the form of (4) in, The length of the received signal, The number of rows and columns in a Hankel matrix is ​​generally equal or close, and satisfies: (5) Since the number of scattering points on the target signal is finite, it can be assumed that the number of scattering points is less than the radar echo Hankel matrix. The number of rows or columns, therefore, according to the properties of the Hankel matrix, the Hankel matrix form of the target signal. It has low-rank properties ( and Having the same dimension, the time-frequency representation of the target signal can be expressed as: (6) Among them, some Fourier matrices It is a full rank, that is Window function matrix It is a diagonal matrix.

[0034] Then, according to the properties of matrix multiplication (7) in, Let be the rank of the matrix.

[0035] Step 2: Since the time-frequency representation of the target body signal is also low-rank, the problem of separating the target body signal from the micro-moving component signal can be constructed as an LRSD model.

[0036] (8) In the formula, The regularization parameter is and , This represents the zero norm. Because... Since the norm is discontinuous, it is difficult to obtain the optimal solution. An effective strategy is to... Norm relaxation is convex. Norm. Furthermore, because the rank function is involved, the problem described by equation (8) is difficult to solve directly. Generally, the rank function can be relaxed to the nuclear norm. (9) In the formula, express Norm, The nuclear norm is represented by equation (9). Under certain conditions, the convex optimization problem described by equation (9) can be solved by RPCA to separate the low-rank matrix. sparse matrix Considering the echo signal in practical applications Typically, noise is present. To reduce the impact of noise on the reconstructed data, equation (9) can be rewritten as follows: (10) In the formula, For noise parameters, This represents the Frobenius norm.

[0037] To facilitate solving, the problem described by equation (10) can be transformed into an unconstrained optimization form. (11) In the formula, This is the penalty parameter.

[0038] Furthermore, by introducing noise variables The problem described by equation (11) is transformed into (12) Step 3: Rewrite the principal component analysis problem of equation (12), and the nuclear norm can be extended to the Schatten-p norm form. The Schatten-p norm is defined as... (13) In the formula, , Defined as The The largest singular value, the Schatten-p norm p The power is defined as (14) when hour, For the nuclear norm; when hour, It is a rank function. Therefore, when The closer to 0, The closer the matrix is ​​to the rank function, the more computationally intensive it becomes. Solving for the Schatten-p norm requires significant time resources when the matrix dimension is large. One feasible method to reduce computational complexity is to relax the rank function using factorization. This involves decomposing the low-rank matrix to be solved into the product of two submatrices and recovering the low-rank matrix by alternately updating these submatrices. While factorization can reduce computational complexity and even avoid singular value decomposition, it requires that the submatrices maintain a certain dimensionality during the computation process. In practical applications It is difficult to obtain in advance, so it is generally necessary to... Set it to a relatively large value, or estimate it dynamically during the solution process. However, regardless of which method is chosen, it creates difficulties in the solution process.

[0039] To address the aforementioned issues, Factor Group-Sparse Regularization (FGSR) is employed to relax the rank function. This regularization method improves the robustness and convergence of the algorithm by adding group sparsity constraints to the submatrix to minimize the non-zero rows or columns of the submatrix. Based on the FGSR method, the rank function can be decomposed into... (15) In the formula, Representative matrix Similarly, the number of non-zero columns, Representative matrix The number of non-zero rows. , , and Since it is a column vector, by relaxing the rank function using the Schatten-1 / 2 norm, we can obtain... (16) Let matrix It can be decomposed into , Each element on the main diagonal is a matrix singular values, and These are the left singular matrix and the right singular matrix, respectively. In summary, the following method for defining the relaxed rank function can be used. (17) in, It is a mixed norm. .according to The relaxation method, the optimization problem described by equation (12) can be transformed into (18) The two constrained convex optimization problems mentioned above can be transformed into the form of augmented Lagrangian functions, therefore equation (18) can be further transformed into (19) In the formula, and For Lagrange multipliers, and Let be the penalty coefficient. Based on the calculation derivation, equation (19) can be rewritten as... (20) Step 4: Both optimization problems in equation (20) can be decomposed into subproblems described by equation (21), making each subproblem easier to solve.

[0040] (twenty one) As shown in equation (21), the matrix The objective function can be simplified to (twenty two) Due to the matrix The existence of makes equation (22) unsolvable directly. Therefore, the problem of solving equation (22) using L-ADMM is specifically solved by approximating the problem (22) by linearizing the quadratic term of the objective function. Based on the linearization derivation of the quadratic term, equation (22) can be transformed into (twenty three) In the formula, For the proximal operator parameters, yes exist gradient at (twenty four) Based on the proximal gradient projection, equation (24) can be transformed into (25) Equation (25) is The norm minimization problem can be solved using the group soft threshold operator. (26) in, For threshold parameters, For a group of soft threshold functions, it can be expressed as: (27) In the formula, for The first of the matrix Row vectors.

[0041] for Problem, matrix The objective function can be simplified to (28) With the update matrix similar, The solution can be obtained through the group soft threshold operator. (29) As shown in equation (21), the matrix The objective function can be simplified to (30) Regarding equation (30) Find the partial derivative, i.e. (31) If we set its value to zero, then the solution to equation (31) is: (32) As shown in equation (21), the matrix The objective function can be simplified to (33) Equation (33) is The norm minimization problem can be solved using a soft thresholding function. (34) for The problem, whose objective function can be simplified to: (35) Find the expression for equation (35) with respect to... The partial derivative can be obtained (36) If we set its value to zero, then the solution to equation (35) is: (37) Figure 1 For based on Method for separating echo signals of target body and micro-moving components (hereinafter referred to as: Method (method) flowchart. Wherein, Lagrange multiplier and ,noise Time-frequency characterization of echo signals from micro-moving components Initialize using a zero matrix. The singular value decomposition is Then the matrix , The initialization can be represented as , Regularization parameters Penalty parameters , and A number greater than 0 is set to balance the energy of the reconstructed target signal, the micro-motion component echo signal, and the noise. This is the relative error. If we take... Figure 1 The method framework becomes based on The process of separating the echo signal from the target body and the micro-moving component requires that... Figure 1 formation The initialization process is replaced with ,Will initialization process And will be updated The steps are replaced with Regarding parameter settings, relative error It should be set to a value less than 0.01 to avoid introducing iteration errors. Typically, and The larger the value, the sparser the generated results; The larger the value, the smaller the time-frequency characterization energy of the estimated noise. Extensive experiments have shown that when... and The value range is 0.001-0.04. The value range is 0.01-0.1. When the value of is in the range of 1-4, the proposed method can achieve good results. (Penalty parameter) and They are equal, it is recommended to... and Set as the reciprocal of the Frobenius norm, which characterizes the time-frequency response of the echo signal. ,in The range is set to 1-4.

[0042] Figure 2 The figures show the results of separating sinusoidal frequency modulated (FM) signals and fixed-frequency signals using different methods. It can be observed from the figures that FGSR1 / 2 and FGSR2 / 3 extract more complete FM signals compared to RPCA.

[0043] Figure 3 The RMSE of the target subject signals separated by different methods under different signal-to-noise ratio conditions shows that FGSR 1 / 2 and FGSR 2 / 3 Compared to RPCA, FGSR has a smaller RMSE for separating the target signal. At high noise levels, FGSR... 1 / 2 Slightly better performance than FGSR 2 / 3 .

[0044] To further verify the proposed method, a principle experiment was designed and carried out in a microwave anechoic chamber. Figure 4 Results of spin target echo signals separated by different methods. Compared to RPCA, FGSR... 1 / 2 and FGSR 2 / 3 The separated target signal is closer to the ideal value. Further comparison reveals that, compared to FGSR, it is closer to the ideal value. 2 / 3 FGSR 1 / 2 The separated rotating component has less background noise.

[0045] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0046] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0047] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A method for separating echo signals of UAV target bodies and micro-moving components based on factor decomposition group sparse regularization, characterized in that, The method includes: Step 1: Construct an additive model of the echo of the UAV micro-moving target, use short-time Fourier transform to perform time-frequency analysis on the non-stationary echo signal, convert the echo signal into Hankel matrix form, and use the low-rank characteristic of the Hankel matrix of the echo of the uniformly moving target body to decompose and obtain the time-frequency representation of the echo signal of the target body, the micro-moving parts, and the noise in the form of Hankel matrix. Step 2: Model the problem of separating the echo signal of the target body and the micro-movement component as a low-rank sparse matrix decomposition model, introduce noise variables to expand it into an optimization problem with three constraint variables, relax the 0 norm to the 1 norm and the rank function to the nuclear norm, and transform the optimization problem into an unconstrained optimization form; Step 3: Relax the rank function by using the factorization group sparsity regularization method. Decompose the low-rank matrix into two sub-matrices and add group sparsity constraints. Combine the Schatten-1 / 2 norm to define the relaxation rank function, and transform the optimization problem into the augmented Lagrangian function form. Step 4: The augmented Lagrangian function is solved using the linearized alternating direction multiplier method. The overall optimization problem is decomposed into multiple sub-problems. Each sub-matrix is ​​solved by near-end gradient projection, group soft thresholding operator, soft thresholding function and partial derivative calculation. The Lagrangian multipliers are updated alternately until the relative error convergence condition is met, thereby achieving the separation of the target body and the echo signal of the micro-moving parts, and simultaneously completing noise estimation and elimination.

2. The method according to claim 1, characterized in that, The additive model for constructing the UAV micro-movement target echo in step one specifically involves constructing the UAV target using a point scattering model. The echo signal is represented as the sum of the echoes from each isolated scattering center on the target, including scattering rate, instantaneous frequency, initial phase, and additive noise term. The short-time Fourier transform uses a Gaussian window or a Hamming window as the window function, and sets the sliding window interval to the minimum value to obtain the short-time signal matrix with maximum overlap, i.e., the Hankel matrix.

3. The method according to claim 1, characterized in that, The construction of the low-rank sparse matrix factorization model in step two specifically involves utilizing the low-rank nature of the target signal's time-frequency representation to establish a convex optimization model that uses the kernel norm to represent low rank and the 1-norm to represent sparsity. Noise parameters are introduced, and the Frobenius norm is used to represent noise energy. By using penalty parameters, the constrained optimization problem is transformed into an unconstrained optimization form.

4. The method according to claim 1, characterized in that, The factorization group sparsity regularization method described in step three relaxes the rank function by decomposing the rank function into the sum of the number of non-zero columns and non-zero rows of two sub-matrices. By adding group sparsity constraints to the sub-matrices, the number of non-zero rows / columns is minimized, thereby improving the robustness and convergence of the algorithm. Combining the characteristics of the Schatten-p norm, the Schatten-1 / 2 norm is selected to relax the rank function, avoiding the high computational cost of solving the Schatten-p norm when the matrix dimension is large.

5. The method according to claim 1, characterized in that, The solution process of the linearized alternating direction multiplier method described in step four specifically involves linearizing the augmented Lagrangian function, approximating the quadratic term of the objective function, introducing the gradient term through the proximal operator parameter, and alternately updating the decomposed submatrices, the micro-motion component signal matrix, and the noise matrix. The optimization subproblem of the target principal decomposition submatrix is ​​solved by using a group soft threshold operator; The optimization subproblem of the echo signal matrix of the micro-motion component is solved by using a soft thresholding function; The optimization subproblem of the noise matrix is ​​solved by taking the partial derivatives and setting them to zero; The Lagrange multipliers are continuously updated based on the iteration results until the relative error of the iteration results is less than a preset threshold.

6. The method according to claim 1, characterized in that, The initialization process of the iteration in step four is as follows: initialize the Lagrange multipliers, noise matrix, and time-frequency characterization matrix of the micro-motion component echo signal to zero matrices; perform singular value decomposition on the Hankel matrix of the target echo signal, and initialize the two decomposition sub-matrices of the target body according to the decomposition results.

7. The method according to claim 1, characterized in that, The method sets both the regularization parameter and the penalty parameter to values ​​greater than 0 to balance the energy of the reconstructed target signal, the echo signal of the micro-movement component, and the noise. The relative error is set to a value less than 0.01 to avoid introducing iteration errors. The regularization parameter ranges from 0.001 to 0.04, the penalty parameter representing sparsity ranges from 0.01 to 0.1, and the parameter representing noise energy ranges from 1 to 4. The penalty coefficients corresponding to the two Lagrange multipliers are equal and are the reciprocal of the Frobenius norm representing the time-frequency response of the echo signal.

8. A radar signal processing system, characterized in that, The system is equipped with the UAV target body and micro-moving component echo signal separation method based on factorization group sparse regularization as described in any one of claims 1-7. It can realize the separation of UAV target body and micro-moving components such as propellers and rotors under narrowband radar detection. It includes a signal acquisition module, a Hankel matrix construction module, a model establishment and optimization module, an iterative solution module, and a signal reconstruction module, wherein: Signal acquisition module: used to acquire echo signals from narrowband radar to UAV targets; Hankel matrix construction module: used to perform short-time Fourier transform on the echo signal and construct the Hankel matrix of the echo signal; Model building and optimization module: used to build a low-rank sparse matrix factorization model, introduce noise variables and relax the rank function using the factorization group sparse regularization method, and convert it into the augmented Lagrangian function form; Iterative solution module: Used to iteratively solve the augmented Lagrange function using the linearized alternating direction multiplier method, alternately updating each matrix and iterating the Lagrange multipliers; Signal reconstruction module: It is used to reconstruct the time-frequency characterization of the echo signals of the target body and the micro-motion component based on the matrix results after iterative convergence, so as to achieve signal separation between the two.

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