CN111610502B - fVEBL-based time-frequency analysis method for space inching target echo signals - Google Patents
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Abstract
The invention discloses a time-frequency analysis method of a space inching target echo signal 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 the space jog target echo signal; solving a time invariant coefficient by using an FVSBL method; and obtaining a time-frequency diagram of the space inching target echo signal according to the power spectral density function of the echo signal time-varying autoregressive model. According to the method, on the premise that the sparseness of the time-invariant coefficients is not required to be obtained, the dimension reduction processing is carried out on the matrix which is required to be inverted in the solving process of the time-invariant coefficients, and the problems that in the prior art, under the condition that the echo data size is large, the time consumption of a calculation process is long and the result convergence is slow due to matrix inversion when the time-invariant coefficients are solved.
Description
Technical Field
The invention belongs to the technical field of radars, and further relates to a time-frequency analysis method of a space micro-motion target echo signal based on a fast-varying decibel leaf FVSBL (Fast Variation Spare Bayesian Learning) in the technical field of radar signal processing. The method can be used for carrying out time-frequency analysis on the space micro-motion target echo signals received by the radar, and provides basis for realizing the instantaneous three-dimensional imaging of the inverse synthetic aperture ISAR (Inverse Synthetic Apeture Radar) 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 the Time-varying non-stationary signal, the relation of the Time-varying signal frequency can be clearly described, so that in order to obtain a Time-frequency diagram with higher resolution to obtain the ISAR instantaneous three-dimensional imaging of the spatial micro-motion target, an effective Time-frequency analysis method needs to be studied.
The micro Doppler analysis method for space target for short-time observation is disclosed in the patent technology 'a micro Doppler analysis method for space target for short-time observation' (application No. 201510375026.9 grant bulletin No. 105044698B) owned by the university of Western-A electronic technology. The method comprises the following specific steps: (1) Representing radar echoes of a space target observed in a short time by using a forward-backward TVAR model; (2) Introducing sparsity into a solution 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 model and the dimension of the basis function by using a minimum description length criterion; (4) Solving a time-invariant coefficient vector of the sparse forward-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 space micro-motion target echo signal, the method still has the following defects: the sparsity of the time-invariant coefficient vector needs to be acquired by means of information criteria before the subsequent solving process can be performed.
Hong Ling in the paper "study on space target perception method based on sparse reconstruction" (university of western electronic science and technology, doctor's academic paper, 2015) a method for performing time-frequency analysis on space inching target echo signals based on parameterization-sparse forward and backward TVAR model of sparse optimization is proposed. The method comprises the following implementation steps: (1) establishing a TVAR model of a space micro-motion target echo signal; (2) Adopting a sparse solving method based on block sparsity to solve the time-varying coefficient of the forward and backward TVAR model; (3) Substituting the solved time-varying coefficient into the power spectral density function to obtain a time-frequency diagram of the echo signal. Although the method realizes the time-frequency analysis of the space micro-motion target echo signal, 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 signals is large, the method is large in calculated amount and slow in convergence speed, and time-frequency analysis of the echo signals of the space jog target is long.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a time-frequency analysis method for a space jog target echo signal based on FVSBL. The method solves the problem that the sparsity of the time-invariant coefficient of the time-variant autoregressive model needs to be obtained when the space jog target echo signal is solved, and solves the problems of large calculated amount and long time consumption caused by matrix inversion by dimension reduction of the matrix needing inversion in each iteration process.
The idea of the invention for achieving the above purpose is: after a matrix form of time-invariant coefficient solving of a time-variant autoregressive model of a space jog target echo signal is obtained, each element in an unknown time-invariant coefficient is set to be 0 by using an FVSBL method, variances follow prior distribution of gamma distribution, mean vectors and covariance matrixes of the time-invariant coefficients are iteratively updated, the matrix which needs to be inverted is subjected to dimension reduction in each iteration process, and when convergence conditions are met, values of each element in the time-invariant coefficients are obtained, so that the time-invariant coefficients can be solved by using the FVSBL method without obtaining sparsity of the time-invariant coefficients, the operand is reduced, and the time cost is reduced.
The specific steps of the invention are as follows:
(1) Substituting the spatial inching 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 space jog target echo signal at the moment N, N represents the total number of time sampling points of the space jog target echo signal, p represents the order of the time-varying autoregressive model, Σ represents the summation operation, a k (n) represents the kth time-varying coefficient value at time n in the time-varying autoregressive model, x (n-i) represents the echo signal value of the spatial inching target echo signal at time n-i, w (n) represents the observed noise value of the spatial inching target echo signal at time n, and q represents a k Expansion dimension of (n), a km Representation a k The kth time-varying coefficient of (n) is the mth time-invariant coefficient spread on a discrete cosine basis, cos represents the cosine operation, pi represents the circumference ratio;
(2) The time-varying autoregressive model of the spatial jog target echo signal at all times is represented as a matrix form as follows:
Y＝-Xb+W
wherein Y represents the spatial jog target echo signal vector at the t-N times, Y= [ x (t), x (t+1), …, x (N), …, x (N)] T The value of T is correspondingly equal to that of p, T represents transposition operation, and X represents the composition of echo signal values of the space inching targets from the 1 st time to the N th time and discrete cosine basis functionsObservation matrix, b represents time invariant coefficient vector, b= [ a ] 11 ,a 12 ,…,a 1m ,…,a 1q ,…a km ,…,a p1 ,a p2 ,…a pm ,…,a pq ] T W represents the observed noise vector at the t-th to nth times, w= [ W (t), W (t+1), …, W (N), …, W (N)]；
(3) The fast variable sparse Bayesian learning FVSBL algorithm is utilized to solve time invariant coefficients:
(3a) Each element in the constant coefficient vector is subjected to Gaussian distribution with the mean value of 0 and the variance of gamma distribution when the constant coefficient vector is set; the constant coefficient vector is subjected to Gaussian distribution with mean vector omega and covariance matrix S when the constant coefficient vector is set; setting the obeying mean value of the observed noise vector as 0, and the covariance matrix as Gaussian distribution of τI, wherein τ represents unknown coefficients of the observed noise vector covariance matrix obeying gamma distribution, and I represents the identity matrix;
(3b) The following variables are initialized according to the following formula:
τ＝1
S＝(X T X+I) -1
ω＝SX T Y
c l ＝(ω s 2 +S h ) -1
wherein S represents the covariance matrix of the time-invariant coefficient vector, -1 represents the inversion operation, l represents the element number of the time-invariant coefficient vector, l=1, 2, …, pq, c l Representing the variance, ω, of the first element in the time-invariant coefficient vector s The S-th element in the mean vector representing the time-invariant coefficient vector, S h The h element on the diagonal of the covariance matrix of the time-invariant coefficient vector is represented, and the values of the three variables, i, s and h, are correspondingly equal;
(3c) The variance of each element in the time-invariant coefficient vector is calculated according to the following formula:
wherein ,cl new Representing the time of recalculationVariance value of the first element in the constant coefficient vector, i represents element number in the time-constant coefficient vector which is not equal to l, c i Representing the variance, e, of the ith element in the time-invariant coefficient vector r Representing a vector with 0 elements except for the element 1 of the r, wherein the value of r is correspondingly equal to the value of l, and e z A vector representing 0 for all elements except the z-th element which is 1;
(3d) Judging whether the variance value of each element of the time-invariant coefficient vector is a finite value, if so, executing the step (3 e), otherwise, executing the step (3 f);
(3e) The j-th column in the observation matrix in the time-varying autoregressive model is reserved, the value of j is correspondingly equal to the value of l, and the covariance matrix of the time-invariant coefficient vector is updated, so that the variance value of the first element in the time-invariant coefficient is updated:
c l ＝c l new
(3f) Deleting the j-th column in the observation matrix in the time-varying autoregressive model, and updating the covariance matrix of the time-invariant coefficient vector, and the vector and the observation matrix formed by the variance values of all elements in the time-invariant coefficient vector:
wherein ,
representing in a time-varying autoregressive modelThe observation matrix deletes the matrix after the j-th column, c represents a vector consisting of variance values of each element in the time-invariant coefficient vector, +.>
Representing the vector after the first element is deleted from c,
representing that the value of each element on the diagonal is equal to +.>
Diagonal matrix of corresponding position element values;
(3g) Updating the mean vector of the time-invariant coefficient vector, observing the covariance matrix coefficient of the noise vector, and the covariance matrix of the time-invariant coefficient vector:
ω＝τ -1 SX T Y
S＝(τ -1 X T X+diag(c)) -1
wherein ,·2 Representing a two-norm, tr (·) represents an operation of summing up diagonal elements of the matrix, diag (c) represents a diagonal matrix in which values of elements on the diagonal are equal to values of elements corresponding to c;
(3h) Judging whether the mean value vector omega of the time-invariant coefficient vector b meets a convergence condition, if so, executing the step (4) when the value of each element in the time-invariant coefficient vector b is the value of the corresponding position element in the mean value vector omega, otherwise, executing the step (3 c);
(4) Calculating a time-varying coefficient of a time-varying autoregressive model of the space jog target echo signal according to the following steps:
(5) Obtaining a time-frequency diagram of a space 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 the time-frequency diagram to obtain the time-frequency diagram of the space inching target echo signal.
Compared with the prior art, the invention has the following advantages:
firstly, the invention utilizes the fast variable sparse Bayesian learning FVSBL algorithm to solve the prior distribution of each element in the time-invariant coefficient set when the time-invariant coefficient is set, solves the problem that the subsequent solving process can be carried out after the sparsity of the time-invariant coefficient vector is acquired by means of the information criterion in the prior art, and has the advantage of high suitability for time-frequency analysis of the space jog target echo signal.
Secondly, in the process of solving the time invariant coefficient of the time varying autoregressive model of the space inching target echo signal, the method reduces the dimension of the matrix which needs to be inverted in each iterative updating process, and solves the problems of large calculated amount and slow convergence speed of the method when the data amount of the echo signal is large, so that the method has the advantage of being capable of carrying out rapid time-frequency analysis on the echo signal with large data amount.
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FIG. 1 is a flow chart of the present invention;
fig. 2 is a simulation diagram of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The steps for carrying out the invention will be described in further detail with reference to fig. 1.
wherein x (N) represents an echo signal value of the space jog target echo signal at the time N, n=1, 2, … N, N represents a time sampling point number of the space jog target echo signal, p represents a time-varying autoregressive model order, Σ represents a summing operation, k represents a sequence number of a time-varying coefficient in the time-varying autoregressive model, and k=1, 2,3 k (n) represents a kth time-varying coefficient value to be obtained at the time n in the time-varying autoregressive model, x (n-i) represents an echo signal value of the space inching target echo signal at the time n-i, the value of i is correspondingly equal to the value of k, w (n) represents an observed noise value of the space inching target echo signal at the time n, and q represents a k (n) the expansion dimension, m represents the number of time-invariant coefficients to be obtained, a km Representation a k The kth time-varying coefficient of (n) is the mth unknown time-invariant coefficient spread on a discrete cosine basis, m=1, 2..q, cos represents a cosine operation, pi represents a circumference ratio;
and 2, representing a time-varying autoregressive model of the space inching target echo signals at all moments as a matrix form.
Y＝-Xb+W
Wherein Y represents the spatial jog target echo signal vector at the t-N times, Y= [ x (t), x (t+1), …, x (N), …, x (N)] T T represents the time T, the value of T is correspondingly equal to the value of p, T represents transposition operation, X represents an observation matrix formed by echo signal values of space inching targets from the 1 st time to the N time and discrete cosine basis functions, b represents a time invariant coefficient vector, and b= [ a ] 11 ,a 12 ,…,a 1m ,…,a 1q ,…a km ,…,a p1 ,a p2 ,…a pm ,…,a pq ] T W represents the observed noise vector at the t-th to nth times, 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 basis of the discrete cosine base function, the value of g is equal to q correspondingly, and each term in X is the product of the discrete cosine base function and the space inching target echo signal.
And 3, solving the time invariant coefficients by utilizing a fast variable sparse Bayesian learning FVSBL algorithm.
Step 2, initializing the following variables according to the following formula:
τ＝1
S＝(X T X+I) -1
ω＝SX T Y
c l ＝(ω s 2 +S h ) -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, l represents element numbers of the time-invariant coefficient vector, l=1, 2, …, pq, c l Representing the variance of the first element in the time-invariant coefficient vector, s represents the element number in the mean vector of the time-invariant coefficient vector, s=1, 2, …, pq, ω s The S-th element in the mean vector representing the time-invariant coefficient vector, h represents the element number on the covariance matrix diagonal of the time-invariant coefficient vector, h=1, 2, …, pq, S h The h element on the diagonal of the covariance matrix of the time-invariant coefficient vector is represented, and the values of the three variables, i, s and h, are correspondingly equal;
step 3, calculating the variance of each element in the time-invariant coefficient vector according to the following formula:
wherein ,cl new Representing the variance value of the first element in the recalculated time-invariant coefficient vector, i representing the element number in the time-invariant coefficient vector not equal to l, c i Representing the variance, e, of the ith element in the time-invariant coefficient vector r Representing a vector with 0 elements except for the element 1 of the r, wherein the value of r is correspondingly equal to the value of l, and e z Representing a vector with 0 for all elements except the z-th element which is 1.
And step 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.
Step 5, reserving the j-th column in the observation matrix in the time-varying autoregressive model, wherein the j-th column is equal to the l-th column in the observation matrix, and updating the covariance matrix of the time-invariant coefficient vector to the variance value of the l-th element in the time-invariant coefficient:
c l ＝c l new
step 6, deleting the j-th column in the observation matrix in the time-varying autoregressive model, and updating the covariance matrix of the time-invariant coefficient vector, and the vector and the observation matrix formed by the variance values of all elements in the time-invariant coefficient vector:
wherein ,
representing the matrix after the j-th column of the observation matrix in the time-varying autoregressive model, c representing the vector consisting of the variance values of the individual elements in the time-invariant coefficient vector, < >>
Representing the vector after the first element is deleted from c,
representing that the value of each element on the diagonal is equal to +.>
A diagonal matrix of corresponding position element values.
Step 7, updating the mean vector of the constant coefficient vector, observing the covariance matrix coefficient of the noise vector, and the covariance matrix of the constant coefficient vector:
ω＝τ -1 SX T Y
S＝(τ -1 X T X+diag(c)) -1
wherein I 2 Representing a two-norm, tr (·) represents the operation of summing the diagonal elements of the matrix, diag (c) represents the diagonal matrix where each element on the diagonal has a value equal to the value of the element corresponding to c.
And 8, judging whether the mean value vector omega of the time-invariant coefficient vector b meets a convergence condition, if so, executing the step 4, otherwise, executing the step 3, wherein the value of each element in the time-invariant coefficient vector b is the value of the corresponding position element in the mean value vector omega.
The convergence condition refers to: ||omega y -ω y-1 || 2 ＜10 -5, wherein ,ωy And omega y-1 And respectively representing the mean value vectors of the time-invariant vectors obtained by the y-th iterative calculation and the y-1 th iterative calculation.
And 4, calculating a time-varying coefficient of the time-varying autoregressive model of the space inching target echo signal according to the following formula:
and step 5, obtaining a time-frequency diagram of the space inching target echo signal.
The power spectral density value of the echo signal at each moment is calculated according to the following power spectral density function formula:
wherein P (f, n) represents the power spectral density value of the space jog target echo signal at the time n, the frequency f represents the echo signal frequency variable, |·| represents the absolute value taking operation, e represents the exponential operation based on the natural constant e, 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 the time-frequency diagram to obtain the time-frequency diagram of the space inching target echo signal.
The effects of the present invention are further described below in connection with simulation experiments.
1. And (5) simulating experimental conditions.
The hardware platform of the simulation experiment of the invention is: the processor is Inter (R) Core (TM) i5-4590 CPU with main frequency of 3.30GHZ and memory of 64GB.
The software platform of the simulation experiment of the invention is: CST study SUITE 2019 and MATLAB R2018b.
2. Simulation content and analysis of results thereof.
The simulation experiment of the invention adopts the invention and two prior arts (short time Fourier transform STFT time-frequency analysis method, sparse Bayesian learning-based time-frequency analysis method) to respectively perform time-frequency analysis on echo signals of a space jog target model shown in fig. 2 (a), so as to obtain time-frequency diagrams corresponding to the three technologies.
The main parameter settings of the air jog target model for the simulation experiment are shown in table 1.
TABLE 1 Main parameter Table of air jog target model
| Parameters (parameters) | Numerical value |
| Bottom radius/m | 0.44 |
| Top radius/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 simulation radar parameters were set as follows:
operating frequency: 8GHZ-12GHz, the center frequency is 10GHZ, the bandwidth is 2GHZ, the sweep frequency step length is 0.05, the distance resolution is 0.0375m, the observation time is 2s, and the heavy frequency is 500HZ.
In a simulation experiment of performing time-frequency analysis on an echo signal of a spatial jog target model shown in fig. 2, two prior arts adopted are:
the STFT time-frequency analysis method of the short-time Fourier transform in the prior art is a signal time-frequency analysis method which is proposed by Yu et al in an OFDM time synchronization method (electronic and information journal, 2004,026 (003): 453-458) based on the short-time Fourier transform, and is called as the STFT time-frequency analysis method for short-time Fourier transform.
The prior art time-frequency analysis method based on sparse Bayesian learning refers to a method for performing time-frequency analysis on a space inching target echo signal based on a parameterization-sparse forward and backward TVAR model, which is proposed in a paper published by Hong Ling (doctor's academic university of electronic science and technology, 2015) based on sparse reconstruction, namely, a time-frequency analysis method based on sparse Bayesian learning
3. Simulation result analysis
Table 2 time-consuming table 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 effects 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 airborne micro-motion target for performing a simulation experiment according to the present invention. Fig. 2 (b) is a time-frequency diagram obtained by performing time-frequency analysis on the air jog target model in 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 air jog target model in 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 air jog target model of fig. 2 (a) by using the time-frequency analysis method of the present invention.
The simulation result analysis is performed on three time-frequency diagrams with time/s on the abscissa and frequency/HZ on the ordinate, and the observation time is within 2 s.
As can be seen from fig. 2 (b) and fig. 2 (c), compared with the result of the time-frequency analysis method based on sparse bayesian learning, the time-frequency analysis result of the time-frequency analysis method of the short-time fourier transform STFT 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 the signal, once the window function is determined, the resolution of the short-time fourier transform on the signal analysis is also determined, so that the time-frequency resolution of the method is not high.
As can be seen from fig. 2 (b), fig. 2 (c) and table 2, compared with the result of the short-time fourier transform STFT time-frequency analysis method, the time-frequency resolution of the time-frequency graph is higher in the time-frequency analysis method based on sparse bayesian learning in the prior art, but the method involves matrix inversion every time iterative updating in the time-frequency analysis process, resulting in longer time-frequency analysis time.
As can be seen from fig. 2 (b), fig. 2 (c), fig. 2 (d) and table 2, compared with the results of the previous two prior art, the time-frequency resolution of the time-frequency chart is higher, and the time consumption is less, which proves that the time-frequency analysis result of the present invention is superior to the time-frequency analysis results of the previous two prior art.
The simulation experiment shows that: the time-frequency analysis method can obtain the time-frequency diagram with higher time-frequency resolution, reduces the time cost by reducing the dimension of the matrix needing to be inverted in the time-frequency analysis process, solves the problem that the time cost needs to be increased when the time-frequency diagram with higher time-frequency resolution is obtained in the prior art method, and is a very effective time-frequency analysis method.
Claims (4)
1. A time-frequency analysis method of a space micro-motion target echo signal based on FVSBL is characterized by comprising the following steps:
(1) Substituting the spatial inching 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 space jog target echo signal at the moment N, N represents the total number of time sampling points of the space jog target echo signal, p represents the order of the time-varying autoregressive model, Σ represents the summation operation, a k (n) represents the kth time-varying coefficient value at time n in the time-varying autoregressive model, x (n-i) represents the echo signal value of the spatial inching target echo signal at time n-i, w (n) represents the observed noise value of the spatial inching target echo signal at time n, and q represents a k Expansion dimension of (n), a km Representation a k The kth time-varying coefficient of (n) is the mth time-invariant coefficient spread on a discrete cosine basis, cos represents the cosine operation, pi represents the circumference ratio;
(2) The time-varying autoregressive model of the spatial jog target echo signal at all times is represented as a matrix form as follows:
Y＝-Xb+W
wherein Y represents the spatial jog target echo signal vector at the t-N times, Y= [ x (t), x (t+1), …, x (N), …, x (N)] T The value of T is correspondingly equal to that of p, T represents transposition operation, X represents an observation matrix formed by echo signal values of the space inching targets at the 1 st to the N th moments and discrete cosine basis functions, and b represents a time invariant coefficientVector b= [ a ] 11 ,a 12 ,…,a 1m ,…,a 1q ,…a km ,…,a p1 ,a p2 ,…a pm ,…,a pq ] T W represents the observed noise vector at the t-th to nth times, w= [ W (t), W (t+1), …, W (N), …, W (N)]；
(3) The fast variable sparse Bayesian learning FVSBL algorithm is utilized to solve time invariant coefficients:
(3a) Each element in the constant coefficient vector is subjected to Gaussian distribution with the mean value of 0 and the variance of gamma distribution when the constant coefficient vector is set; the constant coefficient vector is subjected to Gaussian distribution with mean vector omega and covariance matrix S when the constant coefficient vector is set; setting the obeying mean value of the observed noise vector as 0, and the covariance matrix as Gaussian distribution of τI, wherein τ represents unknown coefficients of the observed noise vector covariance matrix obeying gamma distribution, and I represents the identity matrix;
(3b) The following variables are initialized according to the following formula:
τ＝1
S＝(X T X+I) -1
ω＝SX T Y
c l ＝(ω s 2 +S h ) -1
wherein S represents the covariance matrix of the time-invariant coefficient vector, -1 represents the inversion operation, l represents the element number of the time-invariant coefficient vector, l=1, 2, …, pq, c l Representing the variance, ω, of the first element in the time-invariant coefficient vector s The S-th element in the mean vector representing the time-invariant coefficient vector, S h The h element on the diagonal of the covariance matrix of the time-invariant coefficient vector is represented, and the values of the three variables, i, s and h, are correspondingly equal;
(3c) The variance of each element in the time-invariant coefficient vector is calculated according to the following formula:
wherein ,cl new A method for representing the first element in the recalculated time-invariant coefficient vectorThe difference, i, represents the element number in the time-invariant coefficient vector that is not equal to l, c i Representing the variance, e, of the ith element in the time-invariant coefficient vector r Representing a vector with 0 elements except for the element 1 of the r, wherein the value of r is correspondingly equal to the value of l, and e z A vector representing 0 for all elements except the z-th element which is 1;
(3d) Judging whether the variance value of each element of the time-invariant coefficient vector is a finite value, if so, executing the step (3 e), otherwise, executing the step (3 f);
(3e) The j-th column in the observation matrix in the time-varying autoregressive model is reserved, the value of j is correspondingly equal to the value of l, and the covariance matrix of the time-invariant coefficient vector is updated, so that the variance value of the first element in the time-invariant coefficient is updated:
c l ＝c l new
(3f) Deleting the j-th column in the observation matrix in the time-varying autoregressive model, and updating the covariance matrix of the time-invariant coefficient vector, and the vector and the observation matrix formed by the variance values of all elements in the time-invariant coefficient vector:
wherein ,
representing the matrix after the j-th column of the observation matrix in the time-varying autoregressive model, c representing the vector consisting of the variance values of the individual elements in the time-invariant coefficient vector, < >>
Representing the vector after deletion of the first element from c,/->
Representing that the value of each element on the diagonal is equal to +.>
Diagonal matrix of corresponding position element values;
(3g) Updating the mean vector of the time-invariant coefficient vector, observing the covariance matrix coefficient of the noise vector, and the covariance matrix of the time-invariant coefficient vector:
ω＝τ -1 SX T Y
S＝(τ -1 X T X+diag(c)) -1
wherein I 2 Representing a two-norm, tr (·) represents an operation of summing up diagonal elements of the matrix, diag (c) represents a diagonal matrix in which values of elements on the diagonal are equal to values of elements corresponding to c;
(3h) Judging whether the mean value vector omega of the time-invariant coefficient vector b meets a convergence condition, if so, executing the step (4) when the value of each element in the time-invariant coefficient vector b is the value of the corresponding position element in the mean value vector omega, otherwise, executing the step (3 c);
(4) Calculating a time-varying coefficient of a time-varying autoregressive model of the space jog target echo signal according to the following steps:
(5) Obtaining a time-frequency diagram of a space 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 the time-frequency diagram to obtain the time-frequency diagram of the space inching target echo signal.
2. The ffsbl-based time-frequency analysis method of spatially jog target echo signals according to claim 1, wherein the specific form of the observation matrix X in step (2) is as follows:
wherein the value of g is correspondingly equal to the value of q.
3. The ffsbl-based spatial jog target echo signal time frequency analysis method of claim 1, wherein the convergence condition in step (3 h) is: ||omega y -ω y-1 ||＜10 -5, wherein ,ωy And omega y-1 And respectively representing the mean value vectors of the time-invariant vectors obtained by the y-th iterative calculation and the y-1 th iterative calculation.
4. The ffsbl-based spatial jog target echo signal time frequency analysis method of claim 1, wherein the power spectral density function formula in step (5 a) is as follows:
wherein P (f, n) represents the power spectral density value of the space jog target echo signal at the frequency f at the time of n, f represents the echo signal frequency variable, |·| represents the absolute value taking 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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