CN107219510B - Radar target identification method based on unlimited largest interval linear discriminant projection model - Google Patents

Radar target identification method based on unlimited largest interval linear discriminant projection model Download PDF

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CN107219510B
CN107219510B CN201710351886.8A CN201710351886A CN107219510B CN 107219510 B CN107219510 B CN 107219510B CN 201710351886 A CN201710351886 A CN 201710351886A CN 107219510 B CN107219510 B CN 107219510B
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陈渤
刘宁
文伟
刘宏伟
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Xian University of Electronic Science and Technology
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Abstract

The invention proposes a kind of radar target identification methods based on unlimited largest interval linear discriminant projection model, for solving the low technical problem of discrimination present in existing radar target identification method.Realize step are as follows: obtain power spectrum characteristic training sample set X category label collection y corresponding with its；Construct unlimited largest interval linear discriminant projection model；Define the expression formula that unlimited largest interval linear discriminant projection model combines pseudo- Posterior distrbutionp；Set the initial value that unlimited largest interval linear discriminant projection model combines parameters in the expression formula of pseudo- Posterior distrbutionp；Indicate that unlimited largest interval linear discriminant projection model combines the Condition Posterior Distribution of parameters in pseudo- Posterior distrbutionp；The Condition Posterior Distribution of the parameters represented is sampled；Obtain power spectrum characteristic test sample collectionCategory of test label set corresponding with itsObtain the discrimination of radar target.The present invention can be used for carrying out detection identification to Radar High Range Resolution.

Description

Radar target identification method based on infinite maximum interval linear discriminant projection model
Technical Field
The invention belongs to the technical field of radars, relates to a radar target identification method, and particularly relates to a target identification method of a radar of an infinite interval linear discrimination projection model, which can be used for detecting and identifying a radar high-resolution range profile.
Background
The radar target mark is a technical means adopted by radar for identifying a found target in a search volume of the radar target mark, and the principle is to realize the judgment of the type of the target by utilizing a radar echo signal of the target. The broadband radar usually works in an optical area, a radar target can be regarded as being composed of a large number of scattering points with different intensities, and a high-resolution range profile HRRP is a vector sum of echo signals of all the scattering points on the target body obtained by using broadband radar signals. The method reflects the distribution of scattering points on a target body along the radar sight line, and comprises important structural information of the target, such as the size of the target, the structure of the scattering points and the like. Therefore, at the end of the twentieth century, some scholars proposed a technology for automatically identifying radar targets by using HRRP, and after the twenty-first century, the technology has attracted extensive attention in the radar field, see [ s.p.
In the high frequency region, the scattering center model describes the electromagnetic scattering properties of the target. According to the model, when the target posture is greatly changed, the MTRC of the scattering center range unit walking can occur, namely, part of the scattering centers can move from one range unit to another range unit, and the HRRP of the target is caused to be changed violently; and when the posture is changed slightly, the MTRC does not appear. As described above, the HRRP is sensitive to the target pose, and the HRRP of the same target has a multi-mode distribution characteristic, which tends to make the distribution of data in the HRRP space have non-linear separability, which affects the effect and application of the common target identification method. The HRRP automatic identification method is classified into three categories: template matching based methods, compressed sensing based methods, and classifier model based methods. The template matching based method is that a series of reference images, namely templates, are constructed from marked training images, the testing images and the templates are respectively matched and are classified into the most similar templates, and the complexity of the method is higher because the number and the dimension of the stored templates are generally larger; constructing an over-complete library based on a compressed sensing method, calculating sparse representation of a test sample on a training sample, carrying out image reconstruction and carrying out classification and identification according to a reconstruction error minimum criterion, wherein the identification rate of the method is reduced to a great extent due to the influence of noise or a shelter in HRRP; the method based on the classifier model comprises the steps of firstly carrying out feature extraction on target area slices to obtain a training sample set and a testing sample set, constructing the classifier model through the training samples with labels and carrying out parameter calculation, then inputting the test samples without labels into the classifier model to calculate class labels, and completing target identification.
In the existing machine learning theory, Principal Component Analysis (PCA), Independent Component Analysis (ICA) Factor Analysis (FA) and the like are unsupervised feature extraction methods, and features extracted by the techniques are not necessarily suitable for a rear-end classification task; in order to fully utilize class information, a large number of supervised class feature extraction methods are provided, a representative method is Linear Discriminant Analysis (LDA), the LDA maximizes the inter-class distance of a sample after projection, and simultaneously minimizes the intra-class distance, so that the separability of data can be effectively improved. However, LDA is highly dependent on the distribution of Data, which limits the application of LDA, and for this problem, a large number of researchers have proposed different solutions, among which there are representative Subclass Discriminant Analysis (SDA) methods, which divide the original Data into several subclasses, modify the intra-class and inter-class covariance matrices, and improve the applicability of LDA methods, and although these methods have achieved good results on some Data sets, these methods are two-stage feature extraction methods, which are not tightly coupled with the back-end classification task and may cause a loss of classification performance, in order to avoid this loss [ b.chen, h.zhang, x.zhang et.al, Max-margin discrete projection view Data evaluation [ J ]. IEEE Transactions on Knowledge and Data engineering.2015, (27) (7) SVM 1976, which proposes a Bayesian model, the projection characteristics are used as the input of the hidden variable SVM classifier, and the projection space and the SVM classifier are subjected to combined learning under the framework of a Bayesian model, so that the performance loss caused by stage learning is effectively avoided, and the target recognition rate is improved.
In the above methods, both the staged learning and the joint learning have a common problem: the methods all belong to global feature extraction methods, namely, the samples are expected to be separable in a projection space through a global projection matrix. However, for data which is not linearly separable, especially for data with a multi-mode distribution structure, due to the fact that the data ignores structure information which is implicit in the data, the global projection method may bring loss of classification performance, and the recognition rate is low.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a radar target identification method based on an infinite interval linear discrimination projection model, and aims to solve the technical problem of low identification rate in the conventional radar target identification method.
The technical idea of the invention is as follows: aiming at data with multi-mode distribution, the idea of a mixed expert model is introduced into an MMLDP model, and an infinite-margin linear discriminant projection model (iMMLDP) is provided. Specifically, immlddp divides a data set into 'infinite' subsets by a dp (dirichlet process) hybrid model, learns a local MMLDP classifier on each subset, and combines the local classifiers to achieve global nonlinear projection and classification. In addition, IMMLDP unifies the data set division, the projection subspace learning and the classifier learning under the framework of a Bayesian model, guides the data set division and the projection subspace learning through classification errors, and well ensures the linear separability of each local region.
According to the technical idea, the technical scheme adopted for achieving the purpose of the invention comprises the following steps:
(1) acquiring a power spectrum characteristic training sample set X and a class label set y corresponding to the power spectrum characteristic training sample set X:
(1a) the radar receives the high-resolution range profiles of the N C-type targets to obtain N high-resolution range profiles;
(1b) extracting the power spectrum characteristics of each high-resolution range profile in the N high-resolution range profiles to obtain a power spectrum characteristic training sample set X ═ X1,x2,…,xn,…,xNAnd expressing the class label corresponding to the power spectrum characteristic training sample set X by a class label set y: y ═ y1,y2,…,yn,…,yNN denotes the total number of training samples, xnDenotes the nth sample, ynClass label y indicating class n samplen∈{1,2,…,C}；
(2) Constructing an infinite maximum interval linear discriminant projection model: unifying a Dirichlet process DP mixed model, a projection model and a hidden variable SVM classifier under a Bayesian model framework to obtain an infinite interval linear discrimination projection model;
(3) an infinite maximum interval linear discriminant projection model combined pseudo posterior distribution is defined, and the expression is as follows:
wherein, ω iscRepresenting class c classifier parameters, distribution obeys N (0, beta)c -1I) Classifier hyperparameter betac～Ga(a0,b0) C belongs to {1,2, …, D }, and D represents the initial total cluster number; a. thec＝[ac1,ac2,…,ack，…，acK]Projection matrix representing class c samples, c ∈ {1,2, …, D }, ackIs represented by AcColumn k ofκk～Ga(c0,d0) K represents AcThe total number of columns; z ═ Z1,z2,…,zn,…,zN]Representing a feature sample set obtained by projecting a sample set X and simultaneously being input into a hidden variable SVM classifier, znDenotes the nth sample xnFeature samples, z, obtained after projectionnHas an initial distribution of N (A)Τxn,Ι)；{μc，∑cDenotes the distribution parameter, μ, of the class c samplescRepresents the mean, Σ, of the class c samplecCovariance matrix representing class c samples, class c distribution parameter { μ }c,ΣcThe initial distribution is the Normal-Wishart distribution, i.e. { mu. }c,Σc}～NW({μc,Σc}|μ0,W0,ν0,β0) In which μ0,W0,ν0,β0Is an initial distribution parameter; h ═ h1,h2,…,hn,…,hN]Representing a set of clustering indicator variables, hnRepresenting a training sample xnTo which class, hn∈{1,2,…,D}；υ＝[υ1,υ2,…,υc,…,υC]Representing the parameters of a Dirichlet process DP mixed model based on a Stick-breaking structure, the distribution of upsilon is Beta (1, alpha), and the distribution of alpha is Ga (e)0,f0) (ii) a X represents a training sample, and y represents a class label corresponding to the training sample; n (-) denotes a Gaussian distribution, Ga (-) denotes a Gamma distribution, NW (-) denotes a Normal-Wishart distribution, (. degree)TRepresenting a transpose operation;
(4) setting initial values of all parameters in an expression of the infinite maximum interval linear discriminant projection model combined pseudo posterior distribution:
setting a class c classifier parameter ωcIs a random matrix of K +1 dimensions, obeying an N (0,1) distribution, class c classifier parameters ωcThe initial value of the covariance accuracy beta is Ga (10) compliant31) distributed random vectors, class c sample projection matrix AcThe initial value of (1) is the eigenvector corresponding to the first K large eigenvalues of the covariance matrix of the training sample set X, the initial value of the characteristic sample set Z is a K multiplied by N dimensional random matrix obeying N (0,1) distribution, and the c type distribution parameter { muc,ΣcThe initial value of is a NW ({ mu ] subject to a Normal-Wishart distributionc,Σc}|μ0,W0,ν0,β0) Wherein mu is0＝0,W0＝10-5I,ν0＝K+1,β0＝10-3The initial distribution of the parameter upsilon of the Dirichlet process DP mixed model is Beta (1,1), and the initial value of the aggregation parameter alpha is set to be Ga (1, 10)-10) A distributed random number;
(5) joint pseudo posterior distribution expression of linear discriminant projection model for representing infinite maximum intervalConditional posterior distribution of the individual parameters: class c classifier parameters ωcConditional posterior distribution p (ω)c-, class c sample projection matrix AcThe k-th column a ofc,kConditional posterior distribution of (a) p (a)c,k-), the kth sample line Z of the n sample of the feature sample set Zk,nConditional posterior distribution of (1) p (z)k,n| -), class c distribution parameter { μc,ΣcConditional posterior distribution of p ({ μ })c,ΣcThe method comprises the following steps of } | -, condition posterior distribution p (h | -) of a clustering indication variable h, and condition posterior distribution p (upsilon | -) of a parameter upsilon of a Dirichlet process DP mixed model;
(6) sampling the conditional posterior distribution of each parameter shown in step (5): according to the Gibbs sampling method, combining the infinite maximum interval linear discriminant projection model shown in the step (5) with the pseudo posterior distribution expressionConditional posterior distribution of each parameter, in turn I0Sub-cycle sampling of wherein0Is a natural number from the I0+1 start per interval SPSub-saving the parameter ω in each projection subspacec,AcDistribution parameterSampling the result and saving T0Sampling results of the secondary parameters;
(7) obtaining a power spectrum feature test sample setAnd its corresponding test class label set
(7a) Radar receptionObtaining high-resolution range profile of the C-class targetA high-resolution range profile;
(7b) extraction ofObtaining the power spectrum characteristic test sample set of each high-resolution range profile in the high-resolution range profileAnd testing the sample setCorresponding class label passes the test class label setRepresents:wherein,represents the total number of the test samples,which represents the n-th sample of the sample,class label representing class n sample
(8) Obtaining the recognition rate of the radar target:
(8a) using a cluster indicator variable hnFor test sample setClustering is carried out, and the clustering result passes through a c-th type sample projection matrix AcProjecting the data to a projection subspace of a linear discriminant projection model with infinite maximum intervals to obtain a test feature sample setWherein the test is specificSample collectionComprising a plurality of subsets;
(8b) by saved class c classifier parameters omegacTo the test feature sample setClassifying to obtain a test sample setClass label set of
(8c) Test class label setAnd test sample setClass label set ofAnd comparing to obtain the identification rate of the radar target.
Compared with the prior art, the invention has the following advantages:
1) according to the method, the HRRP radar high-resolution range profile data set is divided into 'infinite' subsets through a DP process, an MMLDP model is learned in each subset, and clustering and classification are jointly learned, so that a hidden linear structure in data can be effectively mined. Compared with the target identification technology of the existing radar, the target identification rate of the radar is improved, and particularly, the effect is more obvious under the condition that the target has the multimode distribution characteristic.
2) The invention unifies the division of the data set, the projection subspace and the learning of the SVM classifier under the Bayesian framework for joint learning, thereby avoiding the classification performance loss caused by a two-stage classification method. Meanwhile, simple projection models and classifiers are respectively learned on each subset, and compared with the prior art that one projection model and one classifier are independently trained on the whole data set, the complexity of the models is reduced.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
the flow of the whole experiment is shown.
FIG. 2 shows the posterior clustering quantity results of the measured data experiment.
Detailed description of the preferred embodiments (explained and illustrated in the technical solution)
The invention is described in detail below with reference to the following figures and specific examples:
referring to fig. 1, the radar target identification method based on the infinite maximum interval linear discriminant projection model includes the following steps:
step (1) obtaining a power spectrum characteristic training sample set X and a corresponding class label set y:
(1a) the radar receives 600 high-resolution range profiles of the 3 types of targets to obtain 600 high-resolution range profiles.
(1b) Extracting the power spectrum characteristics of each high-resolution range profile in 600 high-resolution range profiles to obtain a power spectrum characteristic training sample set X ═ X1,x2,…,xn,…,xNAnd expressing the class label corresponding to the power spectrum characteristic training sample set X by a class label set y: y ═ y1,y2,…,yn,…,yN}，xnDenotes the nth sample, ynClass label y indicating class n samplen∈{1,2,3}。
Step (2) constructing an infinite maximum interval linear discriminant projection model, and the implementation steps are as follows:
(2a) representing a dirichlet process DP hybrid model based on a Stick-breaking construct:
υc|α～Beta(1,α),θc|G0～G0,c＝1,2,…,∞
hn|π(υ)～Mult(π(υ)),xn|hn＝c；θc～p(x|θc),n＝1,...,N
wherein upsilon iscIs a parameter of the proportion of the cutting stick,denotes the length of each truncated stick, alpha is upsiloncA priori distribution parameters of (a) to (e) Ga (e)0,f0)；θcDenotes xnDistribution parameter of thetacHas a distribution of G0，G0Representing the distribution of bases, the distribution of bases being set to Normal-Wishart distribution, i.e. G0～NW({μc,Σc}|μ0,W0,ν0,β0)；hnIs xnWhen h is an indicator ofnWhen c denotes xnBelonging to class c, i.e. xn～p(x|θc)。
(2b) Representing the projection model in each cluster:
the projection model based on the MMLDP model can be represented as: z is a radical ofn～N(AΤxn,I),κk～Ga(c0,d0) Wherein a represents a global projection matrix a ═ a1,a2,…,ak]，akColumn k, x, representing AnDenotes the nth sample, κkIs akA priori distribution parameter of c0And d0Is κkHyper-parameters of the parameters.
The projection model in each cluster can be represented as:
zn|hn＝c,Ac～N(Ac Τxn,Ip),Ac＝[ac1,ac2，…，ack，…，acK]
wherein, when clustering indicates variable hnWhen c is equal, znObey mean value of Ac ΤxnThe covariance matrix is IpP denotes the dimension of the identity matrix I.
(2c) A model representing hidden variable SVM classifiers in each cluster:
setting the parameter of the c hidden variable SVM classifier to obey prior distributionRespectively bringing the prior distribution of each hidden variable SVM classifier into each hidden variable SVM classifier to obtain a model of the hidden variable classifier in each cluster, wherein the model can be expressed as:
wherein λ ═ λ1,λ2,…,λc，…，λC]Representing hidden variables, λ, in a hidden variable SVM classifiercAnd (4) representing the hidden variables in the c-th hidden variable SVM classifier.
(2d) Unifying a Dirichlet process DP mixed model, a projection model and a hidden variable SVM classifier under a Bayesian model framework to obtain an infinite interval linear discrimination projection model, wherein the hierarchical structural formula is as follows:
hn|π(υ)～Disc(π(υ))
xn|hn＝c,{μc,Σc}～p(xn|{μc,Σc}),n＝1,...,N.
yn,{λn}c|{zn,hn＝c},ωc～φ(yn,λn|ωc,zn),c＝1,...,∞
{μc,Σc}～NW(μ0,W0,ν0,β0)
obtaining the nth sample x according to the hierarchical expression of the formulanLikelihood distribution function of (1):
step (3) defines the combined pseudo posterior distribution of the infinite maximum interval linear discriminant projection model, and the concrete expression form is as follows:
setting initial values of all parameters in an expression of the infinite maximum interval linear discriminant projection model combined pseudo posterior distribution:
setting a class c classifier parameter ωcIs a random matrix of K +1 dimensions, obeying an N (0,1) distribution, class c classifier parameters ωcThe initial value of the covariance accuracy beta is Ga (10) compliant31) distributed random vectors, class c sample projection matrix AcThe initial value of (1) is the eigenvector corresponding to the first K large eigenvalues of the covariance matrix of the training sample set X, the initial value of the characteristic sample set Z is a K multiplied by N dimensional random matrix obeying N (0,1) distribution, and the c type distribution parameter { muc,ΣcThe initial value of is a NW ({ mu ] subject to a Normal-Wishart distributionc,Σc}|μ0,W0,ν0,β0) Wherein mu is0＝0,W0＝10-5I,ν0＝K+1,β0＝10-3The initial distribution of the parameter upsilon of the Dirichlet process DP mixed model is Beta (1,1), and the initial value of the aggregation parameter alpha is set to be Ga (1, 10)-10) A distributed random number.
Step (5) represents the combined pseudo posterior distribution expression of the infinite maximum interval linear discriminant projection modelThe condition posterior distribution of each parameter comprises the following steps:
(5a) represents the class c classifier parameters ωcThe condition posterior distribution of (a), expressed as:
wherein:
βcis a hyper-parameter of the class c classifier.
(5b) Representing a projection matrix A of class c samplescThe k-th column a ofc,kConditioned posterior distribution, manifestation thereof
Comprises the following steps:
wherein:
xnrefers to class c samples, κc,kDenotes ac,kThe parameter, κ, within the prior distributionck～Ga(c0,d0)。
(5c) K line Z representing the n sample of the feature sample set Zk,nThe condition posterior distribution of (a), expressed as:
wherein:
wherein Andcorresponding to the mean and covariance matrices of the conditional posterior distribution, respectively.
(5d) Distribution parameter [ mu ] representing class c samplec,ΣcA condition posterior distribution of the form:
wherein:
υ'c＝υ0+Nc
β'c＝β0+Nc
Ncindicates the number of class c samples,represents the mean value of the class c samples,represents the mean of the covariance matrix of the class c samples.
(5e) A conditional posterior distribution representing a cluster indicator variable, expressed in the form of:
p(h|-)＝Disc(h；π)
and picSubject to the constraint of
(5f) The condition posterior distribution, expressed as:
p(υc|-)∝p(h|υ)Beta(υc；1,α)～Beta(υc；ρa,ρb)
where ρ isa＝1+Nc，NkIndicating the number of class k samples.
(5g) Hidden variable lambda representing hidden variable SVM classifiernThe condition posterior distribution of (a), expressed as:
wherein IG (.) represents an inverse gaussian distribution.
(5h) Is represented by betacThe condition posterior distribution of (a), expressed as:
wherein
(5i) Denotes kappac,kThe condition posterior distribution of (a), expressed as:
wherein
(5j) A conditional posterior distribution representing α, expressed as:
wherein e'0＝e0+D-1，
(6) Sampling the conditional posterior distribution of each parameter shown in step (5): according to the Gibbs sampling method, combining the infinite maximum interval linear discriminant projection model shown in the step (5) with the pseudo posterior distribution expressionThe conditional posterior distribution of each parameter is sequentially sampled 400 times in a cycle, and the parameter omega in each projection subspace is saved every 10 times from the 401 st timec,AcDistribution parameterSampling results, and storing the sampling results of the 10 times parameters.
Step (7) obtaining a power spectrum characteristic test sample setAnd its corresponding test class label set
(7a) And the radar receives the high-resolution range profiles of 2400 3 types of targets to obtain 2400 high-resolution range profiles.
(7b) Extracting the power spectrum characteristics of each high-resolution range profile in 2400 high-resolution range profiles to obtain a power spectrum characteristic test sample setAnd testing the sample setCorresponding class label passes the test class label setRepresents:wherein,which represents the n-th sample of the sample,class label representing class n sample
(8) Obtaining the recognition rate of the radar target:
(8a) using a cluster indicator variable hnFor test sample setClustering is carried out, and the clustering result passes through a c-th type sample projection matrix AcProjecting the data to a projection subspace of a linear discriminant projection model with infinite maximum intervals to obtain a test feature sample setWherein the feature sample set is testedComprising a plurality of subsets; cluster indicator variable hnDeterminingThe subset size and number of, hnThe expression is as follows:
p(hn|-)＝Disc(hn(ii) a Pi) and
step (8b) through saved class c classifier parameters omegacTo the test feature sample setClassifying to obtain a test sample setClass label set ofThe method comprises the following implementation steps:
ρ＝[ρ1,ρ2,...,ρc,...,ρD]
wherein,and representing weight coefficients of the hidden variable SVM classifier in the c cluster of the t sample, wherein m is 1,2,3, and t is 1,2cRepresents the average output of the c-th hidden variable SVM classifier,the m value corresponding to the maximum value is shown.
(8c) Test class label setAnd test sample setClass label set ofAnd comparing to obtain the identification rate of the radar target.
The technical effects of the invention are explained in detail by combining simulation experiments and actual measurement data experiments as follows:
1. simulation experiment
(1) Conditions of the experiment
The data set adopted in the experiment is a Benchmark data set in UCI Machine Learning reproducibility, and three more complex data sets of Heart, Splice and Twinorm are selected from the Benchmark data set.
(2) Analysis of experimental content and results
In the experiment, original data is used as input of a model, four methods of LDA + SVM, MMLDP, k-mean + MMLDP and IMMLDP are used for classifying and identifying data sets, each method is repeated for 10 times, 50% of the methods are randomly extracted as training samples each time, and the rest are used as testing samples. The average recognition performance of 10 times is taken as the final recognition rate under different hidden space dimensions, and the optimal recognition rate of each method under different hidden space dimensions is listed in table 1.
TABLE 1 recognition rates of different methods on different data
From table 1 we can see that the classification performance of IMMLDP on different datasets is superior to other methods. Compared with the recognition rate of the MMLDP model, the IMMLDP model shows that the data are clustered firstly, and the learning of one projection model in each cluster is superior to the global projection model method. Compared with the Km + MMLDP model recognition rate, the IMMLDP model shows that the IMMLDP performs joint learning on clustering, classifiers and projection, and discloses a hidden structure of data, so that the recognition performance is remarkably improved.
2 actual measurement data experiment
(1) Conditions of the experiment
The invention adopts c-band radar to process the actually measured HRRP data of three types of airplane targets. The amplitude sensitivity of the HRRP is eliminated by adopting a modulo-2 norm normalization method, the translation sensitivity of the HRRP is eliminated by extracting the power spectrum characteristic of the HRRP, namely the obtained sample data set is the power spectrum characteristic of the HRRP, and in an experiment, the upper limit of the adopted cutting stick is set to be 10.
(2) Analysis of experimental content and results
The identification results obtained by selecting 600 power spectrum features as training samples and 2400 power spectrum features as test samples in the dimensionality of the 3-dimensional hidden space are shown in table 2.
TABLE 2 IMMLDP clustering and Performance analysis on Radar high-resolution range profiles
The posterior number of clusters obtained by IMMLDP is shown in FIG. 2, and it can be seen that the number of effective clusters is three, and it can be seen from Table 2 that better classification precision is obtained inside each cluster, which benefits from that we perform joint learning on a cluster subspace and a classifier, and ensures good classification performance in each cluster, thereby improving the overall classification performance and improving the recognition rate of radar targets.

Claims (4)

1. A radar target identification method based on an infinite interval linear discriminant projection model comprises the following steps:
(1) acquiring a power spectrum characteristic training sample set X and a class label set y corresponding to the power spectrum characteristic training sample set X:
(1a) the radar receives the high-resolution range profiles of the N C-type targets to obtain N high-resolution range profiles;
(1b) extracting the power spectrum characteristics of each high-resolution range profile in the N high-resolution range profiles to obtain a power spectrum characteristic training sample set X ═ X1,x2,···,xn,···,xNAnd expressing the class label corresponding to the power spectrum characteristic training sample set X by a class label set y: y ═ y1,y2,···,yn,···,yNN denotes the total number of training samples, xnDenotes the nth sample, ynClass label y indicating class n samplen∈{1,2,···,C}；
(2) Constructing an infinite maximum interval linear discriminant projection model: unifying a Dirichlet process DP mixed model, a projection model and a hidden variable SVM classifier under a Bayesian model framework to obtain an infinite interval linear discrimination projection model, wherein the implementation steps are as follows:
(2a) representing a dirichlet process DP hybrid model based on a Stick-breaking construct:
υc|α～Beta(1,α),θc|G0～G0,c＝1,2,…，∞
hn|π(υ)～Mult(π(υ)),xn|hn＝c；θc～p(x|θc),n＝1,...,N
wherein upsilon iscIs a parameter of the proportion of the cutting stick,denotes the length of each truncated stick, alpha is upsiloncA priori distribution parameters of (a) to (e) Ga (e)0,f0)；θcDenotes xnDistribution parameter of thetacHas a distribution of G0，G0Representing the distribution of bases, the distribution of bases being set to Normal-Wishart distribution, i.e. G0～NW({μc,Σc}|μ0,W0,ν0,β0)；hnIs xnWhen h is an indicator ofnWhen c denotes xnBelonging to class c, i.e. xn～p(x|θc)；
(2b) Representing the projection model in each cluster:
the projection model based on the MMLDP model can be represented as: z is a radical ofn～N(AΤxn,I),κk～Ga(c0,d0) Wherein a represents a global projection matrix a ═ a1,a2,…，ak]，akColumn k, x, representing AnDenotes the nth sample, κkIs akA priori distribution parameter of c0And d0Is κkA hyper-parameter of the parameter;
the projection model in each cluster can be represented as:
zn|hn＝c,Ac～N(Ac Τxn,Ip),Ac＝[ac1,ac2，…，ack，…，acK]
κk～Ga(c0,d0)
wherein, when clustering indicates variable hnWhen c is equal, znObey mean value of Ac ΤxnThe covariance matrix is IpP represents the dimension of the identity matrix I;
(2c) a model representing hidden variable SVM classifiers in each cluster:
setting the parameter of the c hidden variable SVM classifier to obey prior distributionRespectively bringing the prior distribution of each hidden variable SVM classifier into each hidden variable SVM classifier to obtain a model of the hidden variable classifier in each cluster, wherein the model can be expressed as:
βc～Ga(a0,b0)
wherein λ ═ λ1,λ2,…，λc，…，λC]Representing hidden variables, λ, in a hidden variable SVM classifiercRepresenting hidden variables in the c hidden variable SVM classifier;
(2d) unifying a Dirichlet process DP mixed model, a projection model and a hidden variable SVM classifier under a Bayesian model framework to obtain an infinite interval linear discrimination projection model, wherein the hierarchical structural formula is as follows:
υc|α～Beta(1,α)；α～Ga(e0,f0)
hn|π(υ)～Disc(π(υ))
xn|hn＝c,{μc,Σc}～p(xn|{μc,Σc}),n＝1,...,N.
Ac＝[ac,1,...,ac,K]
yn,{λn}c|{zn,hn＝c},ωc～φ(yn,λn|ωc,zn),c＝1,...,∞
β～Gama(a0,b0)
κc,k～Gama(c0,d0)
{μc,Σc}～NW(μ0,W0,ν0,β0)
obtaining the nth sample x according to the hierarchical expression of the formulanLikelihood distribution function of (1):
(3) an infinite maximum interval linear discriminant projection model combined pseudo posterior distribution is defined, and the expression is as follows:
wherein, ω iscRepresenting class c classifier parameters, distribution obeys N (0, beta)c -1I) Classifier hyperparameter betac～Ga(a0,b0) C belongs to {1,2, …, D }, and D represents the initial total cluster number; a. thec＝[ac1,ac2,…，ack，…，acK]Projection matrix representing class c samples, c ∈ {1,2, …, D }, ackIs represented by AcColumn k ofκk～Ga(c0,d0) K represents AcThe total number of columns; z ═ Z1,z2,…,zn,…，zN]Representing a feature sample set obtained by projecting a sample set X and simultaneously being input into a hidden variable SVM classifier, znDenotes the nth sample xnFeature samples, z, obtained after projectionnHas an initial distribution of N (A)Τxn,Ι)；{μc，∑cDenotes the distribution parameter, μ, of the class c samplescRepresents the mean, Σ, of the class c samplecCovariance matrix representing class c samples, class c distribution parameter { μ }c,ΣcThe initial distribution is the Normal-Wishart distribution, i.e. { mu. }c,Σc}～NW({μc,Σc}|μ0,W0,ν0,β0) In which μ0,W0,ν0,β0Is an initial distribution parameter; h ═ h1,h2,…,hn,…，hN]Representing a set of clustering indicator variables, hnRepresenting a training sample xnTo which class, hn∈{1,2,…，D}；υ＝[υ1,υ2,…,υc,…，υC]Representing the parameters of a Dirichlet process DP mixed model based on a Stick-breaking structure, the distribution of upsilon is Beta (1, alpha), and the distribution of alpha is Ga (e)0,f0) (ii) a X represents a training sample, and y represents a class label corresponding to the training sample; n (-) denotes a Gaussian distribution, Ga (-) denotes a Gamma distribution, NW (-) denotes a Normal-Wishart distribution, (. degree)TDenotes a transpose operation, a0，b0Is betacC of a hyper-parameter of0,d0Is κkHyper-parameters of parameters, e0，f0A hyperparameter of α;
(4) setting initial values of all parameters in an expression of the infinite maximum interval linear discriminant projection model combined pseudo posterior distribution:
setting a class c classifier parameter ωcIs a random matrix of K +1 dimensions, obeying an N (0,1) distribution, class c classifier parameters ωcThe initial value of the covariance accuracy beta is Ga (10) compliant31) distributed random vectors, class c sample projection matrix AcThe initial value of (1) is the eigenvector corresponding to the first K large eigenvalues of the covariance matrix of the training sample set X, the initial value of the characteristic sample set Z is a K multiplied by N dimensional random matrix obeying N (0,1) distribution, and the c type distribution parameter { muc,ΣcThe initial value of is a NW ({ mu ] subject to a Normal-Wishart distributionc,Σc}|μ0,W0,v0,β0) Wherein mu is0＝0,W0＝10-5I,ν0＝K+1,β0＝10-3The initial distribution of the parameter upsilon of the Dirichlet process DP mixed model is Beta (1,1), and the initial value of the aggregation parameter alpha is set to be subject to Ga (1,1)0-10) A distributed random number;
(5) joint pseudo posterior distribution expression of linear discriminant projection model for representing infinite maximum intervalConditional posterior distribution of the individual parameters: class c classifier parameters ωcConditional posterior distribution p (ω)c-, class c sample projection matrix AcThe k-th column a ofc,kConditional posterior distribution of (a) p (a)c,k-), the kth sample line Z of the n sample of the feature sample set Zk,nConditional posterior distribution of (1) p (z)k,n| -), class c distribution parameter { μc,ΣcConditional posterior distribution of p ({ μ })c,ΣcThe method comprises the following steps of } | -, condition posterior distribution p (h | -) of a clustering indication variable h, and condition posterior distribution p (upsilon | -) of a parameter upsilon of a Dirichlet process DP mixed model;
(6) sampling the conditional posterior distribution of each parameter shown in step (5): according to the Gibbs sampling method, combining the infinite maximum interval linear discriminant projection model shown in the step (5) with the pseudo posterior distribution expressionConditional posterior distribution of each parameter, in turn I0Sub-cycle sampling of wherein0Is a natural number from the I0+1 start per interval SPSub-saving the parameter ω in each projection subspacec,AcDistribution parameterAnd storing T0Sampling results of the secondary parameters;
(7) obtaining a power spectrum feature test sample setAnd its corresponding test class label set
(7a) Radar receptionObtaining high-resolution range profile of the C-class targetA high-resolution range profile;
(7b) extraction ofObtaining the power spectrum characteristic test sample set of each high-resolution range profile in the high-resolution range profileAnd testing the sample setCorresponding class label passes the test class label setRepresents:wherein,represents the total number of the test samples,which represents the n-th sample of the sample,class label representing class n sample
(8) Obtaining the recognition rate of the radar target:
(8a) using a cluster indicator variable hnFor test sample setClustering is carried out, and the clustering result passes through a c-th type sample projection matrix AcProjecting the data to a projection subspace of a linear discriminant projection model with infinite maximum intervals to obtain a test feature sample setWherein the feature sample set is testedComprising a plurality of subsets;
(8b) by saved class c classifier parameters omegacTo the test feature sample setClassifying to obtain a test sample setClass label set of
(8c) Test class label setAnd test sample setClass label set ofAnd comparing to obtain the identification rate of the radar target.
2. The radar target recognition method based on the infinity spaced linear discriminant projection model according to claim 1, wherein the step (3) of defining the infinity spaced linear discriminant projection model is combined with the pseudo-posterior distribution, which is expressed in the following specific form:
3. the method for radar target recognition based on the infinity spaced linear discriminant projection model according to claim 1, wherein the expression of the combined pseudo-posterior distribution of the infinity spaced linear discriminant projection model in the step (5)The condition posterior distribution of each parameter comprises the following steps:
(5a) represents the class c classifier parameters ωcThe condition posterior distribution of (a), expressed as:
wherein:
βca hyper-parameter of a class c classifier;
(5b) representing a projection matrix A of class c samplescThe k-th column a ofc,kThe posterior distribution of conditions, expressed as:
wherein:
xnrefers to class c samples, κc,kDenotes ac,kThe parameter, κ, within the prior distributionck～Ga(c0,d0)；
(5c) K line Z representing the n sample of the feature sample set Zk,nThe condition posterior distribution of (a), expressed as:
wherein:
wherein Andrespectively corresponding to the mean and covariance matrices of the conditional posterior distribution;
(5d) distribution parameter [ mu ] representing class c samplec,ΣcA condition posterior distribution of the form:
wherein:
υ'c＝υ0+Nc
β′c＝β0+Nc
Ncindicates the number of class c samples,represents the mean value of the class c samples,means representing a covariance matrix of class c samples;
(5e) a conditional posterior distribution representing a cluster indicator variable, expressed in the form of:
p(h|-)＝Disc(h；π)
and picSubject to the constraint of
(5f) The condition posterior distribution, expressed as:
p(υc|-)∝p(h|υ)Beta(υc；1,α)～Beta(υc；ρa,ρb)
where ρ isa＝1+Nc，NkRepresents the number of class k samples;
(5g) hidden variable lambda representing hidden variable SVM classifiernThe condition posterior distribution of (a), expressed as:
wherein IG (.) represents an inverse gaussian distribution;
(5h) is represented by betacThe condition posterior distribution of (a), expressed as:
wherein
(5i) Denotes kappac,kThe condition posterior distribution of (a), expressed as:
wherein
(5j) A conditional posterior distribution representing α, expressed as:
wherein e'0＝e0+D-1，
4. The method for radar target identification based on the infinite spaced linear discriminant projection model as claimed in claim 1, wherein the step (8b) is performed on the test feature sample setClassifying to obtain a test sample setClass label set ofThe method comprises the following implementation steps:
ρ＝[ρ1,ρ2,...,ρc,...,ρD]
wherein,representing test specimensThe prediction category label of (a) is,the weight coefficients of the hidden variable SVM classifier in the C-th cluster representing the T-th sample are m 1,20，ρcRepresents the average output of the c-th hidden variable SVM classifier,the m value corresponding to the maximum value is shown.
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