Sparse time-frequency-frequency modulation rate representation reconstruction method based on tail minimization

Abstract

The invention relates to a sparse time-frequency-frequency modulation rate representation reconstruction method based on tail minimization, and the method comprises the steps: building a parameterized sparse optimization model, carrying out the solving of the parameterized sparse optimization model through an alternating direction multiplier method, and carrying out the solving of a next round of multiple times of iteration. And calculating a tail support set of frequency-modulation rate reconstruction representation obtained by the current iteration, updating the global optimization variable according to the tail support set, and substituting the global optimization variable into the subsequent solution of the alternating direction multiplier method, so that the target support set energy in the global optimization variable is more prominent in the multiple solution processes, and the target support set energy in the global optimization variable is more accurate. By adopting the method, the target micro-motion features extracted in a complex scene can be more accurate.

Description

Technical Field

[0001] The present application relates to the technical field of radar target micro-motion signal characterization, and in particular to a sparse time-frequency-modulation frequency characterization reconstruction method based on tail minimization. Background Art

[0002] When radar detects and identifies targets, it is critical to accurately analyze micro-motion target signals. In life, small movements of the human body, the rotation of aircraft engine blades, and the shaking of ships on the sea are all micro-motion targets. Processing such signals can obtain target characteristics, achieve accurate identification and tracking, and is widely used in security monitoring, traffic monitoring and other fields. The time-frequency analysis method can show the Doppler characteristics of micro-motion target signals that change over time and extract instantaneous Doppler information, so it is widely used. The instantaneous Doppler rate can also improve imaging quality, extract micro-Doppler features, and enhance the ability to analyze micro-motion targets.

[0003] However, the micro-motion target signal is complex and changes quickly. On the one hand, the time-varying characteristics of the signal are complex, and it is difficult to accurately characterize it with traditional methods; on the other hand, the signal modulation characteristics are complex, and it is difficult to accurately capture the details with existing methods. This makes signal processing difficult, and it is not easy to accurately analyze and process it. Summary of the invention

[0004] Based on this, it is necessary to provide a sparse time-frequency-modulation frequency representation reconstruction method based on tail minimization, which can improve the accuracy of micro-Doppler characteristic analysis in complex scenarios to address the above technical problems.

[0005] A sparse time-frequency-modulation rate representation reconstruction method based on tail minimization, the method comprising: Acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The parameterized sparse optimization model is solved by using an alternating direction multiplier method until the solution satisfies a first preset threshold, then the current iteration is stopped; if the solution does not satisfy a second preset threshold, the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration is calculated; Based on the idea of ​​tail optimization, the frequency-frequency modulation rate reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold until the solution meets the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0006] In one embodiment, after the radar observation data is processed accordingly, the observation data characterized by frequency-modulation frequency at different times is obtained, including: Processing the radar observation data through a sliding time window to obtain a plurality of continuous signal short-time segments; Each short-time segment of the signal is processed into an approximate linear combination of multiple Chirp signals through a second-order parameterized Fourier dictionary, thereby obtaining observation data characterized by frequency-modulation frequency at different moments.

[0007] In one embodiment, the tail optimization concept is expressed as:

[0008] In the above formula, represents the complement of the target support set in the frequency-modulation reconstruction representation, Indicates a short-term segment of the signal The corresponding radar observation vector, represents the downsampling matrix, represents the inverse short-time frequency modulation Fourier transform matrix, where represents the block Chirp dictionary matrix, represents the block inverse Fourier transform matrix, It represents the frequency-modulation frequency characterization vector obtained by stacking the frequency dimension at different times using the alternating direction multiplication method. is the data fidelity term, used to constrain the reconstruction error, express norm, Used to define the noise range.

[0009] In one embodiment, based on the tail optimization concept, when the frequency-modulation frequency reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold, the parameterized sparse optimization model described by the LASSO model is expressed as:

[0010] In the above formula, represent norm, the first term in the formula limits the range of reconstruction error, Sparse prior regularization term modified to add tail optimization.

[0011] In one embodiment, when solving the updated parameterized sparse optimization model using the alternating direction multiplier method: Performing dual decomposition on the variables to be optimized, introducing splitting variables, and converting the updated parameterized sparse optimization model into a constrained optimization problem; The constrained optimization problem is converted into a corresponding augmented Lagrangian function by using an augmented Lagrangian multiplier method; Performing a scale transformation according to the Lagrangian multiplier and the penalty term coefficient, and performing an equivalent transformation on the augmented Lagrangian function; The Gauss-Seidel idea is used to decompose the augmented Lagrangian function after equivalent transformation into three sub-problems. By iteratively solving the three sub-problems multiple times, the frequency-modulation frequency reconstruction representation at different times is obtained.

[0012] In one embodiment, the constrained optimization problem is expressed as:

[0013] In the above formula, Used to characterize the sparse prior regularization term after tail correction, For Hadamard, is the complement matrix of the frequency-modulation frequency representation support set, i.e., the tail support set, and .

[0014] In one embodiment, the three sub-problems are respectively sub-problems for solving global variables, split variables and dual variables; In the process of solving the splitting variables, the soft threshold is calculated only for the sum of the global variables and the dual variables of the index part corresponding to the complement of the support set.

[0015] In one embodiment, when solving the updated parameterized sparse optimization model using the alternating direction multiplier method: When the relative error of the frequency-modulation frequency reconstruction representation obtained by two iterative calculations is less than the first preset threshold, stopping the alternating direction multiplier method; If the number of times the alternating direction multiplier method is currently run is less than a second preset threshold, a tail minimization process is performed on the currently obtained frequency-modulation frequency reconstruction representation, and the tail-optimized frequency-modulation frequency reconstruction representation is continued to use the alternating direction multiplier method to solve the updated parameterized sparse optimization model; Until the number of times the alternating direction multiplier method is currently run is greater than or equal to the second preset threshold, the frequency-modulation frequency representation currently calculated is the frequency-modulation frequency reconstruction representation of the micro-motion target at a certain moment.

[0016] A sparse time-frequency-modulation frequency representation reconstruction device based on tail minimization, the device comprising: An observation data acquisition module is used to acquire radar observation data of a micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The parameterized sparse optimization model building module is used to model the time-frequency-modulation frequency representation reconstruction problem as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; A reconstruction representation tail optimization module is used to solve the parameterized sparse optimization model by using an alternating direction multiplier method until the solution meets a first preset threshold, then stop the current iteration, and if it does not meet a second preset threshold, calculate the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration; The three-dimensional representation reconstruction module is used to solve the frequency-frequency modulation rate reconstruction representation on the tail support set based on the tail optimization idea by using the alternating direction multiplier method under the first preset threshold until the solution result satisfies the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0017] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented: Acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The parameterized sparse optimization model is solved by using an alternating direction multiplier method until the solution satisfies a first preset threshold, then the current iteration is stopped; if the solution does not satisfy a second preset threshold, the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration is calculated; Based on the idea of ​​tail optimization, the frequency-frequency modulation rate reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold until the solution meets the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0018] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps: Acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The parameterized sparse optimization model is solved by using an alternating direction multiplier method until the solution satisfies a first preset threshold, then the current iteration is stopped; if the solution does not satisfy a second preset threshold, the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration is calculated; Based on the idea of ​​tail optimization, the frequency-frequency modulation rate reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold until the solution meets the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0019] The above-mentioned sparse time-frequency-modulation frequency representation reconstruction method based on tail minimization, after constructing a parameterized sparse optimization model, uses the alternating direction multiplier method to solve it. After a round of multiple iterative solutions, it also calculates the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration, and updates the global optimization variables based on the tail support set, and then brings it into the subsequent alternating direction multiplier method solution, so that in the multiple solution processes, the target support set energy in the global optimization variables is more prominent. The use of this method can make the target micro-motion features extracted in complex scenarios more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flowchart of a sparse time-frequency-modulation frequency representation reconstruction method based on tail minimization in one embodiment; Figure 2 A schematic diagram of a specific step flow of Algorithm 1 in an embodiment; Figure 3 A schematic diagram of a specific step flow of Algorithm 2 in an embodiment; Figure 4 is a flowchart of an implementation process of the method in an embodiment; Figure 5 This is a schematic diagram of a sample of darkroom measurement data in a simulation experiment; Figure 6 A darkroom measurement signal with different random sparsity rates in a simulation experiment Schematic diagram comparing frequency-modulation frequency distribution reconstruction methods at different moments; Figure 7 A darkroom measurement signal with different random sparsity rates in a simulation experiment Schematic diagram comparing frequency-modulation frequency distribution reconstruction methods at different moments; Figure 8 A schematic diagram of the time-frequency dimension projection of darkroom measurement signals at different random sparsity rates in a simulation experiment after being enhanced by different methods; Fig. 9 A schematic diagram of the time-frequency modulation dimension projection of darkroom measurement signals at different random sparsity rates in a simulation experiment after being enhanced by different methods; Fig.10 is the measured signal under different random sparsity rates in a measured data experiment Schematic diagram of the comparison of frequency-modulation frequency distribution enhancement methods obtained by using different methods at all times; Fig.11 is the measured signal under different random sparsity rates in a measured data experiment Schematic diagram of the comparison of frequency-modulation frequency distribution enhancement methods obtained by using different methods at all times; Fig.12It is a schematic diagram of the projection of the darkroom measurement data time-frequency-modulation frequency sequence reconstructed at different random sparsity rates using three methods in an actual data experiment on the time-frequency dimension; Fig.13 It is a schematic diagram of the projection of the time-frequency modulation dimension of the measured signal under different random sparsity rates in a measured data experiment after being enhanced by the present method and the traditional ADMM method; Fig.14 It is a structural block diagram of a process device of a sparse time-frequency-modulation frequency representation reconstruction method based on tail minimization in one embodiment; Fig.15 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0022] With respect to the existing technology, the time-frequency-modulation frequency reconstructed under a high random sparsity rate still has obvious interferences such as side lobes and pseudo peaks, which makes the time-frequency-modulation frequency representation accuracy obtained in some complex scenarios insufficient. In this application, Figure 1 As shown, a sparse time-frequency-modulation rate representation reconstruction method based on tail enhancement is provided, comprising the following steps: Step S100, acquiring radar observation data of the micro-motion target, and performing corresponding processing on the radar observation data to obtain observation data characterized by frequency-modulation rate at different times.

[0023] Step S110, the time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction according to the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the sparse observation model of the time-frequency-modulation frequency representation to obtain a parameterized sparse optimization model.

[0024] Step S120, using the alternating direction multiplier method to solve the parameterized sparse optimization model until the solution meets the first preset threshold, then stop the current iteration; if it does not meet the second preset threshold, calculate the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration.

[0025] Step S130, based on the tail optimization idea, the frequency-modulation frequency reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold, until the solution meets the first preset threshold and the second preset threshold, and the frequency-modulation frequency reconstruction representation at different times is obtained, and the three-dimensional time-frequency-modulation frequency reconstruction representation of the micro-motion target is obtained according to the frequency-modulation frequency reconstruction representation at all times.

[0026] In this application, through the analysis of most algorithms in the field of sparse reconstruction, it is found that the upper bound of the difference of the algorithm with the sparsity parameter set to k and the spatial dimension set to N is directly related to the Nk components excluding the largest k components, that is, the energy proportion of the "tail". Therefore, directly minimizing the tail norm of all potential solutions can significantly improve the focusing accuracy and processing and analysis performance of the reconstructed micro-motion signal.

[0027] In step S100, after the radar observation data is processed accordingly, observation data represented by the frequency-modulation rate at different times are obtained, including: the radar observation data is processed through a sliding time window to obtain multiple continuous signal short-time segments, and then each signal short-time segment is processed into an approximate linear combination of multiple Chirp signals through a second-order parameterized Fourier dictionary to obtain observation data represented by the frequency-modulation rate at different times.

[0028] In order to accurately extract the micro-motion features of the target, a highly focused time-frequency-modulation frequency representation must be obtained. Therefore, in step S110, the time-frequency-modulation frequency representation reconstruction problem is modeled as: Reconstructing the frequency-modulation representation The time-frequency-modulation frequency representation sparse observation model is solved, where the observation data It is an incomplete radar echo observation data and has defects. However, since the actual echo observation data is missing and inevitably interfered by noise, the observation matrix is an underdetermined matrix. Therefore, solving the frequency-modulation frequency representation problem belongs to a linear underdetermined inverse problem, and its solution is not unique. The result of calculating the frequency-modulation frequency representation will have significant deviations, that is, the solution model is expressed as: (1) In formula (1), Indicates a short-term segment of the signal The corresponding radar observation vector, represents the downsampling matrix, represents the inverse short-time frequency modulation Fourier transform matrix, where represents the block Chirp dictionary matrix, represents the block inverse Fourier transform matrix, represents the frequency-modulation frequency characterization vector to be solved, represents the additive noise vector.

[0029] To solve this problem, it is usually necessary to combine the unique properties of the frequency-chirp frequency representation and introduce relevant prior information to constrain the solution process, so as to obtain effective recovery results. Since the number of signal components of the micro-motion target is limited and much smaller than the observation points in the short-term segment of the signal, there are usually only a small number of significant scattering points on the two-dimensional frequency-chirp frequency plane, and the rest of the area appears as background noise. This shows that the frequency-chirp frequency representation has significant sparsity. Based on this feature, a sparse regularization prior is introduced, and the problem is modeled using a sparse representation method to achieve the enhancement and recovery of the sparse features of the target. Ideally, the sparse characteristics of the signal can be obtained by norm to quantify, expressed as: (2) In order to solve this optimization problem, greedy algorithms such as Matching Pursuit (MP) or Orthogonal Matching Pursuit (OMP) can be used. However, these methods are based on the principle of maximum likelihood estimation and involve multi-dimensional parameter search, which limits the accuracy of sparse recovery. In addition, due to the The optimization problem of norm minimization is NP-hard and usually requires relaxing constraints to avoid computational complexity. Norm minimization can effectively replace norm, achieving a convex approximation of sparse signals. Specifically, sparsity Constraints can be expressed in the following form: (3) In formula (3), express norm, Used to define the noise range. The problem described in formula (3) belongs to a linear programming problem and can be solved by algorithms such as the interior point method or the simplex method. However, although these methods can guarantee convergence to the global optimal solution, their computational complexity is high and they are sensitive to system errors, so they have certain limitations in practical applications. Based on the Least Absolute Shrinkage and Selection Operator (LASSO) model, it is possible to introduce The norm is used to describe the sparse regularized prior of the target, thereby enhancing the sparse characteristics of the frequency-modulation frequency representation.

[0030] Furthermore, the introduction The norm is used as a sparse prior to model the sparse feature enhancement problem of frequency-modulation frequency representation as a parameterized sparse optimization model. Based on the observation model described by formula (1), the target solution can be expressed as: (4) In formula (4), represent norm, the first term in formula (4) limits the range of reconstruction error, and the second term is used as a sparse constraint by adjusting the regularization parameter The value of can flexibly control the sparsity of the frequency-modulation frequency representation.

[0031] Next, in step S120, the alternating direction multiplier method is used to iteratively solve formula (4) until it converges, and the frequency-modulation frequency representation reconstruction of the current round is obtained. In order to achieve the sparsity of the reconstructible coefficient signal reaching or even exceeding the upper bound of the recoverable sparsity, in this embodiment, the tail optimization idea is proposed, which is that the upper bounds of the errors of the solutions of various existing algorithms are directly related to the Nk components except the largest k components, that is, the "tail" Therefore, a strategy to significantly improve the performance of sparse time-frequency-modulation reconstruction is to directly minimize the tail norm of all potential solutions , so as to make the signal energy more concentrated on the target support set, which is expressed as: (5) However, formula (5) is still a non-convex and NP-hard problem. Therefore, it is more feasible to adopt the idea of ​​iterative operation, that is, in multiple iterations, after estimating each determined support set T, solve the following tail optimization problem, that is, the tail optimization model is expressed as: (6) In formula (6), represents the complement of the target support set in the frequency-modulation reconstruction representation, i.e., the tail support set. Indicates a short-term segment of the signal The corresponding radar observation vector, represents the downsampling matrix, represents the inverse short-time frequency modulation Fourier transform matrix, where represents the block Chirp dictionary matrix, represents the block inverse Fourier transform matrix, It represents the frequency-modulation frequency characterization vector obtained by stacking the frequency dimension at different times using the alternating direction multiplication method. is the data fidelity term, used to constrain the reconstruction error, express norm, Used to define the noise range.

[0032] Further, when updating the target support portion for each frequency-modulation frequency characterization reconstruction obtained by the alternating direction multiplier method, Algorithm 1 may be used, and the algorithm steps are as follows: Figure 2 shown.

[0033] Specifically, in Algorithm 1, the distribution The elements are sorted by absolute value and the first The index of the largest element is , is the process of reconstructing the tail support set based on the frequency-modulation frequency obtained in the current iteration.

[0034] In step S130, further, according to the tail optimization model represented by formula (7), the parameterized sparse optimization model described by the LASSO model is expressed as: (7) In formula (7), represent norm, the first term in the formula limits the range of reconstruction error, Sparse prior regularization term modified to add tail optimization.

[0035] In this embodiment, when the alternating direction method of multipliers (ADMM) is used to solve the updated parameterized sparse optimization model: the variables to be optimized are dually decomposed, split variables are introduced, the parameterized sparse optimization model after the update is converted into a constrained optimization problem, the augmented Lagrangian multiplier method is used to convert the constrained optimization problem into the corresponding augmented Lagrangian function, the scale transformation is performed according to the Lagrangian multiplier and the penalty term coefficient, the augmented Lagrangian function is equivalently transformed, and the Gauss-Seidel idea is used to decompose the augmented Lagrangian function after the equivalent transformation into three sub-problems, and the three sub-problems are iteratively solved alternately for multiple times to obtain frequency-modulation frequency reconstruction representations at different times.

[0036] Specifically, the ADMM algorithm introduces split variables , dual decomposition of the original optimization variables , decompose the complex optimization problem into multiple sub-problems, optimize the solutions of multiple sub-problems, and adopt a collaborative update strategy to ultimately achieve the goal of global optimization.

[0037] Due to the combination of augmented Lagrangian function method and dual ascent idea, ADMM algorithm has good convergence performance and computational complexity. According to ADMM theory, formula (5) can be converted into the following constrained optimization problem: (8) In formula (8), Used to characterize the sparse prior regularization term after tail correction, For Hadamard, is the complement matrix of the frequency-modulation frequency characterization support set, and From formula (8), it can be seen that in this method Global variables in norm , each time ADMM is solved, it is reinitialized. The norm is the tail support set in the previous iteration result, and it is minimized during the solution process through the ADMM algorithm.

[0038] The corresponding optimization equation can be constructed by using the augmented Lagrangian multiplier method. Based on formula (8), the corresponding augmented Lagrangian function can be expressed as: (9) In formula (9), and are the conjugate transpose of the Lagrange multiplier and the penalty term coefficient respectively. Formula (9) is also equivalent to: (10) In formula (10), Defined as a scaling transformation of the Lagrange multipliers.

[0039] Furthermore, based on the Gaussian-Seidel idea, the ADMM method decomposes the formula into the following three sub-optimization problems for iterative alternating solutions, which can be specifically expressed as: (11) In formula (11), the superscript of the variable indicates the corresponding number of iterations. Through the above alternating iterative optimization process, the global variable With split variables It is possible to achieve simultaneous minimization by jointly optimizing the two variables, the dual variable can be updated, thus significantly improving the convergence efficiency of the algorithm.

[0040] Specifically, the three sub-problems are respectively the sub-problems of solving the global variables, the splitting variables and the dual variables.

[0041] Furthermore, when solving these three sub-optimization problems: first optimize the global variables, substitute formula (10) into formula (11)-1, and ignore the global variables Irrelevant terms, the optimization process of frequency-modulation frequency distribution sparse recovery can be obtained as follows: (12) When the augmented Lagrangian function is applied to the global variable When the partial derivative is zero, the least squares problem described by equation (12) can be solved to obtain: (13) because It can be used to avoid the matrix inversion operation, and formula (13) can be rewritten as follows through the matrix inversion theorem: (14) Then the optimization process of global variables can be written as: (15) Furthermore, when performing split variable optimization, formula (10) is substituted into formula (11)-2, and terms irrelevant to the split variable are ignored. The optimization process of frequency-modulation frequency distribution sparse recovery can be obtained as follows: (16) Formula (16) can be equivalent to the one containing the splitting variable Norm optimization problem, using the soft threshold method can get its explicit solution: (17) In formula (17), is a complex soft threshold operator.

[0042] Furthermore, when performing dual variable optimization, the optimization process of the dual variable is shown in formula (11)-3.

[0043] In this embodiment, in order to improve the computational efficiency, the observation matrix formed by the 0 and 1 distribution characteristics of the downsampling matrix and the diagonal structure of the Chirp dictionary matrix and the inverse Fourier transform matrix is ​​used. Sparsity, rewrite each optimization variable into a matrix form, so that matrix multiplication can be replaced by matrix dot multiplication. Specifically, the optimization process of each variable can be rewritten as: (18) In formula (18), , and are the matrix forms of global variables, split variables and dual variables respectively. is the matrix form of the observed sparse residual signal, expressed as:

[0044] In formula (18), is the Chirp dictionary matrix, and are the Fourier transform and inverse Fourier transform operators respectively.

[0045] Furthermore, by bringing the ADMM solution method described by formula (18) into Algorithm 1, we can obtain the tail of the sparse time-frequency-modulation reconstruction: The specific iterative process of the ADMM solution algorithm for the norm is as follows: Figure 3 As shown in Algorithm 2.

[0046] In Algorithm 2, it can be seen that the main difference between the tail ADMM algorithm and the traditional ADMM solution method is that during the update of the split variables, the soft threshold is only calculated for the sum of the global variables and the dual variables corresponding to the index part of the support set complement. The choice of is determined only by the frequency-modulation frequency distribution obtained in this iteration Before The tail optimization algorithm is determined by the index of the largest element. This means that even if the support set is selected incorrectly in a certain iteration, according to the update rule of the support set, the incorrectly selected frequency-modulation frequency component will be discarded in subsequent iterations, thereby avoiding the influence of the incorrect component selection. This self-correction ability of the tail optimization algorithm can bring higher reconstruction accuracy and reliability. Since the tail ADMM method requires multiple rounds of ADMM method iterations, the operation time is longer than the ADMM method.

[0047] In this embodiment, when the alternating direction multiplier method is used to solve the updated parameterized sparse optimization model: when the relative error of the frequency-frequency modulation rate reconstruction representation obtained by two iterative calculations is less than the first preset threshold, the alternating direction multiplier method is stopped, and if the number of times the alternating direction multiplier method is currently run is less than the second preset threshold, the tail of the currently obtained frequency-frequency modulation rate reconstruction representation is minimized, and the tail-optimized frequency-frequency modulation rate reconstruction representation continues to be solved using the alternating direction multiplier method for the updated parameterized sparse optimization model, until the number of times the alternating direction multiplier method is currently run is greater than or equal to the second preset threshold, then the frequency-frequency modulation rate representation currently calculated is the frequency-frequency modulation rate reconstruction representation of the micro-motion target at a certain moment.

[0048] like Figure 4 As shown, it is a schematic diagram of the implementation steps of the whole method.

[0049] In this paper, simulation experiments are also used to prove the effectiveness of this method. The norm minimization ADMM method is used as a comparison. The reconstruction performance of the time-frequency-modulation frequency distribution of the proposed tail ADMM method and the comparison method is verified and analyzed on the darkroom measurement data and radar measured data under three data sparsity conditions of 30%, 50% and 70%. The norm tail minimization ADMM method is abbreviated as Tail-ADMM.

[0050] The radar echo is generated by using the X-band metal cone scattering data measured under darkroom conditions. The precession angle is set to 15°, the precession period is 2s, the radar field of view angle is set to 20°, the radar carrier frequency is 10GHz, the pulse repetition frequency is 200Hz, and the observation time is 3.84 seconds (in order to improve the experimental efficiency, a shorter signal time of 2.56 seconds is used later).

[0051] like Figure 5 The figure shows the time-frequency distribution of the echo of the metal cone model in the precession state. Different from the simulated cone model, on the one hand, the metal cone model measured in the darkroom is approximately a combination of a cone and a cylinder, and on the other hand, the turntable cannot completely simulate the real precession of the space target during measurement. Compared with the simulated point scattering model, its time-frequency distribution is no longer a standard sinusoidal distribution, but an approximate sinusoidal curve with a certain morphological distortion. Therefore, it can be used as a typical data sample of irregular micro-motion. At the same time, the clutter generated by the power and support devices such as the turntable used in the darkroom measurement generates some noise and interference in the time-frequency distribution background of the measurement echo.

[0052] Figure 6 and Figure 7 They are and Frequency-modulation frequency distribution calculated by STCFT, ADMM and the proposed Tail-ADMM method at different sparsity rates at different times. The two peaks in the center of the frequency-modulation frequency represent the signal components corresponding to the two scattering centers of the simulated target. Compared with the sparse time-frequency-modulation frequency of the simulated signal, the frequency-modulation frequency distribution slices reconstructed by the traditional ADMM method at a higher sparsity rate for the darkroom measurement signal contain more pseudo peaks and side lobes. The proposed Tail-ADMM method can remove most of the pseudo peaks of the background species, while limiting the side lobes of the scattering center with a better focusing effect.

[0053] like Figure 8 As shown in the figure, the projections of the time-frequency-frequency sequence of darkroom measurement data reconstructed by the three methods at different sparsity rates on the time-frequency dimension. The time-frequency curve reconstructed by the traditional ADMM method has more burr-like interference sidelobes at 50% and 70% sparsity rates. The burr-like interference sidelobes in the time-frequency dimension projection curve reconstructed by Tail-ADMM are effectively suppressed.

[0054] Tables 1 to 3 list the Renyi entropy, image entropy and contrast of the reconstruction results of the three methods at different sparsity rates projected on the time-frequency dimension. Under the three sparsity rates, the proposed Tail-ADMM method can obtain the minimum Renyi entropy and image entropy, as well as the maximum contrast. Under various sparsity rate conditions, the proposed Tail-ADMM method can obtain the minimum Renyi entropy and image entropy, as well as the maximum contrast.

[0055] Table 1 Comparison of Renyi entropy of time-frequency projection distribution of enhanced darkroom measurement data at different sparsity rates

[0056] Table 2 Comparison of time-frequency projection distribution image entropy after darkroom measurement data enhancement at different sparsity rates

[0057] Table 3 Time-frequency projection distribution contrast after darkroom measurement data enhancement at different sparsity rates

[0058] like Fig. 9 As shown in the figure, the projection of the time-frequency-frequency modulation sequence of the darkroom measurement data reconstructed by the three methods at different sparsity rates on the time-frequency modulation frequency dimension. The sidelobes of the time-frequency modulation frequency distribution of the darkroom measurement data reconstructed by the traditional ADMM become more serious as the sparsity rate increases, and the sidelobe interference in the time-frequency modulation frequency distribution reconstructed by Tail-ADMM is better suppressed.

[0059] Furthermore, in this paper, the measured data is also used for experiments to prove the effectiveness of this method. In the measured data experiment, the AWR2243 multi-channel frequency-modulated continuous-wave (FMCW) radar device is used to collect experimental data. In order to speed up the experimental efficiency, the number of iterations of Tail-ADMM is set. is 4.

[0060] Fig.10 and Fig.11 They are and Schematic diagram of the frequency-modulation frequency distribution of the measured data calculated by STCFT, ADMM and the proposed Tail-ADMM method at different sparsity rates at different times. The two peaks in the center of the frequency-modulation frequency represent the signal components corresponding to the two scattering centers of the simulated target.

[0061] The frequency-modulation frequency distribution in the measured signal time-frequency-modulation frequency sequence has a weaker sidelobe level than the darkroom measurement data, and the reconstruction result of Tail-ADMM has weaker sidelobes and better focusing level. The scattering points with weak energy in the time frequency-modulation frequency slice appear too weak in both the traditional ADMM and Tail-ADMM optimization. The traditional ADMM reconstruction obtained at 50% and 70% sparsity Obvious pseudo peaks and side lobes appeared in the moment frequency-modulation frequency slice, which were well suppressed in the Tail-ADMM reconstruction result.

[0062] like Fig.12 The figure shows the projection of the time-frequency-frequency sequence of the darkroom measurement data reconstructed by the three methods at different sparsity rates on the time-frequency dimension. Compared with the darkroom measurement results, the reconstruction results of the measured data have better continuity in the time-frequency dimension. The Tail-ADMM reconstruction results at the three sparsity rates show a more focused time-frequency curve, especially at 50% and 70% sparsity rates, the Tail-ADMM reconstruction results have weaker burr-like background interference than the traditional ADMM.

[0063] Tables 4 to 6 list the Renyi entropy, image entropy and contrast of the measured data reconstruction results of the three methods at different sparsity rates projected on the time-frequency dimension. Under the three sparsity rates, the proposed Tail-ADMM method can obtain the minimum Renyi entropy and image entropy, as well as the maximum contrast.

[0064] Table 4 Comparison of Renyi entropy of time-frequency projection distribution after enhanced measured data at different sparsity rates

[0065] Table 5 Comparison of image entropy of time-frequency projection distribution after measured data enhancement under different sparsity rates

[0066] Table 6. Time-frequency projection distribution contrast of measured data after enhancement at different sparsity rates

[0067] like Fig.13 Figure 2 shows the time-frequency modulation projection diagram of the measured signal at different sparsity rates after enhancement using the proposed method and the traditional ADMM method. Under the three sparsity rates, the Tail-ADMM reconstruction results show fewer burr-like sidelobes.

[0068] According to the above experimental results, it can be effectively proved that the method proposed in this paper has significant advantages in enhancing micro-motion feature representation and sparse signal reconstruction. It can effectively enhance the time-frequency representation of the target in the absence of echo data and has high engineering application value.

[0069] In the above sparse time-frequency-modulation frequency representation reconstruction method based on tail minimization, after obtaining the radar echo data of the micro-motion target, a sparse regularization prior is introduced to quantify the sparse characteristics of the signal. The Least Absolute Shrinkage and Selection Operator (LASSO) model is established by introducing the support set and transforming the LASSO optimization problem into the tail The norm optimization problem adopts the tail minimization iterative solution strategy. After each round of iteration, the support set is updated. The norm minimization LASSO problem is decomposed into multiple sub-optimization problems based on the Gaussian-Seidel idea by using the ADMM method. The global variable x, split variable z, and dual variable u are solved alternately and iteratively by using collaborative updating, and finally the frequency-modulation frequency distribution is reconstructed. , the frequency-modulation frequency distribution reconstructed in each short-time window of the signal is combined to obtain the sparsely reconstructed time-frequency-modulation frequency distribution. Finally, a comparative experiment is carried out on darkroom measurement data and actual measured data to verify the effectiveness of the method of the present invention.

[0070] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0071] In one embodiment, Fig.14 As shown, a sparse time-frequency-modulation frequency representation reconstruction device based on tail minimization is provided, comprising: an observation data acquisition module 200, a parameterized sparse optimization model construction module 210, a reconstruction representation tail optimization module 220 and a three-dimensional representation reconstruction module 230, wherein: The observation data acquisition module 200 is used to acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation frequency at different times after corresponding processing of the radar observation data; The parameterized sparse optimization model building module 210 is used to model the time-frequency-modulation frequency representation reconstruction problem as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction according to the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The reconstruction representation tail optimization module 220 is used to solve the parameterized sparse optimization model by using an alternating direction multiplier method until the solution meets a first preset threshold, then stop the current iteration, and if it does not meet a second preset threshold, calculate the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration; The three-dimensional representation reconstruction module 230 is used to solve the frequency-frequency modulation rate reconstruction representation on the tail support set based on the tail optimization idea under the first preset threshold value by using the alternating direction multiplier method until the solution result satisfies the first preset threshold value and the second preset threshold value, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0072] For the specific limitations of the sparse time-frequency-modulation frequency characterization reconstruction device based on tail minimization, please refer to the limitations of the sparse time-frequency-modulation frequency characterization reconstruction method based on tail minimization in the above text, which will not be repeated here. Each module in the above-mentioned sparse time-frequency-modulation frequency characterization reconstruction device based on tail minimization can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0073] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Fig.15As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a sparse time-frequency-modulation frequency characterization reconstruction method based on tail minimization is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0074] Those skilled in the art will understand that Fig.15 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0075] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented: Acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The parameterized sparse optimization model is solved by using an alternating direction multiplier method until the solution satisfies a first preset threshold, then the current iteration is stopped; if the solution does not satisfy a second preset threshold, the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration is calculated; Based on the idea of ​​tail optimization, the frequency-frequency modulation rate reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold until the solution meets the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0076] In one embodiment, a computer readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented: Acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The parameterized sparse optimization model is solved by using an alternating direction multiplier method until the solution satisfies a first preset threshold, then the current iteration is stopped; if the solution does not satisfy a second preset threshold, the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration is calculated; Based on the idea of ​​tail optimization, the frequency-frequency modulation rate reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold until the solution meets the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

[0077] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0078] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0079] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A sparse time-frequency-modulation frequency representation reconstruction method based on tail minimization, characterized in that: The method comprises: Acquire radar observation data of the micro-motion target, and obtain observation data characterized by frequency-modulation rate at different times after corresponding processing of the radar observation data; The time-frequency-modulation frequency representation reconstruction problem is modeled as a time-frequency-modulation frequency representation sparse observation model that solves the frequency-modulation frequency representation reconstruction based on the observation data at different times, and uses l The sparse regularized prior of the 1-norm characterization of the micro-motion target in the time-frequency-modulation frequency space is used to optimize the time-frequency-modulation frequency characterization sparse observation model to obtain a parameterized sparse optimization model; The parameterized sparse optimization model is solved by using an alternating direction multiplier method until the solution satisfies a first preset threshold, then the current iteration is stopped; if the solution does not satisfy a second preset threshold, the tail support set of the frequency-modulation frequency reconstruction representation obtained in the current iteration is calculated; Based on the idea of ​​tail optimization, the frequency-frequency modulation rate reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold until the solution meets the first preset threshold and the second preset threshold, thereby obtaining the frequency-frequency modulation rate reconstruction representation at different times, and obtaining the three-dimensional time-frequency-frequency modulation rate reconstruction representation of the micro-motion target according to the frequency-frequency modulation rate reconstruction representation at all times.

2. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 1 is characterized in that: After the radar observation data is processed accordingly, the observation data characterized by frequency-modulation frequency at different times are obtained, including: Processing the radar observation data through a sliding time window to obtain a plurality of continuous signal short-time segments; Each short-time segment of the signal is processed into a linear combination of multiple Chirp signals through a second-order parameterized Fourier dictionary, so as to obtain observation data characterized by frequency-modulation frequency at different moments.

3. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 2 is characterized in that: The tail optimization idea is expressed as: In the above formula, represents the complement of the target support set in the frequency-modulation reconstruction representation, Indicates a short-term segment of the signal The corresponding radar observation vector, represents the downsampling matrix, represents the inverse short-time frequency modulation Fourier transform matrix, where represents the block Chirp dictionary matrix, represents the block inverse Fourier transform matrix, It represents the frequency-modulation frequency characterization vector obtained by stacking the frequency dimension at different times using the alternating direction multiplication method. is the data fidelity term, used to constrain the reconstruction error, express norm, Used to define the noise range.

4. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 3 is characterized in that: Based on the tail optimization concept, when the frequency-modulation frequency reconstruction representation on the tail support set is solved by the alternating direction multiplier method under the first preset threshold, the parameterized sparse optimization model described by the LASSO model is expressed as: In the above formula, represent norm, the first term in the formula limits the range of reconstruction error, Sparse prior regularization term modified to add tail optimization.

5. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 4 is characterized in that: When solving the updated parameterized sparse optimization model using the alternating direction multiplier method: Performing dual decomposition on the variables to be optimized, introducing splitting variables, and converting the updated parameterized sparse optimization model into a constrained optimization problem; The constrained optimization problem is converted into a corresponding augmented Lagrangian function using an augmented Lagrangian multiplier method; Performing a scale transformation according to the Lagrange multiplier and the penalty term coefficient, and performing an equivalent transformation on the augmented Lagrangian function; The Gauss-Seidel idea is used to decompose the augmented Lagrangian function after equivalent transformation into three sub-problems. By iteratively solving the three sub-problems multiple times, the frequency-modulation frequency reconstruction representation at different times is obtained.

6. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 5 is characterized in that: The constrained optimization problem is expressed as: In the above formula, Used to characterize the sparse prior regularization term after tail correction, For Hadamard, is the complement matrix of the frequency-modulation frequency characterization support set, and .

7. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 6 is characterized in that: The three sub-problems are respectively sub-problems for solving global variables, split variables and dual variables; In the process of solving the splitting variables, the soft threshold is calculated only for the sum of the global variables and the dual variables of the index part corresponding to the complement of the support set.

8. The sparse time-frequency-modulation rate representation reconstruction method based on tail minimization according to claim 7 is characterized in that: When solving the updated parameterized sparse optimization model using the alternating direction multiplier method: When the relative error of the frequency-modulation frequency reconstruction representation obtained by two iterative calculations is less than the first preset threshold, stopping the alternating direction multiplier method; If the number of times the alternating direction multiplier method is currently run is less than a second preset threshold, a tail minimization process is performed on the currently obtained frequency-modulation frequency reconstruction representation, and the tail-optimized frequency-modulation frequency reconstruction representation is continued to use the alternating direction multiplier method to solve the updated parameterized sparse optimization model; Until the number of times the alternating direction multiplier method is currently run is greater than or equal to the second preset threshold, the frequency-modulation frequency representation currently calculated is the frequency-modulation frequency reconstruction representation of the micro-motion target at a certain moment.

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