雷达高分辨距离像目标识别方法研究
|
摘要
高分辨距离像(HRRP)是用宽带雷达信号获取的目标散射点子回波在雷达射线上投影的向量和，它提供了目标散射点沿距离方向的分布情况，是目标重要的结构特征，对目标识别与分类十分有价值，因而成为雷达自动目标识别(RATR)领域研究的热点。本论文主要围绕着“十五”和“十一五”国防预研计划项目“目标识别技术”(项目编号：413070501和51307060601)及国家自然科学基金项目“基于高距离分辨回波序列的雷达目标识别技术”(项目编号：60302009)的研究任务，从高分辨距离像的物理特性分析、特征提取和特征选择以及分类器设计这三个基本层次展开对雷达高分辨距离像目标识别的相关理论与技术问题的研究。
论文内容可概括为如下五部分：
·第一部分，从目标的散射点模型出发，对高分辨距离像的物理特性进行了深入的研究，指出方位敏感性、平移敏感性和强度敏感性是雷达HRRP目标识别需要首先解决的三大问题。并针对最常用的模板匹配法，提出雷达高分辨距离像目标识别的基本思路，为后续的研究奠定基础。
·第二部分，研究雷达HRRP目标识别的特征提取和特征选择方法，工作有以下三点。(1)针对高分辨距离像的平移敏感性问题，研究基于高阶谱特征的雷达高分辨距离像目标识别。类似于近年来在目标识别领域中常用的在低维空间实现高维映射空间欧氏距离计算的核方法，本论文通过分析高阶谱域欧氏距离和原始像域欧氏距离的关系，得出在原始像域计算高阶谱域欧氏距离的方法，使高阶谱特征在目标识别中的应用具有现实意义。(2)基于散射点模型理论，提出了一种利用距离像幅度起伏特性的特征提取新方法。新方法提取的加权距离像特征有效地融合了帧距离像的散射点强度分布像和方差像，反映了各个距离单元内目标散射点的分布情况，可以更好地描述目标散射特性。(3)基于Fisher可分性判据，提出了一种加权特征选择方法。该方法根据雷达HRRP目标识别的具体特点，对HRRP的平移不变特征——功率谱特征采用基于Fisher判决率的迭代算法搜索最优权向量。与直接使用原始特征及现有的特征选择方法相比，本论文提出的特征选择方法既可以降维，又提高了识别性能，而且运算简单。
·第三部分，详细讨论雷达HRRP的统计建模问题，主要工作涉及以下三个大的方面。一、讨论在统计识别中解决HRRP样本方位、平移和强度敏感性的方法，为HRRP的统计建模工作奠定基础。二、在HRRP样本各距离单元回波相互独立的假设前提下，提出了一种基于Gamma和Gaussian Mixture两种分布形式的独立双分布复合模型。三、进一步的研究表明HRRP样本各距离单元回波相互独立的假设并不完全成立，因此，我们又研究了更精确的基于HRRP样本各距离单元回波相关统计特性的统计识别方法，具体工作包括以下两点。(1)考虑到用于识别的HRRP样本在2-范数强度归一化后都位于单位超球面上，针对于幂次变换后趋于Joint-Gaussian分布的HRRP数据，提出了一种改进的基于子空间近似的统计识别方法。(2)研究发现HRRP样本各距离单元回波的联合分布近似因子分析(FA)模型描述的Joint-Gaussian分布，这表明在雷达HRRP统计识别中并不需要使用复杂的Joint-Gaussian Mixture模型(如FA Mixture模型)，这大大降低了统计识别的难度。进而，针对基于FA模型的雷达HRRP统计识别，提出了一种自适应模型选择算法。该算法可以同时解决因子个数选择和方位帧划分这两个模型选择问题。
·第四部分，研究基于复数HRRP样本的雷达目标识别方法。在分析复数HRRP样本特性的基础上，指出由于初相敏感性问题，原先适用于实数HRRP样本的方位模板、识别方法和特征提取方法一般都不能直接用于基于复数HRRP的RATR，我们必须重新寻找既与复数HRRP样本的初相无关又能利用其剩余相位信息的方法。进而，在识别方法方面，分析指出基于主分量分析(PCA)子空间的最小重构误差法既可以回避复数HRRP样本的初相敏感性问题又可以利用复数HRRP样本的其余相位信息，因而，该识别方法适用于基于复数HRRP的RATR，并提出了该方法相应的平移匹配快速算法；此外，在特征提取方法方面，提出了一种用于复数HRRP样本的初相无关特征提取方法，对实数HRRP样本适用的识别方法、方位模板和预处理方法同样适用于该复特征向量。因此，本论文的研究使基于复数HRRP的RATR成为可能。而且，基于实测数据的识别实验表明，使用复数HRRP样本可以取得比实数HRRP样本更好的识别性能。
·第五部分，研究如何用少量的简单分类器解决多类目标识别问题。由于HRRP样本的方位敏感性，雷达HRRP目标识别是典型的多类目标识别问题。本论文提出了一种基于超立方体和超网格自组织映射(SOM)编码的多类目标识别方法。该方法的优势体现在：一方面将基于二分类的多类目标识别方法扩展为基于k分类的K(k<A high-resolution range profile (HRRP) is the amplitude of the coherent summations of the complex time returns from target scatterers in each range resolution cell, which represents the projection of the complex returned echoes from the target scattering centers onto the radar line-of-sight (LOS). It contains the target structure signatures, such as target size, scatterer distribution, etc., thereby radar HRRP target recognition has received intensive attention from the radar automatic target recognition (RATR) community. The theory and techniques for radar HRRP target recognition are researched from the three aspects, i.e. analysis on the physical property of HRRP samples, feature extraction and feature selection, and classification methods, in this dissertation, which are supported by Advanced Defense Research Programs of China (No. 413070501 and No. 51307060601) and National Science Foundation of China (No. 60302009).
The main content of this dissertation is summarized as follows.
·Based on the scattering center model, the first part makes a detailed analysis on the physical property of HRRP samples, and points out that how to deal with the target-aspect, time-shift and amplitude-scale sensitivity of HRRP samples is a challenging task for radar HRRP target recognition. Then a framework for HRRP-based RATR by template matching method (TMM) is established, which forms the basis for the following study.
·The second part focuses on feature extraction and feature selection for HRRP-based RATR. The main work includes: 1) Due to the huge storage requirement and the complex computation, higher-order spectra features receive less attention from RATR community. Similar to the well-known kernel method in automatic target recognition (ATR) community, in which the Euclidean distances in the high dimensional mapped space can be calculated in the low dimensional original space, a method for calculating the Euclidean distances in higher-order spectra feature space is proposed in this dissertation, which is performed in original HRRP space directly and can avoid calculating the higher-order spectra, effectively reducing the computation complexity and storage requirement. 2) According to the scattering center model, a new feature extraction method using the amplitude fluctuation property of HRRP samples is proposed in this dissertation. The weighted HRRP vector extracted by the new method can effectively fuse the corresponding frame's stcatterer strength distributing profile and variance profile, and represent the scatterer distribution in every range cell, thereby it can describe the scattering property of a target better. 3) Based on the Fisher's linear discriminant, a weighted feature selection method is proposed. According to the characteristics of radar HRRP target recognition, the proposed weighted feature selection method use the iterative algorithm based on the Fisher's discriminant ratio to search the optimal weight for the time-shift invariant feature, i.e. power spectrum. Compared with using the raw feature vectors and some existing feature selection methods, the weighted feature selection method not only can reduce the feature dimension, but also can improve the recognition performance with low computational complexity.
·The third part is contributed to radar HRRP statistical modeling. The main work concerns the following three aspects. Firstly, we make a detailed analysis on the effect of the three sensitivity problems of HRRP samples on statistical recognition, and propose our corresponding solution, which forms the basis for the study on radar HRRP statistical modeling. Secondly, under the hypothesis that the elements in an HRRP sample are statistically independent, we develop an independent statistical model comprising two distribution forms, i.e. Gamma distribution and Gaussian mixture distribution, to model echoes of different types of range cells as different distribution forms. Thirdly, theoretical analysis and our experimental results based on measured data show that the independence assumption is not true, thus we further make a study on the more accurate statistical recognition methods based on HRRP samples' jointly statistical characteristics. Our work includes: 1) Different from general target recognition problems, L_2 normalized samples are applied to HRRP-based RATR to deal with the amplitude-scale sensitivity problem, therefore, geometrically speaking, HRRP samples spread on a unit hypersphere. We propose a modified statistical recognition method based on subspace approximation for power transformed HRRP samples under the joint-Gaussian distribution hypothesis. 2) According to the experiments based on measured data, HRRP samples approximately follow the joint-Gaussian distribution described by factor analysis (FA) model. Therefore, we can apply FA model to radar HRRP statistical recognition rather than a joint-Gaussian mixture model, e.g. FA mixture model, which is a more accurate choice for modeling non-Gaussian distributed correlations in multidimensional data but with high learning complexity and large computation burden. Furthermore, an iterated algorithm for model selection of FA model in radar HRRP statistical recognition is proposed, which can automatically give the optimal aspect-frame boundaries and determine the optimal number of factors in each aspect-frame.
·The forth part focuses on RATR using complex HRRP samples. Based on the analysis on the physical property of complex HRRP samples, we point out that the frame template, classification algorithm and feature extraction method for complex HRRP samples should be unvaried with the initial phases. In the existing classification methods, the principal component analysis (PCA)-based minimum reconstruction error approximation is independent of the initial phases yet exploits the remaining phase information in complex HRRP samples, therefore, this method can be used in complex HRRP-based RATR, and a fast time-shift compensation algorithm is proposed for this method. In addition, we propose a novel feature extraction method invariant with the initial phases for complex HRRP samples. The recognition algorithms, frame-template establishment methods and preprocessing methods used in the real HRRP-based RATR can also be applied to the proposed complex feature vector-based RATR. Therefore, based on the aforementioned research, complex HRRP-based RATR becomes practical. Furthermore, in the recognition experiments based on measured data, complex HRRP samples can obtain better recognition results than real HRRP samples.
·The fifth part is contributed to multicategory classification by a small number of simple classifiers. Due to the target-aspect sensitivity of HRRP samples, radar HRRP target recognition is a typical multicategory classification problem. We propose a multicategory classification method based on hypercube/hypergrid self-organization mapping (SOM) scheme. The advantageous of this method includes: 1) We can not only use binary classifiers but also k-ary (k<
论文内容可概括为如下五部分：
·第一部分，从目标的散射点模型出发，对高分辨距离像的物理特性进行了深入的研究，指出方位敏感性、平移敏感性和强度敏感性是雷达HRRP目标识别需要首先解决的三大问题。并针对最常用的模板匹配法，提出雷达高分辨距离像目标识别的基本思路，为后续的研究奠定基础。
·第二部分，研究雷达HRRP目标识别的特征提取和特征选择方法，工作有以下三点。(1)针对高分辨距离像的平移敏感性问题，研究基于高阶谱特征的雷达高分辨距离像目标识别。类似于近年来在目标识别领域中常用的在低维空间实现高维映射空间欧氏距离计算的核方法，本论文通过分析高阶谱域欧氏距离和原始像域欧氏距离的关系，得出在原始像域计算高阶谱域欧氏距离的方法，使高阶谱特征在目标识别中的应用具有现实意义。(2)基于散射点模型理论，提出了一种利用距离像幅度起伏特性的特征提取新方法。新方法提取的加权距离像特征有效地融合了帧距离像的散射点强度分布像和方差像，反映了各个距离单元内目标散射点的分布情况，可以更好地描述目标散射特性。(3)基于Fisher可分性判据，提出了一种加权特征选择方法。该方法根据雷达HRRP目标识别的具体特点，对HRRP的平移不变特征——功率谱特征采用基于Fisher判决率的迭代算法搜索最优权向量。与直接使用原始特征及现有的特征选择方法相比，本论文提出的特征选择方法既可以降维，又提高了识别性能，而且运算简单。
·第三部分，详细讨论雷达HRRP的统计建模问题，主要工作涉及以下三个大的方面。一、讨论在统计识别中解决HRRP样本方位、平移和强度敏感性的方法，为HRRP的统计建模工作奠定基础。二、在HRRP样本各距离单元回波相互独立的假设前提下，提出了一种基于Gamma和Gaussian Mixture两种分布形式的独立双分布复合模型。三、进一步的研究表明HRRP样本各距离单元回波相互独立的假设并不完全成立，因此，我们又研究了更精确的基于HRRP样本各距离单元回波相关统计特性的统计识别方法，具体工作包括以下两点。(1)考虑到用于识别的HRRP样本在2-范数强度归一化后都位于单位超球面上，针对于幂次变换后趋于Joint-Gaussian分布的HRRP数据，提出了一种改进的基于子空间近似的统计识别方法。(2)研究发现HRRP样本各距离单元回波的联合分布近似因子分析(FA)模型描述的Joint-Gaussian分布，这表明在雷达HRRP统计识别中并不需要使用复杂的Joint-Gaussian Mixture模型(如FA Mixture模型)，这大大降低了统计识别的难度。进而，针对基于FA模型的雷达HRRP统计识别，提出了一种自适应模型选择算法。该算法可以同时解决因子个数选择和方位帧划分这两个模型选择问题。
·第四部分，研究基于复数HRRP样本的雷达目标识别方法。在分析复数HRRP样本特性的基础上，指出由于初相敏感性问题，原先适用于实数HRRP样本的方位模板、识别方法和特征提取方法一般都不能直接用于基于复数HRRP的RATR，我们必须重新寻找既与复数HRRP样本的初相无关又能利用其剩余相位信息的方法。进而，在识别方法方面，分析指出基于主分量分析(PCA)子空间的最小重构误差法既可以回避复数HRRP样本的初相敏感性问题又可以利用复数HRRP样本的其余相位信息，因而，该识别方法适用于基于复数HRRP的RATR，并提出了该方法相应的平移匹配快速算法；此外，在特征提取方法方面，提出了一种用于复数HRRP样本的初相无关特征提取方法，对实数HRRP样本适用的识别方法、方位模板和预处理方法同样适用于该复特征向量。因此，本论文的研究使基于复数HRRP的RATR成为可能。而且，基于实测数据的识别实验表明，使用复数HRRP样本可以取得比实数HRRP样本更好的识别性能。
·第五部分，研究如何用少量的简单分类器解决多类目标识别问题。由于HRRP样本的方位敏感性，雷达HRRP目标识别是典型的多类目标识别问题。本论文提出了一种基于超立方体和超网格自组织映射(SOM)编码的多类目标识别方法。该方法的优势体现在：一方面将基于二分类的多类目标识别方法扩展为基于k分类的K(k<
The main content of this dissertation is summarized as follows.
·Based on the scattering center model, the first part makes a detailed analysis on the physical property of HRRP samples, and points out that how to deal with the target-aspect, time-shift and amplitude-scale sensitivity of HRRP samples is a challenging task for radar HRRP target recognition. Then a framework for HRRP-based RATR by template matching method (TMM) is established, which forms the basis for the following study.
·The second part focuses on feature extraction and feature selection for HRRP-based RATR. The main work includes: 1) Due to the huge storage requirement and the complex computation, higher-order spectra features receive less attention from RATR community. Similar to the well-known kernel method in automatic target recognition (ATR) community, in which the Euclidean distances in the high dimensional mapped space can be calculated in the low dimensional original space, a method for calculating the Euclidean distances in higher-order spectra feature space is proposed in this dissertation, which is performed in original HRRP space directly and can avoid calculating the higher-order spectra, effectively reducing the computation complexity and storage requirement. 2) According to the scattering center model, a new feature extraction method using the amplitude fluctuation property of HRRP samples is proposed in this dissertation. The weighted HRRP vector extracted by the new method can effectively fuse the corresponding frame's stcatterer strength distributing profile and variance profile, and represent the scatterer distribution in every range cell, thereby it can describe the scattering property of a target better. 3) Based on the Fisher's linear discriminant, a weighted feature selection method is proposed. According to the characteristics of radar HRRP target recognition, the proposed weighted feature selection method use the iterative algorithm based on the Fisher's discriminant ratio to search the optimal weight for the time-shift invariant feature, i.e. power spectrum. Compared with using the raw feature vectors and some existing feature selection methods, the weighted feature selection method not only can reduce the feature dimension, but also can improve the recognition performance with low computational complexity.
·The third part is contributed to radar HRRP statistical modeling. The main work concerns the following three aspects. Firstly, we make a detailed analysis on the effect of the three sensitivity problems of HRRP samples on statistical recognition, and propose our corresponding solution, which forms the basis for the study on radar HRRP statistical modeling. Secondly, under the hypothesis that the elements in an HRRP sample are statistically independent, we develop an independent statistical model comprising two distribution forms, i.e. Gamma distribution and Gaussian mixture distribution, to model echoes of different types of range cells as different distribution forms. Thirdly, theoretical analysis and our experimental results based on measured data show that the independence assumption is not true, thus we further make a study on the more accurate statistical recognition methods based on HRRP samples' jointly statistical characteristics. Our work includes: 1) Different from general target recognition problems, L_2 normalized samples are applied to HRRP-based RATR to deal with the amplitude-scale sensitivity problem, therefore, geometrically speaking, HRRP samples spread on a unit hypersphere. We propose a modified statistical recognition method based on subspace approximation for power transformed HRRP samples under the joint-Gaussian distribution hypothesis. 2) According to the experiments based on measured data, HRRP samples approximately follow the joint-Gaussian distribution described by factor analysis (FA) model. Therefore, we can apply FA model to radar HRRP statistical recognition rather than a joint-Gaussian mixture model, e.g. FA mixture model, which is a more accurate choice for modeling non-Gaussian distributed correlations in multidimensional data but with high learning complexity and large computation burden. Furthermore, an iterated algorithm for model selection of FA model in radar HRRP statistical recognition is proposed, which can automatically give the optimal aspect-frame boundaries and determine the optimal number of factors in each aspect-frame.
·The forth part focuses on RATR using complex HRRP samples. Based on the analysis on the physical property of complex HRRP samples, we point out that the frame template, classification algorithm and feature extraction method for complex HRRP samples should be unvaried with the initial phases. In the existing classification methods, the principal component analysis (PCA)-based minimum reconstruction error approximation is independent of the initial phases yet exploits the remaining phase information in complex HRRP samples, therefore, this method can be used in complex HRRP-based RATR, and a fast time-shift compensation algorithm is proposed for this method. In addition, we propose a novel feature extraction method invariant with the initial phases for complex HRRP samples. The recognition algorithms, frame-template establishment methods and preprocessing methods used in the real HRRP-based RATR can also be applied to the proposed complex feature vector-based RATR. Therefore, based on the aforementioned research, complex HRRP-based RATR becomes practical. Furthermore, in the recognition experiments based on measured data, complex HRRP samples can obtain better recognition results than real HRRP samples.
·The fifth part is contributed to multicategory classification by a small number of simple classifiers. Due to the target-aspect sensitivity of HRRP samples, radar HRRP target recognition is a typical multicategory classification problem. We propose a multicategory classification method based on hypercube/hypergrid self-organization mapping (SOM) scheme. The advantageous of this method includes: 1) We can not only use binary classifiers but also k-ary (k<
引文
[1] Duda R. O., Hart E E., Stork D. G.. Pattem Classification. Second Edition. New York: John Wiley and Sons. 2001.
[2] Skolnik M.. Introduction to Radar Systems, Second Edition, New York: McGraw-Hill. 1980.
[3] 廖学军．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[4] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[5] 邢孟道．基于实测数据的雷达成像方法研究．博士研究生学位论文．西安电子科技大学．2002．
[6] 刘宏伟，杜兰，袁莉，保铮．雷达高分辨距离像目标识别研究进展．电子与信息学报．2005年8月，Vol．27(8)．1328-1334．
[7] Nebabin V. G.. Methods and techniques of radar recognition. Boston: Artech House. 1997.
[8] Barton D. K.. Spumik Ⅱ as observed by C band radar. IRE National Conference. 1959, Vol.7(5). 67-73.
[9] Skolnik M. I.. Radar Handbook. Second Edition. 北京：电子工业出版社. 2003.
[10] Lewis G. N., Postol T. A.. Furore Challenges to Ballistic Missile Defense. IEEE Spectrum, 1997(9). 60-68.
[11] William P. D., William W. W.. Radar Development at Lincoln Laboratory: An overview of the First Fifty Years. Lincoln Laboratory Journal. 2000, Vol.12(2). 147-166.
[12] Lemnios W. Z., Grometestein A.. Overview of the Lincoln Laboratory Ballistic Missile Defense Program. Lincoln Laboratory Journal. 2002, Vol. 13(1). 9-32.
[13] Baum C. E.. On the singularity expansion method for the solution of electromagnetic interaction problem. Air Force Weapon Lab. International Note 88. 1971.
[14] Eesterkamp J.. A Framework for 1D HRR ATR evaluation. AFRL Technical Report. Aug. 1998.
[15] Moving and stationary target acquisition and recognition, Program technology review. Denver, CO. Nov. 1996. http://www.mbvlab.wpafb.af.mil/public/MBVDATA
[16] Zhao Q., Principle J. C., Support vector machines for SAR automatic target recognition. IEEE Trans. A.E.S.. 2001, Vol.37(2). 643-654.
[17] Novak L. M., Owirka G. J., Weaver A. L.. Automatic target recognition using enhanced resolution SAR data. IEEE Trans. A.E.S.. 1999, Vol.35 (1).157-175.
[18] An Overview of automatic target recognition. The Lincoln Laboratory Journal. 1993, Vol.6(1).
[19] Marcoz Y., Miguel T.T., Feature Selection using Genetic Algorithms in SAR Airborne Imagery. http://www.cim.mcgill.ca,2001.
[20] Punkle P. et al.. Multi-aspect target detection for SAR imagery using Hidden Markov models. IEEE Trans. A.E.S.. 2001, Vol.39(1). 46-55.
[21] Bryant M., Garber F.. SVM classifier applied to the MSTAR public data set. Algorithms for Synthetic Aperture Radar Imagery Ⅵ. Proceedings of the SPIE. 2001, Vol. 3721. 355-360.
[22] Musman S., Kerr D., Bachmann C.. Automatic Recognition of ISAR Images. IEEE Trans. A.E.S.. 1996, Vol.32(4). 1392-1403.
[23] Rosenbach K., Schiller J., Construction and Test of a Classifier for Non-Cooperative Air-Target Identification based on 2-D-ISAR Images. Proceedings of IRS'98 International Radar Symposium. Sep. 1998.1023-1033.
[24] Maki A. et al.. ISAR Image Analysis by Subspace Method: Automatic Extraction and Identification of Ship Profile. IEEE Radar 2001. 523-528.
[25] Maki A. et al.. Automatic Ship Identification in ISAR Imagery: An On-line System using CMSM. IEEE Radar 2002.206-211.
[26] Li H.-J., Wang Y. D., Wang L.-H., Matching score properties between range profile of high-resolution radar targets. IEEE trans. A. P.. 1996, 44(4). 444-452.
[27] Zyweck A., Bogner R. E.. Coherent averaging of range profiles. IEEE International Radar Conference. 1995.
[28] Mitchell R. A., Dewall R.. Overview of high range resolution radar target identification. In Proceedings of Automayic Target Recognition 'Working Group. 1994.
[29] Jacobs S. P.. Automatic target recognition using high-resolution radar range profiles. Ph. D. Dissertation. Washington University. 1999.
[30] 王雪松．宽带极化信息处理研究．博士研究生学位论文．国防科学技术大学．1999．
[31] Van der Heiden R., Groen F. C. A.. The Box-Cox Metric for Nearest Neighbour Classification Improvement. Pattern Recognition. 1997, Vol. 30(2). 273-279.
[32] Cohen M. N.. Variability of ultra-high range resolution profiles and some implications for target recognition. SPIE. 1992. 256-266.
[33] Li H.-J., Yang S.-H.. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. A.P.. 1993, Vol.41(3). 261-268.
[34] Zyweck A., Bogner R. E.. Radar target classification of commercial aircraft. IEEE Trans. A.E.S.. 1996, Vol.32(2). 598-606.
[35] Williams R., Westerkamp J., Gross D. et al.. Automatic Target Recognition of Time Critical Moving Targets 1D High Range Resolution (HRR) Radar. IEEE AES System Magazine. 2000, Vol. 15(4). 37-43.
[36] Webb A. R.. Gamma Mixture Models for Target Recognition. Pattern Recognition. 2000, 33.2045-2054.
[37] Du Lan, Liu Hongwei, Bao Zheng, Xing Mengdao. Radar HRRP target recognition based on higher order spectra. IEEE Trans. on Signal Processing. Jul. 2005, Vol.53 (7). 2359-2368.
[38] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Trans. on Signal Processing. Vol.54 (6). 2226-2238.
[39] 杜兰，刘宏伟，保铮．利用目标方位信息改善雷达距离像识别性能．系统工程与电子技术．2004年8月，Vol．26(8)．1040-1043．
[40] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. Signal Processing. 2001, Vol.49(9). 1875-1885.
[41] Kim K. T., Seo D. K., Kim H. T.. Efficient radar target recognition using the MUSIC algorithm and invariant feature. IEEE Trans A.P.. 2002, Vol.50(3). 325-337.
[42] 杜兰，刘宏伟，保铮，张军英．一种利用雷达高分辨距离像幅度起伏特性的特征提取新方法．电子学报．2005年3月，Vol．33(3)．411-415．
[43] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. Radar automatic target recognition using complex high-resolution range profiles. IET Radar, Sonar & Navigation. Feb. 2007, Vol. 1 (1). 18-26.
[44] 杜兰，保铮，刘宏伟，高分辨距离像雷达自动目标识别的模板匹配问题，第九届全国雷达学术年会论文集，2004年8月．509-512．
[45] Li J., Stoica P.. Efficient mixed-spectrum estimation with application to feature extraction. IEEE Trans. on Signal Processing. Feb. 1996, Vol.42(2). 281-295.
[46] Bharadwaj P., Runkle P., Carin L.. Multiaspct classification of airborne targets via physics-based HMMs and matching pursuits. IEEE Trans. on A.E.S.. 2001, Vol.37(2): 595-606.
[47] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A weighted feature reduction method for power spectra of radar HRRPs. Journal of electronics (China). 2006, Vol.23 (3). 365-369.
[48] Du Lan, Zhang Junying, Bao Zheng. Multicategory classification based on the hypercube self-organization mapping (SOM) scheme. Lecture Notes in Computer Science Vol.4221.107-110.
[49] Gorshkov S. A., Leschenko S. P., Orlenko V. M. et al.. Radar Target Backscattering Simulation Software and User's Manual. Boston London: Artech House. 2002.
[50] Sebald D. J., Bucklew J. A.. Support vector machines and the multiple hypothesis test problem. IEEE Trans. on S.P.. 2001, Vol.49(11). 2865-2872.
[51] Dietterich T. G., BaNff. G.. Solving multiclass leaming problems via error-correcting output codes. Journal of Artificial Intelligence Research. 1995(2). 263-286.
[52] T. W. T., G. R.. Coding and decoding strategies for multi-class learning problems. Information Fusion. 2003, Vol.4(1 ). 11-21.
[53] 杜兰，刘宏伟，保铮．一种基于距离一多普勒二维联合的群目标分辨方法．电子学报．2004年6月，Vol．32(6)．881-885．
[54] 杜兰，保铮，邢孟道．直升机雷达回波的分析与检测．西安电子科技大学学报．2003年10月，Vol．30(5)．574-579．
[55] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[1] 廖学车．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[2] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[3] Xing M.-D., Bao Z., Pei B.. The properties of high-resolution range profiles. Optical Engineering. 2002, 41 (2). 493-504.
[4] Jacobs S.P.. Automatic target recognition using high-resolution radar range profiles. Washington University. 1999.
[5] Kim K.-T., Seo D.-K., Kim H.-T.. Efficient radar target recognition using the Music algorithm and invariant features. IEEE Trans. A.P.. 2002, 50 (3). 325-337.
[6] Williams R., Westerkamp J., Gross D. et al.. Automatic Target Recognition of Time Critical Moving Targets 1D High Range Resolution (HRR) Radar. IEEE AES System Magazine. 2000, 15(4). 37-43.
[7] Miller M.I., Grenander U., OSullivan J.A. et al.. Automatic target recognition organized via jump-diffusion algorithms. IEEE Trans. A.P.. 1997, Vol.6(1). 157-173.
[8] 杜兰，刘宏伟，保铮．利用目标方位信息改善雷达距离像识别性能．系统工程与电子技术．2004年8月，Vol．26(8)．1040-1043．
[9] 杜兰，保铮，刘宏伟．高分辨距离像雷达自动目标识别的模板匹配问题．第九届全国雷达学术年会论文集．2004年8月．509-512．
[10] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. New York: John Wiley and Sons, 2001.
[11] Bhatnagar V. Automatic target recognition using high range resolution data. Dayton: Master Thesis. Wright State University. 1998.
[12] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. Signal Processing. 2001, Vol.49(9). 1875-1885.
[13] 杜兰，保铮，邢忑道．飞机目标的雷达一维距离像特性研究．西安电子科技大学学报．2001，Vol．28(增刊)．14-19．
[14] Bao Z., Sun C.-Y., Xing M.-D., Time-Frequency Approaches to ISAR Imaging of Maneuvering Targets and Their Limitations. IEEE Trans. A.E.S.. 2001, Vol. 37(3). 1091-1099.
[15] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[16] Marques de Sa J.P.. Pattern Recognition Concepts, Methods and Applications. New York: Springer. 2001.
[17] 邢孟道．基于实测数据的雷达成像方法研究．博士研究生学位论文．西安电子科技大学．2002．
[18] Li H.-J., Wang Y. D., Wang L.-H., Matching score properties between range profile of high-resolution radar targets. IEEE trans. A. P.. 1996, 44(4). 444-452.
[1] 廖学军．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[2] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[3] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. S. P., 2001, Vol. 49(9). 1875-1885.
[4] Popovici V., Thiran J. P.. Pattern Recognition Using Higher-order Local Autocorrelation Coefficients. 12~(th) IEEE Worshop on Neural Networks for Signal Processing. 2002. 229-238.
[5] Chandran V., Elgar S. L.. Pattern recognition using invariants defined from higher order spectra—One-dimensional inputs. IEEE. Trans. S.P.. 1993, Vol.41(1). 205-212.
[6] Tugnait J. K.. Detection of non-Gaussian signals using integrated polyspectrum. IEEE Trans. S.P.. 1994, Vol.42(11). 3137-3149.
[7] Nikias C. L., Petropulu A. P.. High-order Spectra Analysis: A Nonlinear Signal Processing Framework. NJ: Prentice-Hall. 1993.
[8] 张贤达．现代信号处理．北京：清华大学出版社．1995．
[9] 沈凤麟，叶中付，钱玉美．信号统计分析与处理．合肥：中国科学技术大学出版社．2001．
[10] Marques J. P.. Pattem Recognition Concepts, Methods and Applications. New York: Springer. 2001.
[11] 边肇祺，张学工．模式识别(第二版)．北京：清华大学出版社．2000．
[12] 赵群．基于高分辨一维距离像的雷达目标识别与检测．博士研究生学位论文．西安电子科技大学．1995．
[13] Dietterich T. G.. Approximate Statistical Tests for Comparing Supervised Classification Leaming Algorithms. Neural Computation. 1998, Vol.10. 1895-1923.
[14] Du Lan, Liu Hongwei, Bao Zheng, Xing Mengdao. Radar HRRP target recognition based on higher order spectra. IEEE Trans. on Signal Processing. Jul. 2005, Vol.53 (7). 2359-2368.
[1] Li H.-J., Yang S.-H.. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. A.P.. 1993, Vol.41(3). 261-268.
[2] 廖学军．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[3] Marques de Sa J.P.. Pattern Recognition Concepts, Methods and Applications. New York: Springer. 2001.
[4] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[5] Jacobs S.P.. Automatic target recognition using high-resolution radar range profiles. Washington University. 1999.
[6] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. S. P.. 2001, Vol.49(9). 1875-1885.
[7] Azimi-Sadjadi M. R., Yao D., Huang Q. et. al.. Underwater Target Classification Using Wavelet Packets and Neural Networks. IEEE Trans. On N.N.. 2000, Vol.11(3). 784-794.
[8] 杜兰，刘宏伟，保铮，张军英．一种利用雷达高分辨距离像幅度起伏特性的特征提取新方法．电子学报．2005年3月，Vol．33(3)．411-415．
[9] 杜兰，刘宏伟，保铮，张军英．一种用于雷达HRRP功率谱的加权特征压缩方法．西安电子科技大学学报．2006，Vol．33(2)．173-177．
[10] 刘宏伟，马建华，保铮．BOX-COX变换提高雷达高分辨距离像识别性能的物理机理分析．第九届全国雷达学术年会．2004年．354-357．
[1] Jacobs S. P.. Automatic target recognition using high-resolution radar range profiles. Ph. D. Dissertation. Washington University. 1999.
[2] Van der Heiden R., Groen F. C. A.. The Box-Cox Metric for Nearest Neighbour Classification Improvement. Pattern Recognition. 1997, Vol.30(2). 273-279.
[3] Shaw A. K., Vasgist R., Williams R.. HRR-ATR using Eigen-templates with observation in unknown target scenario. Proceedings of SPIE. 2000, Vol.4053. 467-478.
[4] Webb A. R.. Gamma Mixture Models for Target Recognition. Pattern Recognition. 2000, Vol.33.2045-2054.
[5] Copsey K., Webb A. R.. Bayesian Gamma Mixture Model Approach to Radar Target Recognition. IEEE Trans. on A. E. S.. Oct. 2003, Vol.39(4). 1201-1217.
[6] Xu L., Krzyzak A., Oja E.. Rival Penalized Competitive Learning for Clustering Analysis, RBF Net, and Curve Detection. IEEE Trans. on N. N.. Vol.4. 636-648.
[7] Evans M., Hastings N., Peacock B.. Statistical Distributions. Second Edition. New York: John Wiley and Sons. 1993.
[8] Fukunaga K.. Introduction to Statistical Pattern Recognition. Second Edition. Boston: Academic. 1990.
[9] Skolnik M.. Introduction to Radar Systems. Second Edition. New York: McGraw-Hill. 1980.
[10] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. New York: John Wiley and Sons. 2001.
[11] Abramowitz M., Stegun I. A.. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover. 1972.
[12] Tipping M. E., Bishop C. M.. Mixtures of principal component analysers. Neural Computation. 1999, Vol. 11 (2). 443-482.
[13] Rubin D., Thayer D.. EM algorithms for ML factor analysis. Psychometrika. 1982, Vol. 47(1). 69-76.
[14] Ghahramani Z., Hinton G. E.. The EM algorithm for mixtures of factor analyzers. Technical Report CRG-TR-96-1. Univ. of Toronto. 1996. http://www.gatsby.ucl.ac.uk/～zoubin/papers/tr-96-1 .ps.gz
[15] Akaike H.. Factor analysis and AIC. Psychometrika. 1987, Vol.52(3). 317-332.
[16] Xu L.. BYY harmony learning, structural RPCL, and topological self-organizing on mixture models. Neural Networks. 2002, Vol.15.1125-1151.
[17] Constantinos C., Michalis K. T., Aristidis L.. Bayesian feature and model selection for Gaussian mixture models. IEEE Trans. P.A.M.I.. Jun. 2006, Vol.28(6). 1013-1018.
[18] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[19] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Trans. on S.P.. Jun. 2006, Vol.54(6). 2226-2238.
[20] 杜兰，刘宏伟，保铮．利用目标方位信息改善雷达距离像识别性能．系统工程与电子技术．2004年8月，Vol．26(8)．1040-1043．
[21] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[22] Cheung Y. M.. Maximum weighted likelihood via rival penalized EM for density mixture clustering with automatic model selection. IEEE Trans. K. D. E.. Jun. 2006, Vol. 17(6). 750-761.
[23] Jain A. K., Duin R. P. W., Mao J.. Statistical pattern recognition: A review. IEEE Trans. on P.A.M.I.. Vol.22(1). 4-37.
[24] Stehwien W.. Statistics and Correlation Properties of High Resolution X-band Sea Clutter. Record of the 1994 IEEE National Radar Conference. Mar. 1994, 46-51.
[25] Vapnik V. N.. The Nature of Statistical Learning Theory. Berlin: Spring-Verlag. 1995.
[26] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A compound statistical model based radar HRRP target recognition. Lecture Notes in Computer Science Vol.3497. 369-374.
[27] Williams R., Westerkamp J., Gross D. et. al.. Automatic Target Recognition of Time Critical Moving Targets 1D High Range Resolution (HRR) Radar. IEEE AES System Magazine. 2000, Vol.15(4). 37-43.
[28] Jacobs S. P., O'sollivan J. A.. Automatic target recognition using sequences of high resolution radar range-profiles. IEEE Trans. A.E.S.. 2000, 36 (2). 364-380.
[1] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[2] 邢孟道．基于实测数据的雷达成像方法研究．博士研究生学位论文．西安电子科技大学．2002．
[3] Jacobs S.P.. Automatic target recognition using high-resolution radar range profiles. Washington University. 1999.
[4] Van der Heiden R., Groen F. C. A.. The Box-Cox Metric for Nearest Neighbour Classification Improvement. Pattern Recognition. 1997, Vol.30(2). 273-279.
[5] Shaw A. K., Vasgist R., Williams R.. HRR-ATR using Eigen-templates with observation in unknown target scenario. Proceedings of SPIE. 2000, Vol.4053. 467-4781
[6] Fukunaga K.. Introduction to Statistical Pattern Recognition, Second Edition. Boston: Academic. 1990.
[7] 刘宏伟，马建华，保铮．BOX-COX变换提高雷达高分辨距离像识别性能的物理机理分析．第九届全国雷达学术年会．2004年．354-357．
[8] Liu H.-W., Bao Z.. Radar HRR Profiles Recognition based on SVM with Power-Transformed-Correlation Kernel. Springer Lecture Notes in Computer Science. Berlin: Springer-Verlag. Aug. 2004. 531-536.
[9] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. New York: John Wiley and Sons. 2001.
[10] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. Radar automatic target recognition using complex high-resolution range profiles, IET Radar, Sonar & Navigation. Feb. 2007, Vol.1(1). 18-26.
[11] Du Lan, Liu Hongwei, Bao Zheng. Radar automatic target recognition based on complex high-resolution range profiles. Proceedings of 2006 international conference on radar. 2006. 1415-1419.
[12] Papoulis A., Pillai S. U.. Probability, Random Variables and Stochastic Processes. Forth Edition. New York: The McGraw-Hill Companies. 2002.
[1] Kuncheva L.I.. Using diversity measures for generating error-correcting output codes in classifier ensembles. Pattern Recognition Letters. 2005, Vol.26.83-90.
[2] Dietterich T. G., Bakiri G.. Solving multiclass learning problems via error-correcting output codes. Journal of Artificial Intelligence Research. 1995, Vol.2.263-286.
[3] T.W.T., G. R.. Coding and decoding strategies for multi-class learning problems. Information Fusion. 2003, Vol.4(1). 11-21.
[4] Lin S., Costello D. J.. Error Control Coding. Second Edition. Prentice-Hall. 2004.
[5] Francesco M., Giorgio V., Effectiveness of Error Correcting Output Coding Methods in Ensemble and Monolithic Learning Machines. Pattern Analysis and Applications. 2003, Vol.6(4). 285-300.
[6] Sebald D. J., Bucklew J. A.. Support Vector Machines and the multiple Hypothesis Test Problems. IEEE Trans. on Signal Processing. 2001, Vol.49(11), 865-2872.
[7] Cortes C., Vapnik V.. Support-vector networks. Machine Learning. 1995, Vol.20(3). 273-297.
[8] Vapnik V. N.. Statistical Learning Theory. New York: Wiley. 1998.
[9] Xu L., Krzy2ak A., Oja E.. Rival Penalized Competitive Learning for Clustering Analysis, RBF Net, and Curve Detection. IEEE Trans. on N. N.. Vol.4. 636-648.
[10] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. John Wiley and Sons. 2001.
[11] Kohonen T.. Self-Organizing Maps. Berlin: Springer Verlag. 1995.
[12] Haykin S.. Neural Networks: a comprehensive foundation. Second Edition. Pretice-Hall. 1999.
[13] Liu H.-W., Bao Z.. Radar HRR Profiles Recognition based on SVM with Power-Transformed-Correlation Kernel. Springer Lecture Notes in Computer Science. Berlin: Springer-Verlag. 2004.531-536.
[14] 袁莉，刘宏伟，保铮．基于中心矩特征的雷达HRRP自动目标识别．电子学报，2004，Vol．32(12，)，2078-2081．
[15] Du Lan, Zhang Junying, Bao Zheng. Multicategory classification based on the hypercube self-organization mapping (SOM) scheme. Lecture Notes in Computer Science. 2006, Vol.4221.107-110.
[2] Skolnik M.. Introduction to Radar Systems, Second Edition, New York: McGraw-Hill. 1980.
[3] 廖学军．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[4] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[5] 邢孟道．基于实测数据的雷达成像方法研究．博士研究生学位论文．西安电子科技大学．2002．
[6] 刘宏伟，杜兰，袁莉，保铮．雷达高分辨距离像目标识别研究进展．电子与信息学报．2005年8月，Vol．27(8)．1328-1334．
[7] Nebabin V. G.. Methods and techniques of radar recognition. Boston: Artech House. 1997.
[8] Barton D. K.. Spumik Ⅱ as observed by C band radar. IRE National Conference. 1959, Vol.7(5). 67-73.
[9] Skolnik M. I.. Radar Handbook. Second Edition. 北京：电子工业出版社. 2003.
[10] Lewis G. N., Postol T. A.. Furore Challenges to Ballistic Missile Defense. IEEE Spectrum, 1997(9). 60-68.
[11] William P. D., William W. W.. Radar Development at Lincoln Laboratory: An overview of the First Fifty Years. Lincoln Laboratory Journal. 2000, Vol.12(2). 147-166.
[12] Lemnios W. Z., Grometestein A.. Overview of the Lincoln Laboratory Ballistic Missile Defense Program. Lincoln Laboratory Journal. 2002, Vol. 13(1). 9-32.
[13] Baum C. E.. On the singularity expansion method for the solution of electromagnetic interaction problem. Air Force Weapon Lab. International Note 88. 1971.
[14] Eesterkamp J.. A Framework for 1D HRR ATR evaluation. AFRL Technical Report. Aug. 1998.
[15] Moving and stationary target acquisition and recognition, Program technology review. Denver, CO. Nov. 1996. http://www.mbvlab.wpafb.af.mil/public/MBVDATA
[16] Zhao Q., Principle J. C., Support vector machines for SAR automatic target recognition. IEEE Trans. A.E.S.. 2001, Vol.37(2). 643-654.
[17] Novak L. M., Owirka G. J., Weaver A. L.. Automatic target recognition using enhanced resolution SAR data. IEEE Trans. A.E.S.. 1999, Vol.35 (1).157-175.
[18] An Overview of automatic target recognition. The Lincoln Laboratory Journal. 1993, Vol.6(1).
[19] Marcoz Y., Miguel T.T., Feature Selection using Genetic Algorithms in SAR Airborne Imagery. http://www.cim.mcgill.ca,2001.
[20] Punkle P. et al.. Multi-aspect target detection for SAR imagery using Hidden Markov models. IEEE Trans. A.E.S.. 2001, Vol.39(1). 46-55.
[21] Bryant M., Garber F.. SVM classifier applied to the MSTAR public data set. Algorithms for Synthetic Aperture Radar Imagery Ⅵ. Proceedings of the SPIE. 2001, Vol. 3721. 355-360.
[22] Musman S., Kerr D., Bachmann C.. Automatic Recognition of ISAR Images. IEEE Trans. A.E.S.. 1996, Vol.32(4). 1392-1403.
[23] Rosenbach K., Schiller J., Construction and Test of a Classifier for Non-Cooperative Air-Target Identification based on 2-D-ISAR Images. Proceedings of IRS'98 International Radar Symposium. Sep. 1998.1023-1033.
[24] Maki A. et al.. ISAR Image Analysis by Subspace Method: Automatic Extraction and Identification of Ship Profile. IEEE Radar 2001. 523-528.
[25] Maki A. et al.. Automatic Ship Identification in ISAR Imagery: An On-line System using CMSM. IEEE Radar 2002.206-211.
[26] Li H.-J., Wang Y. D., Wang L.-H., Matching score properties between range profile of high-resolution radar targets. IEEE trans. A. P.. 1996, 44(4). 444-452.
[27] Zyweck A., Bogner R. E.. Coherent averaging of range profiles. IEEE International Radar Conference. 1995.
[28] Mitchell R. A., Dewall R.. Overview of high range resolution radar target identification. In Proceedings of Automayic Target Recognition 'Working Group. 1994.
[29] Jacobs S. P.. Automatic target recognition using high-resolution radar range profiles. Ph. D. Dissertation. Washington University. 1999.
[30] 王雪松．宽带极化信息处理研究．博士研究生学位论文．国防科学技术大学．1999．
[31] Van der Heiden R., Groen F. C. A.. The Box-Cox Metric for Nearest Neighbour Classification Improvement. Pattern Recognition. 1997, Vol. 30(2). 273-279.
[32] Cohen M. N.. Variability of ultra-high range resolution profiles and some implications for target recognition. SPIE. 1992. 256-266.
[33] Li H.-J., Yang S.-H.. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. A.P.. 1993, Vol.41(3). 261-268.
[34] Zyweck A., Bogner R. E.. Radar target classification of commercial aircraft. IEEE Trans. A.E.S.. 1996, Vol.32(2). 598-606.
[35] Williams R., Westerkamp J., Gross D. et al.. Automatic Target Recognition of Time Critical Moving Targets 1D High Range Resolution (HRR) Radar. IEEE AES System Magazine. 2000, Vol. 15(4). 37-43.
[36] Webb A. R.. Gamma Mixture Models for Target Recognition. Pattern Recognition. 2000, 33.2045-2054.
[37] Du Lan, Liu Hongwei, Bao Zheng, Xing Mengdao. Radar HRRP target recognition based on higher order spectra. IEEE Trans. on Signal Processing. Jul. 2005, Vol.53 (7). 2359-2368.
[38] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Trans. on Signal Processing. Vol.54 (6). 2226-2238.
[39] 杜兰，刘宏伟，保铮．利用目标方位信息改善雷达距离像识别性能．系统工程与电子技术．2004年8月，Vol．26(8)．1040-1043．
[40] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. Signal Processing. 2001, Vol.49(9). 1875-1885.
[41] Kim K. T., Seo D. K., Kim H. T.. Efficient radar target recognition using the MUSIC algorithm and invariant feature. IEEE Trans A.P.. 2002, Vol.50(3). 325-337.
[42] 杜兰，刘宏伟，保铮，张军英．一种利用雷达高分辨距离像幅度起伏特性的特征提取新方法．电子学报．2005年3月，Vol．33(3)．411-415．
[43] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. Radar automatic target recognition using complex high-resolution range profiles. IET Radar, Sonar & Navigation. Feb. 2007, Vol. 1 (1). 18-26.
[44] 杜兰，保铮，刘宏伟，高分辨距离像雷达自动目标识别的模板匹配问题，第九届全国雷达学术年会论文集，2004年8月．509-512．
[45] Li J., Stoica P.. Efficient mixed-spectrum estimation with application to feature extraction. IEEE Trans. on Signal Processing. Feb. 1996, Vol.42(2). 281-295.
[46] Bharadwaj P., Runkle P., Carin L.. Multiaspct classification of airborne targets via physics-based HMMs and matching pursuits. IEEE Trans. on A.E.S.. 2001, Vol.37(2): 595-606.
[47] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A weighted feature reduction method for power spectra of radar HRRPs. Journal of electronics (China). 2006, Vol.23 (3). 365-369.
[48] Du Lan, Zhang Junying, Bao Zheng. Multicategory classification based on the hypercube self-organization mapping (SOM) scheme. Lecture Notes in Computer Science Vol.4221.107-110.
[49] Gorshkov S. A., Leschenko S. P., Orlenko V. M. et al.. Radar Target Backscattering Simulation Software and User's Manual. Boston London: Artech House. 2002.
[50] Sebald D. J., Bucklew J. A.. Support vector machines and the multiple hypothesis test problem. IEEE Trans. on S.P.. 2001, Vol.49(11). 2865-2872.
[51] Dietterich T. G., BaNff. G.. Solving multiclass leaming problems via error-correcting output codes. Journal of Artificial Intelligence Research. 1995(2). 263-286.
[52] T. W. T., G. R.. Coding and decoding strategies for multi-class learning problems. Information Fusion. 2003, Vol.4(1 ). 11-21.
[53] 杜兰，刘宏伟，保铮．一种基于距离一多普勒二维联合的群目标分辨方法．电子学报．2004年6月，Vol．32(6)．881-885．
[54] 杜兰，保铮，邢孟道．直升机雷达回波的分析与检测．西安电子科技大学学报．2003年10月，Vol．30(5)．574-579．
[55] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[1] 廖学车．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[2] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[3] Xing M.-D., Bao Z., Pei B.. The properties of high-resolution range profiles. Optical Engineering. 2002, 41 (2). 493-504.
[4] Jacobs S.P.. Automatic target recognition using high-resolution radar range profiles. Washington University. 1999.
[5] Kim K.-T., Seo D.-K., Kim H.-T.. Efficient radar target recognition using the Music algorithm and invariant features. IEEE Trans. A.P.. 2002, 50 (3). 325-337.
[6] Williams R., Westerkamp J., Gross D. et al.. Automatic Target Recognition of Time Critical Moving Targets 1D High Range Resolution (HRR) Radar. IEEE AES System Magazine. 2000, 15(4). 37-43.
[7] Miller M.I., Grenander U., OSullivan J.A. et al.. Automatic target recognition organized via jump-diffusion algorithms. IEEE Trans. A.P.. 1997, Vol.6(1). 157-173.
[8] 杜兰，刘宏伟，保铮．利用目标方位信息改善雷达距离像识别性能．系统工程与电子技术．2004年8月，Vol．26(8)．1040-1043．
[9] 杜兰，保铮，刘宏伟．高分辨距离像雷达自动目标识别的模板匹配问题．第九届全国雷达学术年会论文集．2004年8月．509-512．
[10] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. New York: John Wiley and Sons, 2001.
[11] Bhatnagar V. Automatic target recognition using high range resolution data. Dayton: Master Thesis. Wright State University. 1998.
[12] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. Signal Processing. 2001, Vol.49(9). 1875-1885.
[13] 杜兰，保铮，邢忑道．飞机目标的雷达一维距离像特性研究．西安电子科技大学学报．2001，Vol．28(增刊)．14-19．
[14] Bao Z., Sun C.-Y., Xing M.-D., Time-Frequency Approaches to ISAR Imaging of Maneuvering Targets and Their Limitations. IEEE Trans. A.E.S.. 2001, Vol. 37(3). 1091-1099.
[15] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[16] Marques de Sa J.P.. Pattern Recognition Concepts, Methods and Applications. New York: Springer. 2001.
[17] 邢孟道．基于实测数据的雷达成像方法研究．博士研究生学位论文．西安电子科技大学．2002．
[18] Li H.-J., Wang Y. D., Wang L.-H., Matching score properties between range profile of high-resolution radar targets. IEEE trans. A. P.. 1996, 44(4). 444-452.
[1] 廖学军．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[2] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[3] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. S. P., 2001, Vol. 49(9). 1875-1885.
[4] Popovici V., Thiran J. P.. Pattern Recognition Using Higher-order Local Autocorrelation Coefficients. 12~(th) IEEE Worshop on Neural Networks for Signal Processing. 2002. 229-238.
[5] Chandran V., Elgar S. L.. Pattern recognition using invariants defined from higher order spectra—One-dimensional inputs. IEEE. Trans. S.P.. 1993, Vol.41(1). 205-212.
[6] Tugnait J. K.. Detection of non-Gaussian signals using integrated polyspectrum. IEEE Trans. S.P.. 1994, Vol.42(11). 3137-3149.
[7] Nikias C. L., Petropulu A. P.. High-order Spectra Analysis: A Nonlinear Signal Processing Framework. NJ: Prentice-Hall. 1993.
[8] 张贤达．现代信号处理．北京：清华大学出版社．1995．
[9] 沈凤麟，叶中付，钱玉美．信号统计分析与处理．合肥：中国科学技术大学出版社．2001．
[10] Marques J. P.. Pattem Recognition Concepts, Methods and Applications. New York: Springer. 2001.
[11] 边肇祺，张学工．模式识别(第二版)．北京：清华大学出版社．2000．
[12] 赵群．基于高分辨一维距离像的雷达目标识别与检测．博士研究生学位论文．西安电子科技大学．1995．
[13] Dietterich T. G.. Approximate Statistical Tests for Comparing Supervised Classification Leaming Algorithms. Neural Computation. 1998, Vol.10. 1895-1923.
[14] Du Lan, Liu Hongwei, Bao Zheng, Xing Mengdao. Radar HRRP target recognition based on higher order spectra. IEEE Trans. on Signal Processing. Jul. 2005, Vol.53 (7). 2359-2368.
[1] Li H.-J., Yang S.-H.. Using range profiles as feature vectors to identify aerospace objects. IEEE Trans. A.P.. 1993, Vol.41(3). 261-268.
[2] 廖学军．基于高分辨距离像的雷达目标识别．博士研究生学位论文．西安电子科技大学．1999．
[3] Marques de Sa J.P.. Pattern Recognition Concepts, Methods and Applications. New York: Springer. 2001.
[4] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[5] Jacobs S.P.. Automatic target recognition using high-resolution radar range profiles. Washington University. 1999.
[6] Zhang X., Shi Y., Bao Z.. A New Feature Vector Using Selected Bispectra for Signal Classification with Application in Radar Target Recognition. IEEE Trans. S. P.. 2001, Vol.49(9). 1875-1885.
[7] Azimi-Sadjadi M. R., Yao D., Huang Q. et. al.. Underwater Target Classification Using Wavelet Packets and Neural Networks. IEEE Trans. On N.N.. 2000, Vol.11(3). 784-794.
[8] 杜兰，刘宏伟，保铮，张军英．一种利用雷达高分辨距离像幅度起伏特性的特征提取新方法．电子学报．2005年3月，Vol．33(3)．411-415．
[9] 杜兰，刘宏伟，保铮，张军英．一种用于雷达HRRP功率谱的加权特征压缩方法．西安电子科技大学学报．2006，Vol．33(2)．173-177．
[10] 刘宏伟，马建华，保铮．BOX-COX变换提高雷达高分辨距离像识别性能的物理机理分析．第九届全国雷达学术年会．2004年．354-357．
[1] Jacobs S. P.. Automatic target recognition using high-resolution radar range profiles. Ph. D. Dissertation. Washington University. 1999.
[2] Van der Heiden R., Groen F. C. A.. The Box-Cox Metric for Nearest Neighbour Classification Improvement. Pattern Recognition. 1997, Vol.30(2). 273-279.
[3] Shaw A. K., Vasgist R., Williams R.. HRR-ATR using Eigen-templates with observation in unknown target scenario. Proceedings of SPIE. 2000, Vol.4053. 467-478.
[4] Webb A. R.. Gamma Mixture Models for Target Recognition. Pattern Recognition. 2000, Vol.33.2045-2054.
[5] Copsey K., Webb A. R.. Bayesian Gamma Mixture Model Approach to Radar Target Recognition. IEEE Trans. on A. E. S.. Oct. 2003, Vol.39(4). 1201-1217.
[6] Xu L., Krzyzak A., Oja E.. Rival Penalized Competitive Learning for Clustering Analysis, RBF Net, and Curve Detection. IEEE Trans. on N. N.. Vol.4. 636-648.
[7] Evans M., Hastings N., Peacock B.. Statistical Distributions. Second Edition. New York: John Wiley and Sons. 1993.
[8] Fukunaga K.. Introduction to Statistical Pattern Recognition. Second Edition. Boston: Academic. 1990.
[9] Skolnik M.. Introduction to Radar Systems. Second Edition. New York: McGraw-Hill. 1980.
[10] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. New York: John Wiley and Sons. 2001.
[11] Abramowitz M., Stegun I. A.. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover. 1972.
[12] Tipping M. E., Bishop C. M.. Mixtures of principal component analysers. Neural Computation. 1999, Vol. 11 (2). 443-482.
[13] Rubin D., Thayer D.. EM algorithms for ML factor analysis. Psychometrika. 1982, Vol. 47(1). 69-76.
[14] Ghahramani Z., Hinton G. E.. The EM algorithm for mixtures of factor analyzers. Technical Report CRG-TR-96-1. Univ. of Toronto. 1996. http://www.gatsby.ucl.ac.uk/～zoubin/papers/tr-96-1 .ps.gz
[15] Akaike H.. Factor analysis and AIC. Psychometrika. 1987, Vol.52(3). 317-332.
[16] Xu L.. BYY harmony learning, structural RPCL, and topological self-organizing on mixture models. Neural Networks. 2002, Vol.15.1125-1151.
[17] Constantinos C., Michalis K. T., Aristidis L.. Bayesian feature and model selection for Gaussian mixture models. IEEE Trans. P.A.M.I.. Jun. 2006, Vol.28(6). 1013-1018.
[18] 裴炳南．高分辨雷达自动目标识别方法研究．博士研究生学位论文．西安电子科技大学．2002．
[19] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A two-distribution compounded statistical model for radar HRRP target recognition. IEEE Trans. on S.P.. Jun. 2006, Vol.54(6). 2226-2238.
[20] 杜兰，刘宏伟，保铮．利用目标方位信息改善雷达距离像识别性能．系统工程与电子技术．2004年8月，Vol．26(8)．1040-1043．
[21] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[22] Cheung Y. M.. Maximum weighted likelihood via rival penalized EM for density mixture clustering with automatic model selection. IEEE Trans. K. D. E.. Jun. 2006, Vol. 17(6). 750-761.
[23] Jain A. K., Duin R. P. W., Mao J.. Statistical pattern recognition: A review. IEEE Trans. on P.A.M.I.. Vol.22(1). 4-37.
[24] Stehwien W.. Statistics and Correlation Properties of High Resolution X-band Sea Clutter. Record of the 1994 IEEE National Radar Conference. Mar. 1994, 46-51.
[25] Vapnik V. N.. The Nature of Statistical Learning Theory. Berlin: Spring-Verlag. 1995.
[26] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. A compound statistical model based radar HRRP target recognition. Lecture Notes in Computer Science Vol.3497. 369-374.
[27] Williams R., Westerkamp J., Gross D. et. al.. Automatic Target Recognition of Time Critical Moving Targets 1D High Range Resolution (HRR) Radar. IEEE AES System Magazine. 2000, Vol.15(4). 37-43.
[28] Jacobs S. P., O'sollivan J. A.. Automatic target recognition using sequences of high resolution radar range-profiles. IEEE Trans. A.E.S.. 2000, 36 (2). 364-380.
[1] 叶炜．逆合成孔径雷达运动补偿与成像研究．博士研究生学位论文．西安电子科技大学．1996．
[2] 邢孟道．基于实测数据的雷达成像方法研究．博士研究生学位论文．西安电子科技大学．2002．
[3] Jacobs S.P.. Automatic target recognition using high-resolution radar range profiles. Washington University. 1999.
[4] Van der Heiden R., Groen F. C. A.. The Box-Cox Metric for Nearest Neighbour Classification Improvement. Pattern Recognition. 1997, Vol.30(2). 273-279.
[5] Shaw A. K., Vasgist R., Williams R.. HRR-ATR using Eigen-templates with observation in unknown target scenario. Proceedings of SPIE. 2000, Vol.4053. 467-4781
[6] Fukunaga K.. Introduction to Statistical Pattern Recognition, Second Edition. Boston: Academic. 1990.
[7] 刘宏伟，马建华，保铮．BOX-COX变换提高雷达高分辨距离像识别性能的物理机理分析．第九届全国雷达学术年会．2004年．354-357．
[8] Liu H.-W., Bao Z.. Radar HRR Profiles Recognition based on SVM with Power-Transformed-Correlation Kernel. Springer Lecture Notes in Computer Science. Berlin: Springer-Verlag. Aug. 2004. 531-536.
[9] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. New York: John Wiley and Sons. 2001.
[10] Du Lan, Liu Hongwei, Bao Zheng, Zhang Junying. Radar automatic target recognition using complex high-resolution range profiles, IET Radar, Sonar & Navigation. Feb. 2007, Vol.1(1). 18-26.
[11] Du Lan, Liu Hongwei, Bao Zheng. Radar automatic target recognition based on complex high-resolution range profiles. Proceedings of 2006 international conference on radar. 2006. 1415-1419.
[12] Papoulis A., Pillai S. U.. Probability, Random Variables and Stochastic Processes. Forth Edition. New York: The McGraw-Hill Companies. 2002.
[1] Kuncheva L.I.. Using diversity measures for generating error-correcting output codes in classifier ensembles. Pattern Recognition Letters. 2005, Vol.26.83-90.
[2] Dietterich T. G., Bakiri G.. Solving multiclass learning problems via error-correcting output codes. Journal of Artificial Intelligence Research. 1995, Vol.2.263-286.
[3] T.W.T., G. R.. Coding and decoding strategies for multi-class learning problems. Information Fusion. 2003, Vol.4(1). 11-21.
[4] Lin S., Costello D. J.. Error Control Coding. Second Edition. Prentice-Hall. 2004.
[5] Francesco M., Giorgio V., Effectiveness of Error Correcting Output Coding Methods in Ensemble and Monolithic Learning Machines. Pattern Analysis and Applications. 2003, Vol.6(4). 285-300.
[6] Sebald D. J., Bucklew J. A.. Support Vector Machines and the multiple Hypothesis Test Problems. IEEE Trans. on Signal Processing. 2001, Vol.49(11), 865-2872.
[7] Cortes C., Vapnik V.. Support-vector networks. Machine Learning. 1995, Vol.20(3). 273-297.
[8] Vapnik V. N.. Statistical Learning Theory. New York: Wiley. 1998.
[9] Xu L., Krzy2ak A., Oja E.. Rival Penalized Competitive Learning for Clustering Analysis, RBF Net, and Curve Detection. IEEE Trans. on N. N.. Vol.4. 636-648.
[10] Duda R. O., Hart P. E., Stork D. G.. Pattern Classification. Second Edition. John Wiley and Sons. 2001.
[11] Kohonen T.. Self-Organizing Maps. Berlin: Springer Verlag. 1995.
[12] Haykin S.. Neural Networks: a comprehensive foundation. Second Edition. Pretice-Hall. 1999.
[13] Liu H.-W., Bao Z.. Radar HRR Profiles Recognition based on SVM with Power-Transformed-Correlation Kernel. Springer Lecture Notes in Computer Science. Berlin: Springer-Verlag. 2004.531-536.
[14] 袁莉，刘宏伟，保铮．基于中心矩特征的雷达HRRP自动目标识别．电子学报，2004，Vol．32(12，)，2078-2081．
[15] Du Lan, Zhang Junying, Bao Zheng. Multicategory classification based on the hypercube self-organization mapping (SOM) scheme. Lecture Notes in Computer Science. 2006, Vol.4221.107-110.