CN108133232A - A kind of Radar High Range Resolution target identification method based on statistics dictionary learning - Google Patents

A kind of Radar High Range Resolution target identification method based on statistics dictionary learning Download PDF

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CN108133232A
CN108133232A CN201711350910.2A CN201711350910A CN108133232A CN 108133232 A CN108133232 A CN 108133232A CN 201711350910 A CN201711350910 A CN 201711350910A CN 108133232 A CN108133232 A CN 108133232A
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dictionary
matrix
sample
frame
father
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CN108133232B (en
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袁家雯
刘文波
朱海霞
陈旺才
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2415—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on parametric or probabilistic models, e.g. based on likelihood ratio or false acceptance rate versus a false rejection rate
    • G06F18/24155—Bayesian classification

Abstract

The invention discloses a kind of Radar High Range Resolution target identification methods based on statistics dictionary learning, including obtaining the continuous HRRP original signals of T class targets, and it are pre-processed；Father's frame is divided by two subframes according to maximum probability difference arithmetic, obtains initialization statistics dictionary；Relevant parameter is configured before dictionary training is counted；Training obtains optimal dictionary and transposed matrix；Test identification classification is carried out using transposed matrix to HRRP original signals to be measured.The method of the present invention is applied especially to the HRRP target identifications under Low SNR, has better recognition performance compared to single statistical modeling and dictionary learning method.

Description

A kind of Radar High Range Resolution target identification method based on statistics dictionary learning
Technical field
The present invention relates to Radar Technology, more particularly to a kind of Radar High Range Resolution mesh based on statistics dictionary learning Mark recognition methods.
Background technology
Radar Target Recognition is one of important research direction of Radar Signal Processing.High Range Resolution (HRRP) it is the amplitude wave-shape of vector sum that the target scattering idea echo obtained with radar signal projects on radar ray.By Target physical arrangement information itself can be accurately reflected in HRRP, so being widely used in meteorological, aviation and target identification The fields of grade.
Target identification based on Radar High Range Resolution belongs to grinding for pattern recognition theory and field of radar cross discipline Study carefully scope, therefore the technological difficulties that radar HRRP target identifications are related to are more.Research both at home and abroad is pointed out azimuthal sensitivity, is put down at present It is that radar HRRP target identifications need the primary three major issues solved to move sensibility and strength sensitive.(1) strength sensitive：By In radar it is possible that being operated in the bad weathers such as sleet, the HRRP that same target is received so as to cause radar is deposited in amplitude The different scale calibrations the problem of.Common solution have l1, l2 norm normalization (HRRP echoes amplitude compression to 0 to 1 it Between) and extraction intensity invariant features.(2) sensibility is translated：Since most object to be measured is kept in motion, can not ensure Radar target is in the relative position apart from window, so causing to will appear translation sensibility during intercept signal.It is related Alignment schemes, absolute alignment schemes and extraction shift-invariant operator are to solve the problems, such as this common method.(3) azimuth sensitivity Property：When target reaches certain angle relative to radar rotation, the scattering point of target is with respect to radar line of sight generation distance and angle Range walk phenomenon is got in mobile and then generation scattering causes HRRP to change rapidly.
It is maximum to solve difficulty for azimuthal sensitivity wherein in three big sensitive questions, how effectively to overcome azimuthal sensitivity from And extracting steady target signature becomes the key of radar HRRP target identification technologies.The uniform framing method of original adoption is to HRRP Angular domain divides, and extraction frame inner average HRRP samples are identified as matching template.Later it is found that uniformly framing method is not HRRP statistical natures can be described very well, therefore some correlative studys use the method that angular domain adaptively divides to improve target identification Rate, but how effective solution is not proposed yet to the problems such as reasonable framing of target angular domain and extraction robust feature.
Invention content
Goal of the invention：To solve the deficiencies in the prior art, provide it is a kind of be suitable for Low SNR under, compared to single Statistical modeling and dictionary learning method have better recognition performance based on statistics dictionary learning radar high-resolution distance As target identification method.
Technical solution：The invention discloses a kind of Radar High Range Resolution target identification sides based on statistics dictionary learning Method includes the following steps：
(1) the continuous HRRP original signals of T class targets are obtained, and it is pre-processed；
(2) father's frame is divided by two subframes according to maximum probability difference arithmetic, obtains initialization statistics dictionary；
(3) relevant parameter is configured before dictionary training is counted；
(4) training obtains optimal dictionary and linear classifier；
(5) test identification classification is carried out using linear classifier to HRRP original signals to be measured.
Further, radar continuously receives T classification target radar high resolution range profile numbers successively in the step (1) According to, and it is orderly to the continuous multiple HRRP original signals of the i-th class targetMake l2After norm normalization The pretreatment of power spectrum characteristic is asked for, power spectrum characteristic calculation formula is：
Power spectrum the first half feature is chosen as feature samples collection in father's frameWherein i=1 ..., T, That is, feature samples collection Y in father's frameiIn j-th of sample yjIt is represented by：
yj=[fj(1),fj(2),…,fj(m)] (2)。
Further, the step (2) includes：
(21) Class-conditionaldensity function in father's frame is calculated
According to PPCA models, feature samples collection Y in father's frameiIn j-th of sample yjFollowing form can be represented again：
yj=Aix+μi+εi(3)；
In formula, AiFor feature samples collection Y in father's frameiIn projection matrix；X is hidden variable, Gaussian distributed N (0, In)； μiFor feature samples collection Y in father's frameiAverage vector；εiFor noise vector, N (0, σ is obeyed2Im), so in i-th classification target father's frame Class-conditionaldensity function is as follows：
p(yj|Yi2 π of)=()-n/2|(σi)2Im+AiA'i|-1/2exp[-1/2(yj-μi)'((σi)2Im+AiA'i)-1(yi- μi)] (4)；
Wherein, σiFor noise vector amplitude, ImUnit matrix is tieed up for m；
(22) father's frame is divided into two subframes
Frame boundary line θ is set by feature samples collection Y in father's frameiIt is divided intoWithTwo subframes, estimate by maximum likelihood method MeterThe average vector of subframe PPCA modelsNoise vector amplitudeAnd projection matrix
Wherein,For covariance matrixK-th of characteristic value, () ' table Show the transposition of matrix,And Λ(i,n)The corresponding eigenvectors matrix of respectively preceding n characteristic value and eigenvalue matrix, InFor n Tie up unit matrix, m ImDimension；Simultaneously by feature samples collection Y in father's frameiMiddle sample yjIt substitutes intoClass conditional probability density Function obtains probability valueIts total sample number is Ni；Then by probability valueMaximum probability difference is substituted into calculate Method：
By the power spectrum characteristic corresponding to variable k more new frame boundary θ and record frame boundary θ, so as to which father's frame be divided into Two subframes；
Posterior probability is calculated by Bayesian formula：
Assuming that prior probabilityIt derives
(23) ifTwo frames that then step (22) is generated jump to step as new training sample Suddenly (1)；If otherwiseContinue to execute step (24)；
(24) initialization statistics dictionary D is obtained0
Further, the step (3) includes the following steps：
(31) the feature samples collection Y in every classification target father's frameiIn select before d power spectrum characteristic structure formAnd then Form the training sample set of statistics dictionaryWherein N=T × d；
(32) order matrixAnd by row l2Norm normalization statistics initialization dictionary D0；
(33) according to YtrainAnd D0Said target classification, first definition differentiate sparse coding matrix Q, wherein element qijIt is located at The i-th row jth arranges in Q matrixes, and qijJ-th of sample belongs to same class in i-th of atom and training sample in=1 expression dictionary Not；Secondly class label H, wherein element h are definedijThe i-th row jth arranges in H-matrix, and hijJth in=1 meaning training sample A sample belongs to the i-th class target.
Further, the step (4) includes the following steps：
(41) distinguished number is optimized using the sparse conformance error of atom, constrains the object function of dictionary learning
On the basis of dictionary learning, introduce the sparse conformance error optimization of atom and differentiateConstrain dictionary learning Object function：
In formula, Y is input signal, selects Y heretrainFor input signal, i.e. Y=Ytrain；D=[dj]j∈[1,K]∈Rm×K For excessively complete dictionary, each column vector d in DjReferred to as dictionary atom；X=[xj]j∈[1,K]∈RK×NFor sparse coding matrix, by each A row vector xjIt forms；Q∈RN×KTo differentiate sparse coding matrix；A be linear transformation matrix, define linear transformation g (A, x)= Ax；H∈RT×KFor class label；W is linear classifier, defines linear transformation f (W, x)=Wx；L is the sparse of sparse coefficient vector Degree；E is all 1's matrix；Transposition of the M for sparse codings of the Θ through dictionary D linear expressions, abbreviation transposed matrix, i.e. Θ=DM'；For reconstructed error,To identify sparse error,For error in classification,It is dilute for atom Conformance error is dredged, α, beta, gamma is respectively the weight of corresponding error term；Effect is to constrain sample sparse coefficient as far as possible Similar to the sparse coefficient of Θ, MX essence is inner product of the sparse coding with sample sparse coding of Θ, and MX is got over closer to E, sample With dictionary pattern matching；
In order to solve the object function in formula (11), X can be obtained with OMP algorithms0=OMP (D0,Y,L),M0=OMP (D0, Θ, L) ', it can obtain A with polynary ridge regression model0=(XX'- λ1I)-1XQ', W0=(XX'- λ2I)-1XH' generally takes λ1=λ2 =1.And object function can be converted to K-SVD solution procedurees：
It enables, DnewFor matrixl2Row normalizing under norm Change, so formula (12) is further rewritten into：
(42) training obtains optimal dictionary and linear classifier.
Further, the step (42) includes the following steps：
Step1：L2Row normalization under norm, enables k=0；
Step2：Fixed kth time dictionaryKth time sparse coefficient matrix X is updated by OMP algorithms(k)；
Step3：The dictionary stage is updated by row：
To kth time errorCarry out SVD decomposition：
Update j-th of atom in kth time dictionary
Update jth row vector x in kth time sparse coefficient matrix(k),j：x(k),j=Σ (1,1) V (:,1)；
In above formula, x(k),iFor the i-th row vector in sparse coefficient matrix, U and V are orthogonal matrix, and Σ isIt is unusual Value matrix；
Step4：K=k+1 is enabled, if k>K, training terminate, output dictionary DnewWith transposed matrix Mnew；Otherwise Step2 is returned It continues cycling through；
Step5：It updates to obtain D by K-SVD algorithmsnewIts any one row j has Wherein dj、aj、wjAnd mjThe respectively jth column vector of D, A, W and M, the transposition of () ' representing matrix；So D, W, A, M cannot It is directly tested, it must be converted into respectively Conversion formula is as follows：
So as to obtain optimal dictionaryAnd transposed matrix
Further, the step (5) includes the following steps：
(51) to Radar High Range Resolution test sample stestCarry out l2After norm normalization work(is asked for according to formula (18) The pretreatment of rate spectrum signature, as formula (19) obtains pretreated test feature sample ytest：
ytest=[ftest(1),ftest(2),…,ftest(m)] (19)；
(52) problems with is solved with OMP algorithms：Acquire test feature sample ytestAsk for relatively optimal dictionarySparse coefficient
(53) it enablesThen test sample be judged to Θ (:, maxIndex) belonging to class Not.
Advantageous effect：Compared with prior art, the Radar High Range Resolution mesh of the invention based on statistics dictionary learning Mark recognition methods has the following advantages：
(1) dictionary will be incorporated the advantages of HRRP targe-aspect sensitivities can be effectively solved the problems, such as in traditional statistical modeling algorithm Model is practised, the linear classifier for being more suitable for radar HRRP target identifications is obtained, so as to fulfill the standard to Low SNR signal Really identification.
(2) the method for the present invention is completed to the extraction of robust feature and the design of grader simultaneously in a short time, compared to biography Classifier design after the target identification method elder generation feature extraction of system, had both substantially reduced the time of training stage, and had also improved spy The separability of sign, so as to reach preferable classifying quality in linear classifier.
(3) method of the invention, the HRRP target identifications being applied especially under Low SNR, compared to single statistics Modeling and dictionary learning method have better recognition performance.Wherein, it is gradually increased with the signal-to-noise ratio of signal, counts dictionary Learning method averagely improves 3 percentage points compared to statistical modeling method accuracy of identification, compared to other dictionary learning algorithm accuracy of identification Averagely improve 2 percentage points.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is the normalization HRRP signals and power spectrum characteristic comparison schematic diagram under the conditions of different postures and signal-to-noise ratio, warp It is maximum similar as comparison schematic diagram in the normalization HRRP signal averaging vector sum frames of noise pollution；
Fig. 3 is the probability differential chart based on maximum probability difference arithmetic；
Fig. 4 is the probability distribution graph based on maximum probability difference arithmetic；
Fig. 5 is each method discrimination comparison diagram under different signal-to-noise ratio.
Specific embodiment
Technical scheme of the present invention is described in detail below in conjunction with the accompanying drawings, so that the purpose of the present invention, technical solution And advantage is more explicit.
The present invention proposes a kind of Radar High Range Resolution target identification method based on statistics dictionary learning.First, To target, continuous HRRP original signals do pretreatment and obtain father's frame training sample set；Then with based on probability principal component (PPCA) the maximum probability difference criterion of model realizes the division to father's frame training sample set, and getting frame boundary on this basis Corresponding power spectrum characteristic forms initialization dictionary, so as to eliminate radar HRRP orientation and translation sensibility；Then, in dictionary learning On the basis of, the sparse conformance error optimization criterion of atom is introduced to train to obtain optimal dictionary and transposed matrix.More than Optimization design makes the robust feature extraction of complete paired samples and grader to set simultaneously in its learning process in statistics dictionary It counts, the target identification method of design grader reduces a large amount of training times after more traditional first extraction feature, improves identification Performance and the robustness to noise.
Radar High Range Resolution target identification method proposed by the present invention based on statistics dictionary learning, general flow chart is such as Shown in Fig. 1.(a) and (b) depicts HRRP number of echoes through normalized of the target under different orientations respectively in Fig. 2 According to how rationally the comparison same target of two graph discoveries HRRP peak values under different direction position occur and significantly change, therefore Target angular domain is divided, is one of the problem to be solved in the present invention.Signal shown in (b) is after serious noise pollution in Fig. 2 In Fig. 2 shown in (c), (d) describes in Fig. 2 that HRRP signals ask for power spectrum characteristic in (b) in Fig. 2, finds power spectrum characteristic There is certain robustness to noise.Based on this, the present invention is passed through using initialization atom of the power spectrum characteristic as statistics dictionary The better feature of robustness is extracted to the optimization for counting dictionary.
As shown in Figure 1, the Radar High Range Resolution target identification method based on statistics dictionary learning of the present invention, is divided into Initialize dictionary, dictionary training and test phase.Training stage uses the maximum probability difference principle based on PPCA models first The adaptive target angular domain that divides corresponds to power spectrum characteristic with getting frame boundary, these features are formed initialization statistics dictionary.Its The secondary sparse conformance error optimization criterion of introducing atom so that while dictionary learning is counted, generation one is based on atom The linear classifier of sparse similarity factor.Test phase directly acquires sparse coefficient of the sample to be tested based on statistics dictionary, then Sparse coefficient is substituted into grader and carries out target identification.Specifically include following steps：
Initialize the dictionary stage：
(1) the continuous HRRP original signals of T class targets are obtained, and it is pre-processed
Radar continuously receives T classification target radar high resolution range profile data (HRRP original signals) successively, and orderly To the continuous multiple HRRP original signals S of the i-th class targeti=[s1,s2,…,sN] make l2Power spectrum spy is asked for after norm normalization The pretreatment of sign, power spectrum characteristic calculation formula are：
Power spectrum the first half feature is chosen as feature samples collection Y in father's framei=[y1,y2,…,yNi], wherein i=1 ..., T.That is, feature samples collection Y in father's frameiIn j-th of sample yjIt is represented by：
yj=[fj(1),fj(2),…,fj(m)] (2)。
(2) father's frame is divided by two subframes according to maximum probability difference arithmetic, obtains initialization statistics dictionary
(21) Class-conditionaldensity function in father's frame is calculated
According to PPCA models, feature samples collection Y in father's frameiIn j-th of sample yjFollowing form can be represented again：
yj=Aix+μi+εi(3)；
In formula, AiFor feature samples collection Y in father's frameiIn projection matrix；X is hidden variable, Gaussian distributed N (0, In),；μiFor feature samples collection Y in father's frameiAverage vector；εiFor noise vector, N (0, σ is obeyed2Im).So the i-th classification target Class-conditionaldensity function is as follows in father's frame：
p(yj|Yi2 π of)=()-n/2|(σi)2Im+AiA'i|-1/2exp[-1/2(yj-μi)'((σi)2Im+AiA'i)-1(yi- μi)] (4)；
Wherein, σiFor noise vector amplitude, ImUnit matrix is tieed up for m.
(22) father's frame is divided into two subframes
Frame boundary line θ is set by feature samples collection YiIt is divided intoWithTwo subframes estimate subframe by maximum likelihood method The average vector of PPCA modelsNoise vector amplitudeAnd projection matrix
Wherein,For covariance matrixK-th of characteristic value, () ' table Show the transposition of matrix,And Λ(i,n)The corresponding eigenvectors matrix of respectively preceding n characteristic value and eigenvalue matrix, InFor n Tie up unit matrix, m ImDimension.Simultaneously by feature samples collection Y in father's framei(total sample number Ni) in sample yjIt substitutes into's Class-conditionaldensity function obtains probability valueThen by probability valueMaximum probability difference is substituted into calculate Method：
By the power spectrum characteristic corresponding to variable k more new frame boundary θ and record frame boundary θ, so as to which father's frame be divided into Two subframes.
Posterior probability is calculated by Bayesian formula：
Assuming that prior probabilityIt derivesWith reference to Fig. 3 and Fig. 4 is it is found that be directed to frame boundary line front half section, preceding k sample mean class conditional probabilityIncreasingly greater than frame Interior average class conditional probabilityI.e. preceding k sample mean posterior probabilityIncrease with k；For frame Boundary line second half section, preceding k sample mean class conditional probabilityGradually it is less than frame inner average class conditional probabilityI.e. preceding k sample mean posterior probabilityReduce with k, meaning frame boundary line θ or so targets Attitudes vibration is apparent, thus formula (8) can find frame boundary line and realize that angular domain divides.
(23)Two frames that then step (22) is generated jump to step as new training sample (1)；If otherwiseContinue to execute step (3).
(3) initialization statistics dictionary D is obtained0
Training stage：
(1) relevant parameter configuration is carried out before dictionary training is counted
(11) the feature samples collection Y in every classification target father's frameiIn select before d power spectrum characteristic structure formAnd then Form the training sample set of statistics dictionaryWherein N=T × d；；
(12) order matrixAnd by row l2Norm normalization statistics initialization dictionary D0；
(13) according to YtrainAnd D0Said target classification, first definition differentiate sparse coding matrix Q, wherein element qijIt is located at The i-th row jth arranges in Q matrixes, and qijJ-th of sample belongs to same class in i-th of atom and training sample in=1 expression dictionary Not；Secondly class label H, wherein element h are definedijThe i-th row jth arranges in H-matrix, and hijJth in=1 meaning training sample A sample belongs to the i-th class target.
(2) training obtains optimal dictionary and linear classifier
(21) distinguished number is optimized using the sparse conformance error of atom, constrains the object function of dictionary learning
On the basis of dictionary learning, introduce the sparse conformance error optimization of atom and differentiateConstrain dictionary learning Object function：
In formula, Y is input signal, selects Y heretrainFor input signal, i.e. Y=Ytrain；D=[dj]j∈[1,K]∈Rm×K For excessively complete dictionary, each column vector d in DjReferred to as dictionary atom；X=[xj]j∈[1,K]∈RK×NFor sparse coding matrix, by each A row vector xjIt forms；Q∈RN×KTo differentiate sparse coding matrix；A be linear transformation matrix, define linear transformation g (A, x)= Ax；H is class label；W is linear classifier, defines linear transformation f (W, x)=Wx；L is the degree of rarefication of sparse coefficient vector；E is All 1's matrix；Transposition of the M for sparse codings of the Θ through dictionary D linear expressions, abbreviation transposed matrix, i.e. Θ=DM'. For reconstructed error,To identify sparse error,For error in classification,For the sparse similar mistake of atom Difference, α, beta, gamma are respectively the weight of corresponding error term.Effect is that constraint sample sparse coefficient is as dilute with Θ as possible Sparse coefficient is similar.MX essence is inner product of the sparse coding with sample sparse coding of Θ, and MX is got over and dictionary closer to E, sample Match.
In order to solve the object function in formula (11), X can be obtained with OMP algorithms0=OMP (D0,Y,L),M0=OMP (D0, Θ, L) ', it can obtain A with polynary ridge regression model0=(XX'- λ1I)-1XQ', W0=(XX'- λ2I)-1XH' generally takes λ1=λ2 =1.And object function can be converted to K-SVD solution procedurees：
It enables, DnewFor matrixl2Row normalizing under norm Change.So formula (11) is further rewritten into：
(22) training obtains optimal dictionary and linear classifier
Based on this, the dictionary training step of formula (13) is provided：
Step1：L2Row normalization under norm, enables k=0；
Step2：Fixed kth time dictionaryKth time sparse coefficient matrix X is updated by OMP algorithms(k)；
Step3：The dictionary stage is updated by row：
To kth time errorCarry out SVD decomposition：
Update j-th of atom in kth time dictionary
Update jth row vector x in kth time sparse coefficient matrix(k),j：x(k),j=Σ (1,1) V (:,1)；
In above formula, x(k),iFor the i-th row vector in sparse coefficient matrix, U and V are orthogonal matrix, and Σ isIt is strange Different value matrix；
Step4：K=k+1 is enabled, if k>K, training terminate, output dictionary DnewWith transposed matrix Mnew；Otherwise Step2 is returned It continues cycling through.
Step5：It updates to obtain D by K-SVD algorithmsnewIts any one row j has, Wherein dj、aj、wjAnd mjThe respectively jth column vector of D, A, W and M, the transposition of () ' representing matrix.So D, W, A, M cannot It is directly tested, it must be converted into respectively Conversion formula is as follows：
So as to obtain optimal dictionaryAnd transposed matrix
Test phase：
(1) to Radar High Range Resolution test sample stestCarry out l2After norm normalization work(is asked for according to formula (18) The pretreatment of rate spectrum signature, as formula (19) obtains pretreated test feature sample ytest：
ytest=[ftest(1),ftest(2),…,ftest(m)] (19)。
(2) problems with is solved with OMP algorithms：Acquire test feature sample ytestAsk for relatively optimal dictionarySparse coefficient
(3) it enablesThen test sample be judged to Θ (:, maxIndex) and generic.
This experiment uses the three classes airplane data that certain ISAR experimental radar is surveyed：Amp- 26, the diploma, Ya Ke -42, every section of instruction It is 1300 to practice sample number, i.e., 1300 HRRP time domain samples are randomly selected in data segment, first locate time domain HRRP data in advance After reason again carry out statistics dictionary training, data segment after not extracting remaining HRRP samples (sum is 26000) as test specimens This.Table 1 provides the aircraft HRRP discriminations handled by the present invention.
1 three kinds of aircraft discriminations of table
Fig. 5 describes discrimination change curve obtained by various methods under different signal-to-noise ratio simultaneously, there it can be seen that statistics Dictionary learning method recognition performance under the conditions of low signal-to-noise ratio or high s/n ratio is optimal.Understand from physical significance, Under Low SNR,Reconstructed error constrains influence of the noise to linear model；Under the conditions of high s/n ratio,The sparse conformance error of atom constrains the sparse coefficient of sample similar to the sparse coefficient of matrix Θ.

Claims (7)

1. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning, which is characterized in that including following Step：
(1) the continuous HRRP original signals of T class targets are obtained, and it is pre-processed；
(2) father's frame is divided by two subframes according to maximum probability difference arithmetic, obtains initialization statistics dictionary；
(3) relevant parameter is configured before dictionary training is counted；
(4) training obtains optimal dictionary and linear classifier；
(5) test identification classification is carried out using linear classifier to HRRP original signals to be measured.
2. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning according to claim 1, It is characterized in that, radar continuously receives T classification target radar high resolution range profile data successively in the step (1), and have Sequence to the continuous multiple HRRP original signals of the i-th class targetMake l2Work(is asked for after norm normalization The pretreatment of rate spectrum signature, power spectrum characteristic calculation formula are：
Power spectrum the first half feature is chosen as feature samples collection in father's frameWherein i=1 ..., T, that is, Feature samples collection Y in father's frameiIn j-th of sample yjIt is represented by：
yj=[fj(1),fj(2),…,fj(m)] (2)。
3. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning according to claim 1, It is characterized in that, the step (2) includes：
(21) Class-conditionaldensity function in father's frame is calculated
According to PPCA models, feature samples collection Y in father's frameiIn j-th of sample yjFollowing form can be represented again：
yj=Aix+μi+εi(3)；
In formula, AiFor feature samples collection Y in father's frameiIn projection matrix；X is hidden variable, Gaussian distributed N (0, In)；μiFor Feature samples collection Y in father's frameiAverage vector；εiFor noise vector, N (0, σ is obeyed2Im), so class in i-th classification target father's frame Conditional probability density function is as follows：
p(yj|Yi2 π of)=()-n/2|(σi)2Im+AiA'i|-1/2exp[-1/2(yj-μi)'((σi)2Im+AiA'i)-1(yi- μi)] (4)；
Wherein, σiFor noise vector amplitude, ImUnit matrix is tieed up for m；
(22) father's frame is divided into two subframes
Frame boundary line θ is set by feature samples collection Y in father's frameiIt is divided intoWithTwo subframes, estimate by maximum likelihood method The average vector of subframe PPCA modelsNoise vector amplitudeAnd projection matrix
Wherein,For covariance matrixK-th of characteristic value, () ' represent square The transposition of battle array,And Λ(i,n)The corresponding eigenvectors matrix of respectively preceding n characteristic value and eigenvalue matrix, InIt is tieed up for n single Bit matrix, m ImThe dimension of matrix.Simultaneously by feature samples collection Y in father's frameiMiddle sample yjIt substitutes intoClass conditional probability density Function obtains probability valueIts total sample number is Ni；Then by probability valueMaximum probability difference is substituted into calculate Method：
By the power spectrum characteristic corresponding to variable k more new frame boundary θ and record frame boundary θ, so as to which father's frame is divided into two Subframe；
Posterior probability is calculated by Bayesian formula：
Assuming that prior probabilityIt derives
(23) ifTwo frames that then step (22) is generated jump to step as new training sample (1)；If otherwiseContinue to execute step (24)；
(24) initialization statistics dictionary D is obtained0
The corresponding power spectrum characteristics of all frame boundary θ recorded are formed into initial statistical dictionaryFinally obtain each classification Target initialization statistics dictionary is combined into the initialization statistics dictionary based on radar HRRP target identifications
4. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning according to claim 1, It is characterized in that, the step (3) includes the following steps：
(31) the feature samples collection Y in every classification target father's frameiIn select before d power spectrum characteristic structure formAnd then it forms Count the training sample set of dictionaryWherein N=T × d；
(32) order matrixAnd by row l2Norm normalization statistics initialization dictionary D0；
(33) according to YtrainAnd D0Said target classification, first definition differentiate sparse coding matrix Q, wherein element qijPositioned at Q squares The i-th row jth arranges in battle array, and qijJ-th of sample belongs to same category in i-th of atom and training sample in=1 expression dictionary；Its It is secondary to define class label H, wherein element hijThe i-th row jth arranges in H-matrix, and hijJ-th of sample in=1 meaning training sample Belong to the i-th class target.
5. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning according to claim 1, It is characterized in that, the step (4) includes the following steps：
(41) distinguished number is optimized using the sparse conformance error of atom, constrains the object function of dictionary learning
On the basis of dictionary learning, introduce the sparse conformance error optimization of atom and differentiateConstrain the target of dictionary learning Function：
In formula, Y is input signal, selects Y heretrainFor input signal, i.e. Y=Ytrain；D=[dj]j∈[1,K]∈Rm×KIt is excessively complete Standby dictionary, each column vector d in DjReferred to as dictionary atom；X=[xj]j∈[1,K]∈RK×NFor sparse coding matrix, from each row to Measure xjIt forms；Q∈RN×KTo differentiate sparse coding matrix；A is linear transformation matrix, defines linear transformation g (A, x)=Ax；H∈ RT×KFor class label；W is linear classifier, defines linear transformation f (W, x)=Wx；L is the degree of rarefication of sparse coefficient vector；E is All 1's matrix；Transposition of the M for sparse codings of the Θ through dictionary D linear expressions, abbreviation transposed matrix, i.e. Θ=DM'； For reconstructed error,To identify sparse error,For error in classification,For the sparse similar mistake of atom Difference, α, beta, gamma are respectively the weight of corresponding error term；Effect is that constraint sample sparse coefficient is as dilute with Θ as possible Sparse coefficient is similar, and MX essence is inner product of the sparse coding with sample sparse coding of Θ, and MX is got over and dictionary closer to E, sample Match；
In order to solve the object function in formula (11), X can be obtained with OMP algorithms0=OMP (D0,Y,L),M0=OMP (D0,Θ, L) ', it can obtain A with polynary ridge regression model0=(XX'- λ1I)-1XQ', W0=(XX'- λ2I)-1XH' generally takes λ1=λ2=1. And object function can be converted to K-SVD solution procedurees：
It enablesDnewFor matrixl2Row normalization under norm, So formula (12) is further rewritten into：
(42) training obtains optimal dictionary and linear classifier.
6. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning according to claim 5, It is characterized in that, the step (42) includes the following steps：
Step1：ForL2Row normalization under norm, enables k=0；
Step2：Fixed kth time dictionaryKth time sparse coefficient matrix X is updated by OMP algorithms(k)；
Step3：The dictionary stage is updated by row：
To kth time errorCarry out SVD decomposition：
Update j-th of atom in kth time dictionary
Update jth row vector x in kth time sparse coefficient matrix(k),j：x(k),j=Σ (1,1) V (:,1)；
In above formula, x(k),iFor the i-th row vector in sparse coefficient matrix, U and V are orthogonal matrix, and Σ isSingular value square Battle array；
Step4：K=k+1 is enabled, if k>K, training terminate, output dictionary DnewWith transposed matrix Mnew；Otherwise Step2 is returned to continue Cycle；
Step5：It updates to obtain D by K-SVD algorithmsnewIts any one row j has Wherein dj、aj、wjAnd mjThe respectively jth column vector of D, A, W and M, the transposition of () ' representing matrix, so D, W, A, M cannot It is directly tested, it must be converted into respectivelyConversion formula is as follows：
So as to obtain optimal dictionaryAnd transposed matrix
7. a kind of Radar High Range Resolution target identification method based on statistics dictionary learning according to claim 1, It is characterized in that, the step (5) includes the following steps：
(51) to Radar High Range Resolution test sample stestCarry out l2After norm normalization power spectrum is asked for according to formula (18) The pretreatment of feature, as formula (19) obtains pretreated test feature sample ytest：
ytest=[ftest(1),ftest(2),…,ftest(m)] (19)；
(52) problems with is solved with OMP algorithms：Acquire test feature sample ytestIt asks for Relatively optimal dictionarySparse coefficient
(53) it enablesThen test sample be judged to Θ (:, maxIndex) and generic.
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