CN113960539B - Target micro Doppler cluster estimation method of forward and backward TVAR models - Google Patents
Target micro Doppler cluster estimation method of forward and backward TVAR models Download PDFInfo
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Abstract
The invention provides a target micro Doppler clustering estimation method of a forward and backward TVAR model, which solves the problem of insufficient time-frequency resolution of micro Doppler analysis of the existing time-frequency analysis method. The implementation steps comprise: collecting target radar echo data; representing the target HRRP range bin data in a TVAR model; converting the target time-varying coefficient to obtain a matrix form of target distance unit data in a BS-FBTVAR model; estimating a time-invariant coefficient of the target by using a clustering structure a priori; and using the time-varying coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram of the target. And reflecting the number, shape and attitude information of scattering points of the radar target according to the micro Doppler time-frequency diagram, and identifying the target. The invention utilizes the interaction between adjacent super-parameters of the intra-block sparse coefficients and the prior information of the known block boundaries of the rigid body target. The micro Doppler time-frequency resolution and the noise immunity are improved. The method is used for micro-motion characteristic analysis of the space cone target and further used for target identification.
Description
Technical Field
The invention belongs to the technical field of radars, and further relates to micro Doppler analysis of radar targets, in particular to a target micro Doppler clustering estimation method of a forward-backward TVAR model, which can be used as an important basis for identifying targets.
Background
Micro-motion is common in nature, such as swinging of the hands and legs of a pedestrian, rotation of motors, helicopter rotors, vibration of bridges, spin, precession, nutation, etc. of ballistic missile targets. The micro-motion of the radar target can generate additional frequency modulation on the target, so that the target echo Doppler is time-varying, reflects the fine characteristics of the target, and can be used as an important basis for identifying the target. The time-frequency analysis method is used as an effective means of micro Doppler analysis, the instantaneous frequency of the target is extracted and separated, and the characteristics of the structure, the gesture, the electromagnetic parameters of surface materials, the stress state and the like of the target can be calculated by utilizing the instantaneous frequency, so that the structural characteristics and the micro-motion characteristics obtained by the time-frequency analysis of the target are applied to the identification of the space cone target.
The time-frequency analysis method is used for micro Doppler analysis of radar target micro motion to extract the fine features of the target, and is mainly divided into two main categories: parameterized and non-parameterized time-frequency analysis. Wherein:
Non-parametric time-frequency analysis methods, including linear time-frequency methods and Cohen classes. For example, v.c.chen, published paper "Doppler signatures of radar backscattering from objects with micro motions"(IET Signal Process.,vol.2,no.3,pp.291–300,Sep.2008) therein proposes that the Wigner-Ville distribution be used to analyze micro-doppler characteristics of vibrating or rotating targets or target structures to overcome the Hisenbergur boundary of time-frequency resolution, since the conventional Cohen class is severely disturbed by cross terms when the signal of interest contains multiple components.
C.Cai, W.Liu, J.S.Fu, Y.Lu in its published paper "Radar micro-Doppler signature analysis with HHT"(IEEE Trans.Aerosp.Electron.Syst.,vol.46,no.2,pp.929–938,Apr.2010), hilbert-Huang transform was used to analyze the radar micro-Doppler characteristics of vibrating targets and obtain better performance than the traditional Cohen-type TF method, which is very sensitive to noise.
T.Thayaparan, S.Abrol, E.Riseborough, L.Stankovic, D.Lamothe, G.Duff, in its published paper "Analysis of radar micro-Doppler signatures from experimental helicopter and human data"(IET Radar Sonar Navigat.,vol.1,no.4,pp.289–299,Aug.2007), utilizes a wavelet transform method in combination with time-frequency analysis to extract micro-doppler features from radar echo signals of helicopters and human targets.
In order to alleviate the limitation of the uncertainty principle of the linear time-frequency analysis method, X.Chen, J.Guan, Z.Bao, Y.He, a short-time fractional fourier transform is proposed in the published paper "Detection and extraction of target with micromotion in spiky sea clutter via short-time fractional Fourier transform"(IEEE Trans.Geosci.Remote Sens.,vol.52,no.2,pp.1002–1018,Feb.2014) for target detection and micro-doppler signal extraction with high detection probability under a low signal-to-noise ratio environment. Although the above methods may improve the performance of linear time-frequency analysis methods or the Cohen class to some extent, processing complex signals is still difficult.
In the parameterized time-frequency analysis method, H.ling, F.Dai, and X.Wang, a BS-FBTVAR model is proposed in a published paper "Micro-Doppler Analysis of Rigid-Body Targets via Block-Sparse Forward-Backward Time-Varying Autoregressive Model"(IEEE Geosci.Remote Sens.Lett.,vol.13,no.9,pp.1-5,2016), micro Doppler analysis is performed on a rigid body target by utilizing block sparsity in model parameters, good frequency resolution and effective noise reduction in a relatively short time window are utilized, and a block sparse Bayesian learning algorithm is applied to coefficient solution of the model. However, the micro-Doppler analysis of the target using BSBL algorithm is somewhat different from the ideal time-frequency resolution.
The prior art can be severely interfered by cross terms when Cohen types are used in non-parameterized time-frequency analysis; the short-time fractional Fourier transform cannot process complex signals when overcoming the interference of cross terms; the use of the Hilbert-Huang transform can be very sensitive to noise; the parameterized time-frequency analysis method based on BSBL algorithm has good frequency resolution and noise immunity, but has a certain gap from ideal time-frequency resolution, and the obtained instantaneous frequency resolution is difficult to meet the requirement of extracting the fine features of the target.
Disclosure of Invention
Aiming at overcoming the defects of the prior art, the invention provides a target micro Doppler clustering estimation method of a forward-backward TVAR model with higher time-frequency resolution and noise resistance of target micro Doppler analysis.
The invention relates to a target micro Doppler cluster estimation method of a forward and backward TVAR model, which is characterized by comprising the following steps:
Step 1, radar echo data of a target are acquired: the method comprises the steps that a radar emits electromagnetic waves to irradiate a ballistic missile target and receives echoes of the ballistic missile target, the ballistic missile target is subjected to line demodulation, fast time Fourier transform is carried out on the ballistic missile target, residual video items and envelopment oblique items are removed, high-resolution range profile HRRP data of the ballistic missile target are obtained, data x (N) in a range unit are taken, N is the number of points of the target HRRP range unit data, n=0, 1, and N x-1,Nx is the total length of the target HRRP range unit data;
Step 2 representation of HRRP range bin data for the target in TVAR model: substituting the collected high-resolution range profile HRRP range bin data of the radar target into a front-back time-varying autoregressive TVAR model, wherein the HRRP range bin data of the target in the TVAR model is expressed as
Wherein m is the model order of forward and backward TVAR; n x is the length of the signal; i represents the variation of the target scattering point in the forward and backward TVAR model, i=1. a i (n) is the time-varying coefficient in the front-to-back TVAR model; Is the conjugation of a i (n); w (n) represents Gaussian white noise with zero mean and variance/>
Step 3, converting the time-varying coefficient a i (n) of the target into a time-invariant coefficient to obtain a matrix form of target HRRP distance unit data in a BS-FBTVAR model: estimating a time-varying coefficient a i (n) of the target in a forward-backward TVAR model, and converting the estimation of the time-varying coefficient into the estimation of a time-invariant coefficient; and obtaining a matrix form of a target block sparse forward and backward time-varying autoregressive BS-FBTVAR model by utilizing the block sparse property of the time-invariant coefficient, which comprises the following steps of
3.1 Develop the estimate of the time-varying coefficient of the object a i (n) into an estimate of the time-invariant coefficient a ij: the time-varying coefficient a i (n) in the forward and backward TVAR models is expressed as a set of discrete cosine-based linear combination formulas
Wherein f j (n) is a discrete cosine base, j represents a superimposed variable linearly combined using the discrete cosine base, j=1..q, q is the dimension of the discrete cosine base function, i represents a variable of the target scattering point in the forward-backward TVAR model, i=1..m; a ij is a time-invariant coefficient developed by a time-varying coefficient a i (n);
3.2 obtaining a matrix form of a target BS-FBTVAR model: substituting the time-invariant coefficients a ij into the forward-backward TVAR model of the target, the target HRRP range bin data is represented in this model as
Wherein,Is the conjugation of a ij,Is the conjugation of f j (n);
The matrix form of the target HRRP distance unit data in the BS-FBTVAR model is expressed as follows by utilizing the block sparse property of the time invariant coefficient model:
Yf=-Zfβ+wf
Yb=-Zbβ*+wb
Wherein Y f represents the m+1st to nth x th data of the target HRRP range bin data x (N), where all subscripts f represent forward TVAR model data of the target; y b represents the 1 st through N x -m data of the target HRRP distance unit data x (N), where all subscripts b represent the backward TVAR model data of the target; z f represents the observation matrix on the m+1st to N x th target HRRP distance-cell data; z b represents the observation matrix on the 1 st through N x -m target HRRP distance cell data; beta represents a time-invariant coefficient vector to be estimated by the target, and beta * is the conjugate of beta; w f and w b represent gaussian white noise with a mean of zero and a variance of γ 0; Wherein/> A block of target time invariant coefficients, having the property of non-sparsity within inter-block sparse blocks, j=1,..q;
Step 4, obtaining a clustering structure priori of a time-invariant coefficient beta of the target: obtaining a block sparse compressed sensing matrix form of an unknown block boundary through a potential relation of an artificially constructed model of an augmentation vector by using an improved algorithm EBSBL, and obtaining a clustering structure priori form of a target time-invariant coefficient beta by using interaction between the super-parameters of the time-invariant coefficient beta and adjacent super-parameters of the super-parameters;
Step 5, estimating a time-invariant coefficient beta of the target: the ballistic missile rigid body target is known in block boundary, prior information of the known block boundary is introduced into an improved algorithm of EBSBL, a block sparse recovery algorithm based on a Bayesian learning framework is used for recovering a known block boundary compressed sensing matrix form, and a time-invariant coefficient beta of the target is estimated;
Step 6, using the estimated time-varying coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram of the target: converting the time-invariant coefficient beta into a time-variant coefficient a i (n) through a linear combination formula of a discrete cosine base, and calculating to obtain an instantaneous power spectrum PS (f, n) of the target by utilizing an instantaneous power formula according to the time-variant coefficient a i (n) of TVAR, wherein the instantaneous power spectrum PS (f, n) is expressed as:
where f is the frequency at which the frequency is, Is an estimate of the noise variance;
Substituting the instantaneous power spectrum of the target into the frequency of the target point by point to obtain a micro Doppler frequency curve graph of the echo signal of the target; and reflecting the number, shape and attitude information of scattering points of the radar target according to the micro Doppler frequency, and identifying the target.
The invention solves the technical problems of insufficient time-frequency resolution and poor noise resistance of micro Doppler analysis in the existing time-frequency analysis method.
Compared with the prior art, the invention has the following advantages:
The time-frequency resolution of target micro Doppler analysis is improved: according to the invention, dependence is applied to adjacent sparse coefficients in a block by using a clustering structure priori, the super parameters of the neighborhood are properly processed to promote the correlation of the adjacent coefficients to estimate the time-invariant coefficients, the estimation performance of the time-invariant coefficients is improved, and the estimation accuracy of the time-invariant coefficients is also improved by adding the information with known block boundaries to a forward-backward TVAR model of the clustering structure priori, so that the estimation performance of instantaneous frequency is improved, namely the time-frequency resolution of target micro Doppler analysis is improved.
The anti-noise performance is improved, namely, as the block boundary of the rigid body target is known, the information of the block boundary is added into a forward-backward TVAR model based on a clustering priori structure, the accuracy of time invariant coefficient estimation of an algorithm is improved, and the convergence rate of the algorithm is accelerated; the Gaussian white noise in the environment affects the model order in the forward and backward TVAR models, and the noise resistance is improved by properly increasing the model order.
According to the invention, the prior information of the known boundary and the prior estimation of the clustering structure in the EBSBL-based improved algorithm are utilized, so that the interaction between the super parameter of the time-invariant block sparse coefficient and the adjacent super parameter is considered, the estimation performance of the time-invariant coefficient of the target is improved, the time-frequency resolution and the noise resistance of micro Doppler analysis can be improved, and an important basis is provided for target identification.
Drawings
FIG. 1 is a block diagram of an implementation flow of the present invention;
FIG. 2 is a schematic diagram of a spatial cone object model of a simulation experiment of the present invention;
FIG. 3 (a) is a micro Doppler analysis of noise-free radar target data using STFT time-frequency analysis method, wherein FIG. 3 (b) is a micro Doppler analysis of noise-free radar target data using BSBL-based BS-FBTVAR model time-frequency analysis method, wherein FIG. 3 (c) is a micro Doppler analysis of noise-free radar target echo data according to the present invention;
FIG. 4 (a) is a micro Doppler analysis of 20dB noise radar target data using STFT time-frequency analysis method, wherein FIG. 4 (b) is a micro Doppler analysis of 20dB noise radar target data using BSBL-based BS-FBTVAR model time-frequency analysis method, wherein FIG. 4 (c) is a micro Doppler analysis of 20dB noise radar target echo data according to the present invention;
fig. 5 (a) is a micro-doppler analysis of 10dB noise radar target data using the STFT time-frequency analysis method, wherein fig. 5 (b) is a micro-doppler analysis of 10dB noise radar target data using the BSBL-based BS-FBTVAR model time-frequency analysis method, and wherein fig. 5 (c) is a micro-doppler analysis of 10dB noise radar target echo data according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples.
Example 1
In the micro Doppler analysis of a space cone target, a parameterized time-frequency analysis and a non-parameterized time-frequency analysis method are generally used for carrying out micro Doppler characteristic analysis on the target, and the prior art uses a Wigner-Ville distribution method in the non-parameterized time-frequency analysis, so that the method has higher time-frequency aggregation, can overcome Hisenbergur boundaries of time-frequency resolution, has higher resolution, and has serious interference of cross terms on multi-component signals; the short-time fractional Fourier transform relieves the limitation of the uncertainty principle of the linear time-frequency analysis method, is simple to calculate, but cannot process complex signals when the interference of cross terms is overcome; the Hilbert-Huang transformation method is adopted to obtain better performance than the traditional Cohen TF method, but is very sensitive to noise; the parameterized time-frequency analysis method based on BSBL algorithm has good frequency resolution and noise immunity, but has a certain gap from ideal time-frequency resolution, and the obtained instantaneous frequency is difficult to meet the requirement of extracting the fine features of the target. The invention provides a target micro-Doppler analysis method based on a clustering prior estimation block sparse forward-backward TVAR model, which aims to solve the problem of insufficient time-frequency resolution of micro-Doppler analysis of the existing time-frequency analysis method, so as to improve the time-frequency resolution and noise resistance of micro-Doppler analysis of a space cone target.
The invention relates to a target micro Doppler clustering estimation method of a forward and backward TVAR model, referring to fig. 1, fig. 1 is a flow chart for realizing the method, which comprises the following steps:
step 1, radar echo data of a target are acquired: the radar emits electromagnetic waves to irradiate and receive echoes of the ballistic missile target, and the micro-motion of the target comprises spin, precession and nutation, and the generated micro-motion parameters are displayed and analyzed through a micro-Doppler frequency graph. Firstly, carrying out line demodulation on the acquired electromagnetic waves, then carrying out fast time Fourier transform on the electromagnetic waves, finally removing residual video items and envelop oblique items to obtain high-resolution range profile HRRP data of a ballistic missile target, taking data x (N) in a range unit, wherein N is the number of points of the target HRRP range unit data, n=0, 1, and N x-1,Nx is the total length of the target HRRP range unit data.
Step 2 representation of HRRP range bin data for the target in TVAR model: the time-varying autoregressive TVAR model of forward and backward prediction is used for analyzing the instantaneous frequency characteristic of a non-stationary random signal, the HRRP distance unit data of a target is the non-stationary random signal, the collected HRRP distance unit data of the radar target is substituted into the TVAR model of forward and backward, and the HRRP distance unit data x (n) of the target in the TVAR model is expressed as:
forward data:
backward data: Wherein m is the model order of forward and backward TVAR; n x is the length of the signal; i is a variable of a target scattering point in a forward-backward TVAR model, and represents delay information of target HRRP distance unit data x (n) corresponding to the 1 st to m-th scattering points, i=1; a i (n) is the time-varying coefficient in the front-to-back TVAR model; /(I) Is the conjugation of a i (n); w (n) represents Gaussian white noise with zero mean and varianceVariance/>, of Gaussian white noise at actual solutionUsing estimated value substitution, expressed as
Wherein the method comprises the steps ofTime-varying coefficients are estimated for solving forward and backward TVAR model algorithms of the object.
In order to utilize the observed data as much as possible, the invention utilizes the forward and backward prediction error average minimization to estimate TVAR the time-varying coefficients of the model. The forward and backward prediction errors are respectively
Forward prediction error:
backward prediction error: the sum of the forward and backward prediction errors is
Solving a time-varying coefficient a i(n),i=1,...,m,n=0,1,...,Nx -1 of a target in the TVAR model, wherein the minimum sum of forward and backward prediction errors is required to be met, and the time-varying coefficient a i (n) corresponding to the minimum sum of the forward and backward prediction errors is required to be the most accurate.
Step 3, converting the time-varying coefficient a i (n) of the target into a time-invariant coefficient to obtain a matrix form of target HRRP distance unit data in a BS-FBTVAR model: estimating a time-varying coefficient a i (n) of the target in a forward-backward prediction TVAR model, and converting the estimation of the time-varying coefficient into the estimation of a time-invariant coefficient; obtaining a matrix form of a target block sparse forward and backward time-varying autoregressive BS-FBTVAR model by utilizing the block sparse property of the time-invariant coefficient in the forward and backward TVAR model, which comprises the following steps:
3.1 develop the estimate of the time-varying coefficient of the object a i (n) into an estimate of the time-invariant coefficient a ij: the time-varying parameters a i (n) in the forward and backward TVAR models are expressed as a linear combination formula of a set of basis functions
Where f j (n) is a discrete cosine basis function, j represents a superposition variable that is linearly combined using the basis function, j=1,..q, q is the dimension of the basis function; i represents the variation of the target scattering point in the forward and backward TVAR model, i=1. a ij is a time-invariant coefficient developed by time-variant coefficient a i (n), i.e., does not vary over time n.
The common basis functions comprise discrete cosine basis, discrete Fourier basis, chebyshev basis, polynomial basis and the like, and the discrete cosine basis function is selected because the TVAR coefficients in the acquired radar target data are best in sparsity when developed under the discrete cosine basis function.
3.2 Obtaining a matrix form of a target BS-FBTVAR model: the invention converts the estimation of the time-invariant coefficient into the reconstruction of the time-invariant coefficient vector by using the compressed sensing theory, and the time-invariant coefficient vector is estimated by adopting an algorithm based on a Bayesian framework. Specifically, the time-invariant coefficient a ij is substituted into a BS-FBTVAR model of a target, and target HRRP distance unit data is expressed as in the model
Forward TVAR model:
Backward TVAR model: Wherein/> Is the conjugation of a ij,Is the conjugation of f j (n).
Obtaining target HRRP distance unit data by utilizing the block sparse property of the time invariant coefficient model and representing the target HRRP distance unit data in a matrix form of a BS-FBTVAR model as
Block sparse forward TVAR model matrix representation: y f=-Zfβ+wf
Block sparse backward TVAR model matrix representation: y b=-Zbβ*+wb
Wherein Y f represents the m+1st to nth x th data of the target HRRP range bin data x (N), where all subscripts f represent forward TVAR model data of the target; y b represents the 1 st through N x -m data of the target HRRP distance unit data x (N), where all subscripts b represent the backward TVAR model data of the target; z f represents the observation matrix on the m+1st to N x th target HRRP distance-cell data; z b represents the observation matrix on the 1 st through N x -m target HRRP distance cell data; beta represents a time-invariant coefficient vector to be estimated of the target in a BS-FBTVAR model, and beta * is the conjugate of beta; w f and w b represent Gaussian white noise with a mean of zero and a variance of gamma 0,γ0, the variance of Gaussian white noise WhereinOne block of the target time-invariant coefficient vector β has the property of non-sparsity within inter-block sparse blocks, j=1. The time-invariant coefficient a ij of the solution target is converted into a matrix form, so that the time-invariant coefficient vector beta can be conveniently reconstructed by using a Bayesian framework-based algorithm, and a foundation is laid for solving the time-invariant coefficient vector beta of the target.
Step 4, obtaining a clustering structure priori of a time-invariant coefficient vector beta of the target: the method comprises the steps of obtaining a block sparse compressed sensing matrix form of an unknown block boundary through a potential relation of an artificially constructed model of an augmentation vector by using an improved algorithm of EBSBL, obtaining a clustering structure priori form of a target block sparse constant coefficient beta by using interaction between super parameters of the block sparse constant coefficient beta and adjacent super parameters thereof, wherein each super parameter of the block sparse constant coefficient beta is a linear combination of super parameters of adjacent m independent Gaussian distributions. The invention considers the correlation of the sparse coefficient in the block by utilizing the clustering structure priori of the constant coefficient in the block sparse, and improves the accuracy of the constant coefficient estimation in the target time.
Step 5, introducing prior information of block boundary known in an algorithm based on EBSBL cluster structure prior to solve a time-invariant coefficient beta of the target: the improved algorithm EBSBL is used for solving the problem of block sparseness with unknown boundaries, the ballistic missile rigid body target is known in block boundaries, the prior information of the block boundaries is introduced, the convergence speed of the algorithm is accelerated, the estimation accuracy of the algorithm is improved, the prior information of the block boundaries is introduced into the improved algorithm EBSBL, the block sparseness recovery algorithm based on a Bayesian learning framework is used for recovering the known block boundary compressed sensing matrix form, and the time invariant coefficient beta of the target is obtained through estimation.
When solving the time invariant coefficients, whether the selection of the model order m and the basis function number q is proper or not is one of key problems that whether the TVAR model can successfully describe data or not.
Step 6, using the estimated time-varying coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram of the target: converting the time-invariant coefficient beta obtained in the step 5 into a time-variant coefficient a i (n) through a linear combination formula of a discrete cosine base, and calculating to obtain an instantaneous power spectrum PS (f, n) of the target by utilizing an instantaneous power formula according to the time-variant coefficient a i (n) of TVAR, wherein the instantaneous power spectrum PS (f, n) is expressed as
Where f is the frequency at which the frequency is,For the estimated value of the noise variance, substituting the instantaneous power spectrum of the target into the frequency of the target point by point to obtain a micro Doppler frequency curve graph of the target, observing the sine change rule in the curve graph on a display, analyzing the movement of the space cone target such as spin, precession, nutation and the like, comparing the degree of coincidence between the sine change rule of the micro Doppler curve obtained by the method and the actual ideal time frequency curve graph and the definition instant frequency resolution of the curve graph, and intuitively finding that the accuracy of the micro Doppler time frequency curve is higher; according to the micro Doppler reaction radar target, the number, shape and attitude information of scattering points are used for identifying the target, and the time-frequency resolution and the noise resistance are higher.
The prior art uses Wigner-Ville in non-parameterized time-frequency analysis, has higher time-frequency aggregation, can overcome Hisenbergur boundaries of time-frequency resolution, has higher resolution, but has serious interference of cross terms on multi-component signals; the short-time fractional Fourier transform relieves the limitation of the uncertainty principle of the linear time-frequency analysis method, is simple to calculate, and cannot process complex signals when the interference of cross terms is overcome. The use of the Hilbert-Huang transform achieves better performance than the traditional Cohen-type TF method, but is very sensitive to noise. The parameterized time-frequency analysis method based on BSBL algorithm has good time-frequency resolution and noise immunity, but does not consider the correlation of adjacent sparse coefficients in the block, has a certain gap with the time-frequency resolution of ideal micro Doppler analysis, and is difficult to meet the requirement of extracting the fine features of the target through the obtained instantaneous frequency resolution.
The invention aims to improve the time-frequency resolution and the noise immunity of target micro Doppler analysis, and the HRRP distance unit data of target echo is represented by using a forward-backward TVAR model, the dependence is applied to adjacent sparse coefficients in blocks in a block sparse time-invariant coefficient beta in the forward-backward TVAR model by using a clustering structure prior, the time-invariant coefficients are estimated by processing the correlation of adjacent coefficients promoted by the hyper-parameters of a neighborhood, the estimation performance of the time-invariant coefficients is improved, and the time-frequency resolution of the target micro Doppler analysis is further improved.
The method acquires radar echo data of a target to obtain high-resolution range profile HRRP range unit data x (n) of the ballistic missile target, the HRRP range unit data of the target are expressed in a forward-backward TVAR model, time-varying parameters a i (n) of a forward-backward TVAR model of the target are estimated, the estimation of time-varying coefficients is converted into the estimation of time-invariant coefficients, the matrix form of a sparse forward-backward time-varying autoregressive BS-FBTVAR model of the target block is obtained by utilizing the block sparse property of the time-invariant coefficients, the cluster structure priori form of the time-invariant coefficients beta of the target is obtained by using the interaction between the super-parameters of the time-invariant coefficients beta and the adjacent super-parameters of the target, and priori information of known block boundaries is applied, so that the accuracy of the estimation of the time-invariant coefficients is improved, and the time-frequency resolution of micro Doppler of the target is improved. When the model order m is selected, the value of m is properly increased to improve the anti-noise performance. The method estimates the time-invariant coefficient beta of the target, converts the time-invariant coefficient beta into a time-variant coefficient a i (n) through a linear combination formula of a discrete cosine base, and uses the estimated time-variant coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram of the target. The method improves the time-frequency resolution and the noise immunity of the micro Doppler analysis of the radar target.
Example 2
The method for estimating the micro-Doppler cluster of the target in the forward and backward TVAR models is the same as that in the embodiment 1, and the clustering structure priori of the time invariant coefficient beta of the target is obtained in the step 4, and the method comprises the following steps:
4.1 obtaining a combined representation of the time invariant coefficients β of the target: using EBSBL model, an extended hidden block set z k is introduced, with a fixed block size h, k representing the variable of the number of blocks, k=1:g, g being the number of blocks, g=n β-h+1,Nβ being the length of β, N β =mq, m being the model order, q being the dimension of the discrete cosine basis function, then the time invariant coefficient β is expressed as using a linear transformation
Where E k is a zero matrix of N β x h dimensions except that the part of rows k to k+h-1 is replaced by an identity matrix,Such a partitioned vector z is an equally partitioned block sparse signal having a block size h. The time-invariant coefficient β is represented as a combination of g equally divided block sparse signals of block size h.
4.2 Get a multivariate gaussian distribution for each block: restoring a block sparse compressed sensing matrix form of a block boundary with unknown target time-invariant coefficients, wherein each block meets the multi-element Gaussian distribution, and capturing the related structure of the kth block; the probability of a block is expressed as
Where z k is the kth block, γ k is the unknown hyper-parameter that controls the sparsity of the kth block, and B k is the positive definite matrix of the kth block. Each block obeys a multivariate gaussian distribution with a mean of zero and a variance of gamma k.
4.3 Obtaining the clustering structure priori of the time invariant coefficient beta of the target: beta is expressed as normal distribution
Wherein, beta l is the first data of the target time invariant coefficient beta, gamma l-(h-1)/2 is the super parameter of the first- (h-1)/2 data distribution of the target time invariant coefficient beta, gamma l+h/2 is the super parameter of the first +h/2 data distribution of the target time invariant coefficient beta, and beta l is related to the interaction of the target time invariant coefficient beta from the first- (h-1)/2 data to the first +h/2 data super parameter. p (β l;γl-(h-1)/2,...,γl,...,γl+h/2) is the probability of β l with parameter γ l-(h-1)/2,...,γl,...,γl+h/2, γ l is the superparameter of the first data distribution of the target time invariant coefficient β, l=1, 2
P (β; γ) is a cluster structure prior of β, also referred to as the probability of β with a parameter vector γ.
According to the invention, the dependence is applied to adjacent sparse coefficients in the block by using the clustering structure prior, the correlation of the adjacent coefficients is promoted by properly processing the hyper-parameters of the neighborhood to solve the time-invariant coefficients, the estimation performance of the time-invariant coefficients is improved, and the time-frequency resolution of the target micro Doppler analysis is further improved.
Example 3
The method for estimating the target micro Doppler cluster of the forward-backward TVAR model is the same as that of the embodiment 1-2, and the step 5 estimates the time-invariant coefficient beta of the target, and comprises the following steps:
5.1 obtaining likelihood functions of the BS-FBTVAR signal model: the invention uses the known property of the rigid block boundary of the space cone object to set the block size as m, and re-represents the clustering structure priori of the time-invariant coefficient beta of the object obtained in the step 4 as
Wherein, gamma l-(m-1)/2 is the super parameter of the target time invariant coefficient beta first- (m-1)/2 data distribution, and gamma l+m/2 is the super parameter of the target time invariant coefficient beta first+m/2 data distribution.
The likelihood function of the clustering structure prior of the time-invariant coefficient beta is expressed by using a sparse recovery algorithm of a Bayesian framework, and the likelihood function of the BS-FBTVAR signal model is expressed as follows:
Wherein p (Y f|βf,γf0) is a likelihood function of the block sparse forward TVAR signal model, Likelihood functions of the block sparse backward TVAR signal model; beta f is a forward time invariant coefficient, beta b is a forward time invariant coefficient; gamma f0 and gamma b0 are the noise variances of gaussian white noise in the forward TVAR and backward TVAR models, respectively; y f is the forward HRRP distance bin data of the target, including the m+1th to N x th data of x (N); y b is the targeted backward HRRP distance bin data, including the 1 st through N x -m data of x (N)Is the conjugation of Y b; /(I)For Y f length,A length of Y b; z f and Z b, wherein Z f is the forward observation matrix of the target HRRP distance unit data, including the observation matrix on the (m+1) -th to (N x) -th targets, and Z b is the forward observation matrix of the target HRRP distance unit data, including the observation matrix on the (1) -th to (N x -m) -th targets,Is the conjugation of Z b; i M is an identity matrix of M dimensions.
5.2 Obtaining a target time invariant coefficient beta: according to the forward and backward likelihood function of the target and the clustering priori of the time-invariant coefficient beta of the target, the posterior of the obtained time-invariant coefficient beta is Gaussian distribution, and the posterior distribution mean values of the forward and backward time-invariant coefficient beta are respectively expressed as
Posterior distribution mean value of forward time invariant coefficient beta :μf=γf0 -1ΣfZf HYf=DZf H(γf0I+ZfDZf H)-1Yf
Posterior distribution mean of the backward time invariant coefficient beta: Wherein mu f is the mean value of the forward time invariant coefficient beta, and mu b is the mean value of the backward time invariant coefficient beta; Σ f is the variance of the forward time invariant coefficient β, Σ b is the variance of the backward time invariant coefficient β; z f H is the conjugate transpose of Z f, and Z b H is the conjugate transpose of Z b; d is the diagonal matrix of the first element (gamma l-(m-1)/2+...+γl+...+γl+m/2)-1, I is the identity matrix, (. Cndot.) -1 is the matrix inversion operation.
Since the posterior distribution mean μ f of the forward time invariant coefficient β f and the posterior distribution mean μ b of the backward time invariant coefficient β b of the target are both estimated β in essence, when using a bayesian framework-based sparse recovery algorithm, the average μ= (μ f+μb)/2 is taken for each iteration, and μ is the time invariant coefficient vector β to be solved when the algorithm converges.
According to the invention, the prior information of the block boundary is added into the forward and backward TVAR models based on the clustering prior structure, so that the accuracy of the algorithm for solving the time invariant coefficients is improved, the convergence speed of the algorithm is accelerated, and the time-frequency resolution of micro Doppler analysis is further improved. When the block boundary m is selected, the AIC criterion and the MDL criterion are adopted for automatic selection, when the noise is large, the m is larger than the number of scattering points contained in the target, and the noise environment is adapted by properly increasing the m, so that the anti-noise performance is improved.
A more detailed example is given below to further illustrate the invention.
Example 4
The method for estimating micro-Doppler cluster of the target in forward and backward TVAR models is the same as that of the embodiments 1-3, and the electromagnetic simulation tool software CST STUDIO SUITE 2019 is used for generating broadband radar echo data of the target to carry out simulation experiments.
Referring to fig. 1, the implementation steps of the present embodiment are as follows.
Step 1, simulation data of a target model: the target adopts a simple spherical tip cone model, and the material is an ideal good conductor (PEC). Wherein, the cone height is 1.5m, the bottom radius is 0.9m, three hemispherical grooves are carved on the surface of 0.5m from the bottom at equal intervals, and the groove depth is 0.05m. The simulated radar parameters were set as follows: the carrier frequency was 10GHz, the PRF was 800Hz, and the residence time was 1s. The spin frequency of the target is 1r/s, the precession frequency is 1r/s, the included angle between the precession axis and the spin axis is 10 degrees, the pitch angle is 45 degrees, and the radar incident direction is perpendicular to the cone central axis.
Step 2, representation of distance unit data of target in front-back direction TVAR model: and generating broadband radar echo data by using electromagnetic simulation tool software, reading the broadband radar echo data into a mat format file by using matlab 2018b software, namely, data of slow distance frequency and slow time at the moment, performing fast Fourier transform on a distance frequency dimension, changing the distance frequency dimension into a distance dimension, taking data x (n) in a distance unit, and substituting the data x (n) into a forward-backward TVAR model.
The distance unit data of the target is represented as a model in the front-back direction TVAR
Forward data:
backward data:
In order to utilize the observed data as much as possible, the invention utilizes the forward and backward prediction error average minimization to obtain the solution of TVAR model parameters. The forward and backward prediction errors are respectively
Forward prediction error:
backward prediction error: the sum of forward and backward prediction errors is/>
Solving a time-varying coefficient a i(n),i=1,...,m,n=0,1,...,Nx -1 of a target in the TVAR model, wherein the minimum xi is required to be satisfied, and the time-varying coefficient a i (n) corresponding to the minimum xi is the most accurate.
Step 3, obtaining a matrix form of the BS-FBTVAR model: the TVAR model of the target is converted into an estimated form, the time-varying coefficient a i (n) is not easy to solve by directly solving, the time-varying coefficient can be converted into a time-invariant coefficient vector for solving, and the time-invariant coefficient vector can be reconstructed in a new matrix form by using a compressed sensing theory and a Bayesian framework-based sparse recovery algorithm, so that the estimation of the time-invariant coefficient is obtained. Therefore, firstly, the time-varying coefficient a i (n) of the TVAR model of the target is expressed by a group of linear combinations of discrete cosine bases, the estimation problem of the time-varying coefficient is converted into the estimation problem of the time-invariant coefficient, and the matrix form of the BS-FBTVAR model is obtained by utilizing the block sparse property of the time-varying coefficient.
(3.1) Representing the time-varying coefficients of the object as a linear combination of a set of discrete cosine bases
Then a i (n) can be converted into a time-invariant coefficient vector consisting of a ij, a ij is independent of time n and no longer time-varying, and the time-invariant coefficient model obtained by linear combination representation is expressed as
Forward TVAR model:
Backward TVAR model:
(3.2) the vector composed of the time-invariant coefficients of the above formula has a block sparse property, and a matrix form of a BS-FBTVAR model obtained by using the property is expressed as:
Yf=-Zfβ+wf
Yb=-Zbβ*+wb
Wherein/> Can be regarded as a block, and has the property of non-sparsity in sparse blocks among blocks.
Step 4, using the known prior information of the block boundary and the prior estimation of the clustering structure, the constant coefficient beta: the algorithm based on EBSBL is a block sparse recovery algorithm for unknown block boundaries, the invention uses a clustering structure priori method in an improved algorithm based on EBSBL to estimate time invariant coefficients in a block sparse forward and backward TVAR model, considers interaction between adjacent super parameters of intra-block sparse coefficients of a target time invariant coefficient beta, uses a formulated structure prior to apply dependence on the adjacent sparse coefficients in the block, and applies prior information known by a rigid body target block boundary of a spatial cone target, wherein each super parameter of the block sparse time invariant coefficient beta is a linear combination of super parameters of adjacent m independent Gaussian distributions, when the time invariant coefficient beta is estimated by using a Bayesian frame-based sparse algorithm, the estimation accuracy of the time invariant coefficient beta is improved, and the method specifically comprises the following implementation steps:
(4.1) representing the time-invariant coefficients β as linear combinations of the set of concealment blocks: using the EBSBL model, an extended hidden block set z i is introduced, which has a fixed block size h, i=1:g, g=n β-h+1,Nβ =pq, g being the number of blocks, N β being the length of β, expressed by a linear transformation as β
Wherein the method comprises the steps ofIs a zero matrix in which a part other than the i-th row to the i+h-1-th row is replaced by an identity matrix. The block vector z is a combination of equally divided block sparse signals having a block size h, and the time-invariant coefficient β is expressed as g equally divided block sparse signals having a block size h.
(4.2) Representing the obeyed distribution of each block z i, introducing interaction between adjacent super parameters of sparse coefficients in the blocks, and obtaining a clustering structure priori of a time-invariant coefficient vector beta: introducing a priori information of which the boundary condition is known, the time-invariant coefficients β are divided into equally divided block sparse signals having a block size p. Each block satisfying the multivariate gaussian distribution is expressed as:
Wherein gamma i is an unknown hyper-parameter of control block sparsity, B i is a positive definite matrix, and the related structure of the ith block is captured. Introducing interaction between adjacent super-parameters of intra-block sparse coefficients, each beta i sparse coefficient in the target time-invariant coefficient beta is expressed as following normal distribution
Each beta i is a linear combination of super parameters of m adjacent coefficients, when the block boundary m is selected, the AIC criterion and the MDL criterion are adopted to automatically select, when the noise is large, m is larger than the number of scattering points contained in a target, the noise environment is adapted by properly increasing m, and the anti-noise performance is improved.
The clustering structure of the time-invariant coefficient vector beta is expressed as a priori
Wherein γ=γ i,i=1,2,...,Nβ, wherein γ i obeys the inverse gamma distribution
Wherein the shape parameter a 0 > 0, the scale parameter b 0 > 0 is a minimum number,Being a gamma function, the present invention sets a 0 to 1e -2 and b 0 to 1e -3. The clustering structure priori of the time-invariant coefficient vector beta is obtained, and the clustering structure priori of the time-invariant coefficient vector beta in the invention considers the correlation of adjacent sparse coefficients in the block to improve the estimation accuracy of the time-invariant coefficient vector beta.
(4.3) Obtaining likelihood functions of the block sparse forward TVAR signal model: and (3) using the clustering structure priori of the time-invariant coefficient beta obtained in the step (4.2), and expressing a sparse recovery algorithm for estimating the time-invariant coefficient beta under a Bayesian framework. The likelihood function of the BS-FBTVAR signal model of the target is expressed as
Likelihood function of forward BS-FBTVAR signal model:
likelihood function of backward BS-FBTVAR signal model:
Wherein, gamma f0 and gamma b0 are noise variances of Gaussian white noise in forward TVAR and backward TVAR models respectively and respectively obey inverse gamma distribution, the shape parameter c 0 of the Gaussian white noise is set to be 1e -2, and the proportion parameter d 0 is set to be 1e -3;Yf as forward HRRP distance unit data of a target; y b is the targeted backward HRRP range unit data, Is the conjugation of Y b; For Y f length,/> A length of Y b; wherein Z f is the forward observation matrix of the target HRRP distance unit data, Z b is the forward observation matrix of the target HRRP distance unit data,For the conjugate of Z b, I M is an identity matrix of M dimensions.
(4.4) Constant coefficient β at the time of estimation: according to likelihood function of target block sparse forward TVAR signal model and clustering priori property of target time-invariant coefficient beta, using Bayes sparse recovery algorithm to obtain posterior property of target time-invariant coefficient beta as Gaussian distribution, and the posterior distribution mean value of forward and backward time-invariant coefficient beta is respectively expressed as
Posterior distribution mean :μf=γf0 -1ΣfZf HYf=DZf H(γf0I+ZfDZf H)-1Yf of forward time invariant coefficients β posterior distribution mean of backward time invariant coefficients β:
Since the posterior distribution mean μ f of the forward time invariant coefficient β f and the posterior distribution mean μ b of the backward time invariant coefficient β b of the target are both estimated β in essence, when using a bayesian framework-based sparse recovery algorithm, the average μ= (μ f+μb)/2 is taken for each iteration, the convergence threshold is set to 1e -3, and μ is the time invariant coefficient vector β to be estimated when the algorithm converges. According to the invention, the time-frequency resolution of the obtained micro Doppler analysis is improved by utilizing the prior information of the block boundary and the prior estimation time-invariant coefficient of the clustering structure, and the micro Doppler characteristics generated by the micro motion of the space cone target are more clearly depicted.
Step 5, obtaining a micro Doppler frequency curve chart: converting the time-invariant coefficient beta obtained in the step 4 into a time-variant coefficient a i (n) through a linear combination formula of a discrete cosine base, and using the obtained time-variant coefficient a i (n) in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram. Wherein the instantaneous power spectrum of the target is expressed as
Where f is the frequency at which the frequency is,Is an estimate of the noise variance. The instantaneous power spectrum of the target is substituted into the frequency of the target point by point, so that a micro Doppler frequency curve graph of the echo signal of the target can be obtained. By comparing the degree of coincidence of the sine change rule of the micro Doppler curve obtained by the method with the actual ideal time-frequency curve and the definition of the curve, namely the time-frequency resolution, the accuracy of the micro Doppler time-frequency curve is higher, the micro Doppler characteristics generated by micro motion of the space cone target, namely the fine characteristics of the scattering point number, the gesture, the shape and the like of the target, are better, and the method is more convenient to use in the identification of the target.
The invention is based on the target micro Doppler analysis of the clustering prior estimation block sparse forward and backward TVAR model, and is mainly used for giving a clearer time-frequency diagram and good noise immunity compared with the traditional method. The implementation steps are as follows: using electromagnetic simulation tool software CST STUDIO SUITE 2019 to generate radar echo data of the target; obtaining a forward-backward TVAR model by utilizing radar echo data of a target; the TVAR coefficients are represented by a group of linear combinations of discrete cosine bases, the estimation problem of the time-varying coefficients is converted into the estimation problem of the time-invariant coefficients, and the matrix form of the BS-FBTVAR model is obtained by utilizing the block sparse property of the block sparse coefficients; the prior information of the block boundary is utilized, and the block sparse coefficient is unchanged when the prior estimation is carried out on the clustering structure in the improved algorithm based on EBSBL; and using the estimated time-varying coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram. According to the method, the BS-FBTVAR model is solved based on the clustering structure priori, the dependence is applied to adjacent sparse coefficients in the block, and the effect of improving the time-frequency resolution of micro Doppler analysis is achieved.
The effects of the present invention can be illustrated by the following simulation experiments.
Example 5
The method for estimating the target micro Doppler cluster of the forward and backward TVAR models is the same as that of the embodiment 1-4.
Simulation experiment conditions:
the hardware platform of the simulation experiment of the invention is: the processor is Inter (R) Xeon (R) CPU E5-1630 v4, the main frequency is 3.70GHZ, and the memory is 64GB.
The software platform of the simulation experiment of the invention is: CST study SUITE 2019 and MATLAB R2019b.
Simulation experiment contents:
Simulation experiment: fig. 2 is a target model, and the electromagnetic simulation tool software CST study SUITE 2019 is used to generate radar target echo. The target adopts a simple spherical tip cone model, and the material is an ideal good conductor (PEC). Wherein, the cone height is 1.5m, and bottom radius is 0.9m, and from bottom equidistant three hemisphere recess of carving in 0.5m department surface, the recess degree of depth is 0.05m, and simulation radar parameter sets up as follows: the carrier frequency was 10GHz, the PRF was 800Hz, and the residence time was 1s. The spin frequency of the target is 1r/s, the precession frequency is 1r/s, the included angle between the precession axis and the spin axis is 10 degrees, the pitch angle is 45 degrees, and the radar incident direction is perpendicular to the cone central axis.
Fig. 3 (a) -3 (c) are graphs of the results of micro-doppler analysis of noise-free radar target echo data using the STFT time-frequency analysis method, the BSBL-based BS-FBTVAR model time-frequency analysis method, and the present invention, respectively, fig. 4 (a) -4 (c) are graphs of the results of micro-doppler analysis of 20dB noise radar target echo data using the STFT time-frequency analysis method, the BSBL-based BS-FBTVAR model time-frequency analysis method, and the present invention, respectively, and fig. 5 (a) -5 (c) are graphs of the results of micro-doppler analysis of 10dB noise radar target echo data using the STFT time-frequency analysis method, the BSBL-based BS-FBTVAR model time-frequency analysis method, and the present invention, respectively.
In the above figures, the abscissa indicates time in s, the ordinate indicates frequency in Hz. The curves in the figure are all micro-Doppler time-frequency results of the target, two sinusoidal curves with smaller frequency peaks correspond to vertexes A and B of the target model in fig. 2, namely sliding scattering centers A and B, and a C point is invisible due to the shielding effect. The three middle sinusoids with larger frequency peaks correspond to three pits D, E and F, namely a general scattering center, and three grooves on a cone target are observed by a radar in turn due to a shielding effect, so that the condition of incomplete curve on a time-frequency surface occurs.
Simulation result analysis:
Fig. 3 (a) is a diagram showing the result of micro-doppler analysis on noise-free radar target echo data using the STFT time-frequency analysis method, where the micro-doppler time-frequency graph generated by the general scattering centers D, E, F in the target model of fig. 2 is blurred, the micro-doppler features generated by the micro-motion corresponding to the sliding scattering centers a, B cannot be analyzed, and the two intersecting curves closer to each other cannot be distinguished. Fig. 3 (b) is a diagram of a result of micro-doppler analysis on noise-free radar target echo data by using a BS-FBTVAR model time-frequency analysis method based on BSBL, which improves the accuracy of time-frequency resolution, can distinguish two intersecting curves with relatively close distances, and can completely analyze micro-doppler frequencies generated by spin and precession of an equivalent scattering center and a general scattering center of a target model, but can see that error components appear at upper peaks and lower peaks of each period of a sinusoidal curve when micro-motion of the general scattering centers D, E and F is analyzed in a time-frequency diagram, and the time-frequency diagram is relatively turbid. Fig. 3 (c) is a graph of the result of micro-doppler analysis on noise-free radar target echo data by using the forward-backward TVAR model target micro-doppler clustering estimation method, which can completely extract micro-doppler frequencies generated by spin and precession of a sliding scattering center and a general scattering center of a space cone target, and can obviously distinguish two intersecting curves with a relatively short distance, so that a time-frequency graph is clearer. As can be seen from comparison of fig. 3 (a), fig. 3 (b) and fig. 3 (c), the micro doppler curve obtained by the present invention has higher time-frequency resolution and is closer to an ideal time-frequency curve.
Example 6
The method for estimating the target micro Doppler cluster of the forward and backward TVAR models is the same as that of the embodiments 1-4, and the simulation experiment conditions and contents are the same as those of the embodiment 5.
Simulation result analysis:
Fig. 4 (a) is a diagram showing the result of micro-doppler analysis on radar target echo data in a 20dB noise environment using the STFT time-frequency analysis method, which is insensitive to noise and cannot extract micro-doppler frequencies generated by micro-motion of a sliding scattering center and a general scattering center. Fig. 4 (b) is a diagram showing the result of micro-doppler analysis on radar target echo data in a 20dB noise environment by using a BSBL-based BS-FBTVAR model time-frequency analysis method, in which error components appear above the peak in the second period, below the peak in the first period, and below the peak in the penultimate period when micro-motion of the general scattering centers D, E, F is analyzed. In fig. 4 (c), the result diagram of the micro-doppler analysis on the radar target echo data in the 20dB noise environment by using the forward-backward TVAR model target micro-doppler clustering estimation method of the present invention can completely extract the micro-doppler frequencies generated by the spin and precession of the sliding scattering centers a, B and the general scattering centers D, E, F of the spatial cone target, and has clear time-frequency surface and better anti-noise performance than that of fig. 4 (B). Comparing the micro Doppler time frequency chart 3 (c) obtained under the noiseless condition, and the micro Doppler time frequency chart of the simulation target generated under the noise environment condition of 20dB in fig. 4 (c), the two are compared, and the noise immunity of the invention is realized.
Example 7
The method for estimating the target micro Doppler cluster of the forward and backward TVAR models is the same as that of the embodiments 1-4, and the simulation experiment conditions and contents are the same as those of the embodiment 5.
Fig. 5 (a) is a graph of the result of micro-doppler analysis of radar target echo data in a 10dB noise environment using the STFT time-frequency analysis method, and is not sensitive to noise, and cannot extract micro-doppler frequencies generated by micro-motion of a sliding scattering center and a general scattering center, as in fig. 3 (a). Fig. 5 (b) is a diagram of a result of micro-doppler analysis on radar target echo data in a 10dB noise environment by using a BS-FBTVAR model time-frequency analysis method based on BSBL, when micro-motion of general scattering centers D, E, F is analyzed, an error component appears at the position above the vertex on the second period, and obvious concave-convex points appear at each position of the time-frequency diagram, so that noise resistance is slightly poor. In fig. 5 (c), the result graph of the micro-doppler analysis on the radar target echo data in the 10dB noise environment by using the forward-backward TVAR model target micro-doppler clustering estimation method of the present invention shows slight concave-convex points on the time-frequency surface, but does not affect the definition of the time-frequency graph. As can be seen from comparison of fig. 5 (a), 5 (b) and 5 (c), the noise immunity of the present invention is higher.
In summary, the method for estimating the target micro-Doppler cluster of the forward and backward TVAR models solves the technical problem that the micro-Doppler analysis time-frequency resolution of the existing time-frequency analysis method is insufficient. The implementation steps are as follows: collecting radar echo data of a target; representing HRRP range bin data of the target in a TVAR model; converting the time-varying coefficient of the target to obtain a matrix form of target HRRP distance unit data in a BS-FBTVAR model; obtaining a clustering structure priori of a time-invariant coefficient of the target by using interaction between adjacent super-parameters of the intra-block sparse coefficient; solving a time invariant coefficient of the target; and using the solved time-varying coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram of the target. And reflecting the number, shape and attitude information of scattering points of the radar target according to the micro Doppler frequency, and identifying the target. The invention utilizes the interaction between adjacent super-parameters of the intra-block sparse coefficients and the prior information of the known block boundaries of the rigid body target. The micro Doppler time-frequency resolution and the noise immunity are improved. The method is used for micro-motion characteristic analysis of the space cone target and further used for target identification.
Claims (1)
1. A target micro Doppler cluster estimation method of a forward-backward TVAR model is characterized by comprising the following steps:
Step 1, radar echo data of a target are acquired: the method comprises the steps that a radar emits electromagnetic waves to irradiate a ballistic missile target and receives echoes of the ballistic missile target, the ballistic missile target is subjected to line demodulation, fast time Fourier transform is carried out on the ballistic missile target, residual video items and envelopment oblique items are removed, high-resolution range profile HRRP data of the ballistic missile target are obtained, data x (N) in a range unit are taken, N is the number of points of the target HRRP range unit data, n=0, 1, and N x-1,Nx is the total length of the target HRRP range unit data;
Step 2 representation of HRRP range bin data for the target in TVAR model: substituting the collected high-resolution range profile HRRP range bin data of the radar target into a front-back time-varying autoregressive TVAR model, wherein the HRRP range bin data of the target in the TVAR model is expressed as:
Wherein m is the model order of forward and backward TVAR; n x is the length of the signal; i represents the variation of the target scattering point in the forward and backward TVAR model, i=1. a i (n) is the time-varying coefficient in the front-to-back TVAR model; Is the conjugation of a i (n); w (n) represents Gaussian white noise with zero mean and variance/>
Step 3, converting the time-varying coefficient a i (n) of the target into a time-invariant coefficient to obtain a matrix form of target HRRP distance unit data in a BS-FBTVAR model: estimating a time-varying coefficient a i (n) of the target in a forward-backward TVAR model, and converting the estimation of the time-varying coefficient into the estimation of a time-invariant coefficient; and obtaining a matrix form of a target block sparse forward and backward time-varying autoregressive BS-FBTVAR model by utilizing the block sparse property of the time-invariant coefficient, which comprises the following steps of
3.1 Develop the estimate of the time-varying coefficient of the object a i (n) into an estimate of the time-invariant coefficient a ij: the time-varying coefficient a i (n) in the forward and backward TVAR models is expressed as a set of discrete cosine-based linear combination formulas
Where f j (n) is a discrete cosine base, j represents a superimposed variable that is linearly combined using the discrete cosine base, j=1,..q, q is the dimension of the discrete cosine base function, i represents a variable of the target scattering point in the forward-backward TVAR model,
I=1.. m; a ij is a time-invariant coefficient developed by a time-varying coefficient a i (n);
3.2 obtaining a matrix form of a target BS-FBTVAR model: substituting the time-invariant coefficients a ij into the forward-backward TVAR model of the target, the target HRRP range bin data is represented in this model as
Wherein,Is the conjugation of a ij, f j * (n) is the conjugation of f j (n);
The matrix form of the target HRRP distance unit data in the BS-FBTVAR model is expressed as follows by utilizing the block sparse property of the time invariant coefficient model:
Yf=-Zfβ+wf
Yb=-Zbβ*+wb
Wherein Y f represents the m+1st to nth x th data of the target HRRP range bin data x (N), where all subscripts f represent forward TVAR model data of the target; y b represents the 1 st through N x -m data of the target HRRP distance unit data x (N), where all subscripts b represent the backward TVAR model data of the target; z f represents the observation matrix on the m+1st to N x th target HRRP distance-cell data; z b represents the observation matrix on the 1 st through N x -m target HRRP distance cell data; beta represents a time-invariant coefficient vector to be estimated by the target, and beta * is the conjugate of beta; w f and w b represent gaussian white noise with a mean of zero and a variance of γ 0;
Wherein/> A block of target time invariant coefficients, having the property of non-sparsity within inter-block sparse blocks, j=1,..q;
Step 4, obtaining a clustering structure priori of a time-invariant coefficient beta of the target: obtaining a block sparse compressed sensing matrix form of an unknown block boundary through a potential relation of an artificially constructed model of an augmentation vector by using an improved algorithm EBSBL, and obtaining a clustering structure priori form of a target time-invariant coefficient beta by using interaction between the super-parameters of the time-invariant coefficient beta and adjacent super-parameters of the super-parameters; the method comprises the following steps:
4.1 obtaining a combined representation of the time invariant coefficients β of the target: using the EBSBL model, an extended hidden block set z k is introduced, with a fixed block size h, k representing the variable of the number of blocks, k=1:g, g being the number of blocks, g=n β-h+1,Nβ being the length of β, N β =mq, the time-invariant coefficient β being expressed as using a linear transformation
Where E k is a zero matrix of N β x h dimensions except that the part of rows k to k+h-1 is replaced by an identity matrix,Such a partitioned vector z is an equally partitioned block sparse signal with a block size h;
4.2 get a multivariate gaussian distribution for each block: restoring a block sparse compressed sensing matrix form of a block boundary with unknown target time-invariant coefficients, wherein each block meets the multi-element Gaussian distribution, and capturing the related structure of the kth block; the probability of a block is expressed as
Wherein z k is the kth block, γ k is an unknown hyper-parameter controlling the sparsity of the kth block, and B k is the positive definite matrix of the kth block;
4.3 obtaining the clustering structure priori of the time invariant coefficient beta of the target: beta is expressed as normal distribution
Wherein, β l is the target time invariant coefficient β1st data, γ l is the superparameter of the target time invariant coefficient β1st data distribution, l=1, 2
Wherein, gamma l-(h-1)/2 is the super parameter of the target time invariant coefficient beta (1- (h-1)/2 data distribution, gamma l+h/2 is the super parameter of the target time invariant coefficient beta (1+h/2 data distribution), and beta l is related to the interaction of the target time invariant coefficient beta from the first- (h-1)/2 data to the first+h/2 data super parameter;
step 5, estimating a time-invariant coefficient beta of the target: the ballistic missile rigid body target is known in block boundary, prior information of the known block boundary is introduced into an improved algorithm of EBSBL, a block sparse recovery algorithm based on a Bayesian learning framework is used for recovering a known block boundary compressed sensing matrix form, and a time-invariant coefficient beta of the target is estimated; the method comprises the following steps:
5.1 obtaining likelihood functions of the BS-FBTVAR signal model: introducing the known information of the boundary of a rigid object block, wherein the block size is m, and the clustering structure priori re-representing the time-invariant coefficient beta of the object is
Wherein, gamma l-(m-1)/2 is the super parameter of the first- (m-1)/2 data distribution of the target time invariant coefficient beta, and gamma l+m/2 is the super parameter of the first +m/2 data distribution of the target time invariant coefficient beta;
The likelihood function of the clustering structure prior of the time-invariant coefficient beta is expressed by using a sparse recovery algorithm of a Bayesian framework, and the likelihood function of the BS-FBTVAR signal model is expressed as follows:
Wherein p (Y f|βf,γf0) is a likelihood function of the block sparse forward TVAR signal model, Likelihood functions of the block sparse backward TVAR signal model; beta f is a forward time invariant coefficient, beta b is a forward time invariant coefficient; gamma f0 and gamma b0 are the noise variances of gaussian white noise in the forward TVAR and backward TVAR models, respectively; y f is the forward HRRP distance bin data of the target, including the m+1th to N x th data of x (N); y b is the targeted backward HRRP distance bin data, including the 1 st through N x -m data of x (N)Is the conjugation of Y b; /(I)For Y f length,A length of Y b; z f and Z b, wherein Z f is the forward observation matrix of the target HRRP distance unit data, including the observation matrix on the (m+1) -th to (N x) -th targets, and Z b is the forward observation matrix of the target HRRP distance unit data, including the observation matrix on the (1) -th to (N x -m) -th targets,Is the conjugation of Z b; i M is an identity matrix of M dimensions;
5.2 obtaining a target time invariant coefficient beta: according to the forward and backward likelihood function of the target and the clustering priori of the time-invariant coefficient beta of the target, the posterior of the obtained time-invariant coefficient beta is Gaussian distribution, and the posterior distribution mean values of the forward and backward time-invariant coefficient beta are respectively expressed as
μf=γf0 -1ΣfZf HYf=DZf H(γf0I+ZfDZf H)-1Yf
Wherein mu f is the mean value of the forward time invariant coefficients beta f, and mu b is the mean value of the backward time invariant coefficients beta b; Σ f is the variance of the forward time invariant coefficient β f, Σ b is the variance of the backward time invariant coefficient β b; z f H is the conjugate transpose of Z f, and Z b H is the conjugate transpose of Z b; d is the first element which is the diagonal matrix of (gamma l-(m-1)/2+...+γl+...+γl+m/2)-1) (. Cndot. -1) is the matrix inversion operation;
Since the posterior distribution mean value mu f of the forward time invariant coefficient beta f and the posterior distribution mean value mu b of the backward time invariant coefficient beta b of the target are both estimated beta, taking the average value mu= (mu f+μb)/2, namely the time invariant coefficient vector beta to be estimated;
Step 6, using the estimated time-varying coefficient in instantaneous frequency estimation to obtain a micro Doppler time-frequency diagram of the target: converting the time-invariant coefficient beta into a time-variant coefficient a i (n) through a linear combination formula of a discrete cosine base, and calculating to obtain an instantaneous power spectrum PS (f, n) of the target by utilizing an instantaneous power formula according to the time-variant coefficient a i (n) of TVAR, wherein the instantaneous power spectrum PS (f, n) is expressed as:
where f is the frequency at which the frequency is, Is an estimate of the noise variance;
Substituting the instantaneous power spectrum of the target into the frequency of the target point by point to obtain a micro Doppler frequency curve graph of the echo signal of the target; and reflecting the number, shape and attitude information of scattering points of the radar target according to the micro Doppler frequency, and identifying the target.
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