摘要
电磁波的极化特征是信号幅度、相位、频率和波形等信息外,另一个可资利用的重要特征信息。对极化信息的充分挖掘和利用,有利于提高雷达和通信等系统的性能。电磁矢量传感器构成的极化敏感阵列在雷达、通信、声纳和生物医学等众多领域具有广阔的应用前景。另一方面,MIMO雷达以其在目标检测、参数估计等方面的独特优势,使其成为近十年的一个研究热点。而参数估计(如波达方向、极化状态角等)是雷达和通信等系统的主要任务之一。故本文主要研究基于电磁矢量传感器以及电磁矢量传感器在MIMO雷达应用中的波达方向、极化状态角等参数估计问题。具体内容可概括为如下四个部分。
第一部分,研究电磁矢量传感器对相干信源波达方向的估计问题。首先建立传统共点式电磁矢量传感器对完全极化入射信源响应的信号模型,接着回顾几种基于共点式电磁矢量传感器的波达方向估计算法。然后针对传统极化平滑算法解相干源时没有利用子阵互相关信息导致分辨率较差的问题,提出一种新的解相干源预处理方法：加权极化平滑算法。该算法利用了电磁矢量传感器阵列的六个分量组成子阵的全部自相关和互相关信息,对接收阵列协方差矩阵的子矩阵做加权滑动平均,得到等效的阵列协方差矩阵,以该协方差矩阵对角化为约束,推导最优加权系数的理论表达式,并分析等效信源协方差矩阵的秩,得到加权极化平滑算法最大的解相干源数为6。计算机仿真结果表明加权极化平滑算法比传统的极化平滑算法具有更高的分辨性能和估计精度。
第二部分,提出四种分离式电磁矢量传感器阵列结构,并研究其波达方向和(或)极化状态角联合估计问题。传统共点式电磁矢量传感器阵元间互耦效应明显,导致电磁矢量传感器硬件实现困难、波达方向和极化状态角估计性能严重下降。较之传统的共点式电磁矢量传感器,分离式电磁矢量传感器能够显著降低阵元间互耦,且非共点结构在硬件设计上更易于实现。故提出分离式电磁矢量传感器阵列结构来解决互耦问题。为实现两维高精度波达方向估计,首先提出由单个分离式全电磁矢量传感器和单个电偶极子组成的单三角阵列结构。在不增加任何阵元个数的前提下,提出一种双三角形阵列结构来实现两维波达方向的高精度估计。该矢量传感器空间结构分两个步骤设计：第一步,设计空间分离式电磁矢量传感器的空间结构使之满足矢量叉积传播矢量估计算法：第二步,在第一步基础上,设计阵列结构使之满足两维孔径扩展。上述两种阵列结构只使用六个或七个阵元,在实际的阵列雷达中往往不能满足检测概率和估计精度的需求,故提出一种稀疏均匀分离式电磁矢量传感器矩形阵列,针对该阵列提出了一种二维波达方向和极化参数的联合估计算法。但是全电磁矢量传感器中的电偶极子和磁偶极子的响应往往不一致,导致参数估计精度下降。故提出一种全电偶极子组成的三正交分离式矢量传感器阵列。上述所提阵列结构在降低阵元间互耦的同时,都采用稀疏阵列结构来扩展阵列的物理孔径,提高了波达方向估计精度。
第三部分,研究双基地MIMO雷达的发射角和接收角估计问题。由于MIMO雷达的自由度等于发射阵元数和接收阵元数的Kronecker积,使MIMO雷达在提供高精度参数估计的同时,计算复杂度大大增加。此外,在双基地MIMO雷达中发射角和接收角的配对亦是一个重要问题。因此,提出一种实值ESPRIT方法和波束域求根MUSIC方法,利用全程实值操作的ESPRIT算法来降低复数域的ESPRIT算法的计算量。利用波束域的转换及求根算法来降低常规阵元域MUSIC算法的计算量。另外,从提高估计精度的角度出发,针对发射阵和接收阵均为分布式子阵的双基地MIMO雷达,研究实值双尺度ESPRIT方法来估计发射角和接收角。相对于半波长均匀分布的发射阵和接收阵组成的双基地MIMO雷达,分布式阵列能够扩展阵列的物理孔径,在不增加硬件复杂度的情况下,提高了角度估计性能。而且所提三种方法均能够实现发射角和接收角的自动配对。
第四部分,研究电磁矢量传感器MIMO雷达的波达方向估计问题。鉴于MIMO雷达在参数估计方面的独特优势,考虑电磁矢量传感器在MIMO雷达中的应用,提出一种干涉式矢量传感器MIMO雷达,利用干涉发射阵列的长、短基线空间平移不变性采用双尺度ESPRIT算法获取发射角的高精度估计值；同理,利用矢量接收阵的双尺度空间平移不变特性得到高精度接收角估计值。该干涉矢量传感器MIMO阵列雷达,可同时获取MIMO雷达的波形分集和矢量传感器的极化分集,且在不增加阵元数和硬件复杂度情况下扩展有效孔径,提高了角度估计精度。另一方面,针对常规电磁矢量传感器MIMO雷达采用固定极化的发射极化方式,极化信息并没有得到充分利用,提出一种CRB最小化的发射极化优化算法来估计目标的波达方向。所提优化算法的波达方向估计精度高于采用固定极化的波达方向估计算法,并能保持固定极化波达方向估计算法的两维波达方向估计可自动配对、发射电磁矢量传感器位置可任意的优点。
Polarization of electromagnetic wave is another important signal information besides amplitude, phase, frequency and waveform. The performance of radar and communication systems can be significantly improved by fully utilizing the polarization. Therefore, the polarization sensitive array consisted of electromagnetic vector sensor has broad applications in radar, communication, sonar and biomedicine. On the other hand, MIMO radar is a hot research topic in recent years with its advantages in target detection and parameter estimation. Parameter (such as DOA and polarization state angle) estimation is one of the main tasks of radar and communication systems. Therefore, this paper studies on DOA and polarization state estimation with electromagnetic vector sensor array and its applications in MIMO radar. Specific contents can be summarized as the following four parts.
The first part studies the problem of DOA estimation of coherent incident signals for electromagnetic vector sensor. First, signal model is built with the scenario that completely polarized signal impinges upon traditional spatially collocating electromagnetic vector sensor, followed by reviewing of several DOA estimation algorithms based on electromagnetic vector sensor. Furthermore, no utilization of the cross-correlation information among the smoothed subarrays leads to low resolution of polarization smoothing algorithm. An improved polarization smoothing algorithm of direction-of-arrival estimation for coherent sources is proposed, which is called weighted polarization smoothing algorithm. Full use of auto-correlation and cross-correlation of the subarrays composed of six components of electromagnetic vector-sensor array is performed in weighted polarization smoothing algorithm. An equivalent covariance matrix is obtained by a weighted sum of36sub-matrixes. The derivation of theoretical formula of optimal weighting coefficients and analysis of the rank of equivalent signal covariance matrix constrained by its diagonalization are accomplished. Simulation results are presented to illustrate higher resolution and accuracy of weighted polarization smoothing against polarization smoothing.
The second part proposes four structures of spatially noncollocating electromagnetic vector sensor (EMVS) array and studies its DOA and/or polarization estimation. Traditional spatially collocating EMVS array has strong mutual coupling, resulting the difficulty of the implementation of EMVS hardware, and the decline of the DOA and polarization estimation performance seriously. Spatially noncollocating EMVS (SNC-EMVS) can reduce greatly the mutual coupling and the hardware cost compared with the spatially collocating EMVS (SC-EMVS). Therefore, we propose SNC-EMVS array to solve the problem of strong mutual coupling in SC-EMVS. For two dimensional high accuracy DOA estimation, we firstly propose a new SNC-EMVS array with triangular configuration, which is composed of a single SNC-EMVS and a single dipole. Without adding sensors, we then propose a double-triangular configuration array to achieve two dimensional (2-D) high accuracy DOA estimation. The double-triangular configuration array is obtained by a two-step design. The first step aims to make the configurations of SNC-EMVS satisfy the "vector cross-product" Poynting-vector estimator. The second step focuses on extending the2-D array apertures of SNC-EMVS. Detection probability and estimation accuracy of an actual array radar often cannot be satisfied by only using six or seven sensors of the above two array structures. Therefore, we thirdly propose a sparse uniform rectangular SNC-EMVS array and a novel2-D DOA and polarization parameters estimation algorithm. But in practical applications, electric-field response and magnetic-field response in EMVS are often inconsistent, which leads to estimation performance degradation. Therefore, we fourth propose a sparse uniform rectangular SNC-EMVS array consisted of only electric-dipoles. The above four array structures not only reduce mutual coupling but also extend the2-D apertures to improve DOA estimation accuracy by using sparse structures.
The third part studies the problem of DOD and DOA estimation for bistatic MIMO radar. Since the degree of freedom of MIMO radar is equal to Kronecker product between the number of transmitter and receiver, MIMO radar greatly increases computational complexity besides providing high accuracy parameter estimates. Furthermore, the pairing of DODs and DOAs in bistatic MIMO radar is also an important issue. Therefore, we propose unitary ESPRIT and beamspace root MUSIC method to reduce the computational complexity. Unitary ESPRIT uses real-valued operations throughout ESPRIT algorithm to reduce the computational complexity of the complex-valued ESPRIT algorithm. Beamspace root MUSIC uses beamspace transformation and root-like method to reduce the computational complexity of conventional MUSIC algorithm. In addition, from the perspective of improving the estimation accuracy, we propose distributed array bistatic MIMO radar and unitary two-size ESPRIT to estimate the DOD and DOA. Compared to the uniform linear array with the half-wavelength element spacing, distributed array can extend the physical aperture without increasing the hardware complexity to greatly improve the angle estimation performance. Moreover, the proposed three methods are able to achieve automatic pairing between DODs and DOAs.
The fourth part studies the problem of DOA estimation for the EMVS MIMO radar. Considering the advantages of parameter estimation using MIMO radar, the EMVS is applied to MIMO radar and propose an interferometric EMVS MIMO radar. A short baseline and a long baseline of the transmitting array are utilized to obtain high accuracy DOD estimation via the two-size ESPRIT. Similarly, the high accuracy DOA estimation can be obtained by utilizing the EMVS receive array. The proposed system can obtain the waveform diversity offered by MIMO radar and the polarization diversity offered by EMVS simultaneously. Also, it is capable of extending array aperture without increasing sensors and hardware costs, which can improve the angle estimation accuracy greatly. Moreover, for the problem of the bad direction of arrival (DOA) estimation accuracy because of no utilization of the transmitted polarization information in EMVS MIMO radar, a transmitted polarization optimization algorithm based on minimizing the Cramer-Rao bound is proposed. The proposed algorithm can provide better estimation accuracy than the fixed polarization DOA estimation algorithm, and remain the advantages of the automatic pairing between the2-D DOA estimation and arbitrary placement of the transmitted electromagnetic vector sensor antennas.
引文
[1]庄钊文,徐振海,肖顺平,等.极化敏感阵列信号处理[M].北京：国防工业出版社,2005.
[2]徐友根,刘志文,龚晓峰.极化敏感阵列信号处理[M].北京：北京理工大学出版社,2013.
[3]Li J. Direction and polarization estimation using arrays with small loops and short dipoles [J]. IEEE Transactions on Antennas and Propagation,1993,41(3):379-387.
[4]Nehorai A, Paldi E. Vector-sensor array processing for electromagnetic source localization[J]. IEEE Transactions on Signal Processing,1994,42(2):376-398.
[5]Li J, Compton R T. Angle and polarization estimation using ESPRIT with a polarization sensitive array[J]. IEEE Transactions on Antennas and Propagation,1991, 39(9):1376-1383.
[6]Li J, Compton R T. Two-dimensional angle and polarization estimation using the ESPRIT algorithm[J]. IEEE Transactions on Antennas and Propagation,1992,40(5): 550-555.
[7]Compton R T. The tripole antenna:an adaptive array with full polarization flexibility[J]. IEEE Transactions on Antennas and Propagation,1981,29(6):944-952.
[8]Li J, Stoica P and Zheng D. Efficient direction and polarization estimation with a COLD array [J]. IEEE Transactions on Antennas and Propagation,1996,44(4), 539-547.
[9]Mir H S and Sahr J D. Passive direction finding using airborne vector sensors in the presence of manifold perturbations [J]. IEEE Transactions on Signal Processing,2007, 55(1):156-164.
[10]Wong K T, Zoltowski M D. Closed-form direction-finding with arbitrarily spaced electromagnetic vector-sensors at unknown locations. IEEE Transactions on Antennas and Propagation,2000,48(5):671-681.
[11]Zoltowski M D, Wong K T. ESPRIT-based 2D direction finding with a sparse array of electromagnetic vector-sensors. IEEE Transactions on Signal Processing,2000,48(8): 2195-2204.
[12]Zoltowski M D, Wong K T. Closed-form eigenstructure-based direction finding using arbitrary but identical subarrays on a sparse uniform rectangular array grid[J]. IEEE Transactions on Signal Processing,2000,48(8):2205-2210.
[13]Forsythe K W, Bliss D W and Fawcett G S. Multiple-Input Multiple-Output (MIMO) radar:performance issues [C]. Proceedings of IEEE Radar Conference,2004,1: 310-315.
[14]Robey F C, Coutts S, Weikle D, et al. MIMO radar theory and experimental results [C]. Proceedings of the 38th Asilomar Conference on Signals, Systems and Computers, 2004,1:300-304.
[15]Forsythe K W, Bliss D W. Waveform correlation and optimization issues for MIMO radar [C]. Proceedings of the 39th Asilomar Conference on Signals, Systems and Computers,2005:1306-1310.
[16]Aittomaki T and Koivunen V. Perfermance of MIMO radar with angular diversity under swerling scattering models [J]. IEEE Journal on Selected Topics in Signal Processing,2010,4(1):101-114.
[17]谢荣.MIMO雷达角度估计算法研究[D].西安：西安电子科技大学,2011.
[18]Xu L, Li J, Stoica P. Target detection and parameter estimation for MIMO radar systems[J]. IEEE Transactions on Aerospace and Electronic Systems,2008,44(3): 927-939.
[19]Joachim Ender H G and Jens K. System architectures and algorithms for radar imaging by MIMO-SAR [C]. Proceedings of 2009 IEEE Radar Conference,2009.
[20]刘波.MIMO雷达正交波形设计及信号处理研究[D].成都：电子科技大学,2007.
[21]Fuhrmann D R and Antonio G S. Transmit beamforming for MIMO radar systems using signal cross-correlation[J]. IEEE Transactions on Aerospace and Electronic Systems,2008,44(1):171-186.
[22]Errara E R and Paws T M. Direction finding with an array of antennas having diverse polarizations[J]. IEEE Transactions on Antennas and Propagation,1983,31(2): 231-236.
[23]Capon J. High-resolution frequency-wavenumber spectrum analysis[J]. Proceeding of the IEEE,1969,57(8):1408-1418.
[24]Schmidt R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas and Propagation,1986,34(3):276-280.
[25]Li J. and Compton R T. Angle estimation using a polarization sensitive array[J]. IEEE Transactions on Antennas and Propagation,1991,39(10):1539-1543.
[26]Li J. and Compton R T. Angle and polarization estimation in a coherent signal environment[J]. IEEE Transactions on Aerospace and Electronic Systems,1993,29(3): 706-716.
[27]Weiss A J and Friedlander B. Performance analysis of diversely polarized antenna arrays[J]. IEEE Transactions on Signal Processing 1991,39(7):1589-1603.
[28]Friedlander B and Weiss A J. Performance of diversely polarized antenna arrays for correlated signals[J]. IEEE Transactions on Aerospace and Electronic Systems,1992, 38(3):869-879.
[29]Weiss A J and Friedlander B. A direction finding algorithm for diversely polarized arrays[J]. Digital Signal Processing,1992,2(3):123-134.
[30]Weiss A J and Friedlander B. Direction finding for diversely polarized signals using polynomial rooting[J]. IEEE Transactions on Signal Processing,1993,41(5): 1893-1905.
[31]Weiss A J and Friedlander B. Analysis of a signal estimation algorithm for diversely polarized arrays[J]. IEEE Transactions on Signal Processing,1993,41(8):2628-2638.
[32]Weiss A J and Friedlander B. Maximum likelihood signal estimation for polarization sensitive arrays[J]. IEEE Transactions on Signal Processing,1993,41(7):918-925.
[33]Ziskind I and Wax M. Maximum likelihood localization of diversely polarized sources by simulated annealing[J]. IEEE Transactions on Antennas and Propagation,1990, 38(7):1111-1114.
[34]Hua Y. A pencil-MUSIC algorithm for finding two-dimensional angles and polarizations using crossed dipoles[J]. IEEE Transactions on Antennas and Propagation,1993,41(3):370-376.
[35]Swindlehurst A and Viberg M. Subspace fitting with diversely polarized antenna arrays[J]. IEEE Transactions on Antennas and Propagation,1993,41(12):1687-1694.
[36]Ho K C, Tan K C, Ser W. An investigation on number of signals whose directions of arrival are uniquely determinable with an electromagnetic vector sensor [J]. Signal Processing,1995,47(1):41-54.
[37]Hochwald B and Nehorai A. Identifiability in array processing models with vector-sensor applications[J]. IEEE Transactions on Signal Processing,1996,44(1): 83-95.
[38]Tan K C, Ho K C, Nehorai A. Linear independence of steering vectors of an electromagnetic vector sensor[J]. IEEE Transactions on Signal Processing,1996, 44(12):3099-3107.
[39]Tan K C, Ho K C, Nehorai A. Uniqueness study of measurements obtainable with arrays of electromagnetic vector sensors[J]. IEEE Transactions on Signal Processing, 1996,44(4):1036-1039.
[40]Ho K C, Tan K C and Tan B T G. Efficient method for estimating directions-of-arrival of partially polarized signals with electromagnetic vector sensors[J]. IEEE Transactions on Signal Processing,1997,45(10):2485-2497.
[41]Nehorai A, Tichavsky P. Cross-product algorithms for source tracking using an EM vector sensor[J]. IEEE Transactions on Signal Processing,1999,47(10):2863-2867.
[42]Ko C C, Zhang J, Nehorai A. Separation and tracking of multiple broadband sources with one electromagnetic vector sensor[J]. IEEE Transactions on Aerospace and Electronic Systems,2002,38(3):1109-1116.
[43]See C-M S, Nehorai A. Source localization with distributed electromagnetic component sensor array processing[C]. IEEE Seventh International Symposium on Signal Processing and Its Applications, IEEE Press,2003,1:177-180.
[44]Hurtado M, Nehorai A. Performance analysis of passive low-grazing-angle source localization in maritime environments using vector sensors. IEEE Transactions on Aerospace and Electronic Systems,2007,43(2):780-789.
[45]Monte L L, Elnour B, Erricolo D, et al. Design and realization of a distributed vector sensor for polarization diversity applications [C]. IEEE International Waveform Diversity and Design Conference, Pisa, Italy, IEEE Press,2007:358-361.
[46]Monte L L, Elnour B, Erricolo D. Distributed 6D vector antennas design for direction of arrival application[C]. IEEE International Conference on Electromagnetics in Advanced Applications, Torino, Italy, IEEE Press,2007:431-434.
[47]Monte L L, Elnour B, Rajagopalan A, et al. Circularly and linearly distributed narrowband vector antennas for direction of arrival applications [C]. North American Radio Science Conference, Ottawa, Ontario, Canada,2007:22-26.
[48]Wong K T, Zoltowski M D. Uni-vector-sensor ESPRIT for multi-source azimuth, elevation, and polarization estimation[J]. IEEE Transactions on Antennas and Propagation,1997,45(10):1467-1474.
[49]Wong K T, Zoltowski M D. Self-initiating MUSIC direction finding and polarization estimation in spatio-polarizational beamspace[J]. IEEE Transactions on Antennas and Propagation,2000,48(8):1235-1245.
[50]Zoltowski M D, Wong K T. ESPRIT-based 2D direction finding with a sparse array of electromagnetic vector-sensors[J]. IEEE Transactions on Signal Processing,2000, 48(8):2195-2204.
[51]Zoltowski M D, Wong K T. Closed-form eigenstructure-based direction finding using arbitrary but identical subarrays on a sparse uniform rectangular array grid[J]. IEEE Transactions on Signal Processing,2000,48(8):2205-2210.
[52]Wong K T, Zoltowski M D. Closed-form direction-finding with arbitrarily spaced electromagnetic vector-sensors at unknown locations [J]. IEEE Transactions on Antennas and Propagation,2000,48(5):671-681.
[53]Wong K T. Direction finding/polarization estimation-dipole and/or loop triad(s) [J]. IEEE Transactions on Aerospace and Electronic Systems,2001,37(2):679-684.
[54]Wong K T, Li L Zoltowski M D. Root-MUSIC-based direction-finding and polarization estimation using diversely polarized possibly collocated antennas[J]. IEEE Antennas and Wireless Propagation Letters,2004,3:129-132.
[55]Wong K T and Yuan X. "Vector cross-product direction-finding" with an electromagnetic vector-sensor of six orthogonally oriented but spatially noncollocating dipoles/loops[J]. IEEE Transactions on Signal Processing,2011,59(1):160-171.
[56]Luo F, Yuan X. Enhanced "vector-cross-product" direction-finding using a constrained sparse triangular-array[J]. EURASIP Journal on Advances in Signal Processing,2012,2012:115.
[57]Yuan X. Estimating the DOA and the polarization of a polynomial-phase signal using a single polarized vector-sensor[J]. IEEE Transactions on Signal Processing,2012, 60(3):1270-1282.
[58]Yuan X, Wong K T, Agrawal K. Polarization estimation with a dipole-dipole pair, a dipole-loop pair, or a loop-loop pair of various orientations [J]. IEEE Transactions on Antennas and Propagation,2012,60(5):2442-2452.
[59]Yuan X, Wong K T, Xu Z, et al. Various triads of collocated dipoles/loops, for direction finding & polarization estimation[J]. IEEE Sensors Journal,2012,12(6): 1763-1771.
[60]Yuan X. Quad compositions of collocated dipoles and loops:for direction finding and polarization estimation[J]. IEEE Antennas and Wireless Propagation Letters, 2012:1044-1047.
[61]Yuan X. Diversely polarized antenna-array signal processing[D]. [Ph.D. dissertation], Hong Kong:The Hong Kong Polytechnic University,2012.
[62]Tabrikian J, Shavi R, Rahamim D. An efficient vector sensor configuration for source localization [J]. IEEE Singal Processing Letters,2004,11(8):690-693.
[63]Rahamim D, Tabrikian J, Shavit R. Source localization using vector sensor array in a multipath environment [J]. IEEE Transactions on Signal Processing,2004,52(11): 3096-3103.
[64]Bihan N L, Mars J. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal Processing,2004,84(7):1177-1199.
[65]Miron S, Bihan N L, Mars J. Quaternion-MUSIC for vector-sensor array processing[J]. IEEE Transactions on Signal Processing,2006,54(4):1218-1229.
[66]Bihan N L, Miron S, Mars J. MUSIC algorithm for vector-sensors array using biquaternions[J]. IEEE Transactions on Signal Processing,2007,55(9):4523-4533.
[67]Zhang Y, Obeidat B A, Amin M G. Spatial polarimetric time-frequency distributions for direction-of-arrival estimations[J]. IEEE Transactions on Signal Processing,2006, 54(4):1327-1340.
[68]Chevalier P, Ferreol A, Albera L, et al. Higher order direction finding from arrays with diversely polarized antennas:The PD-2q-MUSIC algorithms[J]. IEEE Transactions on Signal Processing,2007,55(11):5337-5350.
[69]Korso M N, Boyer R, Renaux A. Statistical resolution limit of the uniform linear cocentered orthogonal loop and dipole array[J]. IEEE Transactions on Signal Processing,2011,59(1):425-431.
[70]Costa M, Richter A, Koivunen V. DoA and polarization estimation for arbitrary array configurations[J]. IEEE Transactions on Antennas and Propagation.
[71]徐友根,刘志文,王四平.二维正交矢量天线导向矢量的秩-1模糊问题研究[J].电路与系统学报,2006,02：20-23.
[72]徐友根,刘志文,王四平.三维正交矢量天线导向矢量的秩1模糊[J].系统工程与电子技术,2005,27(1)：1-5.
[73]徐友根,刘志文,王四平.四维正交矢量天线导向矢量的秩-1模糊[C].第十二届全国信号处理学术年会,中国江苏苏州,2005
[74]徐友根,刘志文,王四平.五维正交矢量天线导向矢量的秩-1模糊问题研究[J].电子与信息学报,2005,(05)：749-752.
[75]徐友根,刘志文.电磁矢量传感器及其阵列累量域虚拟导向矢量的线性无关度[J].电子与信息学报,2005,27(6)：983-986.
[76]Xu Y, Liu Z, Wong K T, et al. Virtual-manifold ambiguity in HOS-based direction-finding with electromagnetic vector-sensors[J]. IEEE Transactions on Aerospace and Electronic Systems,2008,44(4):1291-1308.
[77]徐友根,刘志文电磁矢量传感器阵列相干信号源波达方向和极化参数的同时估计：空间平滑方法[J].通信学报,2004,25(5)：28-38.
[78]Xu Y, Liu Z. Polarimetric angular smoothing algorithm for an electromagnetic vector-sensor array[J]. IET Radar Sonar Navigation,2007,1(3):230-240.
[79]徐友根,刘志文.基于累积量的极化敏感阵列信号DOA和极化参数的同时估计[J].电子学报,2004,32(12)：1962-1966.
[80]徐友根,刘志文.广义信号子空间拟合角度-极化联合估计[J].北京理工大学学报,2010 30(7)：835-839.
[81]徐振海,王雪松,冯德军,等.极化域-空域动态联合谱估计[J].电波科学学报2005,20(1)：25-28.
[82]徐振海,王雪松,肖顺平,等.极化域一空域联合谱估计[J].国防科技大学学报 2004,26(3)：63-67.
[83]徐振海,肖顺平,王雪松,等.极化域一空域联合谱估计精度研究[J].信号处理,2006,22(3)：317-320.
[84]徐振海,肖顺平,王雪松,等.极化域一空域联合谱分辨力研究[J].信号处理2008,24(1)：7-10.
[85]龚晓峰,刘志文,徐友根.电磁矢量传感器阵列信号波达方向估计：双模MUSIC[J].2008电子学报,36(9)：1698-1673.
[86]龚晓峰,徐友根,刘志文.四四元数域低秩逼近及其在矢量阵列波达方向估计中的应用[J].北京理工大学学报,2008,28(11)：1013-1017.
[87]Gong X F, Liu Z W, Xu Y G. Quad-quaternion MUSIC for DOA Estimation using electromagnetic vector sensors[J]. EURASIP Journal on Advances in Signal Processing,2008,2008:1-14.
[88]Gong X F, Liu Z W, Xu Y G. Regularised parallel factor analysis for the estimation of direction-of-arrival and polarisation with a single electromagnetic vector-sensor[J]. IET Signal Processing,2011,5(4):390-396.
[89]Gong X F, Liu Z W, Xu Y G. Direction finding via biquaternion matrix diagonalization with vector-sensors [J]. Signal Processing,2011,91(4):821-831.
[90]Gong X F, Wang K, Lin Q H. Simultaneous source localization and polarization estimation via non-orthogonal joint diagonalization with vector-sensors[J]. Sensors, 2012,12:3394-3417.
[91]Gong X F, Liu Z W, Xu Y G. Coherent source localization:bicomplex polarimetric smoothing with electromagnetic vector-sensors[J]. IEEE Transactions on Aerospace and Electronic Systems,2011,47(3):2268-2285.
[92]He J, Liu Z. Computationally efficient 2D direction finding and polarization estimation with arbitrarily spaced electromagnetic vector sensors at unknown locations using the propagator method[J]. Digital Signal Processing,2009,19(3):491-503.
[93]He J, Jiang S, Wang J, et al. Polarization difference smoothing for direction finding of coherent signals[J]. IEEE Transactions on Aerospace and Electronic Systems,2010, 46(1):469-480.
[94]Gu C, He J, Zhu X, et al. Efficient 2D DOA estimation of coherent signals in spatially correlated noise using electromagnetic vector sensors[J], Multidimensional Systems and Signal Processing,2010,21:239-254.
[95]Liu Z, He J and Liu Z. Computationally efficient DOA and polarization estimation of coherent sources with linear electromagnetic vector-sensor array [J], EURASIP Journal on Advances in Signal Processing,2011, Article ID 490289, doi:10.1155/2011/490289.
[96]Jiang J F, Zhang J Q. Geometric algebra of Euclidean 3-space for electromagnetic vector-sensor array processing:Part Ⅰ-Modeling[J], IEEE Transactionson Antennas and Propagation,2010,58(12):3961-3973.
[97]Jiang J F, Zhang J Q. A weighted inner product estimator in the geometric algebra of euclidean 3-space for source localization using an EM vector-sensor [J]. Chinese Journal of Aeronautics,2012,25(1):83-93.
[98]Li Y, Zhang J Q. An Enumerative NonLinear Programming approach to direction finding with a general spatially spread electromagnetic vector sensor array [J]. Signal Processing,2013,93(4):856-865.
[99]Zhang X F, Xu D Z. Novel blind joint direction of arrival and polarization estimation for polarization sensitive uniform circular array [J]. Progress In Electromagnetics Research,2008,86:19-37.
[100]Zhang X F, Chen C, Li J, et al. Blind DOA and polarization estimation for polarization-sensitive array using dimension reduction MUSIC[J]. Multidimensional Systems and Signal Processing,2013, DOI 10.1007/s11045-012-0186-3.
[101]Tao J, Liu L, Lin Z Q. Joint DOA, range and polarization estimation of sources in the Fresnel region via a sparse line dual-polarization sensor array [J]. IEEE Transactions on Aerospace and Electronic Systems,47(4):2657-2672.
[102]王建英,陈天麒.频率、二维到达角和极化联合估计[J].电子学报,1999,27(11)：74-76.
[103]王建英,陈天麒.用四阶累积量实现频率、两维到达角和极化的联合估计[J].中国科学(E辑),2000,30(5)：424-429.
[104]王建英,王激扬,陈天麒.宽频段空间信号频率、二维到达角和极化联合估计[J].中国科学(E辑),2001,31(6)：526-532.
[105]Fishler E, Haimovich A, Blum R, et al. MIMO radar:an idea whose time has come[C]. In:Proc IEEE Radar Conf, Honolulu, Hawaii, USA, Apr.2004,2:71-78
[106]Fishler E, Haimovich A, Blum R, L. et al. Spatial diversity in radars-models and detection performance[J]. IEEE Transactions on Signal Processing,2006,54(3): 823-838.
[107]Li J, Stoica P. MIMO radar with colocated antennas[J]. IEEE Signal Processing Magazine,2007,24(5):106-114.
[108]Haimovich A, Blum R, Cimini L. MIMO radar with widely separated antennas[J]. IEEE Signal Processing Magazine,2008,25(1):116-129.
[109]Bekkerman I, Tabrikian J. Target detection and localization using MIMO radars and sonars[J]. IEEE Transactions on Signal Processing,2006,54(10):3873-3883.
[110]Li J, Stoica P, Xu, L, et al. On parameter identifiability of MIMO radar[J]. IEEE Signal Processing Letters,2007,14(12):968-971.
[111]Xu L, Li J, Stoica P. Target detection and parameter estimation for MIMO radar systems[J]. IEEE Transactions on Aerospace and Electronic Systems,2008,44(3): 927-939.
[112]Chen D F, Chen B X, Qin G D. Angle estimation using ESPRIT in MIMO radar[J]. Electronics Letters,2008,44(12):770-771.
[113]Chen J, Gu H, Su W. Angle estimation using ESPRIT without pairing in MIMO radar [J]. Electronics Letters,2008,44(24):1422-1423.
[114]Jin M, Liao G., Li J. Joint DOD and DOA estimation for bistatic MIMO radar [J]. Signal Processing,2009,89(2),244-251.
[115]陈金立,顾红,苏为民.一种双基地MIMO雷达快速多目标定位方法[J].电子与信息学报,2009,31(7)：1664-1668.
[116]Liu N, Zhang L R, Zhang J. Direction finding of MIMO radar through ESPRIT and Kalman filter [J]. Electronics Letters,2009,45(17):908-910.
[117]Zhang J, Zhang L R, Yang Z W, et al. Signal subspace reconstruction method of MIMO radar [J]. Electronics Letters,2010,46(7):531-533.
[118]Zhang X, Xu D. Angle estimation in MIMO radar using reduced-dimension Capon [J]. Electronics Letters,2010,46(12):860-861.
[119]Zhang X, Xu L, Xu L, et al. DOD and DOA estimation in MIMO radar with reduced-dimension MUSIC [J]. IEEE Communications Letters,2010,14(12): 1161-1163.
[120]Yang M L, Chen B X, Yang X.Y. Conjugate ESPRIT algorithm for bistatic MIMO radar [J]. Electronics Letters,2010,46(25):1692-1694.
[121]Xie R, Liu Z, Zhang Z. DOA estimation for monostatic MIMO radar using polynomial rooting [J]. Signal Processing,2010,90(12),3284-3288.
[122]Liu J, Liu Z, Xie R. Low angle estimation in MIMO radar [J]. Electronics Letters, 2010,46(23):1565-1566.
[123]Chen J, Gu H, Weimin Su. A new method for joint DOD and DOA estimation in bistatic MIMO radar [J]. Signal Processing,2010,90(2):714-718.
[124]Bencheikh M L, Wang Y, He H. Polynomial root finding technique for joint DOA DOD estimation in bistatic MIMO radar [J]. Signal Processing,2010,90(9), 2723-2730.
[125]Bencheikh M L, Wang Y. Joint DOD-DOA estimation using combined ESPRIT-MUSIC approach in MIMO radar [J]. Electronics Letters,2010,46(15): 1081-1083.
[126]刘晓莉,廖桂生.多基线数据融合的双基地MIMO雷达角度估计[J].电波科学学报,2010,25(06)：1199-1205.
[127]刘晓莉,廖桂生.基于MUSIC和ESPRIT的双基地MIMO雷达角度估计算法[J].电子与信息学报,2010,32(9)：2179-2182.
[128]谢荣,刘峥,刘韵佛.基于L型阵列MIMO雷达的多目标分辨和定位[J].系统工程与电子技术,2010,32(01)：49-52.
[129]谢荣,刘峥.基于多项式求根的双基地MIMO雷达多目标定位方法[J].电子与信息学报,2010,32(9)：2197-2220.
[130]Guo Y D, Zhang Y S, Tong N N. Beamspace ESPRIT algorithm for bistatic MIMO radar [J]. Electronics Letters,2011,47(15):876-878.
[131]Guo Y D, Zhang Y S, Tong N N. ESPRIT-like angle estimation for bistatic MIMO radar with gain and phase uncertainties[J]. Electronics Letters,2011,47(17):996-997.
[132]郭艺夺,张永顺,张林让,等.双基地MIMO雷达收发阵列互耦条件下目标定位方法[J].西安电子科技大学学报,2011,38(06)：94-101.
[133]Guo Y D, Zhang Y S, Tong N N. Central angle estimation of coherently distributed targets for bistatic MIMO radar [J]. Electronics Letters,2011,47(7):462-463.
[134]郭艺夺,张永顺,张林让等.双基地MIMO雷达相干分布式目标快速角度估计算法[J].电子与信息学报,2011,33(07)：1684-1688.
[135]Zhang X, Xu D. Low-complexity ESPRIT-based DOA estimation for colocated MIMO radar using reduced-dimension transformation [J]. Electronics Letters,2011, 47(4):283-284.
[136]Li C, Liao G, Zhu S, et al. An ESPRIT-like algorithm for coherent DOA estimation based on data matrix decomposition in MIMO radar [J]. Signal Processing,2011, 91(8):1803-1811.
[137]符渭波,苏涛,赵永波,等.空间色噪声环境下基于时空结构的双基地MIMO雷达角度和多普勒频率联合估计方法[J].电子与信息学报,2011,33(7)：1649-1654.
[138]符渭波,苏涛,赵永波,等.空间色噪声环境下双基地MIMO雷达角度和多普勒频率联合估计方法[J].电子与信息学报,2011,33(12)：2858-2862.
[139]张娟,张林让,刘楠,等.一种有效的MIMO雷达相干信源波达方向估计方法[J].电子学报,2011,39(3)：680-684.
[140]郑志东,张剑云,杨瑛.基于发射波束域-平行因子分析的MIMO雷达收发角度估计[J].电子与信息学报,2011,33(12)：2875-2880.
[141]Zhang Y, Amin M G, Himed B, Joint DOD/DOA estimation in MIMO radar exploiting time-frequency signal representations[J]. EURASIP Journal on Advances in Signal Processing 2012 2012:102. DOI:10.1186/1687-6180-2012-102.
[142]Xie R, Liu Z, Wu J X. Direction finding with automatic pairing for bistatic MIMO radar [J]. Signal Processing,2012,92(1):198-203
[143]Zheng G, Chen B, Yang M. Unitary ESPRIT algorithm for bistatic MIMO radar[J]. Electronics Letters.2012,48(3),179-181.
[144]李建峰,张小飞,汪飞.基于四元数的Root-MUSIC的双基地MIMO雷达中角度估计算法[J].电子与信息学报,2012,34(02)：300-304.
[145]程院兵,顾红,苏卫民.一种新的双基地MIMO雷达快速多目标定位算法[J].电子与信息学报,2012 34(02)：312-317.
[146]符渭波,苏涛,赵永波,等.双基地MIMO雷达相干源角度估计方法[J].西安电子科技大学学报,2012,39(02)：143-152.
[147]Zhang X and Xu D. Angle estimation in bistatic MIMO radar using improved reduced dimension Capon algorithm [J]. Journal of Systems Engineering and Electronics,2013, 24(1):84-89.
[148]Zhang X. Chen C. Li J. Angle estimation using quaternion-ESPRIT in bistatic MIMO radar [J]. Wireless Personal. Communications,2013,1-10. DOI 10.1007/s11277-012-0589-3.
[149]Chen C, Zhang X, Chen H, et al. A low-complexity algorithm for coherent DOA estimation in monostatic MIMO radar[J]. Wireless Personal Communications,2013, 72:549-563.
[150]Li J, Zhang X, Cao R, et al. Reduced-dimension MUSIC for angle and array gain-phase error estimation in bistatic MIMO radar [J]. IEEE Communications Letters, 2013,17(3):443-446.
[151]Li J, Zhang X. Closed-Form Blind 2D-DOD and 2D-DOA Estimation for MIMO radar with arbitrary arrays [J], Wireless Personal Communications,2013,69:175-186.
[152]Li J, Zhang X. Unitary subspace-based method for angle estimation in bistatic MIMO radar[J]. Circuits Systems and Signal Processing,2013, published online, DOI 10.1007/s00034-013-9653-9.
[153]Cheng Y, Yu R, Gu H, et al. Multi-SVD based subspace estimation to improve angle estimation accuracy in bistatic MIMO radar[J]. Signal Processing,2013,93(7): 2003-2009.
[154]Wong W, Wang X, Xin L. Conjugate unitary ESPRIT algorithm for bistatic MIMO Radar[J]. IEICE Transactions on. Electronics,2013,96(1):124-126.
[155]Wong W, Wang X, Song H, et al. Conjugate ESPRIT for DOA estimation in monostatic MIMO radar[J]. Signal Processing,2013,93(7):2070-2075.
[156]Jiang H, Wang D and Liu C. Joint parameter estimation of DOD DOA/polarization for bistatic MIMO radar[J]. The Journal of China Universities of Posts and Telecommunications,2010,17(5):32-37.
[157]Bencheikh M L, Wang Y. Combined ESPRIT-RootMUSIC for DOD-DOA estimation in polarimetric bistatic MIMO radar[J]. Progress In Electromagnetics Research Letters, 2011,22:109-117.
[158]王克让,朱晓华,何劲.基于矢量传感器MIMO雷达的DOD DOA和极化联合估计算法[J].电子与信息学报,2012,34(1)：160-165.
[159]王克让,何劲,贺亚鹏,等.基于矢量传感器的扩展孔径双基地MIMO雷达多目标定位算法[J],电子与信息学报,2012,34(4)：582-586.
[160]郑桂妹,杨明磊,陈伯孝,等.干涉式矢量传感器MIMO雷达的DOD/DOA和极化联合估计[J].电子与信息学报,2012,34(11)：2635-2641.
[161]Jiang H, Zhang Yu, Li J et al. A PARAFAC-based algorithm for multidimensional parameter estimation in polarimetric bistatic MIMO radar [J]. EURASIP Journal on Advances in Signal Processing,2013,2013:133. doi:10.1186/1687-6180-2013-133.
[162]Gu C, He J, Li H, et al. Target localization using MIMO electromagnetic vector array systems[J]. Signal Processing,2013,93(7):2103-2107.
[163]Zheng G, Chen B. Optimal polarization design for direction finding using MIMO electromagnetic vector-sensor array [J]. Progress In Electromagnetics Research C, 2013,42:205-212.
[164]樊劲宇,顾红,苏卫民,等,偶极子分离的矢量阵MIMO雷达多维角度估计算法[J],电子与信息学报,2013,35(8)：1841-1846.
[165]Roy R, Kailath T. ESPRIT-estimation of signal parameters via rotational invariance techniques[J]. IEEE Transactions on Acoustics, Speech and Signal Processing,1989, 37(7):984-995.
[166]Stoica P, Sharman K C. Maximum likelihood methods for direction-of-arrival[J]. IEEE Transactions on Acoustics, Speech and Signal Processing,1990,38(7):1132-1143.
[167]Viberg M, Ottersten B. Sensor array processing based on subspace fitting[J]. IEEE Transactions on Signal Processing,1991,39(5):1110-1121.
[168]王永良,陈辉,彭应宁,等.空间谱估计理论与算法[M].北京：清华大学出版社.
[169]郑桂妹,陈伯孝,杨明磊.基于电磁矢量阵列的加权极化平滑解相干算法[J].系统工程与电子技术,2012,34(4)：637-643.
[170]Golub G H, Loan C F. Matrix Computations[M],3th ed., The John Hopkins University Press, Baltimore,1996.
[171]王布宏,王永良,陈辉.相干信源波达方向估计的加权空间平滑算法[J].通信学报,2003,24(4)：31-40.
[172]Zhang Q T. Probability of resolution of the MUSIC algorithm [J]. IEEE Transactions on Signal Processing,1995,43(4):978-987.
[173]Miron S, Bihan N L, Mars J. Vector-MUSIC for polarized seismic sources localization [J]. EURASIP Journal on Applied Signal Processing,2005(1):74-84.
[174]Chiu C Y, Yan J B, Murch R D, et al. Design and implementation of a compact 6-port antenna[J]. IEEE Antennas and Wireless Propagation Letters,2009,8:767-770.
[175]Wong K T. Geolocation for partially polarized electromagnetic sources using multiple sparely and uniformly spaced "spatially stretched vector sensors" [C]. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems, Orlando, Florida, USA, IEEE Press,1999:170-174.
[176]Wong K T, Zoltowski M. D. Direction-finding with sparse rectangular dual-size spatial invariance array [J]. IEEE Transactions on Aerospace and Electronic Systems, 1998,34(4):1320-1336.
[177]Lemma A N, Veen A J, Deprettere E F. Multiresolution ESPRIT algorithm[J]. IEEE Transactions on Signal Processing,1999,47(6):1722-1726.
[178]Trees H L. Detection, Estimation, and Modulation Theory, Part IV:Optimum Array Processing. New York:Wiley,2002.
[179]Haardt M, Nossek J A. Unitary ESPRIT:how to obtain increased estimation accuracy with a reduced computational burden. IEEE Transactions on Signal Processing,1995, 43(5):1232-1242
[180]Zoltowski M D, Haardt M, Mathews C P. Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT [J]. IEEE Transactions on Signal Processing,1996,44(2):316-328.
[181]Zoltowski M D, Kautz G M, Silverstein S D. Beamspace Root-MUSIC [J]. IEEE Transactions on Signal Processing,1993,41(1):344-364.
[182]Nilsson J E, Warston H. Radar with separated subarray antennas [C]. In:Proc IEEE Radar Conf, Australia,2003,194-199.
[183]Coutts S, Cuomo K, Robey F. Distributed coherent aperture measurements for next generation BMD radar [C]. In:Proc IEEE Sensor Array and Multichannel Signal Process Workshop,2005,390-393.
[184]Chen G H, Chen B X. Eigenstructure-based ambiguity resolution algorithm for distributed subarray antennas VHF radar [J]. Electronics Letters,2012, 48(13):788-789.
[185]Hurtado M, Xiao J J, Nehorai A. Target estimation, detection, and tracking:a look at adaptive polarimetric design[J]. IEEE Signal Processing Magazine,2009,26(1): 42-52.
[186]Gogineni S, Nehorai A. Polarimetric MIMO radar with distributed antennas for target detection[J]. IEEE transaction on Signal Processing,2010,58(3):1689-1697.
[187]Jiang H, Wang D and Liu C. Joint parameter estimation of DOD DOA/polarization for bistatic MIMO radar [J]. The Journal of China Universities of Posts and Telecommunications,2010,17(5):32-37.
[188]Bencheikh M L, Wang Y. Combined ESPRIT-ROOTMUSIC for DOA-DOD estimation in polarimetric bistatic MIMO radar[J]. Progress In Electromagnetics Research Letters,2011,22:109-117.
[189]王克让,朱晓华,何劲.基于矢量传感器MIMO雷达的DOD DOA和极化联合估计算法[J].电子与信息学报,2012,34(1)：160-165.
[190]王克让,何劲,贺亚鹏,等.基于矢量传感器的扩展孔径双基地MIMO雷达多目标定位算法[J],电子与信息学报,2012,34(4)：582-586.
[191]郑桂妹,杨明磊,陈伯孝,等.干涉式矢量传感器MIMO雷达的DOD/DOA和极化联合估计[J].电子与信息学报,2012,34(11)：2635-2641.
[192]Gu C, He J, Li H, et al. Target localization using MIMO electromagnetic vector array systems[J]. Signal Processing,2013,93(7):2103-2107.
[193]Zheng G, Chen B. Optimal polarization design for direction finding using MIMO electromagnetic vector-sensor array [J]. Progress In Electromagnetics Research C, 2013,42:205-212.
[194]Hurtado M, Nehorai A. Optimal polarized waveform design for active target parameter estimation using electromagnetic vector sensors [C], IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Toulouse, France,2006, 1125-1128.
