CN111610502A - FVSBL-based time-frequency analysis method for echo signal of space micro-motion target - Google Patents
FVSBL-based time-frequency analysis method for echo signal of space micro-motion target Download PDFInfo
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Abstract
The invention discloses a space micro-motion target echo signal time-frequency analysis method based on FVSBL, which comprises the following steps: substituting the radar echo signal of the space micro-motion target into a time-varying autoregressive model; obtaining a matrix form of time-invariant coefficient solution of a time-varying autoregressive model of a spatial micro-motion target echo signal; solving the time invariant coefficient by using an FVSBL method; and obtaining a time-frequency diagram of the spatial micro-motion target echo signal according to a power spectral density function of the echo signal time-varying autoregressive model. According to the invention, on the premise that the sparsity of the time invariant coefficient is not required to be obtained, the dimension reduction processing is carried out on the matrix to be inverted in the solving process of the time invariant coefficient, so that the problems that in the prior art, under the condition of large echo data volume, the time consumption of the calculating process is long and the result convergence is slow due to the matrix inversion in the process of solving the time invariant coefficient are solved.
Description
Technical Field
The invention belongs to the technical field of radar, and further relates to a space micro-motion target echo signal time-frequency analysis method based on fast Variation Bayes FVSBL (fast Variation spark Bayesian learning) in the technical field of radar signal processing. The invention can be used for time-frequency analysis of the echo signal of the space micro-motion target received by the radar, and provides a basis for realizing the inverse Synthetic aperture ISAR (inverse Synthetic aperture Radar) instantaneous three-dimensional imaging of the space micro-motion target.
Background
Because the micro doppler Frequency caused by the non-stationary motion of the spatial micro-motion target is often in a Time-varying curve form, and the Time-Frequency Analysis JTFA (Joint Time-Frequency Analysis) is used as a powerful tool for analyzing Time-varying non-stationary signals, the relationship of the signal Frequency changing along with Time can be clearly described, so that an effective Time-Frequency Analysis method needs to be researched in order to obtain a Time-Frequency diagram with higher resolution so as to obtain the ISAR instantaneous three-dimensional imaging of the spatial micro-motion target.
The patent technology of the university of electronic science and technology of west 'an analysis method of micro doppler of space target suitable for short-time observation' (application No. 201510375026.9 grant No. 105044698B) discloses a time-frequency analysis method of echo signal of space micro moving target by micro doppler analysis method of space target suitable for short-time observation. The method comprises the following specific steps: (1) expressing the radar echo of the space target observed in a short time by using a forward and backward TVAR model; (2) introducing sparsity into a solving method of a forward-backward TVAR model based on least square, and constructing a sparse forward-backward TVAR model; (3) determining the order of the sparse forward and backward model and the dimensionality of a basis function by using a minimum description length criterion; (4) solving the time-invariant coefficient vector of the sparse forward and backward TVAR model; (5) and calculating the instantaneous signal power spectrum of the space target according to the solved time-invariant coefficient vector. Although the method realizes the time-frequency analysis of the echo signal of the spatial micro-motion target, the method still has the following defects: the subsequent solving process can be carried out after the sparsity of the time-invariant coefficient vector is acquired by means of an information criterion.
Hongling proposed a parametric-sparse forward and backward TVAR model based on sparse optimization for time-frequency analysis of spatial micro-motion target echo signals in the published paper "sparse reconstruction-based spatial target perception method research" (the university of electronic technology, Phd. academic papers, 2015). The method comprises the following implementation steps: (1) establishing a TVAR model of a spatial micro-motion target echo signal; (2) solving time-varying coefficients of the forward and backward TVAR models by adopting a sparse solving method based on block sparsity; (3) and substituting the solved time-varying coefficient into a power spectral density function to obtain a time-frequency graph of the echo signal. Although the method realizes the time-frequency analysis of the echo signal of the spatial micro-motion target, the method still has the following defects: in the method, matrix inversion is involved in the iterative updating process of solving the time invariant coefficients, so that when the data volume of the echo signal is large, the method has large calculated amount and low convergence speed, and the time consumption for performing time-frequency analysis on the echo signal of the spatial micro-motion target is long.
Disclosure of Invention
The invention aims to provide a space micro-motion target echo signal time-frequency analysis method based on FVSBL aiming at the defects of the prior art. The method solves the problem that the sparsity of the time-invariant coefficient of the time-varying autoregressive model of the echo signal of the space micro-motion target needs to be obtained when the time-invariant coefficient of the time-varying autoregressive model of the echo signal of the space micro-motion target is solved, and solves the problems of large calculation amount and long time consumption caused by matrix inversion by dimension reduction of the matrix needing to be inverted in each iteration process.
The idea of the invention for realizing the above purpose is as follows: after a matrix form of time-invariant coefficient solving of a time-variant autoregressive model of a spatial micro-motion target echo signal is obtained, each element in an unknown time-invariant coefficient is set to be 0 by using an FVSBL method, the variance obeys the prior distribution of gamma distribution, the mean vector and the covariance matrix of the time-invariant coefficient are subjected to iterative updating, the matrix needing to be inverted is subjected to dimension reduction in each iterative process, and when a convergence condition is met, the value of each element in the time-invariant coefficient is obtained, so that the time-invariant coefficient can be solved by using the FVSBL method without obtaining the sparsity of the time-invariant coefficient, the operation amount is reduced, and the time cost is reduced.
The method comprises the following specific steps:
(1) substituting the spatial micro-motion target echo signals at N moments to be analyzed into the following time-varying autoregressive model:
wherein x (N) represents the echo signal value of the echo signal N moment of the space micro-motion target, and N represents the space micro-motion targetThe total number of time-sampled points of the target echo signal, p denotes the order of the time-varying autoregressive model, ∑ denotes the summing operation, ak(n) represents the k time-varying coefficient value at the time n in the time-varying autoregressive model, x (n-i) represents the echo signal value of the spatial micro-motion target echo signal at the time n-i, w (n) represents the observation noise value of the spatial micro-motion target echo signal at the time n, and q represents ak(n) extended dimension, akmDenotes ak(n) an mth time invariant coefficient of the kth time variant coefficient spread on a discrete cosine basis, cos represents cosine operation, and pi represents circumference ratio;
(2) the time-varying autoregressive model of the spatial micro-motion target echo signals at all the time instants is expressed as a matrix form as follows:
Y＝-Xb+W
wherein, Y represents the space inching target echo signal vector from the t th to the N th time, Y is [ x (t), x (t +1), …, x (N), …, x (N)]TT is equal to p, T represents transposition operation, X represents an observation matrix composed of an echo signal value of the spatial inching target at the 1 st to nth moments and a discrete cosine basis function, b represents a time invariant coefficient vector, and b ═ a11,a12,…,a1m,…,a1q,…akm,…,ap1,ap2,…apm,…,apq]TW represents an observation noise vector at time t to N, W ═ W (t), W (t +1), …, W (N), …, W (N)]；
(3) And (3) solving the time invariant coefficient by using a fast variational sparse Bayesian learning FVSBL algorithm:
(3a) when in setting, each element in the invariant coefficient vector obeys the Gaussian distribution with the mean value of 0 and the variance of gamma distribution; when setting, the invariant coefficient vector obeys Gaussian distribution with mean vector as omega and covariance matrix as S; setting the observation noise vector obeying mean value as 0, the covariance matrix as the Gaussian distribution of tau I, wherein tau represents the unknown coefficient of the observation noise vector covariance matrix obeying gamma distribution, and I represents the unit matrix;
(3b) the following variables are initialized as follows:
τ＝1
S＝(XTX+I)-1
ω＝SXTY
cl＝(ωs 2+Sh)-1
where S denotes a covariance matrix of the time-invariant coefficient vector, -1 denotes an inversion operation, l denotes an element number of the time-invariant coefficient vector, and l is 1,2, …, pq, clRepresenting the variance, ω, of the l-th element in the time-invariant coefficient vectorsThe S-th element, S, in the mean vector representing the time-invariant coefficient vectorhValues of the h element, l, s and h variables on the diagonal of the covariance matrix representing the time-invariant coefficient vector are correspondingly equal;
(3c) the variance of each element in the time-invariant coefficient vector is calculated as follows:
wherein ,cl newRepresenting the variance value of the ith element in the recalculated time-invariant coefficient vector, i representing the number of elements in the time-invariant coefficient vector not equal to l, ciRepresenting the variance of the ith element in the time-invariant coefficient vector, erRepresenting a vector of 0 except the r-th element as 1, the value of r is equal to that of l, ezRepresents a vector whose elements are 0 except the z-th element which is 1;
(3d) judging whether the variance value of each element of the invariant coefficient vector is a finite value, if so, executing the step (3e), otherwise, executing the step (3 f);
(3e) keeping the jth column in an observation matrix in the time-varying autoregressive model, wherein the value of j is correspondingly equal to the value of l, and updating the variance value of the covariance matrix of the invariant coefficient vector and the ith element in the invariant coefficient:
cl＝cl new
(3f) deleting the jth column in an observation matrix in the time-varying autoregressive model, and updating a covariance matrix of a time-invariant coefficient vector, wherein the vector and the observation matrix are composed of variance values of all elements in the time-invariant coefficient vector:
wherein ,
c represents a vector composed of variance values of each element in the time-invariant coefficient vector,
representing the vector after the l-th element is deleted from c,
representing the value of each element on the diagonal equal to
A diagonal matrix corresponding to the position element values;
(3g) updating a mean vector of the time invariant coefficient vector, observing a covariance matrix coefficient of the noise vector, and updating a covariance matrix of the time invariant coefficient vector:
ω＝τ-1SXTY
S＝(τ-1XTX+diag(c))-1
wherein | · | purple sweet2Expressing a two-norm, tr (-) expresses the operation of summing diagonal elements of the matrix, diag (c) expresses a diagonal matrix with the value of each element on the diagonal equal to the value of the element at the corresponding position of c;
(3h) judging whether the mean vector omega of the time invariant coefficient vector b meets the convergence condition, if so, taking the value of each element in the time invariant coefficient vector b as the value of the corresponding position element in the mean vector omega, and executing the step (4), otherwise, executing the step (3 c);
(4) calculating the time-varying coefficient of a time-varying autoregressive model of the echo signal of the spatial micro-motion target according to the following formula:
(5) obtaining a time-frequency diagram of a spatial micro-motion target echo signal:
(5a) calculating the power spectral density value of the echo signal at each moment according to a power spectral density function formula;
(5b) and taking the corresponding values of the power density values at all the moments on the two-dimensional coordinate system as element values in a time-frequency graph to obtain the time-frequency graph of the spatial micro-motion target echo signal.
Compared with the prior art, the invention has the following advantages:
firstly, the invention utilizes the fast variational sparse Bayesian learning FVSBL algorithm to solve the prior distribution of each element in the invariant coefficient when the invariant coefficient is set, and overcomes the problem that the subsequent solving process can be carried out only after the sparsity of the invariant coefficient vector is acquired by means of an information criterion in the prior art, so that the invention has the advantage of high time-frequency analysis adaptability to the spatial micro-motion target echo signal.
Secondly, in the process of solving the time-invariant coefficient of the time-variant autoregressive model of the spatial micro-motion target echo signal, the dimension reduction is carried out on the matrix to be inverted in each iteration updating process, and the problems of large calculated amount and low convergence speed of the method when the data volume of the echo signal is large are solved, so that the method has the advantage of carrying out rapid time-frequency analysis on the echo signal with large data volume.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a simulation of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings.
The steps for carrying out the present invention will be described in further detail with reference to FIG. 1.
where x (N) represents an echo signal value at the time of the spatial fine motion target echo signal N, N is 1,2, … N, N represents the number of time sampling points of the spatial fine motion target echo signal, p represents the order of the time-varying autoregressive model, ∑ represents the summation operation, k represents the number of time-varying coefficients in the time-varying autoregressive model, k is 1,2,3k(n) represents the k time-varying coefficient value to be acquired at the time n in the time-varying autoregressive model, x (n-i) represents the echo signal value of the space micro-motion target echo signal at the time n-i, the value of i is equal to the value of k correspondingly, w (n) represents the observation noise value of the space micro-motion target echo signal at the time n, q represents ak(n) an extension dimension, m denotes the number of time-invariant coefficients to be acquired, akmDenotes ak(n) an mth unknown time-invariant coefficient of the kth time-varying coefficient spread on a discrete cosine basis, m being 1,2.. q, cos representing a cosine operation and pi representing a circumference ratio;
and 2, expressing the time-varying autoregressive model of the spatial micro-motion target echo signals at all the moments as a matrix form as follows.
Y＝-Xb+W
Wherein, Y represents the space inching target echo signal vector from the t th to the N th time, Y is [ x (t), x (t +1), …, x (N), …, x (N)]TT represents the T-th moment, the value of T is equal to the value of p correspondingly, T represents the transposition operation, X represents an observation matrix consisting of the echo signal value of the spatial inching target at the 1 st moment to the Nth moment and the discrete cosine basis function, b represents a time-invariant coefficient vector, and b is [ a ═ a [ [ a ]11,a12,…,a1m,…,a1q,…akm,…,ap1,ap2,…apm,…,apq]TW represents an observation noise vector at time t to N, W ═ W (t), W (t +1), …, W (N), …, W (N)]。
The specific form of the observation matrix X is as follows:
wherein g represents the g-th base of the discrete cosine base function, the value of g is equal to the value of q correspondingly, and each term in X is the product of the discrete cosine base function and the spatial micro-motion target echo signal.
And 3, solving the time invariant coefficient by using a fast variational sparse Bayesian learning FVSBL algorithm.
Step 2, initializing the following variables according to the following formula:
τ＝1
S＝(XTX+I)-1
ω＝SXTY
cl＝(ωs 2+Sh)-1
wherein S represents a covariance matrix of the time invariant coefficient vector, -1 represents an inversion operation, ω represents a mean vector of the time invariant coefficient vector, and l is a tableThe element numbers of the time invariant coefficient vector, l ═ 1,2, …, pq, clDenotes the variance of the ith element in the time-invariant coefficient vector, s denotes the number of the element in the mean vector of the time-invariant coefficient vector, s is 1,2, …, pq, ωsDenotes the S-th element in the mean vector of the time-invariant coefficient vector, h denotes the number of elements on the diagonal of the covariance matrix of the time-invariant coefficient vector, h is 1,2, …, pq, ShValues of the h element, l, s and h variables on the diagonal of the covariance matrix representing the time-invariant coefficient vector are correspondingly equal;
and 3, calculating the variance of each element in the time-invariant coefficient vector according to the following formula:
wherein ,cl newRepresenting the variance value of the ith element in the recalculated time-invariant coefficient vector, i representing the number of elements in the time-invariant coefficient vector not equal to l, ciRepresenting the variance of the ith element in the time-invariant coefficient vector, erRepresenting a vector of 0 except the r-th element as 1, the value of r is equal to that of l, ezRepresenting a vector whose elements are 0 except the z-th element, which is 1.
And 4, judging whether the variance value of each element of the time-invariant coefficient vector is a finite value, if so, executing the step 5 of the step, otherwise, executing the step 6 of the step.
And 5, reserving a jth column in an observation matrix in the time-varying autoregressive model, wherein j is equal to l correspondingly, and updating a covariance matrix of an invariant coefficient vector and a variance value of an l element in an invariant coefficient:
cl＝cl new
and 6, deleting the jth column in the observation matrix in the time-varying autoregressive model, and updating the covariance matrix of the time-invariant coefficient vector, the vector and the observation matrix which are formed by the variance values of all elements in the time-invariant coefficient vector:
wherein ,
c represents a vector composed of variance values of each element in the time-invariant coefficient vector,
representing the vector after the l-th element is deleted from c,
representing the value of each element on the diagonal equal to
A diagonal matrix of corresponding position element values.
And 7, updating the mean vector of the time-invariant coefficient vector, observing the covariance matrix coefficient of the noise vector, and determining the covariance matrix of the time-invariant coefficient vector:
ω＝τ-1SXTY
S＝(τ-1XTX+diag(c))-1
wherein | · | purple sweet2Express a binary equationThe number tr (·) represents the operation of summing the diagonal elements of the matrix, and diag (c) represents the diagonal matrix in which the values of the elements on the diagonal are equal to the values of the elements at the corresponding positions of c.
And 8, judging whether the mean vector omega of the time-invariant coefficient vector b meets a convergence condition, if so, taking the value of each element in the time-invariant coefficient vector b as the value of the corresponding position element in the mean vector omega, and executing the step 4, otherwise, executing the step 3.
The convergence condition refers to: i omegay-ωy-1||2＜10-5, wherein ,ωyAnd omegay-1Respectively representing the mean value vector of the time-invariant vectors obtained by the y-th iteration calculation and the y-1 st iteration calculation.
Step 4, calculating a time-varying coefficient of a time-varying autoregressive model of the spatial micro-motion target echo signal according to the following formula:
and 5, obtaining a time-frequency diagram of the echo signal of the space micro-motion target.
Calculating the power spectral density value of the echo signal at each moment according to the following power spectral density function formula:
wherein, P (f, n) represents the power spectral density value of the spatial micro-motion target echo signal at the time n and the frequency f, f represents the echo signal frequency variable, | · | represents the absolute value operation, e represents the exponential operation with the natural constant e as the base, and j represents the imaginary unit symbol.
And taking the corresponding values of the power density values at all the moments on the two-dimensional coordinate system as element values in a time-frequency graph to obtain the time-frequency graph of the spatial micro-motion target echo signal.
The effect of the present invention will be further described with reference to simulation experiments.
1. And (5) simulating experimental conditions.
The hardware platform of the simulation experiment of the invention is as follows: the processor is Inter (R) core (TM) i5-4590 with the CPU master frequency of 3.30GHZ and the memory of 64 GB.
The software platform of the simulation experiment of the invention is as follows: CST STUDIO SUITE 2019 and MATLAB R2018 b.
2. And (5) analyzing simulation contents and results thereof.
The simulation experiment of the invention is to respectively perform time-frequency analysis on echo signals of the space micro-motion target model shown in the figure 2(a) by adopting the invention and two prior arts (a short-time Fourier transform (STFT) time-frequency analysis method and a sparse Bayesian learning-based time-frequency analysis method) to obtain time-frequency graphs corresponding to the three technologies.
The main parameter settings of the aerial jiggle target model used for the simulation experiment are shown in table 1.
TABLE 1 Main parameter table of air jiggle target model
| Parameter(s) | Numerical value |
| Radius of the bottom/m | 0.44 |
| Radius of the top part/m | 0.0488 |
| Target height/m | 1.77 |
| Spin angular frequency/HZ | 2.5 |
| Precession angular frequency/HZ | 0.5 |
| Nutation angular frequency/HZ | 4 |
The simulated radar parameters are set as follows:
the working frequency is as follows: 8GHz-12GHz, the center frequency is 10GHz, the bandwidth is 2GHz, the sweep step length is 0.05, the distance resolution is 0.0375m, the observation time is 2s, and the repetition frequency is 500 HZ.
In a simulation experiment for performing time-frequency analysis on an echo signal of a space micro-motion target model shown in fig. 2, two prior arts are adopted:
the short-time Fourier transform STFT time-frequency analysis method in the prior art refers to a signal time-frequency analysis method proposed by Kuang Yun et al in' an OFDM time synchronization method (electronic and information science and report, 2004,026(003): 453-.
The time-frequency analysis method based on sparse Bayesian learning in the prior art refers to a method for performing time-frequency analysis on spatial micro-motion target echo signals by a sparse optimization-based parameterized sparse forward and backward TVAR model, which is proposed by Hongling in a paper published by Hongling in the study of sparse reconstruction-based spatial target perception method (doctor academic thesis of university of electronic technology, Xian, 2015), and is called sparse Bayesian learning-based time-frequency analysis method for short
3. Analysis of simulation results
TABLE 2 time consumption chart for three time-frequency analysis methods
| Time frequency method | Time consuming |
| Short Time Fourier Transform (STFT) | 0.074s |
| Sparse Bayesian learning based | 2.148s |
| The time frequency analysis method of the invention | 0.067s |
The effect of the present invention will be further described with reference to the simulation diagram of FIG. 2
FIG. 2(a) is a model diagram of an aerial jiggle target in a simulation experiment according to the present invention. Fig. 2(b) is a time-frequency diagram obtained by performing time-frequency analysis on the aerial micro-motion target model of fig. 2(a) by using a short-time fourier transform time-frequency analysis method in the prior art. Fig. 2(c) is a time-frequency diagram obtained by performing time-frequency analysis on the aerial micro-motion target model of fig. 2(a) by using a time-frequency analysis method based on sparse bayesian learning in the prior art. FIG. 2(d) is a time-frequency diagram obtained by performing time-frequency analysis on the aerial micro-motion target model of FIG. 2(a) by using the time-frequency analysis method of the present invention.
The simulation result analysis is the result analysis of three time-frequency graphs with the abscissa of time/s, the ordinate of frequency/HZ and the observation time of 2 s.
As can be seen from fig. 2(b) and fig. 2(c), compared with the time-frequency analysis method based on sparse bayes learning, the time-frequency analysis result of the short-time fourier transform STFT time-frequency analysis method in the prior art is not high in time-frequency resolution of the time-frequency graph, mainly because the method uses a fixed window function to perform sliding window fourier analysis on a signal, once the window function is determined, the resolution of the short-time fourier transform on the signal analysis is also determined, and thus the time-frequency resolution of the method is not high.
As can be seen from fig. 2(b), fig. 2(c) and table 2, the time-frequency analysis result of the time-frequency analysis method based on the sparse bayes learning in the prior art is higher in time-frequency resolution of the time-frequency graph than the result of the short-time fourier transform STFT time-frequency analysis method, but the time-frequency analysis takes longer because the method involves matrix inversion during each iteration update in the time-frequency analysis process.
As can be seen from fig. 2(b), fig. 2(c), fig. 2(d) and table 2, the time-frequency analysis results of the time-frequency analysis method of the present invention are higher in time-frequency resolution of the time-frequency map and less in time consumption compared with the results of the first two prior art, which proves that the time-frequency analysis results of the present invention are superior to the results of the first two prior art.
The above simulation experiments show that: the time-frequency analysis method can obtain the time-frequency graph with higher time-frequency resolution, reduces the time cost by reducing the dimension of the matrix needing inversion in the time-frequency analysis process, solves the problem that the time cost is increased when the time-frequency graph with higher time-frequency resolution needs to be obtained in the prior art, and is an effective time-frequency analysis method.
Claims (4)
1. A space micro-motion target echo signal time-frequency analysis method based on FVSBL is characterized by comprising the following steps:
(1) substituting the spatial micro-motion target echo signals at N moments to be analyzed into the following time-varying autoregressive model:
wherein x (N) represents the echo signal value of the spatial micro-motion target echo signal at the time of N, N represents the total number of time sampling points of the spatial micro-motion target echo signal, p represents the order of the time-varying autoregressive model, ∑ represents the summation operation, ak(n) represents the k time-varying coefficient value at the time n in the time-varying autoregressive model, x (n-i) represents the echo signal value of the spatial micro-motion target echo signal at the time n-i, w (n) represents the observation noise value of the spatial micro-motion target echo signal at the time n, and q represents ak(n) extended dimension, akmDenotes ak(n) the mth time-invariant coefficient of the kth time-varying coefficient spread on the basis of a discrete cosine, cos represents a cosine operation, and pi represents a circleThe cycle rate;
(2) the time-varying autoregressive model of the spatial micro-motion target echo signals at all the time instants is expressed as a matrix form as follows:
Y＝-Xb+W
wherein, Y represents the space inching target echo signal vector from the t th to the N th time, Y is [ x (t), x (t +1), …, x (N), …, x (N)]TT is equal to p, T represents transposition operation, X represents an observation matrix composed of an echo signal value of the spatial inching target at the 1 st to nth moments and a discrete cosine basis function, b represents a time invariant coefficient vector, and b ═ a11,a12,…,a1m,…,a1q,…akm,…,ap1,ap2,…apm,…,apq]TW represents an observation noise vector at time t to N, W ═ W (t), W (t +1), …, W (N), …, W (N)]；
(3) And (3) solving the time invariant coefficient by using a fast variational sparse Bayesian learning FVSBL algorithm:
(3a) when in setting, each element in the invariant coefficient vector obeys the Gaussian distribution with the mean value of 0 and the variance of gamma distribution; when setting, the invariant coefficient vector obeys Gaussian distribution with mean vector as omega and covariance matrix as S; setting the observation noise vector obeying mean value as 0, the covariance matrix as the Gaussian distribution of tau I, wherein tau represents the unknown coefficient of the observation noise vector covariance matrix obeying gamma distribution, and I represents the unit matrix;
(3b) the following variables are initialized as follows:
τ＝1
S＝(XTX+I)-1
ω＝SXTY
cl＝(ωs 2+Sh)-1
where S denotes a covariance matrix of the time-invariant coefficient vector, -1 denotes an inversion operation, l denotes an element number of the time-invariant coefficient vector, and l is 1,2, …, pq, clRepresenting the variance, ω, of the l-th element in the time-invariant coefficient vectorsThe S-th element, S, in the mean vector representing the time-invariant coefficient vectorhWhen it is indicatedValues of the h element, l, s and h variables on the diagonal line of the covariance matrix of the invariant coefficient vector are correspondingly equal;
(3c) the variance of each element in the time-invariant coefficient vector is calculated as follows:
wherein ,cl newRepresenting the variance value of the ith element in the recalculated time-invariant coefficient vector, i representing the number of elements in the time-invariant coefficient vector not equal to l, ciRepresenting the variance of the ith element in the time-invariant coefficient vector, erRepresenting a vector of 0 except the r-th element as 1, the value of r is equal to that of l, ezRepresents a vector whose elements are 0 except the z-th element which is 1;
(3d) judging whether the variance value of each element of the invariant coefficient vector is a finite value, if so, executing the step (3e), otherwise, executing the step (3 f);
(3e) keeping the jth column in an observation matrix in the time-varying autoregressive model, wherein the value of j is correspondingly equal to the value of l, and updating the variance value of the covariance matrix of the invariant coefficient vector and the ith element in the invariant coefficient:
cl＝cl new
(3f) deleting the jth column in an observation matrix in the time-varying autoregressive model, and updating a covariance matrix of a time-invariant coefficient vector, wherein the vector and the observation matrix are composed of variance values of all elements in the time-invariant coefficient vector:
wherein ,
c represents a vector composed of variance values of each element in the time-invariant coefficient vector,
representing the vector after the l-th element is deleted from c,
representing the value of each element on the diagonal equal to
A diagonal matrix corresponding to the position element values;
(3g) updating a mean vector of the time invariant coefficient vector, observing a covariance matrix coefficient of the noise vector, and updating a covariance matrix of the time invariant coefficient vector:
ω＝τ-1SXTY
S＝(τ-1XTX+diag(c))-1
wherein | · | purple sweet2Expressing a two-norm, tr (-) expresses the operation of summing diagonal elements of the matrix, diag (c) expresses a diagonal matrix with the value of each element on the diagonal equal to the value of the element at the corresponding position of c;
(3h) judging whether the mean vector omega of the time invariant coefficient vector b meets the convergence condition, if so, taking the value of each element in the time invariant coefficient vector b as the value of the corresponding position element in the mean vector omega, and executing the step (4), otherwise, executing the step (3 c);
(4) calculating the time-varying coefficient of a time-varying autoregressive model of the echo signal of the spatial micro-motion target according to the following formula:
(5) obtaining a time-frequency diagram of a spatial micro-motion target echo signal:
(5a) calculating the power spectral density value of the echo signal at each moment according to a power spectral density function formula;
(5b) and taking the corresponding values of the power density values at all the moments on the two-dimensional coordinate system as element values in a time-frequency graph to obtain the time-frequency graph of the spatial micro-motion target echo signal.
2. The FVSBL-based time-frequency analysis method for the echo signal of the spatial micro-motion target of claim 1, wherein the observation matrix X in the step (2) has the following specific form:
wherein, the value of g is correspondingly equal to the value of q.
3. The FVSBL-based spatial jiggle target echo signal time-frequency analysis method according to claim 1, wherein the convergence condition in step (3h) is: i omegay-ωy-1||＜10-5, wherein ,ωyAnd omegay-1Respectively representing the mean value vector of the time-invariant vectors obtained by the y-th iteration calculation and the y-1 st iteration calculation.
4. The FVSBL-based spatial jiggle target echo signal time-frequency analysis method according to claim 1, wherein the power spectral density function formula in step (5a) is as follows:
wherein, P (f, n) represents the power spectral density value of the spatial micro-motion target echo signal at the frequency f at the time n, f represents the frequency variable of the echo signal, | · | represents the absolute value operation, e represents the exponential operation with the natural constant e as the base, and j represents the imaginary unit symbol.
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