基于核方法的雷达高分辨距离像目标识别方法研究
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摘要
高分辨距离像(HRRP)是宽带雷达获取的目标各散射中心沿雷达视线方向的回波向量和，反映了目标散射点沿距离上的分布情况，是目标识别中重要的结构特征，在雷达目标识别领域一直受到广泛的关注。核方法是近十几年机器学习领域内的研究热点，对于处理非线性问题具有高效性。由于HRRP目标识别中目标之间往往表现出较为复杂的非线性关系，因此，近几年核方法被逐步应用于HRRP目标识别，表现出了强大的优势。本文针对HRRP目标识别，围绕着雷达目标识别中的两大基本问题——特征提取和分类器设计，从基于核方法的HRRP特征提取、核分类器设计以及基于核方法的HRRP在线识别三个方面展开了深入的研究。研究内容主要包括四大部分：
1.研究了HRRP的非线性特征提取问题。首先，明确了线性判别分析(LDA)和局部均值判别分析(LMDA)本质上均属于线性特征提取算法，难以获取目标的非线性特征，不能有效地描述目标之间的非线性关系。其次，由于目标HRRP之间往往表现出较为复杂的非线性关系，LMDA在复杂HRRP目标识别中难以获得良好的效果，为此本文利用核方法在处理非线性问题方面的高效性，提出了核局部均值判别分析(KLMDA)算法。测试结果表明，该算法与传统线性、非线性特征提取方法相比，有效增强了目标之间的可分性，提高了目标识别性能。
2.针对雷达目标识别领域目标类样本充分、非目标类样本多样化的两类分类问题展开研究，主要工作包括以下两方面。1)通过分析HRRP在支持向量数据描述(SVDD)超球空间中的分布特性，从理论上明确了若直接使用训练超球半径进行分类，SVDD将无法获得最优泛化性能；针对该问题，定义了二次训练的概念，使用接收机工作特性(ROC)曲线选择最优超球半径，提出了基于SVDD的雷达HRRP分类方法(简称常规SVDD分类方法)。2)针对常规SVDD分类方法抗噪性能差的问题，利用两类目标概率密度分布随信噪比的变化关系分析了主要原因，建立了最优超球半径与信噪比之间的自适应超球半径模型，提出了基于自适应SVDD的雷达高分辨距离像分类方法，大大提高低信噪比下的目标分类性能。
3.对雷达高分辨距离像多目标识别的识别算法设计问题展开研究。首先，通过将SVDD超球空间划分为内空间和延拓空间，分析了内空间和延拓空间样本对目标的不同归属特性和单空间SVDD识别方法的不足。其次，为了能够充分利用延拓样本的分布信息，将先验样本分为模型训练样本和泛化样本，分别使用三种模型对延拓空间样本分布进行建模，从而描述了延拓样本与目标的隶属度关系；根据测试样本在所有目标SVDD超球空间的分布特性，将测试样本定义为松弛样本和紧缩样本，使用不同的判别方式进行识别，提出了基于双空间SVDD的雷达高分辨距离像识别方法。与以往的单空间SVDD识别方法相比，该方法只要延拓样本分布模型选择适当，能够显著提高目标的识别性能。
4.针对雷达目标识别对在线识别的重要需求，研究了小规模训练样本条件下的HRRP在线识别问题，主要工作有三个方面。1)通过分析SVDD对增量样本的泛化性能，获得了一系列重要的结论和定理，从理论上证明了增量学习机理在SVDD上的可行性。2)针对SVDD的在线学习问题，从理论上给出了增量支持向量数据描述(ISVDD)算法样本系数变化的依据，深入分析了在线增量样本与已有样本的集合划分问题，提出一种适于在线学习的ISVDD算法。3)在雷达目标识别的工程应用中，往往存在着不完整的数据库，因此边录取、边学习、边建模成为目前雷达目标在线识别的一种主要方式。针对小规模训练样本条件下的HRRP在线识别问题，提出了基于ISVDD的HRRP在线识别方法。相比于标准SVDD在线识别方法，由于ISVDD在在线识别中的应用，该方法能够大大减少增量样本的训练时间，而且能够获得良好的识别效果。同时，它避免了对大规模HHRP训练样本集的需求。
High-resolution range profile(HRRP) is the vectorial sum of returns from thetarget’s scattering centers projected onto the radar line of sight, which represents theradial distribution of a target’s scattering centers and contains important target structuresignatures. Therefore, HRRP target recognition keeps drawing great attention from theradar target recognition community. Kernel methods, as effective approachs on dealingwith nonlinear problem, have being a hot spot of research in the machine learning fieldin the latest decade. Owing to the complicated nonlinear relationship among HRRPs ofdifferent targets, kernel methods have been successfully applied in HRRP targetrecognition in recent years, obtaining excellent performance. Therefore, from the threeaspects, i.e., kernel feature extraction, kernel classifier designing and kernel methodbased HRRP online recognition, the theory and techniques for HRRP target recognitionare deeply studied in this dissertation. The main content contains four parts:
1. The nonlinear feature extraction of HRRP is studied. Firstly, it is clarified thatthe linear discriminant analysis(LDA) and the local mean discriminant analysis(LMDA)belong to the linear feature extraction algorithms in essence, which can’t extractnonlinear features of targets to describe the nonlinear relationship among differenttargets. Secondly, as nonlinear separability is the main relationship among HRRPs ofdifferent targets, it is difficult for LMDA to obtain excellent recognition performance inthe complicated HRRP target recognition. Accordingly, in this dissertation, consideringthe high efficiency of kernel methods in dealing with nonlinear problem, the kernellocal mean discriminant analysis(KLMDA) algorithm is proposed. The experimentalresults indicate that, compared with the classical linear and nonlinear feature extractionalgorithms, the proposed algorithm can enhance the separability of different targets andimprove the recognition performance.
2. For sufficient samples of the target and multiplex samples of nontargets, theissue of classification is addressed. The main work concerns the following two aspects.1) By analyzing the distribution characteristic of HRRPs in the support vector datadescription(SVDD) hypersphere space, it is theoretically confirmed that the optimalgeneralization performance of SVDD is unachievable while directly utilizing thetraining radius of SVDD for classification. Therefore, the concept of second training isdefined and the receiver operating characteristic(ROC) curve is employed to obtain theoptimal hypersphere radius. Thereafter, a method of radar HRRP classification based onSVDD is proposed, which is referred to as classical SVDD classification method.2) It isproved that the anti-noise capability of the classical SVDD classification method isinsufficient, whose main causes are explored by analyzing the variation of probabilitydensity distribution versus SNR. Then, an adaptive model of optimal hypersphere radius versus SNR is constructed. Consequently, a method of radar HRRP classification basedon adaptive SVDD is proposed, which can greatly improve the classificationperformance under low SNR conditions.
3. The recognition algorithm designing of mutli-targets is focused on. Firstly, bydividing the SVDD hypersphere space into the inner space and the extended space, thedifferent ascription characteristics of HRRPs in the dual spaces are analyzed, and thedeficiency of the single space SVDD recognition method is revealed. Secondly, in orderto using the sufficient prior information of extended samples, the prior samples aredivided into two parts, i.e., model training samples and generalization samples.Afterward, three models are respectively employed to describe the sample distributioncharacteristic in the extended space, which can reflect the memberships of extendedsamples to the target. In accordance with test HRRPs’ multi-space distributingcharacteristics in multi-target hypersphere spaces, they are divided into two types, i.e.,shrink sample and slack sample, which can be determined by two different discriminantrules, respectively. Ultimately, a radar HRRP recognition method based on dual spaceSVDD is proposed. Compared with the recognition method based on single spaceSVDD, as long as the extended distribution model is appropriate, the proposed methodcan improve the recognition performance evidently.
4. Considering the important requirement of online recognition in radar targetrecognition, under the condition of small scale training samples, the HRRP onlinerecognition issue is deeply researched. The main work includes:1) By analysing thegeneralization performance of SVDD to incremental samples, a series of importantconclusions are obtained, which have verified the feasibility of incremental learning onSVDD.2) The principle of samples’ coefficient adjustment is provided, and then thedivision of the set composed of online-updating incremental sample and existed samplesis analyzed in detail. Afterward, an incremental SVDD(ISVDD) algorithm is proposedfor online learning.3) In practical application of radar target recognition, incompletedatabase always exists. Thereby data enrolling, learning and modeling interactively andconcurrently is the primary approach to achieve target recognition. For the HRRP onlinerecognition with small scale training samples, a method of HRRP online recognitionbased on ISVDD is proposed. Compared with the HRRP online recognition methodbased on SVDD, in virtue of the application of ISVDD, the proposed method not onlyreduces the training time of incremental samples but also achieves excellent recognitionperformance. Moreover, it can avoid the requirement of large scale training samples.
1.研究了HRRP的非线性特征提取问题。首先，明确了线性判别分析(LDA)和局部均值判别分析(LMDA)本质上均属于线性特征提取算法，难以获取目标的非线性特征，不能有效地描述目标之间的非线性关系。其次，由于目标HRRP之间往往表现出较为复杂的非线性关系，LMDA在复杂HRRP目标识别中难以获得良好的效果，为此本文利用核方法在处理非线性问题方面的高效性，提出了核局部均值判别分析(KLMDA)算法。测试结果表明，该算法与传统线性、非线性特征提取方法相比，有效增强了目标之间的可分性，提高了目标识别性能。
2.针对雷达目标识别领域目标类样本充分、非目标类样本多样化的两类分类问题展开研究，主要工作包括以下两方面。1)通过分析HRRP在支持向量数据描述(SVDD)超球空间中的分布特性，从理论上明确了若直接使用训练超球半径进行分类，SVDD将无法获得最优泛化性能；针对该问题，定义了二次训练的概念，使用接收机工作特性(ROC)曲线选择最优超球半径，提出了基于SVDD的雷达HRRP分类方法(简称常规SVDD分类方法)。2)针对常规SVDD分类方法抗噪性能差的问题，利用两类目标概率密度分布随信噪比的变化关系分析了主要原因，建立了最优超球半径与信噪比之间的自适应超球半径模型，提出了基于自适应SVDD的雷达高分辨距离像分类方法，大大提高低信噪比下的目标分类性能。
3.对雷达高分辨距离像多目标识别的识别算法设计问题展开研究。首先，通过将SVDD超球空间划分为内空间和延拓空间，分析了内空间和延拓空间样本对目标的不同归属特性和单空间SVDD识别方法的不足。其次，为了能够充分利用延拓样本的分布信息，将先验样本分为模型训练样本和泛化样本，分别使用三种模型对延拓空间样本分布进行建模，从而描述了延拓样本与目标的隶属度关系；根据测试样本在所有目标SVDD超球空间的分布特性，将测试样本定义为松弛样本和紧缩样本，使用不同的判别方式进行识别，提出了基于双空间SVDD的雷达高分辨距离像识别方法。与以往的单空间SVDD识别方法相比，该方法只要延拓样本分布模型选择适当，能够显著提高目标的识别性能。
4.针对雷达目标识别对在线识别的重要需求，研究了小规模训练样本条件下的HRRP在线识别问题，主要工作有三个方面。1)通过分析SVDD对增量样本的泛化性能，获得了一系列重要的结论和定理，从理论上证明了增量学习机理在SVDD上的可行性。2)针对SVDD的在线学习问题，从理论上给出了增量支持向量数据描述(ISVDD)算法样本系数变化的依据，深入分析了在线增量样本与已有样本的集合划分问题，提出一种适于在线学习的ISVDD算法。3)在雷达目标识别的工程应用中，往往存在着不完整的数据库，因此边录取、边学习、边建模成为目前雷达目标在线识别的一种主要方式。针对小规模训练样本条件下的HRRP在线识别问题，提出了基于ISVDD的HRRP在线识别方法。相比于标准SVDD在线识别方法，由于ISVDD在在线识别中的应用，该方法能够大大减少增量样本的训练时间，而且能够获得良好的识别效果。同时，它避免了对大规模HHRP训练样本集的需求。
High-resolution range profile(HRRP) is the vectorial sum of returns from thetarget’s scattering centers projected onto the radar line of sight, which represents theradial distribution of a target’s scattering centers and contains important target structuresignatures. Therefore, HRRP target recognition keeps drawing great attention from theradar target recognition community. Kernel methods, as effective approachs on dealingwith nonlinear problem, have being a hot spot of research in the machine learning fieldin the latest decade. Owing to the complicated nonlinear relationship among HRRPs ofdifferent targets, kernel methods have been successfully applied in HRRP targetrecognition in recent years, obtaining excellent performance. Therefore, from the threeaspects, i.e., kernel feature extraction, kernel classifier designing and kernel methodbased HRRP online recognition, the theory and techniques for HRRP target recognitionare deeply studied in this dissertation. The main content contains four parts:
1. The nonlinear feature extraction of HRRP is studied. Firstly, it is clarified thatthe linear discriminant analysis(LDA) and the local mean discriminant analysis(LMDA)belong to the linear feature extraction algorithms in essence, which can’t extractnonlinear features of targets to describe the nonlinear relationship among differenttargets. Secondly, as nonlinear separability is the main relationship among HRRPs ofdifferent targets, it is difficult for LMDA to obtain excellent recognition performance inthe complicated HRRP target recognition. Accordingly, in this dissertation, consideringthe high efficiency of kernel methods in dealing with nonlinear problem, the kernellocal mean discriminant analysis(KLMDA) algorithm is proposed. The experimentalresults indicate that, compared with the classical linear and nonlinear feature extractionalgorithms, the proposed algorithm can enhance the separability of different targets andimprove the recognition performance.
2. For sufficient samples of the target and multiplex samples of nontargets, theissue of classification is addressed. The main work concerns the following two aspects.1) By analyzing the distribution characteristic of HRRPs in the support vector datadescription(SVDD) hypersphere space, it is theoretically confirmed that the optimalgeneralization performance of SVDD is unachievable while directly utilizing thetraining radius of SVDD for classification. Therefore, the concept of second training isdefined and the receiver operating characteristic(ROC) curve is employed to obtain theoptimal hypersphere radius. Thereafter, a method of radar HRRP classification based onSVDD is proposed, which is referred to as classical SVDD classification method.2) It isproved that the anti-noise capability of the classical SVDD classification method isinsufficient, whose main causes are explored by analyzing the variation of probabilitydensity distribution versus SNR. Then, an adaptive model of optimal hypersphere radius versus SNR is constructed. Consequently, a method of radar HRRP classification basedon adaptive SVDD is proposed, which can greatly improve the classificationperformance under low SNR conditions.
3. The recognition algorithm designing of mutli-targets is focused on. Firstly, bydividing the SVDD hypersphere space into the inner space and the extended space, thedifferent ascription characteristics of HRRPs in the dual spaces are analyzed, and thedeficiency of the single space SVDD recognition method is revealed. Secondly, in orderto using the sufficient prior information of extended samples, the prior samples aredivided into two parts, i.e., model training samples and generalization samples.Afterward, three models are respectively employed to describe the sample distributioncharacteristic in the extended space, which can reflect the memberships of extendedsamples to the target. In accordance with test HRRPs’ multi-space distributingcharacteristics in multi-target hypersphere spaces, they are divided into two types, i.e.,shrink sample and slack sample, which can be determined by two different discriminantrules, respectively. Ultimately, a radar HRRP recognition method based on dual spaceSVDD is proposed. Compared with the recognition method based on single spaceSVDD, as long as the extended distribution model is appropriate, the proposed methodcan improve the recognition performance evidently.
4. Considering the important requirement of online recognition in radar targetrecognition, under the condition of small scale training samples, the HRRP onlinerecognition issue is deeply researched. The main work includes:1) By analysing thegeneralization performance of SVDD to incremental samples, a series of importantconclusions are obtained, which have verified the feasibility of incremental learning onSVDD.2) The principle of samples’ coefficient adjustment is provided, and then thedivision of the set composed of online-updating incremental sample and existed samplesis analyzed in detail. Afterward, an incremental SVDD(ISVDD) algorithm is proposedfor online learning.3) In practical application of radar target recognition, incompletedatabase always exists. Thereby data enrolling, learning and modeling interactively andconcurrently is the primary approach to achieve target recognition. For the HRRP onlinerecognition with small scale training samples, a method of HRRP online recognitionbased on ISVDD is proposed. Compared with the HRRP online recognition methodbased on SVDD, in virtue of the application of ISVDD, the proposed method not onlyreduces the training time of incremental samples but also achieves excellent recognitionperformance. Moreover, it can avoid the requirement of large scale training samples.
引文
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