CN109932716A - A kind of low target micro-Doppler feature extracting method - Google Patents
A kind of low target micro-Doppler feature extracting method Download PDFInfo
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Abstract
A kind of low target micro-Doppler feature extracting method is disclosed, including the following steps: the reception and pretreatment of the target echo signal through external sort algorithm irradiation；Target fine motion frequency is extracted and constructs redundant observation vector model；Construct target micro-Doppler feature Parameter Dictionary；The micro-Doppler feature of low target extracts.Under the premise of land clutter and other clutters can be filtered out well, the present invention can realize that good micro-Doppler feature extracts to the low target under the conditions of Gaussian white noise channel.
Description
Technical field
The present invention relates to external illuminators-based radar signal processing technologies, and in particular to a kind of low target micro-Doppler feature
Extracting method.
Background technique
Current low clearance area is opened gradually, a large amount of general purpose vehicles, especially unmanned plane, into low latitude field, war electricity
Magnetic environment is increasingly sophisticated, and the air defence early warning and aerial training to vital area are exerted heavy pressures on.External illuminators-based radar has good
Good " four is anti-" (Anti-antiradiation missile, anti-interference, resist stealthy, anti-low-level penetration) ability.It is based especially on commercial communication signal
External illuminators-based radar, can make full use of existing mobile communication facility, construct large-scale passive detection network, fighting
Striving has very strong survival ability in environment.It is effectively micro- more to low target to defend state sovereignty and Homeland air defense
General Le feature extracts, and to realize effective tracking and imaging to low latitude, ultra-low altitude penetration target, differentiates low target
Attribute, intention and threat degree are to realize significantly more efficient low-altitude surveillance, obtain one of key factor of initiative in war.
Currently used micro-Doppler feature extracting method has: time frequency analysis combination Hough transformation (HT) method, this side
The features such as method is simple, effective due to its is a kind of common micro-Doppler feature extracting method.But its extraction accuracy is by radar
The influence of long, time frequency analysis image the resolution ratio of echo data matrix size, the window of time frequency analysis.Orthogonal matching pursuit method,
It is a kind of efficient feature extractive technique that Y.C.Pati was proposed in 1993.This method is built upon the base of matching pursuit algorithm
On plinth, by the way that the atom in dictionary is orthogonalized processing according to Schmidt process, by signal decomposition, this is excessively complete
On standby orthogonal basis, to realize the Breaking Recurrently of signal.This method decomposition efficiency is high, fast convergence rate and simple and easy, is owing
It stands good under sampling condition.But this method it is maximum the disadvantage is that, the atomicity when characteristic parameter of extraction increases, in dictionary
Amount is significantly increased, and the operand that algorithm decomposes increases by geometric progression.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of low target micro-Doppler feature extracting method, packet
Include the following steps:
Step 1: the reception and pretreatment of the target echo signal through external sort algorithm irradiation
External sort algorithm emits LTE communication signal, after being irradiated to target, is known as target echo letter by the signal that target reflects
Number, after receiver receives signal, sampling reception is carried out to it and exports reception signal；
External sort algorithm output signal of communication be
Wherein, N is sub- carrier frequency number, and K is code length, and n is the label of sub- carrier frequency, and k is the label of code length, anFor
The weighting coefficient of n-th of sub- carrier frequency, AreFor the real part index of modulation, AimFor the imaginary part index of modulation, TpFor orthogonal frequency division multiplexing
(OFDM) symbol duration, f0For carrier frequency, Δ f is sub- carrier frequency interval；Wherein, Δ f meets OFDM orthogonality item
Part
Wherein, i, j are the number of sub- carrier frequency, indicate that the sub- carrier frequency of any two is all satisfied orthogonality condition, i.e.,
Δ f=1/Tp (3)
The target echo signal then received is
Wherein, tmFor slow time, tkFor the fast time, σ is the scattering coefficient of target, r (tm) be target respectively with external radiation
Source, receiver sum of the distance, c be vacuum in the light velocity；
Reference signal is receiver to the direct-path signal of external sort algorithm, is represented by
Wherein, D is the distance between external sort algorithm and receiver；
Assuming that the multipath clutter received in signal is preferably inhibited, more clean target echo and straight has been obtained
Up to wave, then by echo-signal and reference signal conjugate multiplication, obtains base band echo and be represented by
Wherein,For sr(tk, tm) conjugated signal；
Step 2: being extracted to target fine motion frequency and constructing redundant observation vector model
(a) redundant observation vector model
If there are a n dimensional vector n x=[x (1) ..., x (U)]TThe coordinate α under orthonormal basis Ψ, which is tieed up, in U only contains B
Nonzero element, B < < U, then claiming α is B sparse；Wherein, (1) x ..., x (U) are the coordinates under ordinary coor system；Ψ claims
For the sparse basis array of x；If in the presence of with the incoherent observing matrix Φ of ΨV×U(V < U) carries out Systems with Linear Observation, observation to vector x
As a result it can be denoted as y=Φ x=Φ Ψ α=Θ α, Θ=Φ Ψ is known as perceiving matrix in formula；Original N-dimensional signal phasor x is reduced to
The vector y of M dimension；When meeting constraint isometry condition, the rarefaction representation of signal phasor x, which can pass through, solves minimum l0Norm Solution
Certainly, i.e.,
α=arg min | | α | |0 (8)
In formula, α is the rarefaction representation of above-mentioned vector x, and α meets condition y=Φ Ψ α；
Consider the L information sources with identical sparsity structure if it exists, is denoted as X=[x1..., xL]T, by L x, i.e., X is
x1..., xLThe matrix of composition, then can use identical observing matrix, and observed result is represented by
Y=Φ X=Φ [x1..., xL] (9)
This model is known as redundant observation vector MMV model, tuple L；Using signal have identical sparsity structure this
Prior information is solved, i.e. the following equation group of simultaneous by sparse matrix order minimum
In formula, A is the rarefaction representation of X, αlIt indicates that first of information source ties up the coordinate under orthonormal basis in U, and meets item
Part Y=Φ Ψ [α1..., αL]；
(b) redundant observation vector model is constructed
For the base band echo-signal of first step output, if slow time tmWith fast time tkSampling M ' and N ' are a respectively, then
Echo-signal is represented by matrix form Sr∈RN′×M′, R indicates real number matrix in formula；Due to the variation of targeted attitude, Wu Fazhi
Resulting echo matrix will be observed as redundant observation vector S by connecingr；Therefore, the fast moment time t ' of the identical posture of target is extracteds
Base band echo, construct have identical sparsity structure redundant observation vector model, so as to ask its sparse expression
Solution；
Due to needing to extract the echo at a certain fast moment time, it is therefore desirable to this prior information of target fine motion frequency；Benefit
Target fine motion frequency f is extracted with sine FM Fourier's bessel transform；Using the fine motion frequency f ' of extraction, wherein f ' is to mention
The estimated result of the target fine motion frequency taken constructs the redundant observation vector model of base band echo
S (f ')=[sb(t′s1, t 'm1), sb(t′s2, t 'm2) ..., sb(t′sN′, t 'mN′)] (11)
Wherein, T=1/f ' is the fine motion period of target, t 'siFor fast moment time of label, t 'miFor fast moment time
t′siCorresponding slow time series, i.e. t 'mi=t 'si, t 'si+ T ..., t 'si+ LT,It is shone for same posture in radar
The number of time t appearance is penetrated,It indicates to be rounded downwards, sb(t′si, t 'mi) indicate with t 'si, t 'miFor the base band echo of parameter
Signal, i=1,2 ..., N '；
Step 3: building target micro-Doppler feature Parameter Dictionary
For specific external sort algorithm signal, the signal received in practical application contains target echo signal, direct wave letter
Number and other clutters, wherein noise signal is filtered out by existing clutter recognition means and methods；
For passing through pretreated target echo signal, redundant observation vector model is constructed according to second step, utilizes OFDM
The echo that the orthogonality of signal extracts a certain sub- carrier frequency is handled, then the carrier frequency of target is known quantity in base band echo；Assuming that
Signal amplitude and phase number are respectively P and Q in sparse dictionary, then can be expressed as { A1..., APAnd { θ1...,
θQ, then it is represented by for the sparse dictionary Ψ (f ') of parameter with matrix with f '
Wherein, sparse dictionary matrix Ψ (f ') size is M ' × PQ,For slow moment time of extraction, matrix
In row vectorThe feature vector for indicating target micro-doppler, m=1 ..., L in formula, and
Wherein,
Step 4: the micro-Doppler feature of low target extracts
After completing communication emitter Signals characteristic data set dictionary construction, for target base band echo-signal, use is orthogonal
Matching pursuit algorithm realizes that the micro-Doppler feature of low target extracts；
The micro-Doppler feature Parameter Dictionary constructed using third step, then x=Ψ α can be rewritten as
S (f ')=Ψ (f ') X (15)
Wherein, information source matrix S (f ') size is M × L, and sparse representation matrix X size is PQ × L, sparse basis array Ψ
(f ') size is M ' × PQ；
Defining down-sampled rate is
η=L/M ' (16)
Wherein M ' is slow time sampling points；
Under noise conditions, the sparse expression solution of redundant observation vector MMV model can pass through l0Norm minimum carries out
It solves
X=arg min | | X | |0 (17)
Wherein, X meets conditionε is admissible error；
In solution procedure, meet A and if only if formula (13) and (14)p=AiAnd θq=θiWhen, the X in matrix Ψ (f ')
|q+(p-1)QRow is not zero, then by extracting the non-zero row vector in matrix, therefrom extracts the amplitude and phase of target echo signal
The information such as position, are converted to the information such as radius of turn, the initial phase of target by formula and realize low target micro-doppler
The extraction of feature.
The method have the advantages that the micro-Doppler feature information of target directly can be obtained to echo signal processing,
Without carrying out feature extraction from image, the problem of image resolution ratio influences characteristic parameter extraction precision is evaded；Using multiple
Measurement vector model processes target base band echo-signal, with the increase of model tuple, in characteristic parameter extraction precision
It rises, while in the case where tuple size reaches certain condition, can all realize preferable low target micro-Doppler feature abstraction function；
Also, relative to the method using substance measurement vector model, the invention is less to the time-consuming of target signature parameter extraction.By
This all has stronger robust as it can be seen that the present invention extracts the micro-Doppler feature of low target under the conditions of different signal-to-noise ratio
Property.
Detailed description of the invention
Fig. 1 shows the location diagram between target and external sort algorithm and receiver；
Fig. 2 shows the sparse solving result figures of target base band echo-signal；
Fig. 3 shows target scattering point Doppler curve, and wherein Fig. 3 (a) shows target micro-doppler theoretical curve, and 3 (b)
Target micro-doppler reconstruct curve is shown；
Fig. 4 shows the normalized mean squared error under different tuples, and wherein Fig. 4 (a) shows radius of turn under different tuples
Normalized mean squared error, 4 (b) show the normalized mean squared error of initial phase under different tuples；
Fig. 5 shows a kind of time-consuming of low target micro-Doppler feature extracting method of the present invention under different tuples；
Fig. 6 shows the flow diagram of the method for the present invention.
Specific embodiment
Technical solution of the present invention and implementation process is discussed in detail below with reference to specific example.
Low target micro-Doppler feature extracting method of the invention includes the following steps:
Step 1: the reception and pretreatment of the target echo signal through external sort algorithm irradiation；
Location diagram between target and external sort algorithm and receiver is as shown in Figure 1, the external sort algorithm selected emits length
Phase evolution (LTE) signal of communication after being irradiated to target, is known as target echo signal by the signal that target reflects, receiver receives
After signal, sampling reception is carried out to it and exports reception signal；
External sort algorithm output signal of communication be
Wherein, N is sub- carrier frequency number, and K is code length (related with modulation system), and n is the label of sub- carrier frequency, and k is coding
The label of length, anFor the weighting coefficient of n-th of sub- carrier frequency, AreFor the real part index of modulation, AimFor the imaginary part index of modulation, TpIt is positive
Hand over frequency division multiplexing (OFDM) symbol duration, f0For carrier frequency, Δ f is sub- carrier frequency interval；
Wherein, Δ f meets OFDM orthogonality condition
Wherein, i, j are the number of sub- carrier frequency, indicate that the sub- carrier frequency of any two is all satisfied orthogonality condition herein, i.e.,
Δ f=1/Tp (3)
The target echo signal then received is
Wherein, tmFor slow time, tkFor the fast time, σ is the scattering coefficient of target, r (tm) be target respectively with external radiation
Source, receiver sum of the distance, c be vacuum in the light velocity；
Reference signal is receiver to the direct-path signal of external sort algorithm, is represented by
Wherein, D is the distance between external sort algorithm and receiver；
Assuming that the multipath clutter received in signal is preferably inhibited, more clean target echo and straight has been obtained
Up to wave, then by echo-signal and reference signal conjugate multiplication, obtains base band echo and be represented by
Wherein,For sr(tk, tm) conjugated signal；
Step 2: being extracted to target fine motion frequency and constructing redundant observation vector model；
Strong scattering point in actual environment in aerial target and extraterrestrial target is always limited, therefore aerial target and sky
Between target echo itself there is sparsity.The present invention constructs redundant observation vector model to base band echo, reduces echo matrix
Data volume, to reduce the operand of feature extraction algorithm.Redundant observation vector model is the general of substance vector observation model
It promotes, is repeatedly observed the signal of identical sparsity structure, i.e., not only each column of signal is all sparse, but also non-zero
The position of element be also it is identical, than substance measurement vector model have higher reconstruction accuracy and better anti-noise ability；
(a) redundant observation vector model
If there are a n dimensional vector n x=[x (1) ..., x (U)]TThe coordinate α under orthonormal basis Ψ, which is tieed up, in U only contains B (B
< < U) a nonzero element, then claiming α is B sparse.Wherein, (1) x ..., x (U) are the coordinates under ordinary coor system.Ψ claims
For the sparse basis array of x.If in the presence of with the incoherent observing matrix Φ of ΨV×U(V < U) carries out Systems with Linear Observation, observation to vector x
As a result it can be denoted as y=Φ x=Φ Ψ α=Θ α, Θ=Φ Ψ is known as perceiving matrix in formula.Original N-dimensional signal phasor x is reduced to
The vector y of M dimension.When meeting constraint isometry condition (condition is known to those skilled in the art), signal phasor x's is dilute
Thin expression can be by solving minimum l0Norm solves, i.e.,
α=arg min | | α | |0 (8)
In formula, α is the rarefaction representation of above-mentioned vector x, and α meets condition y=Φ Ψ α；
Consider the L information sources with identical sparsity structure if it exists, is denoted as X=[x1..., xL]T(by L x, i.e., X is
x1..., xLThe matrix of composition), then identical observing matrix can be used, observed result is represented by
Y=Φ X=Φ [x1..., xL] (9)
This model is known as redundant observation vector (MMV) model, tuple L.Using signal have identical sparsity structure this
One prior information can be minimized by sparse matrix order and be solved, is i.e. the following equation group of simultaneous
In formula, A is the rarefaction representation of X, αlIt indicates that first of information source ties up the coordinate under orthonormal basis in U, and meets item
Part Y=Φ Ψ [α1..., αL]；
(b) redundant observation vector model is constructed
For the base band echo-signal of first step output, if slow time tmWith fast time tkSampling M ' and N ' are a respectively, then
Echo-signal is represented by matrix form Sr∈RN′×M′, R indicates real number matrix in formula.Due to the variation of targeted attitude, Wu Fazhi
Resulting echo matrix will be observed as redundant observation vector S by connecingr.Therefore, the fast moment time t ' of the identical posture of target is extracteds
Base band echo, construct have identical sparsity structure redundant observation vector model, so as to ask its sparse expression
Solution；
Due to needing to extract the echo at a certain fast moment time, it is therefore desirable to this prior information of target fine motion frequency.This
Invention extracts target fine motion frequency f using sine FM Fourier bessel transform, and this method can directly carry out base band echo
Operation extracts target fine motion frequency, and precision is higher.Using the fine motion frequency f ' of extraction, wherein f ' is that the target of extraction is micro-
The estimated result of dynamic frequency constructs the redundant observation vector model of base band echo
S (f ')=[sb(t′s1, t 'm1), sb(t′s2, t 'm2) ..., sb(t′sN′, t 'mN′)] (11)
Wherein, T=1/f ' is the fine motion period of target, t 'stFor fast moment time of label, t 'miFor fast moment time
t′siCorresponding slow time series, i.e. t 'mi=t 'si, t 'si+ T ..., t 'si+ LT,It is shone for same posture in radar
The number of time t appearance is penetrated,It indicates to be rounded downwards, sb(t′si, t 'mi) indicate with t 'si, t 'miFor the base band echo of parameter
Signal, i=1,2 ..., N '；
Step 3: building target micro-Doppler feature Parameter Dictionary；
After constructing base band echo redundant observation vector model, need to carry out the model feature extraction, construction target is micro- more
General Le characteristic parameter dictionary；Using the amplitude of target base band echo-signal, initial phase, fine motion frequency as the micro- more of target
General Le characteristic parameter, due to obtaining the fine motion frequency of target by other methods, therefore with the amplitude of target base band echo-signal
With initial phase composition characteristic vector；
For specific external sort algorithm signal, the signal received in practical application contains target echo signal, direct wave letter
Number and other clutters, wherein noise signal is filtered out by existing clutter recognition means and methods；
For passing through pretreated target echo signal, redundant observation vector model is constructed according to second step, utilization is orthogonal
The echo that the orthogonality of frequency division multiplexing (OFDM) signal extracts a certain sub- carrier frequency is handled, then in base band echo target load
Frequency is known quantity.Assuming that signal amplitude and phase number are respectively P and Q in sparse dictionary, then can be expressed as
{A1..., APAnd { θ1..., θQ, then it is represented by for the sparse dictionary Ψ (f ') of parameter with matrix with f '
Wherein, sparse dictionary matrix Ψ (f ') size is M ' × PQ,For slow moment time of extraction, matrix
In row vectorThe feature vector for indicating target micro-doppler, m=1 ..., L in formula, and
Wherein,
Step 4: the micro-Doppler feature of low target extracts；
After completing communication emitter Signals characteristic data set dictionary construction, for target base band echo-signal, the present invention is adopted
Realize that the micro-Doppler feature of low target extracts with orthogonal matching pursuit algorithm；
The micro-Doppler feature Parameter Dictionary constructed using third step, then x=Ψ α can be rewritten as
S (f ')=Ψ (f ') X (15)
Wherein, information source matrix S (f ') size is M × L, and sparse representation matrix X size is PQ × L, sparse basis array Ψ
(f ') size is M ' × PQ；
Defining down-sampled rate is
η=L/M ' (16)
Wherein M ' is slow time sampling points；
Under noise conditions, the sparse expression solution of redundant observation vector (MMV) model can pass through l0Norm minimum into
Row solves
X=arg min | | X | |0 (17)
Wherein, X meets conditionε is admissible error；
In solution procedure, meet A and if only if formula (13) and (14)p=AiAnd θq=θiWhen, in matrix Ψ (f ')
X|q+(p-1)QRow is not zero, then by extracting the non-zero row vector in matrix, can therefrom extract the width of target echo signal
The information such as degree and phase, are converted to the information such as radius of turn, the initial phase of target by formula and realize that low target is micro-
The extraction of Doppler Feature.
Example test
In order to verify feasibility and robustness of the present invention in the extraction of target micro-Doppler feature, this experiment is to rotation
The micro-Doppler feature of multiple scattering points carries out Computer Simulation verifying in target, and speed is 25Hz, and to emulation
As a result it is analyzed.
Test one: the feasibility test that low target micro-doppler theory characteristic extracts
The target point of rotation to feature extraction has 3, and initial phase is respectively pi/2,5 π/3,4 π/3, radius of turn difference
For 0.68m, 3.12m, 2.94m, the test present invention extracts feasibility, test result such as Fig. 2 to low target micro-Doppler feature
It is shown.Rolling target scattering point micro-doppler curve is reconstructed using extraction result and rotates scattering point micro-doppler with target
Theoretical curve comparison, as a result as shown in Figure 3.
It can be seen that target there are three scattering point is rotated from Fig. 2 test result, the rotation of target gone out using formula scales
Radius and initial phase are respectively { 0.680m, 1.571rad }, { 2.932m, 5.759rad }, { 3.136m, 3.884rad }.From
The micro-doppler that Fig. 3 result can be seen that target scattering point reconstructs curve and its theoretical curve is more close, although initial phase
There are certain deviations on position, but swing circle is closer to amplitude, it can be achieved that preferable low target micro-Doppler feature mentions
Take function.The above test result demonstrates the present invention and realizes the feasibility that low target micro-Doppler feature extracts.
Test two: the robustness test that low target micro-doppler theory characteristic extracts
In order to verify the robustness of proposed method, consider the influence of Gaussian noise, Signal to Noise Ratio (SNR) from -10dB to 20dB,
Changed at equal intervals with 5dB, carry out 1000 Monte Carlo Experiments, in this test, the target echo signal for feature extraction is
Result under the conditions of the different signal-to-noise ratio that target echo signal passes through Matlab function awgn construction in experiment one.Fig. 4 is shown
Eigen extracting method is under the conditions of different signal-to-noise ratio to the result of low target micro-Doppler feature extraction accuracy.It is surveyed from Fig. 4
It is found that this method is in the increase with model tuple, characteristic parameter extraction precision rises test result, while reaching in tuple size
To under certain condition, preferable low target micro-Doppler feature abstraction function can be all realized.Fig. 5 show eigen extraction
Method extracts time-consuming result to low target micro-Doppler feature under the conditions of different down-sampled rates.From Fig. 5 test result
It is found that this method is relative to the method using substance measurement vector model, energy less to the time-consuming of target signature parameter extraction
It is enough more fast and effeciently to carry out feature extraction.It is right under the conditions of different signal-to-noise ratio that the above test result also demonstrates the present invention
The robustness that low target micro-Doppler feature extracts.
For the sake of illustrating to understand, Fig. 6 shows the flow diagram of the method for the present invention.
The present invention provides the low target micro-Doppler feature extracting method in the case of a kind of Gaussian white noise channel, can
Applied to automatically extracting for target micro-Doppler feature.
Claims (1)
1. a kind of low target micro-Doppler feature extracting method, including the following steps:
Step 1: the reception and pretreatment of the target echo signal through external sort algorithm irradiation
External sort algorithm emits LTE communication signal, after being irradiated to target, is known as target echo signal by the signal that target reflects, connects
After receipts machine receives signal, sampling reception is carried out to it and exports reception signal；
External sort algorithm output signal of communication be
Wherein, N is sub- carrier frequency number, and K is code length, and n is the label of sub- carrier frequency, and k is the label of code length, anFor n-th of son
The weighting coefficient of carrier frequency, AreFor the real part index of modulation, AimFor the imaginary part index of modulation, TpContinue for orthogonal frequency division multiplex OFDM symbol
Time, f0For carrier frequency, Δ f is sub- carrier frequency interval；
Wherein, Δ f meets OFDM orthogonality condition
Wherein, i, j are the number of sub- carrier frequency, indicate that the sub- carrier frequency of any two is all satisfied orthogonality condition, i.e.,
Δ f=1/Tp (3)
The target echo signal then received is
Wherein, tmFor slow time, tkFor the fast time, σ is the scattering coefficient of target, r (tm) be target respectively with external sort algorithm, connect
The sum of the distance of receipts machine, c are the light velocity in vacuum；
Reference signal is receiver to the direct-path signal of external sort algorithm, is represented by
Wherein, D is the distance between external sort algorithm and receiver；
Assuming that the multipath clutter received in signal is preferably inhibited, more clean target echo and direct wave have been obtained,
Then by echo-signal and reference signal conjugate multiplication, obtains base band echo and be represented by
Wherein,For sr(tk, tm) conjugated signal；
Step 2: being extracted to target fine motion frequency and constructing redundant observation vector model
(a) redundant observation vector model
If there are a n dimensional vector n x=[x (1) ..., x (U)]TThe coordinate α under orthonormal basis Ψ, which is tieed up, in U only contains B non-zero entry
Element, B < < U, then claiming α is B sparse；Wherein, (1) x ..., x (U) are the coordinates under ordinary coor system；Ψ is known as the dilute of x
Dredge basic matrix；If in the presence of with the incoherent observing matrix Φ of ΨV×U(V < U) carries out Systems with Linear Observation to vector x, and observed result can be remembered
For y=Φ x=Φ Ψ α=Θ α, Θ=Φ Ψ is known as perceiving matrix in formula；Original N-dimensional signal phasor x is reduced to the vector of M dimension
y；When meeting constraint isometry condition, the rarefaction representation of signal phasor x, which can pass through, solves minimum l0Norm solves, i.e.,
α=argmin | | α | |0 (8)
In formula, α is the rarefaction representation of above-mentioned vector x, and α meets condition y=Φ Ψ α；
Consider the L information sources with identical sparsity structure if it exists, is denoted as X=[x1..., xL]T, X is by L x, i.e. x1..., xL
The matrix of composition, then can use identical observing matrix, and observed result is represented by
Y=Φ X=Φ [x1..., xL] (9)
This model is known as redundant observation vector MMV model, tuple L；There is this priori of identical sparsity structure using signal
Information is solved, i.e. the following equation group of simultaneous by sparse matrix order minimum
In formula, A is the rarefaction representation of X, αlIt indicates that first of information source ties up the coordinate under orthonormal basis in U, and meets condition Y=Φ
Ψ[α1..., αL]；
(b) redundant observation vector model is constructed
For the base band echo-signal of first step output, if slow time tmWith fast time tkSampling M ' and N ' are a respectively, then echo is believed
Number it is represented by matrix form Sr∈RN′×M′, R indicates real number matrix in formula；Due to the variation of targeted attitude, will can not directly see
Resulting echo matrix is surveyed as redundant observation vector Sr；Therefore, the fast moment time t ' of the identical posture of target is extractedsBase band
Echo constructs the redundant observation vector model with identical sparsity structure, so as to solve to its sparse expression；
Due to needing to extract the echo at a certain fast moment time, it is therefore desirable to this prior information of target fine motion frequency；Using just
String frequency modulation Fourier's bessel transform extracts target fine motion frequency f；Using the fine motion frequency f ' of extraction, wherein f ' is the mesh extracted
The estimated result of fine motion frequency is marked, the redundant observation vector model of base band echo is constructed
S (f ')=[sb(t′s1, t 'm1), sb(t′s2, t 'm2) ..., sb(t′sN′, t 'mN′)] (11)
Wherein, T=1/f ' is the fine motion period of target, t 'siFor fast moment time of label, t 'miFor fast moment time t 'siIt is right
The slow time series answered, i.e. t 'mi=t 'si, t 'si+ T ..., t 'si+ LT,It is same posture in radar illumination
Between t occur number,It indicates to be rounded downwards, sb(t′si, t 'mi) indicate with t 'si, t 'miFor the base band echo-signal of parameter, i
=1,2 ..., N '；
Step 3: building target micro-Doppler feature Parameter Dictionary
For specific external sort algorithm signal, the signal received in practical application contain target echo signal, direct-path signal and
Other clutters, wherein noise signal is filtered out by existing clutter recognition means and methods；
For passing through pretreated target echo signal, redundant observation vector model is constructed according to second step, utilizes ofdm signal
Orthogonality extract the echo of a certain sub- carrier frequency and handled, then the carrier frequency of target is known quantity in base band echo；Assuming that sparse
Signal amplitude and phase number are respectively P and Q in dictionary, then can be expressed as { A1..., APAnd { θ1..., θQ, then
It is represented by for the sparse dictionary Ψ (f ') of parameter with matrix with f '
Wherein, sparse dictionary matrix Ψ (f ') size is M ' × PQ,For slow moment time of extraction, in matrix
Row vectorThe feature vector for indicating target micro-doppler, m=1 ..., L in formula, and
Wherein,
Step 4: the micro-Doppler feature of low target extracts
After completing communication emitter Signals characteristic data set dictionary construction, for target base band echo-signal, using orthogonal matching
Tracing algorithm realizes that the micro-Doppler feature of low target extracts；
The micro-Doppler feature Parameter Dictionary constructed using third step, then x=Ψ α can be rewritten as
S (f ')=Ψ (f ') X (15)
Wherein, information source matrix S (f ') size is M × L, and sparse representation matrix X size is PQ × L, and sparse basis array Ψ (f ') is big
Small is M ' × PQ；
Defining down-sampled rate is
η=L/M ' (16)
Wherein M ' is slow time sampling points；
Under noise conditions, the sparse expression solution of redundant observation vector MMV model can pass through l0Norm minimum is solved
X=argmin | | X | |0 (17)
Wherein, X meets conditionε is admissible error；
In solution procedure, meet A and if only if formula (13) and (14)p=AiAnd θq=θiWhen, the X in matrix Ψ (f ') |q+(p-1)Q
Row is not zero, then by extracting the non-zero row vector in matrix, therefrom extracts the letter such as amplitude and phase of target echo signal
Breath, is converted to the information such as radius of turn, the initial phase of target by formula and realizes low target micro-Doppler feature
It extracts.
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