CN112485794B - Stable time-frequency analysis method for ISAR echo signals - Google Patents

Stable time-frequency analysis method for ISAR echo signals Download PDF

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CN112485794B
CN112485794B CN202011236518.7A CN202011236518A CN112485794B CN 112485794 B CN112485794 B CN 112485794B CN 202011236518 A CN202011236518 A CN 202011236518A CN 112485794 B CN112485794 B CN 112485794B
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CN112485794A (en
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王泽龙
刘吉英
谭欣桐
余奇
郭文博
舒小虎
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National University of Defense Technology
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Abstract

The invention relates to a steady time-frequency analysis method of ISAR echo signals. The method comprises the following steps: obtaining an ISAR echo signal; determining a time slice signal set of the ISAR echo signal according to the ISAR echo signal; determining a frequency domain representation basis for each time slice signal in the set of time slice signals; constructing a time-frequency over-complete convolution frame according to the frequency domain representation basis; establishing a joint optimization model according to the time-frequency over-complete convolution frame and the ISAR echo signal; and solving by using an iterative threshold algorithm according to the joint optimization model to determine the time-frequency spectrum of the ISAR echo signal. The invention effectively improves the time-frequency resolution of the ISAR echo signal.

Description

Stable time-frequency analysis method for ISAR echo signals
Technical Field
The invention relates to the field of signal analysis and processing, in particular to a steady time-frequency analysis method for ISAR echo signals.
Background
Time and frequency are two most important physical quantities for describing the ISAR echo signals, and time-frequency analysis provides the joint distribution of the time and the frequency of the ISAR echo signals by researching the change rule of the signal frequency along with the time. Through many years of research, traditional time-frequency analysis has been widely applied to ISAR echo signal analysis.
The common time-frequency analysis methods are mainly classified into three categories: linear time-frequency analysis, bilinear time-frequency analysis and data-driven time-frequency analysis. The linear time-frequency analysis mainly comprises short-time Fourier transform, continuous wavelet transform, Gabor transform, S transform and the like, the time-frequency analysis algorithm is simple and easy to realize, but the time-frequency resolution is limited, and the self-adaptive capacity of strong nonlinearity, mutation and the like in ISAR echo signals is insufficient. Bilinear time-frequency analysis mainly comprises wigner distribution, smooth pseudo-wigner distribution, Cohn-like time-frequency distribution and the like, the time-frequency analysis obviously improves the time-frequency resolution of signals, but cross terms influence exists on multi-component components in ISAR echo signals, and phenomena of spurious frequency, blurring and the like exist on a spectrogram. The data-driven time-frequency analysis method mainly comprises empirical mode decomposition, variational mode decomposition and other methods, can well process non-stationary signals and overcome adverse factors such as cross term interference, but the theoretical basis of the methods is not complete, and the stability in the ISAR echo signal time-frequency analysis is insufficient. In addition, some practical conditions of the ISAR echo signal, such as missing signal portion, low signal-to-noise ratio, etc., may have a serious impact on the frequency analysis thereof.
The performance and robustness of the steady time-frequency analysis are improved by mining the prior information of the time-frequency spectrum in the ISAR echo signal, and the steady time-frequency analysis mainly relates to two key factors: the time-frequency represents the basis and prior constraints. The traditional time-frequency representation base is difficult to give consideration to representation performance and representation efficiency no matter in a harmonic analysis class or an overcomplete dictionary; the analysis model often applies prior constraints to a plurality of time slice signals, and the robustness needs to be improved.
Disclosure of Invention
The invention aims to provide a steady time-frequency analysis method of ISAR echo signals, which can effectively improve the time-frequency resolution of the ISAR echo signals.
In order to achieve the purpose, the invention provides the following scheme:
a steady time-frequency analysis method of ISAR echo signals comprises the following steps:
obtaining an ISAR echo signal;
determining a time slice signal set of the ISAR echo signal according to the ISAR echo signal;
determining a frequency domain representation basis for each time slice signal in the set of time slice signals;
constructing a time-frequency over-complete convolution frame according to the frequency domain representation basis;
establishing a joint optimization model according to the time-frequency over-complete convolution frame and the ISAR echo signal;
and solving by using an iterative threshold algorithm according to the joint optimization model to determine the time-frequency spectrum of the ISAR echo signal.
Optionally, the constructing a time-frequency overcomplete convolution frame according to the frequency domain representation basis specifically includes:
constructing a time-frequency over-complete convolution frame by using a formula x ═ Σ s;
wherein x is an ISAR echo signal, ΣIs a time-frequency over-complete convolution frame,
Figure BDA0002766881470000021
Figure BDA0002766881470000022
as convolution operator, CM×MA complex matrix space of dimension M × M, S being a matrix S ═ S1,s2,…,sN]∈CM×NAnd vectorizing the vectors obtained by column-by-column end-to-end connection, wherein N is the length of the ISAR echo signal.
Optionally, the establishing a joint optimization model according to the time-frequency overcomplete convolution frame and the ISAR echo signal specifically includes:
using formulas
Figure BDA0002766881470000023
Determining an approximation term of the joint optimization model;
using formulas
Figure BDA0002766881470000024
Determining a priori constraint terms of s;
and determining a joint optimization model according to the approximation term and the prior constraint term.
Optionally, the determining a joint optimization model according to the approximation term and the prior constraint term specifically includes:
using formulas
Figure BDA0002766881470000031
Determining a joint optimization model, wherein>And 0 is the regularization parameter of the joint optimization model.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a steady time-frequency analysis method of ISAR echo signals, which comprises the following steps of firstly, constructing a time-frequency over-complete convolution frame according to the ISAR echo signals; and secondly, establishing a joint optimization model, and then solving the joint optimization model to obtain a time-frequency spectrum of the ISAR echo signal, so as to realize the steady time-frequency analysis of the ISAR echo signal. The time-frequency over-complete convolution frame can effectively improve the time-frequency resolution of the ISAR echo signals and can avoid cross term interference such as false frequency and fuzziness in the ISAR echo signals. The problems of signal part missing, over-low signal-to-noise ratio and the like in the ISAR echo signal can be solved by the combined optimization modeling and numerical algorithm design.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a schematic flow chart of a robust time-frequency analysis method for an ISAR echo signal according to the present invention;
FIG. 2 is a flow chart of a joint optimization model numerical algorithm provided by the present invention;
FIG. 3 is a schematic diagram of a time domain signal according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a time-frequency overcomplete convolution framework constructed in an embodiment of the present disclosure;
FIG. 5 is a diagram illustrating processing results of various time-frequency analysis methods according to an embodiment of the present disclosure.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a steady time-frequency analysis method of ISAR echo signals, which can effectively improve the time-frequency resolution of the ISAR echo signals.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a schematic flow chart of a robust time-frequency analysis method for an ISAR echo signal provided by the present invention, and as shown in fig. 1, the robust time-frequency analysis method for an ISAR echo signal provided by the present invention includes:
s101, obtaining ISAR echo signals x ═ x [1 ═ x],x[2],…,x[N]]T∈RN(ii) a Where N is the echo signal length, RNIs an N-dimensional real space.
And S102, determining a time slice signal set of the ISAR echo signal according to the ISAR echo signal.
The slice signal set for the ISAR echo signals is:
Figure BDA0002766881470000041
wherein M is the time slice length.
S103, determining a frequency domain representation base phi of each time slice signal in the time slice signal set. Wherein phi is [ phi ]1,φ2,…,φM]∈CM×MThe frequency domain representation base Φ of the time slice signal can be set to fourier base, wavelet base, or other forms. Wherein, CM×MA complex matrix space with dimension of M multiplied by M, a time-frequency representation is carried out, and a time slice signal xnThe linearity over Φ is expressed as:
xn＝Φsn,n＝1,2,…,N。
wherein s isnTo represent a coefficient, i.e. xnAnd S ═ S1,s2,…,sN]∈CM×NNamely a time frequency spectrum of time frequency analysis; accordingly, if a constraint model is built under the representation model to reconstruct the representation coefficients, a traditional robust time-frequency analysis can be obtained.
And S104, constructing a time-frequency over-complete convolution frame according to the frequency domain representation basis.
S104 specifically comprises the following steps:
and constructing a time-frequency over-complete convolution frame by using the formula x ═ Σ s.
Wherein x is ISAR echo signal, sigma is time-frequency over-complete convolution frame,
Figure BDA0002766881470000051
Figure BDA0002766881470000052
as convolution operator, CM×MA complex matrix space of dimension M × M, S being a matrix S ═ S1,s2,…,sN]∈CM×NAnd vectorizing the vectors obtained by column-by-column end-to-end connection, wherein N is the length of the ISAR echo signal.
The specific process of constructing the time-frequency over-complete convolution frame is as follows:
the vector format is rewritten into a matrix format X ═ Φ S by combining the N linear representation models.
Wherein X ═ X1,x2,…,xN]Is a hank matrix of ISAR echo signals x, and S is a time-frequency diagram of x. The above formula can be further represented by X ═ Φ SE.
Wherein E ═ E1,e2,…,eN]∈RN×NIs an identity matrix, RN×NIs a real matrix space of dimension N × N.
As known from the basic theory of convolution frameworks, the ISAR echo signal x has an overcomplete representation on the convolution framework formed by Φ and E, i.e., x ═ Σ s.
And S105, establishing a joint optimization model according to the time-frequency over-complete convolution frame and the ISAR echo signal.
S105 specifically comprises the following steps:
using formulas
Figure BDA0002766881470000053
Determining an approximation term of the joint optimization model.
Wherein | · | purple sweet2Representing vector l2And (4) norm. Furthermore, for ISAR echo signals, the time spectrum is typically sparse, and therefore passes through l1The norm excavates sparse prior information, and notes S and S ═ S1,s2,…,sN]Thus using the formula
Figure BDA0002766881470000054
An a priori constraint term for s is determined.
And determining a joint optimization model according to the approximation term and the prior constraint term.
The determining a joint optimization model according to the approximation term and the prior constraint term specifically includes:
using formulas
Figure BDA0002766881470000055
Determining a joint optimization model, wherein>And 0 is a regularization parameter of the joint optimization model.
And S106, solving by using an iterative threshold algorithm according to the combined optimization model, and determining the time-frequency spectrum of the ISAR echo signal.
The specific process of S106 is shown in fig. 2, and the specific steps are as follows:
s3.1: initializing the model parameter lambda>0. Stop threshold τ>0. Iteration step k is 0 and initial solution s0＝(ΣTΣ)-1ΣTx；
S3.2: performing iteration:
sk+1＝Π2λ(sk+ΣT(x-Σsk))
wherein, pi (·) is a threshold operator defined as
Figure BDA0002766881470000061
S3.3: if | | | sk+1-sk||2If tau is less, the iteration stops; otherwise, k is k +1, and the process proceeds to the previous step S3.2.
S3.4: output model solution
Figure BDA0002766881470000063
Rearranging the time-frequency matrix into an M multiplied by N matrix which is the ISAR echo signal obtained by the steady time-frequency analysis based on the convolution frameTime spectrum of (2).
As a specific example, the ISAR echo signal is shown in fig. 3, and is formed by overlapping 4 same chirp signals, the signal duration is 23.33 μ s, and the sampling frequency is 20MHz, so the relevant parameters in this embodiment are shown in table 1, and table 1 is as follows:
TABLE 1
N M λ τ
467 63 12 0.02
The steady time-frequency analysis method of the ISAR echo signal comprises the following specific steps:
s1: and (5) constructing a time-frequency over-complete convolution frame.
Let the frequency domain representation base phi of the time slice signal be ═ phi1,φ2,…,φM]∈CM×MIs Fourier-based, E ═ E1,e2,…,eN]∈RN×NAs an identity matrix, the convolution frame formed by convolution of phi and E is
Figure BDA0002766881470000062
The specific result (the real part of Σ) is shown in fig. 4, and is used for joint optimization modeling and numerical algorithm design.
S2: joint optimization modeling
Considering the joint representation of the time-frequency over-complete convolution frame to the original signal, a joint optimization model can be established through an approximation term and a prior constraint term, and the constraint solution of the time-frequency spectrum is realized. And (3) combining the approximation term and the prior constraint term to establish a joint optimization model of time-frequency analysis:
Figure BDA0002766881470000071
wherein λ >0 is a model regularization parameter. The model not only performs time-frequency representation on an original signal by using a time-frequency over-complete convolution frame, but also combines joint sparse prior constraint of time-frequency representation, so that the time-frequency resolution performance of time-frequency representation can be improved, cross term interference such as false images and fuzziness can be avoided, and the problems of partial signal loss, low signal-to-noise ratio and the like in ISAR echo signals can be solved.
S3: numerical algorithm design
For the above joint optimization model
Figure BDA0002766881470000072
And (4) carrying out model solution by using an iterative threshold algorithm to realize the design of a numerical algorithm. The numerical algorithm comprises the following steps:
s3.1: initializing the model parameter lambda>0. Stop threshold τ>0. Iteration step k is 0 and initial solution s0＝(ΣTΣ)-1ΣTx；
S3.2: performing iteration:
sk+1＝Π2λ(sk+ΣT(x-Σsk))
wherein, pi (·) is a threshold operator defined as
Figure BDA0002766881470000073
S3.3: if | | | sk+1-sk||2If tau is less, the iteration stops;otherwise, k is k +1, and the process proceeds to the previous step S3.2.
S3.4: output model solution
Figure BDA0002766881470000074
The time spectrum of the ISAR echo signal is obtained by rearranging the time spectrum into an M multiplied by N matrix.
The robust time-frequency analysis result of the ISAR echo signal is shown in fig. 5(c), and as a comparison method, the time-frequency analysis results based on the short-time fourier transform and the smooth pseudo wigner distribution are shown in fig. 5(a) and fig. 5(b), respectively. Compared with short-time Fourier transform, the method disclosed by the invention has higher time-frequency resolution; compared with smooth pseudo-wigner distribution, the method disclosed by the invention effectively avoids the influence of cross terms. Therefore, the method provided by the invention has better time-frequency analysis performance for ISAR echo signals.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (3)

1. A steady time-frequency analysis method for ISAR echo signals is characterized by comprising the following steps:
obtaining an ISAR echo signal;
determining a time slice signal set of the ISAR echo signal according to the ISAR echo signal; the slice signal set for the ISAR echo signals is: dividing ISAR echo signals into a plurality of signals according to a certain time slice length;
determining a frequency domain representation basis for each time slice signal in the set of time slice signals;
constructing a time-frequency over-complete convolution frame according to the frequency domain representation basis;
establishing a joint optimization model according to the time-frequency over-complete convolution frame and the ISAR echo signal;
solving by using an iterative threshold algorithm according to the joint optimization model to determine a time-frequency spectrum of the ISAR echo signal;
the constructing of the time-frequency overcomplete convolution frame according to the frequency domain representation basis specifically includes:
constructing a time-frequency over-complete convolution frame by using a formula x ═ Σ s;
wherein x is ISAR echo signal, sigma is time-frequency over-complete convolution frame,
Figure FDA0003599654230000011
Figure FDA0003599654230000012
as convolution operator, CM×MNIs a complex matrix space of M × MN dimension, S is a matrix S ═ S1,s2,…,sN]∈CM×NVector obtained by vectorization of column-by-column end-to-end, S is time frequency spectrum of time frequency analysis, phi is frequency domain representation base of time slice signal, phi ═ phi1,φ2,…,φM]E is an identity matrix, E ═ E1,e2,…,eN]M is the time slice length, and N is the length of the ISAR echo signal.
2. The robust time-frequency analysis method for an ISAR echo signal according to claim 1, wherein the building of a joint optimization model according to the time-frequency overcomplete convolution frame and the ISAR echo signal specifically includes:
using formulas
Figure FDA0003599654230000013
Determining an approximation term of the joint optimization model;
using a formula
Figure FDA0003599654230000014
Determining a priori constraint terms of s;
and determining a joint optimization model according to the approximation term and the prior constraint term.
3. The robust time-frequency analysis method for an ISAR echo signal according to claim 2, wherein the determining a joint optimization model according to the approximation term and the prior constraint term specifically includes:
using formulas
Figure FDA0003599654230000021
Determining a joint optimization model, wherein>And 0 is the regularization parameter of the joint optimization model.
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