Sparse Time-Frequency-Chirp Rate Representation Reconstruction Method Based on Tail Minimization

Abstract

The present application relates to a sparse time-frequency-chirp rate characterization reconstruction method based on tail minimization. After constructing a parametric sparse optimization model and using the alternating direction method of multipliers (ADMM) to solve it, at the end of multiple iterations in one round of solution, the tail support set of the frequency-chirp rate reconstruction characterization obtained in the current iteration is calculated, and the global optimization variable is updated according to the tail support set, and then it is brought into the subsequent solution of the ADMM, so that in the process of multiple solutions, the energy of the target support set in the global optimization variable is more prominent. Using this method can make the target micro-motion features extracted in complex scenarios 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:

[0006] 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;

[0007] 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 1 The sparse regularized prior of the 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;

[0008] 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;

[0009] Based on the tail optimization idea, the frequency - chirp rate reconstruction representation on the tail support set is solved by the alternating direction method of multipliers under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then the frequency - chirp rate reconstruction representation at different times is obtained, and the three - dimensional time - frequency - chirp rate reconstruction representation of the micro - motion target is obtained according to the frequency - chirp rate reconstruction representations at all times.

[0010] In one embodiment, after performing corresponding processing on the radar observation data, the observation data of the frequency - chirp rate representation at different times is obtained, including:

[0011] Processing the radar observation data through a sliding time window to obtain a plurality of consecutive short - time signal segments;

[0012] Processing each of the short - time signal segments into a linear combination of approximate Chirp signals through a second - order parametric Fourier dictionary, to obtain the observation data of the frequency - chirp rate representation at different times.

[0013] In one embodiment, the tail optimization idea is expressed as:

[0014]

[0015] In the above formula, represents the complement of the target support set in the frequency - chirp rate reconstruction representation, represents the short - time signal segment corresponding radar observation vector, represents the down - sampling matrix, represents the inverse short - time frequency - modulated Fourier transform matrix, where, represents the block - Chirp dictionary matrix, represents the block inverse Fourier transform matrix, represents the frequency - chirp rate representation vector stacked by frequency dimension at the current time obtained by the alternating direction method of multipliers, is the data fidelity term, used to constrain the reconstruction error, represents norm, is used to define the noise range.

[0016] In one embodiment, when solving the frequency - chirp rate reconstruction representation on the tail support set by the alternating direction method of multipliers based on the tail optimization idea under the first preset threshold, the parametric sparse optimization model described by the LASSO model is expressed as:

[0017]

[0018] In the above formula, represents the norm. The first term in the formula restricts the range of the reconstruction error, and

[0019] In one embodiment, when using the alternating direction method of multipliers to solve the updated parameterized sparse optimization model:

[0020] Perform dual decomposition on the variable to be optimized, introduce a splitting variable, and transform the updated parameterized sparse optimization model into a constrained optimization problem;

[0021] Use the augmented Lagrangian multiplier method to transform the constrained optimization problem into a corresponding augmented Lagrangian function;

[0022] Perform scale transformation according to the Lagrangian multiplier and the penalty term coefficient, and perform equivalent transformation on the augmented Lagrangian function;

[0023] Use the Gauss-Seidel idea to decompose the equivalent transformed augmented Lagrangian function into three sub-problems, and obtain the frequency-tuning frequency reconstruction representation at different times by alternately solving the three sub-problems through multiple iterations.

[0024] In one embodiment, the constrained optimization problem is expressed as:

[0025]

[0026] In the above formula, is used to represent the sparse prior regularization term after tail correction, is the Hadamard product, is the complement matrix of the frequency-tuning frequency representation support set, i.e., the tail support set, and .

[0027] In one embodiment, the three sub-problems are respectively sub-problems for solving the global variable, the splitting variable, and the dual variable;

[0028] Among them, in the process of solving the splitting variable, only the soft threshold is calculated for the sum of the global variable and the dual variable corresponding to the index part of the complement of the support set.

[0029] In one embodiment, when using the alternating direction method of multipliers to solve the updated parameterized sparse optimization model:

[0030] When the relative error between the frequency-tuning frequency reconstruction representations obtained by two iterations is less than the first preset threshold, stop the alternating direction method of multipliers;

[0031] If the current number of times of running the alternating direction method of multipliers is less than the second preset threshold, perform tail minimization processing on the currently obtained frequency-tuning frequency reconstruction representation, and continue to use the alternating direction method of multipliers to solve the updated parameterized sparse optimization model for the frequency-tuning frequency reconstruction representation after tail optimization;

[0032] Until the current number of times of running the alternating direction method of multipliers is greater than or equal to the second preset threshold, the currently calculated frequency-tuning frequency representation is the frequency-tuning frequency reconstruction representation of the micro-motion target at a certain moment.

[0033] A sparse time-frequency-tuning frequency representation reconstruction device based on tail minimization, the device includes:

[0034] An observation data acquisition module, configured to acquire radar observation data of a micro-motion target, and after performing corresponding processing on the radar observation data, obtain observation data of the frequency-tuning frequency representation at different times;

[0035] A parameterized sparse optimization model construction module, configured to model the time-frequency-tuning frequency representation reconstruction problem as a time-frequency-tuning frequency representation sparse observation model for solving the frequency-tuning frequency representation reconstruction according to the observation data at different times, and use l 1 The norm represents the sparse regular prior of the micro-motion target in the time-frequency-tuning frequency space to optimize the time-frequency-tuning frequency representation sparse observation model, and obtain a parameterized sparse optimization model;

[0036] A reconstruction representation tail optimization module, configured to use the alternating direction method of multipliers to solve the parameterized sparse optimization model until the solution result meets the first preset threshold, then stop the current iteration, if it does not meet the second preset threshold, then calculate the tail support set of the frequency-tuning frequency reconstruction representation obtained in the current iteration;

[0037] A three-dimensional representation reconstruction module, configured to, based on the tail optimization idea, use the alternating direction method of multipliers to solve the frequency-tuning frequency reconstruction representation on the tail support set under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then obtain the frequency-tuning frequency reconstruction representation at different times, and obtain the three-dimensional time-frequency-tuning frequency reconstruction representation of the micro-motion target according to the frequency-tuning frequency reconstruction representation at all times.

[0038] A computer device, including a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0039] Obtain the radar observation data of the micro-motion target. After performing corresponding processing on the radar observation data, obtain the observation data characterized by frequency - chirp rate at different times;

[0040] Model the time - frequency - chirp rate representation reconstruction problem as a time - frequency - chirp rate representation sparse observation model for solving the frequency - chirp rate representation reconstruction based on the observation data at different times, and use l 1 The norm to represent the sparse regular prior of the micro - motion target in the time - frequency - chirp rate space to optimize the time - frequency - chirp rate representation sparse observation model, and obtain a parameterized sparse optimization model;

[0041] Use the alternating direction multiplier method to solve the parameterized sparse optimization model until the solution result 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 - chirp rate reconstruction representation obtained in the current iteration;

[0042] Based on the tail optimization idea, use the alternating direction multiplier method to solve the frequency - chirp rate reconstruction representation on the tail support set under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then obtain the frequency - chirp rate reconstruction representation at different times, and obtain the three - dimensional time - frequency - chirp rate reconstruction representation of the micro - motion target according to the frequency - chirp rate reconstruction representations at all times.

[0043] A computer - readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0044] Obtain the radar observation data of the micro - motion target. After performing corresponding processing on the radar observation data, obtain the observation data characterized by frequency - chirp rate at different times;

[0045] Model the time - frequency - chirp rate representation reconstruction problem as a time - frequency - chirp rate representation sparse observation model for solving the frequency - chirp rate representation reconstruction based on the observation data at different times, and use l 1 The norm to represent the sparse regular prior of the micro - motion target in the time - frequency - chirp rate space to optimize the time - frequency - chirp rate representation sparse observation model, and obtain a parameterized sparse optimization model;

[0046] Use the alternating direction multiplier method to solve the parameterized sparse optimization model until the solution result 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 - chirp rate reconstruction representation obtained in the current iteration;

[0047] Based on the idea of tail optimization, the alternating direction multiplier method is used to solve the frequency - chirp rate reconstruction representation on the tail support set under the first preset threshold until the solution result satisfies the first preset threshold and the second preset threshold, then the frequency - chirp rate reconstruction representation at different times is obtained, and the three - dimensional time - frequency - chirp rate reconstruction representation of the micro - motion target is obtained according to the frequency - chirp rate reconstruction representations at all times.

[0048] In the above - mentioned sparse time - frequency - chirp rate representation reconstruction method based on tail minimization, after constructing the parametric sparse optimization model and using the alternating direction multiplier method to solve it, after the end of multiple iterations in one round of solution, the tail support set of the frequency - chirp rate reconstruction representation obtained in the current iteration is also calculated, and the global optimization variable is updated according to the tail support set, and then it is brought into the subsequent solution of the alternating direction multiplier method, so that in the process of multiple solutions, the energy of the target support set in the global optimization variable is more prominent. Using this method can make the target micro - motion features extracted in complex scenarios more accurate. Description of the Drawings

[0049] Figure 1 It is a schematic flow chart of the sparse time - frequency - chirp rate representation reconstruction method based on tail minimization in an embodiment;

[0050] Figure 2 It is a schematic flow chart of the specific steps of Algorithm 1 in an embodiment;

[0051] Figure 3 It is a schematic flow chart of the specific steps of Algorithm 2 in an embodiment;

[0052] Figure 4 It is a block diagram of the implementation process of this method in an embodiment;

[0053] Figure 5 It is a schematic diagram of a sample of dark - room measurement data in a simulation experiment;

[0054] Figure 6 It is about the comparison schematic diagram of different methods for reconstructing the frequency - chirp rate distribution of the dark - room measurement signal at different times under different random sparsity rates in a simulation experiment ;

[0055] Figure 7 It is about the comparison schematic diagram of different methods for reconstructing the frequency - chirp rate distribution of the dark - room measurement signal at different times under different random sparsity rates in a simulation experiment ;

[0056] Figure 8 It is a schematic diagram of the time - frequency dimension projection after enhancement of the dark - room measurement signal under different random sparsity rates in a simulation experiment using different methods;

[0057] Figure 9 Schematic diagram of the time - chirp rate dimension projection of the darkroom measurement signals enhanced by different methods at different random sparsity rates in a simulation experiment;

[0058] Figure 10 For the measured signals at different random sparsity rates in a measured data experiment Schematic diagram for comparing the enhancement methods of the frequency - chirp rate distribution obtained by different methods at a certain moment;

[0059] Figure 11 For the measured signals at different random sparsity rates in a measured data experiment Schematic diagram for comparing the enhancement methods of the frequency - chirp rate distribution obtained by different methods at a certain moment;

[0060] Figure 12 Schematic diagram of the projection of the time - frequency - chirp rate sequence of the reconstructed darkroom measurement data at different random sparsity rates in a measured data experiment on the time - frequency dimension;

[0061] Figure 13 Schematic diagram of the time - chirp rate dimension projection of the measured signals enhanced by the present method and the traditional ADMM method at different random sparsity rates in a measured data experiment;

[0062] Figure 14 Structural block diagram of the process device of the sparse time - frequency - chirp rate characterization reconstruction method based on tail minimization in an embodiment;

[0063] Figure 15 Internal structure diagram of a computer device in an embodiment. Specific implementation manners

[0064] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to 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.

[0065] Aiming at the existing technology, there are still obvious interferences such as side lobes and false peaks in the reconstructed time - frequency - chirp rate results at a relatively high random sparsity rate, which makes the accuracy of the reconstructed time - frequency - chirp rate characterization insufficient in some complex scenarios. In the present application, as Figure 1 shown, a sparse time - frequency - chirp rate characterization reconstruction method based on tail enhancement is provided, including the following steps:

[0066] Step S100, obtain the radar observation data of the micro - motion target, and after performing corresponding processing on the radar observation data, obtain the observation data of the frequency - chirp rate characterization at different moments.

[0067] Step S110, model the time-frequency-tuning frequency representation reconstruction problem as a time-frequency-tuning frequency representation sparse observation model that solves the frequency-tuning frequency representation reconstruction based on the observation data at different times, and use l 1 the norm to represent the sparse regular prior of the micro-motion target in the time-frequency-tuning frequency space to optimize the time-frequency-tuning frequency representation sparse observation model, and obtain a parameterized sparse optimization model.

[0068] Step S120, use the alternating direction multiplier method to solve the parameterized sparse optimization model until the solution result 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-tuning frequency reconstruction representation obtained in the current iteration.

[0069] Step S130, based on the tail optimization idea, use the alternating direction multiplier method to solve the frequency-tuning frequency reconstruction representation on the tail support set under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then obtain the frequency-tuning frequency reconstruction representations at different times, and obtain the three-dimensional time-frequency-tuning frequency reconstruction representation of the micro-motion target according to the frequency-tuning frequency reconstruction representations at all times.

[0070] In this application, through the analysis of the vast majority of algorithms in the sparse reconstruction field, it is found that the upper bound of the difference of the algorithms with the sparse degree parameter set to k and the space dimension set to N is directly related to the energy ratio of the N-k components other than the largest k components, that is, 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.

[0071] In step S100, after corresponding processing of the radar observation data, the observation data of the frequency-tuning frequency representation at different times is obtained, including: processing the radar observation data through a sliding time window to obtain multiple consecutive short-time signal segments, and then processing each short-time signal segment into an approximate linear combination of multiple Chirp signals through a second-order parameterized Fourier dictionary, so as to obtain the observation data of the frequency-tuning frequency representation at different times.

[0072] In order to accurately extract the micro-motion characteristics of the target, it is necessary to obtain a highly focused time-frequency-tuning frequency representation. Therefore, in step S110, the time-frequency-tuning frequency representation reconstruction problem is modeled as reconstructing the frequency-tuning frequency representation to solve the time-frequency-tuning frequency representation sparse observation model, where the observation data is incomplete radar echo observation data with defects. However, due to the missing actual echo observation data and inevitably being affected by noise interference, the observation matrix is an underdetermined matrix. Therefore, solving the problem of frequency-chirp rate characterization belongs to a linear underdetermined inverse problem, and its solution is not unique. If directly through calculate the frequency-chirp rate characterization, the result will have a significant deviation. That is, the solution model at this time is expressed as:

[0073] (1)

[0074] In formula (1), represents the radar observation vector corresponding to the short-time segment of the signal , 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-chirp rate characterization vector to be solved represents the additive noise vector

[0075] To solve this problem, it is usually necessary to combine the unique properties of the frequency-chirp rate characterization and introduce relevant prior information to constrain the solution process, so as to obtain an effective recovery result. Since the number of signal components of the micro-motion target is limited and much smaller than the number of observation points within the short-time segment of the signal, in the two-dimensional frequency-chirp rate plane, there are usually only a few significant scattering points, and the rest of the region shows background noise. This indicates that the frequency-chirp rate characterization has significant sparsity. Based on this characteristic, a sparse regularization prior is introduced, and the sparse representation method is used to model the problem to enhance and recover the sparse features of the target. In an ideal situation, the sparse characteristic of the signal can be quantified by norm, which is expressed as:

[0076] (2)

[0077] 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, resulting in limited accuracy of sparse recovery. In addition, since the optimization problem based on norm minimization belongs to an NP-hard problem, it is usually necessary to avoid computational complexity by relaxing the constraints. And norm minimization can effectively replace The norm realizes a convex approximation of the sparse signal. Specifically, the sparsity constraint can be expressed in the following form:

[0078] (3)

[0079] In formula (3), denotes the norm, which is used to define the noise range. The problem described by formula (3) belongs to the 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 relatively high and they are sensitive to system errors. Therefore, there are certain limitations in practical applications. Based on the Least Absolute Shrinkage and Selection Operator (LASSO) model, the norm can be introduced to describe the sparse regularization prior of the target, thereby enhancing the sparse characteristics of the frequency - chirp rate representation.

[0080] Furthermore, introducing the norm as the sparse prior, the problem of enhancing the sparse characteristics of the frequency - chirp rate representation is modeled as a parametric sparse optimization model. Based on the observation model described by formula (1), the target solution can be expressed as:

[0081] (4)

[0082] In formula (4), represents the norm. The first term in formula (4) restricts the range of the reconstruction error, and the second term serves as the sparse constraint. By adjusting the value of the regularization parameter , the sparse degree of the frequency - chirp rate representation can be flexibly controlled.

[0083] Next, in step S120, the alternating direction multiplier method is used to iteratively solve formula (4) until it converges, obtaining the frequency - chirp rate representation reconstruction of the current round. To achieve a reconstructible coefficient signal sparsity that reaches or even exceeds the upper bound of the recoverable sparsity, in this embodiment, the tail optimization idea is proposed. The error upper bounds of the solutions of existing multiple algorithms are directly related to the N - k components other than the largest k components, that is, the "tail" in terms of the energy proportion. Therefore, a strategy aimed at significantly improving the sparse time - frequency - chirp rate reconstruction efficiency is to directly minimize the tail norm of all potential solutions, thereby promoting the concentration of signal energy on the target support set, which is expressed as:

[0084] (5)

[0085] However, formula (5) still belongs to 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:

[0086] (6)

[0087] In formula (6), represents the complement of the target support set in the frequency-chirp rate reconstruction representation, that is, the tail support set, represents the short-time segment of the signal 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-chirp rate representation vector stacked by frequency dimension at different times in the current iteration obtained by using the alternating direction method of multipliers, is the data fidelity term, which is used to constrain the reconstruction error, represents norm, is used to define the noise range.

[0088] Furthermore, when updating the target support part for the frequency-chirp rate representation reconstruction obtained by using the alternating direction method of multipliers each time, Algorithm 1 can be used, and its algorithm steps are as Figure 2 shown.

[0089] Specifically, in Algorithm 1, the elements of the distribution are sorted according to the absolute value size, and the indexes of the top largest elements are selected to form , which is the process of obtaining the tail support set of the frequency-chirp rate reconstruction representation according to the current iteration.

[0090] In step S130, further, according to the tail optimization model represented by formula (7), a parametric sparse optimization model described by the LASSO model is expressed as:

[0091] (7)

[0092] In formula (7), represents norm, and the first term in the formula restricts the range of the reconstruction error, It is the sparse prior regularization term after adding the tail optimization correction.

[0093] In this embodiment, when using the Alternating Direction Method of Multipliers (ADMM) to solve the updated parameterized sparse optimization model: the variable to be optimized is dually decomposed, a splitting variable is introduced, and the updated parameterized sparse optimization model is transformed into a constrained optimization problem. The augmented Lagrangian multiplier method is used to transform the constrained optimization problem into the corresponding augmented Lagrangian function. Scale transformation is performed according to the Lagrange multiplier and the penalty term coefficient, and the augmented Lagrangian function is equivalently transformed. The Gaussian - Seidel idea is used to decompose the equivalently transformed augmented Lagrangian function into three sub - problems. By alternately solving the three sub - problems iteratively for multiple times, the frequency - tuning frequency reconstruction representation at different times is obtained.

[0094] Specifically, the ADMM algorithm introduces a splitting variable to dually decompose the original optimization variable

[0095] and decomposes the complex optimization problem into multiple sub - problems. By optimizing the solutions of multiple sub - problems and adopting a collaborative update strategy, the goal of global optimization is finally achieved.

[0096] (8)

[0097] In formula (8), is used to represent the sparse prior regularization term after tail correction, is the Hadamard product, is the complement matrix of the support set of the frequency - tuning frequency representation, and . From formula (8), it can be seen that in this method the global variable in the norm, is re - initialized every time ADMM is solved,

[0098] and the

[0099] (9)

[0100] In Equation (9), and are the conjugate transpose of the Lagrange multiplier and the penalty term coefficient, respectively. Equation (9) is also equivalent to:

[0101] (10)

[0102] In Equation (10), is defined as the scaling transformation of the Lagrange multiplier.

[0103] Furthermore, based on the Gaussian-Seidel idea, the ADMM method decomposes the equation into the following three sub-optimization problems for iterative alternating solution, which can be specifically expressed as:

[0104] (11)

[0105] In Equation (11), the superscript of the variable represents its corresponding iteration number. Through the above alternating iterative optimization process, the global variable and the split variable can achieve synchronous minimization. With the joint optimization of these two variables, the dual variable is updated, thus significantly improving the convergence efficiency of the algorithm.

[0106] Specifically, the three sub-problems are sub-problems for solving the global variable, the split variable, and the dual variable, respectively.

[0107] Furthermore, when solving these three sub-optimization problems: first, optimize the global variable, substitute Equation (10) into Equation (11)-1, and ignore the terms unrelated to the global variable , the optimization process of frequency-tuning frequency distribution sparse recovery can be obtained as follows:

[0108] (12)

[0109] When the partial derivative of the augmented Lagrangian function with respect to the global variable is zero, the least squares problem described by Equation (12) can be solved to obtain:

[0110] (13)

[0111] Since can be used to avoid the matrix inversion operation, and Equation (13) can be rewritten by the matrix inversion theorem as:

[0112] (14)

[0113] Then the optimization process of the global variable can be written as:

[0114] (15)

[0115] Furthermore, when performing split variable optimization, substituting formula (10) into formula (11)-2 and ignoring the terms unrelated to the split variables, the optimization process for sparse recovery of the frequency-tuning frequency distribution can be obtained as follows:

[0116] (16)

[0117] Formula (16) can be equivalently transformed into a norm optimization problem involving split variables, and its explicit solution can be obtained using the soft thresholding method:

[0118] (17)

[0119] In formula (17), is the complex soft thresholding operator.

[0120] Furthermore, when performing dual variable optimization, the optimization process of the dual variables is as shown in formula (11)-3.

[0121] In this embodiment, to improve the operation efficiency, an observation matrix formed by the 0, 1 distribution characteristics of the downsampling matrix and the diagonal structures of the Chirp dictionary matrix and the inverse Fourier transform matrix is used for sparsity. Each optimization variable is rewritten in matrix form to facilitate replacing the multiplication operation between matrices with matrix dot multiplication. Specifically, the optimization process of each variable can be rewritten as:

[0122] (18)

[0123] In formula (18), , and are the matrix forms of the global variable, split variable, and dual variable, respectively. is the matrix form of the observed sparse residual signal, expressed as:

[0124]

[0125] In formula (18), is the Chirp dictionary matrix, and are the Fourier transform and inverse Fourier transform operators, respectively.

[0126] Furthermore, substituting the ADMM solution method described by formula (18) into Algorithm 1, the specific iterative process of the ADMM solution algorithm for the norm at the tail of sparse time-frequency-tuning frequency reconstruction can be obtained, as shown in Figure 3As shown in Algorithm 2.

[0127] In Algorithm 2, it can be seen that compared with the traditional ADMM solution method, the main difference of the tail ADMM algorithm lies in that during the update process of the split variable, the soft threshold is calculated only for the sum of the global variable and the dual variable corresponding to the index part of the complement of the support set. And the selection of the support set is only determined by the index of the first several largest elements of the frequency-tuning frequency distribution obtained in this iteration. This shows that even if the support set selection in a certain iteration is incorrect, according to the update rule of the support set, the misselected frequency-tuning frequency components will be discarded in subsequent iterations, thus avoiding the influence of misselected component selection. This self-correcting 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 that of the ADMM method.

[0128] In this embodiment, when using the alternating direction multiplier method to solve the updated parametric sparse optimization model: when the relative error of the frequency-tuning frequency reconstruction representation calculated in two iterations is less than the first preset threshold, the alternating direction multiplier method is stopped. If the number of times the alternating direction multiplier method is currently running is less than the second preset threshold, the tail of the currently obtained frequency-tuning frequency reconstruction representation is minimized, and the frequency-tuning frequency reconstruction representation optimized at the tail is continued to be used to solve the updated parametric sparse optimization model by the alternating direction multiplier method until the number of times the alternating direction multiplier method is currently running is greater than or equal to the second preset threshold, then the currently calculated frequency-tuning frequency representation is the frequency-tuning frequency reconstruction representation of the micro-motion target at a certain moment.

[0129] As Figure 4 shown, it is a schematic diagram of the implementation steps of the whole method.

[0130] In this article, the effectiveness of this method is also demonstrated through simulation experiments. In the simulation experiments, the short-time frequency modulation transform and the traditional norm minimization ADMM method are selected for comparison. On the darkroom measurement data and the radar measured data, the reconstruction performance of the proposed tail ADMM method and the comparison method for the time-frequency-tuning frequency distribution under three data sparsity rates of 30%, 50% and 70% is verified and analyzed. For the convenience of representation, the proposed norm tail minimization ADMM method is abbreviated as Tail-ADMM.

[0131] The radar echo of an X-band metal cone is generated using the scattering data measured under darkroom conditions. It is set to precess at a precession angle of 15° with a period of 2 s. The radar horizon angle is set to 20°, the radar carrier frequency is 10 GHz, the pulse repetition frequency is 200 Hz, and the observation duration is 3.84 s (to improve the experimental efficiency, a shorter signal duration of 2.56 s is used subsequently).

[0132] As Figure 5 shown, it is the time-frequency distribution of the echo in the precessing state of the metal cone model. Different from the simulated cone model, on the one hand, since the metal cone model measured in the darkroom is approximately a combination of a cone and a cylinder, and on the other hand, since it is difficult for the turntable to fully simulate the real precession of a spatial target during measurement, the shape of its time-frequency distribution is no longer a standard sine distribution compared to the simulated point scattering model, but an approximate sine curve shape with a certain shape distortion, so it can be used as a typical data sample of non-regular micro-motion. At the same time, the clutter generated by the power and support devices such as the turntable used in the darkroom measurement produces some noise and interference in the background of the time-frequency distribution of the measured echo.

[0133] Figure 6 and Figure 7 are respectively and the frequency-tuning frequency distributions calculated by using the STCFT, ADMM, and the proposed Tail-ADMM methods at different sparsity rates at the moments of

[0134] As Figure 8 shown, it is the projection of the time-frequency-tuning frequency sequences of the darkroom measurement data reconstructed by the three methods at different sparsity rates in the time-frequency dimension. The time-frequency curves reconstructed by the traditional ADMM method have more spiky interference side lobes at sparsity rates of 50% and 70%. The spiky interference side lobes are effectively suppressed in the time-frequency dimension projection curve reconstructed by Tail-ADMM.

[0135] Tables 1 to 3 list the Renyi entropy, image entropy, and contrast of the projections of the reconstruction results of the three methods in the time-frequency dimension at different sparsity rates. At the three sparsity rates, the proposed Tail-ADMM method can obtain the minimum Renyi entropy and image entropy, and the maximum contrast. Under various sparsity rate conditions, the proposed Tail-ADMM method can obtain the minimum Renyi entropy and image entropy, and the maximum contrast.

[0136] Table 1 Comparison of Renyi entropy of time-frequency projection distribution of enhanced darkroom measurement data at different sparsity rates

[0137]

[0138] Table 2 Comparison of image entropy of time-frequency projection distribution of enhanced darkroom measurement data at different sparsity rates

[0139]

[0140] Table 3 Contrast of time-frequency projection distribution of enhanced darkroom measurement data at different sparsity rates

[0141]

[0142] As Figure 9 shown, it is the projection of the time-frequency-chirp rate sequences of the darkroom measurement data reconstructed by three methods at different sparsity rates in the time-chirp rate dimension. The sidelobes of the time-chirp rate distribution reconstructed from the darkroom measurement data by traditional ADMM become more serious with the increase of the sparsity rate, and the sidelobe interference in the time-chirp rate distribution reconstructed by Tail-ADMM is better suppressed.

[0143] Furthermore, in this paper, measured data is also used for experiments to prove the effectiveness of the proposed method. In the measured data experiment, an AWR2243 multi-channel Frequency-Modulated Continuous-Wave (FMCW) radar device is used to collect experimental data. To improve the experimental efficiency, the number of iterations of Tail-ADMM is set to 4.

[0144] Figure 10 and Figure 11 are respectively and Schematic diagrams of the frequency-chirp rate distribution of measured data calculated by STCFT, ADMM and the proposed Tail-ADMM methods at different sparsity rates at different times. The two peaks in the center of the frequency-chirp rate represent the signal components corresponding to the two scattering centers of the simulation target.

[0145] The frequency-chirp rate distribution in the measured signal time-frequency-chirp rate sequence has a weaker sidelobe level compared with the darkroom measurement data, and the reconstruction result of Tail-ADMM has weaker sidelobes and better focusing level. At 70% sparsity rate Scattering points with weak energy in the time-frequency - frequency modulation rate slice showed an overly weak phenomenon in both traditional ADMM and Tail-ADMM optimizations. At sparsity rates of 50% and 70%, the time-frequency - frequency modulation rate slice reconstructed by traditional ADMM showed obvious false peaks and side lobes, which were well suppressed in the Tail-ADMM reconstruction results.

[0146] As Figure 12 shown, the projections of the time-frequency - frequency modulation rate sequences of the anechoic chamber measurement data reconstructed by the three methods at different sparsity rates on the time-frequency dimension are presented. Compared with the anechoic chamber measurement results, the reconstructed projections of the measured data in the time-frequency dimension have better continuity. At the three sparsity rates, the Tail-ADMM reconstruction results show more focused time-frequency curves. Especially at sparsity rates of 50% and 70%, the Tail-ADMM reconstruction results have weaker spiky background interference than traditional ADMM.

[0147] Tables 4 to 6 list the Renyi entropy, image entropy, and contrast of the projections of the reconstructed measured data of the three methods at different sparsity rates on the time-frequency dimension. At the three sparsity rates, the proposed Tail-ADMM method can obtain the minimum Renyi entropy and image entropy, as well as the maximum contrast.

[0148] Table 4 Comparison of Renyi entropy of the time-frequency projection distribution of the enhanced measured data at different sparsity rates

[0149]

[0150] Table 5 Comparison of image entropy of the time-frequency projection distribution of the enhanced measured data at different sparsity rates

[0151]

[0152] Table 6 Contrast of the time-frequency projection distribution of the enhanced measured data at different sparsity rates

[0153]

[0154] As Figure 13 shown, the schematic diagrams of the projections of the measured signals enhanced by the proposed method and the traditional ADMM method on the time - frequency modulation rate dimension at different sparsity rates are presented. At the three sparsity rates, the Tail-ADMM reconstruction results show fewer spiky side lobes.

[0155] Based on the above experimental results, it can be effectively proven that the method proposed in this paper has significant advantages in enhancing micro - motion feature representation and sparse signal reconstruction, can effectively enhance the time-frequency representation of the target in the case of missing echo data, and has high engineering application value.

[0156] In the above sparse time-frequency-chirp rate 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. For the non-convex and NP-hard problem, a least absolute shrinkage and selection operator (LASSO) model is established through the norm. By introducing the support set, the LASSO optimization problem is transformed into a tail norm optimization problem. A tail minimization iterative solution strategy is adopted. After each round of iteration, the support set is updated. For the tail norm minimization LASSO problem on each support set, based on the Gaussian-Seidel idea, the ADMM method is used to decompose it into multiple sub-optimization problems, and collaborative update is used to alternately iterate and solve the global variable x, the splitting variable z, and the dual variable u. Finally, the frequency-chirp rate distribution is reconstructed . The frequency-chirp rate distributions reconstructed within each short time window of the signal are combined to obtain the sparse reconstructed time-frequency-chirp rate distribution. Finally, comparative experiments are also carried out on the measured data in the darkroom and the measured data to verify the effectiveness of the method of the present invention.

[0157] It should be understood that although the steps in the Figure 1 flowchart are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, Figure 1 at least a part of the steps in the

[0158] 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 either, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps. Figure 14 In one embodiment, as

[0159] shown, a sparse time-frequency-chirp rate representation reconstruction device based on tail minimization is provided, including: an observation data acquisition module 200, a parametric sparse optimization model construction module 210, a reconstructed representation tail optimization module 220, and a three-dimensional representation reconstruction module 230, where:

[0160] The observation data acquisition module 200 is configured to acquire radar observation data of the micro-motion target, and after performing corresponding processing on the radar observation data, obtain the observation data of the frequency-chirp rate representation at different times;

[0160] The parametric sparse optimization model construction module 210 is configured to model the time-frequency-tuning frequency representation reconstruction problem as a time-frequency-tuning frequency representation sparse observation model that solves the frequency-tuning frequency representation reconstruction based on the observation data at different times, and uses l 1 the norm to represent the sparse regular prior of the micro-motion target in the time-frequency-tuning frequency space to optimize the time-frequency-tuning frequency representation sparse observation model, and obtain a parametric sparse optimization model;

[0161] The reconstructed representation tail optimization module 220 is configured to use the alternating direction multiplier method to solve the parametric sparse optimization model until the solution result 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-tuning frequency reconstruction representation obtained in the current iteration;

[0162] The three-dimensional representation reconstruction module 230 is configured to, based on the tail optimization idea, use the alternating direction multiplier method to solve the frequency-tuning frequency reconstruction representation on the tail support set under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then obtain the frequency-tuning frequency reconstruction representations at different times, and obtain the three-dimensional time-frequency-tuning frequency reconstruction representation of the micro-motion target according to the frequency-tuning frequency reconstruction representations at all times.

[0163] For the specific limitations of the sparse time-frequency-tuning frequency representation reconstruction device based on tail minimization, reference can be made to the limitations of the sparse time-frequency-tuning frequency representation reconstruction method based on tail minimization in the above text, which will not be elaborated here. Each module in the above sparse time-frequency-tuning frequency representation reconstruction device based on tail minimization can be implemented in whole or in part by software, hardware, and their combination. The above modules can be embedded in the processor in the computer device in hardware form or independent of it, or stored in the memory in the computer device in software form, so that the processor can call and execute the operations corresponding to the above modules.

[0164] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as Figure 15As shown in the figure. 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 computer programs. The internal memory provides an environment for the operation of the operating system and computer programs 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, it realizes a sparse time-frequency-chirp rate representation reconstruction method based on tail minimization. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covered on the display screen, or a button, a trackball, or a touchpad set on the computer device housing, or an external keyboard, touchpad, or mouse, etc.

[0165] Those skilled in the art can understand that Figure 15 the structure shown in the figure is only a block diagram of some structures 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 some components, or have different component arrangements.

[0166] In one embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory. When the processor executes the computer program, the following steps are implemented:

[0167] Obtain the radar observation data of the micro-motion target. After performing corresponding processing on the radar observation data, obtain the observation data of the frequency-chirp rate representation at different times;

[0168] Model the time-frequency-chirp rate representation reconstruction problem as a time-frequency-chirp rate representation sparse observation model for solving the frequency-chirp rate representation reconstruction according to the observation data at different times, and use l 1 the norm to represent the sparse regular prior of the micro-motion target in the time-frequency-chirp rate space to optimize the time-frequency-chirp rate representation sparse observation model, and obtain a parameterized sparse optimization model;

[0169] Use the alternating direction multiplier method to solve the parameterized sparse optimization model until the solution result 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-chirp rate reconstruction representation obtained in the current iteration;

[0170] Based on the tail optimization idea, the alternating direction multiplier method is used to solve the frequency - chirp rate reconstruction representation on the tail support set under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then the frequency - chirp rate reconstruction representation at different times is obtained, and the three - dimensional time - frequency - chirp rate reconstruction representation of the micro - motion target is obtained according to the frequency - chirp rate reconstruction representations at all times.

[0171] In one embodiment, a computer - readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0172] Obtain the radar observation data of the micro - motion target. After performing corresponding processing on the radar observation data, the observation data of the frequency - chirp rate representation at different times is obtained;

[0173] Model the time - frequency - chirp rate representation reconstruction problem as a time - frequency - chirp rate representation sparse observation model for solving the frequency - chirp rate representation reconstruction according to the observation data at different times, and use l 1 The norm to represent the sparse regular prior of the micro - motion target in the time - frequency - chirp rate space to optimize the time - frequency - chirp rate representation sparse observation model, and a parameterized sparse optimization model is obtained;

[0174] Use the alternating direction multiplier method to solve the parameterized sparse optimization model until the solution result 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 - chirp rate reconstruction representation obtained in the current iteration;

[0175] Based on the tail optimization idea, the alternating direction multiplier method is used to solve the frequency - chirp rate reconstruction representation on the tail support set under the first preset threshold until the solution result meets the first preset threshold and the second preset threshold, then the frequency - chirp rate reconstruction representation at different times is obtained, and the three - dimensional time - frequency - chirp rate reconstruction representation of the micro - motion target is obtained according to the frequency - chirp rate reconstruction representations at all times.

[0176] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. 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 methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided in the present application can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can 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 (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0177] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0178] The above-described embodiments merely represent several implementation manners of the present application. The description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended 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 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.

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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