卫星导航简化分布式矢量天线抗干扰和多径抑制技术研究
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摘要
卫星导航系统采用扩频通信体制,传播到地面的卫星导航信号淹没在热噪声中;同时由于接收环境复杂,导航信号不可避免的会产生反射或绕射信号;因此,导航接收机极易受到有意或无意射频干扰以及多径干扰。在局域增强系统、联合精密进近与着陆系统等高性能导航应用中,需要补偿抗干扰天线阵波束形成的等效相位中心变化和群时延引入的测距误差。矢量天线元偶极子天线具有稳定的相位中心性能,非常适合导航测量应用;由其构成的简化分布式矢量天线可以垂直层叠布阵、立体布阵;具有极化识别、极化分集接收的能力;性能优于传统天线阵。本文针对高性能卫星导航简化分布式矢量天线如何抑制射频干扰和多径干扰及天线阵波束形成后的相位中心和群时延的校正展开研究,具体内容如下:
     (1)首先对简化分布式矢量天线工作原理进行研究分析。应用球坐标系到直角坐标系的变换和磁场分量转化为电场分量的关系推导出考虑矢量天线元辐射模式的矢量天线数学模型;推导过程物理意义简单明晰,模型精确表达了矢量天线的实际测量数据,为简化分布式矢量天线的应用奠定了基础。仿真给出了矢量天线三个电偶极子和三个磁环测量出的三个正交电场分量和三个正交磁场分量叉乘方法来波方向估计的误差。战时,干扰源的测向定位尤为重要。本文首次提出两个磁环远大于半波长距离安装、消除阵元间互耦的一维稀疏简化分布式矢量天线,采用多信号分类(MUSIC)算法结合矢量天线叉乘方法来波方向估计,叉乘方法的估计结果去除了MUSIC算法由于大阵元间距引入的估计模糊度,获得高精度的来波方向估计。
     (2)研究简化分布式矢量天线在抗射频干扰中的应用。提出三维简化分布式矢量天线,给出其几种抗干扰算法波束形成的对比仿真。提出基于简化分布式矢量天线估计出射频干扰信号来波方向和极化状态的阵元选择极化分集接收抗射频干扰方法。该方法在保证有用卫星信号接收的同时,抑制与卫星信号来波方向相同或相近、与阵元极化方式正交的无线通讯等垂直线极化方式干扰和广播电视信号等水平线极化方式干扰。三维简化分布式矢量天线在估计出来波仰角、方位角的基础上,其结构中垂直L型矢量天线元测量数据相位幅度分离实现来波匹配,进一步估计出来波的极化状态。
     (3)研究简化分布式矢量天线在抗多径干扰中的应用。多径干扰随反射角度的不同具有不同的极化状态,已经不是卫星导航信号的右旋圆极化极化状态。本文三维简化分布式矢量天线来波方向与来波极化状态联合估计,解决了多径干扰与卫星直达信号来波方向估计的解相干问题,可估计出来波的二维方向并在极化域上实现了多径干扰的识别;天线阵波束形成零陷抑制多径方法,解决了信号处理抑制多径算法中无法抑制相对时延较小的短时延多径干扰问题。文中给出工程中应用的圆极化抑制多径扼流圈天线反映多径抑制能力的期望(卫星信号)接收与不期望(多径干扰)接收比值的暗室测试结果。通过对比可以看出,本文方法基本消除了接收机伪距测量多径误差,明显优于扼流圈天线及导航增强接收的确定性波束形成(DBF)方法。应用阵元接收数据来波方向估计得到射频干扰信号来波方向;应用各个阵元接收信号相关后得到的某颗卫星的载波相位测量数据来波方向估计,得到该颗卫星信号和其强反射多径信号的来波方向;在每颗卫星的数据通道内,采用本文提出的改进的最小方差无失真响应(MVDR)波束形成算法获得权值,理论实现了波束形成指向卫星信号、几个零陷指向射频干扰和多径干扰。
     (4)研究简化分布式矢量天线波束形成相位中心和群时延的校正问题。给出了天线相位中心变化对接收机载波相位测距的影响和天线群时延对接收机伪码测距的影响,及天线的相位中心变化和群时延的暗室测试结果。仿真了多种波束形成算法波束形成后的等效天线相位中心特性;首次提出幅相建模改进的MVDR波束形成算法。算法使实际非理想天线阵波束形成指向有用卫星信号且该有用信号接收方向上的等效天线载波相位中心恒为零,省去了波束形成相位中心变化的校正问题;并且波束形成零陷了估计出的射频干扰和多径干扰;进一步通过仿真得到波束形成有用信号接收方向上的群时延特性,其可用来补偿接收机伪距测量值。
     综上所述,本文研究内容为高性能卫星导航天线阵抗干扰和多径抑制的工程实现提供了理论参考和方法支撑。
The satellite navigation system adopting the spread spectrum technology, the satellite signal is submerged by the mechanical thermal noise when it reaches the ground. And the receiving circumstance is complicated, inducing the multipaths by reflection and diffraction. So, the satellite navigation receiver is easily interfered by the intent jamming, some electromagnetic signals used in civilian applications and multipath. The high performance satellite navigation system like Local Area Augmentation System (LAAS) and Joint Precision Approach and Landing System (JPALS) require the compensation of the measurement error induced by the Phase Center Variance (PCV) and the Group Delay (GD) after antenna array beamforming. The vector sensor element electric dipole has the stable phase characteristic, and it is prefect for the navigation measurements. The reduced distributed vector sensor constructed by the electric dipoles can form the vertical linear array and the three dimensional array, distinguish signals by polarization state and receive signals by polarization diversity. It has many advantages compared to the tranditional antenna array. In this dissertation, the high performance satellite navigation reduced distributed vector sensor anti-jamming, multipath mitigation, and the Phase Center Variance and the Group Delay calibration after beamforming are researched. The contents are as follows:
     (1) First the theory of the reduced distributed vector sensor is researched. The vector sensor model considering the vector sensor element patterns is deduced by using the spherical to rectangular coordinate transfer and the relationship between electric field and magnetic field. It is easy to understand. The model simulates the real measurement data, and it is the foundation of the reduced distributed vector sensor application. The direction of arrival estimation errors by the Cross Product method are presented using the three orthogonal electric fields and the three orthogonal magnetic fields measured by the three dipoles and three loops which formed the vector sensor. In war, the direction and position estimation of the jamming machine is very important. The reduced distributed vector sensor consists of two magnetic loops can be installed far away from each other compared to the half wavelength of the wave propogated, eliminating the mutual coupling. The result of the direction of arrival by vector sensor Cross Product method can choose the right peak of the Multiple Signal Classification (MUSIC) algorithm estimated, suppressing the ambiguity caused by the large array elements spacing.
     (2) The reduced distributed vector sensor using in anti-jamming is researched. The reduced distributed vector sensor with a three dimensional structure is presented. And the comparisons of several anti-jamming algorithms are simulated based on it. The distributed vector sensor gives out the direction of the radio frequency jamming and the polarization state of the jamming. Polarization diversity reception of the elements selected by the reduced distributed vector sensor can eliminate the vertically polarized wireless communication signals and the horizontal polarized TV broadcast signals which are orthogonally polarized compared to the receiving vector sensor elements with the same or near direction of the satellite signal, while ensuring the satellite signal receiving. On the basis of elevation and azimuth estimated, the vertical L shape sensors in the reduced distributed vector sensor depart the phase and amplitude of the vector data received to realize the signal match, then the polarization state is eatimated.
     (3) The reduced distributed vector sensor using in multipath mitigation is researched. The polarization state of the multipaths varies with the reflection angle, and it is not the satellite signal’s right-circular polarization any more. The direction and the polarization state estimations of the arrivals by the three dimensional reduced distributed vector sensor presented in the dissertation solve the problem of the direction of arrival estimation of the correlated signals, give out the directions of arrivals and realize distinguishing the multipaths in the polarization field. The reduced distributed vector sensor multipath mitigation method researched in the dissertation solves the problem that the short delay multipath can’t be eliminated in the signal processing multipath mitigation technique. The anechoic chamber test result of the circularly polarized chock ring antenna’s Desired-to-Undesired Ratio (satellite signal to multipath signal ratio) which is the description of the multipath mitigation ability is also presented in the dissertation. Through comparison, it is clear that the multipath error of the pseudorange measurements is almost eliminated by the method presented in the dissertation, and it is greatly better than the chock ring antenna which is operated in most systems and the deterministic beamforming (DBF). The data received estimates the direction of the radio frequency jamming, and the carrier phase data obtained after correlation estimates the direction of the multipaths and the satellite signal. The reduced distributed vector sensor beamforming points at the desired satellite signal estimated, and places nulls at the direction of the radio frequency jamming and the multipaths estimated.
     (4) The calibrations of the Phase Center Variance and the Group Delay after beamforming are researched. The effect on the receiver carrier phase measurements by the Phase Center Variance and the effect on the receiver pseudorange measurements by the antenna Group Delay are presented, and the anechoic chamber test results of the Phase Center Variance and the Group Delay of the antenna are presented. The phase characteristics after beamforming by several anti-jamming algorithms are analyzed. Then the amplitude and phase modeling improved Minimum Variance Distortionless Response (MVDR) beamforming algorithm is proposed in the dissertation. By the algorithm, the non ideal antenna array beamforming points at the satellite signal and the equivalent phase center in this direction is always zero degree, and places nulls on the directions of the radio frequency jamming and multipath estimated. Calculate the Group Delay after beamforming in the direction of the satellite signal further, and the receiver pseudorange measurements error can be compensated.
     The reduced distributed vector sensor researched in this dissertation can provide the theory reference and the method support for the project of antenna array anti-jamming and multipath mitigation in the high performance satellite navigation system.
引文
[1]干国强,邱致和,王万义. GPS干扰与抗干扰文集:第1集[C].西安:信息产业部电子第二十研究所, 1999,前言.
    [2] Braasch M. Optimum antenna design for DGPS ground reference stations [C]. ION GPS 1994. Salt Lake City, UT: 1994:1291-1297.
    [3]刘经南,夏林元.“GPS在DH-10任务规划系统中的应用”项目研究报告[R].航天工业总公司第三研究院,武汉大学泰通卫星技术发展有限责任公司,2000.
    [4] Georgiadou Y, Kleusberg A. On Carrier Signal Multipath Effects in Relative GPS Positioning [J]. Manuscripta Geodetica, 1988:172-179.
    [5]刘荟萃.卫星导航系统中的多径误差分析与抑制技术研究[D].长沙:国防科技大学研究生院, 2010: 83.
    [6]李跃,邱致和.导航与定位[M].北京:国防工业出版社, 2008: 192~196, 158~160, 588~590.
    [7] Nehorai A, Paldi E. Vector Sensor Processing for Electromagnetic Source Localization [J]. Proceedings of 25th Asilomar Conference on Signals, Systems & Computers. Pacific Grove, CA: 1991: 566~572.
    [8] Nehorai A, Paldi E. Vector-Sensor Array Processing for Electromagnetic Source Localization [J]. IEEE Trans. Signal Processing, 1994, 42(2): 376~398.
    [9] Giuli D. Polarization Diversity in Radars [J]. Proceedings of the IEEE, 1986, 74(2): 245~269.
    [10] Hochwald B, Nehorai A. Polarimetric Modeling and Parameter Estimation with Applications to Remote Sensing [J]. IEEE Trans. Signal Processing, 1995, 43(8): 1923~1935.
    [11] Miron S, Le Bihan N, Mars J I. Vector-Sensor MUSIC for Polarized Seismic Sources Localization [J]. EURASIP Journal on Applied Signal Processing, 2005, 1(1): 74~84.
    [12] Andrews M R, Mitra P P, deCarvalho R. Tripling the Capacity of Wireless Communications using Electromagnetic Polarization [J]. Nature, 2001, 409(18): 316~318.
    [13] Stand D D, Berson A, Van’t Hof J P, et al. Doubling Wireless Channel Capacity using Co-Polarised, Co-Located Electric and Magnetic dipoles [J]. Electronics Letters, 2002, 38(14): 746~747.
    [14] Konanur A K, Gosalia K, Krishnamurthy S H, et al. Increasing Wireless Channel Capacity through MIMO Systems Employing Co-Located Antennas [J]. IEEE Trans. Microwave Theory and Techniques, 2005, 53(6): 1837~1844.
    [15] Jan S S, Enge P. Finding Source of Electromagnetic Interference to GPS using Network Sensors r [C]∥ION NTM 2001. Long Beach, CA: 2001: 533-540.
    [16] Shemar S, Bond G, Edmonds P, et al. Trial Results of a Preototype System to Locate GPS Radio Interference Sources using Time-difference-of-arrival Measurements [C]∥ION NTM 2004. San Diego, CA: 2004: 1018-1025.
    [17] Fitch J. GPS Jamming Environment Prediction Based on Discrete Data Sampling [C]∥ION NTM 2004. San Diego, CA: 2004: 1011-1017.
    [18] Ramos J, Zoltowski M, Burgos M. Robust Blind Adaptive Array. A prototype forGPS [C]∥1996 IEEE International Symposium on Phased Array Systems and Technology. Boston, MA, USA: 1996: 406~410.
    [19] Fante R L, Vaccaro J J. Wideband Cancellation of Interference in a GPS Receive Array [J]. IEEE Trans. Aerospace and Electronic Systems, 2000, 36(2): 549~564.
    [20] Ulrey J A, Gupta I J. Optimum Element Distribution for Circular Adaptive Antenna Systems [C]∥ION NTM 2006. Monterey, CA: 2006: 76-81.
    [21] Demissie B. Algebraic Method for Deterministic Blind Beamforming with Unknown Receiver Gain and Phases [C]∥2007 IEEE International Conference on Signal Processing and Communications. Dublin, Ireland: 2007: 448~451.
    [22]吴仁彪,孙擎宇,胡铁乔等.基于功率倒置算法的GPS抗干扰实时系统实现[J].中国民航大学学报, 2010, 28(3): 45~48.
    [23] Trinkle M, Cheuk W C. Null-steering GPS Dual-polarised Antenna Arrays [C]∥The 6th International Symposium on Satellite Navigation Technology including Mobile Positioning & Location Services. Melbourne, Australia: 2003: 1~10.
    [24] Fante R L. Principles of Adaptive Space-Time-Polarization Cancellation of Broadband Interference [R]. Massachusetts: The MITRE Corporation, 2003: 1~22.
    [25]战永红,李双勋,王展等. GPS单孔径双极化天线抗干扰算法与性能分析[J].国防科技大学学报, 2009, 31(1): 95~98.
    [26] Amin M G, Sun W. A Novel Interference Suppression Scheme for Global Navigation Satellite Systems Using Antenna Array [J]. IEEE Journal on Selected Areas in Communications, 2005, 23(5): 999~1012.
    [27] Sun W, Amin M G. A Self-Coherence Anti-Jamming GPS Receiver [J]. IEEE Trans. Signal Processing, 2005, 53(10): 3910~3915.
    [28] Sahmoudi M, Amin M G. Unitary Cyclic MUSIC for Direction Finding in GPS Receivers [C]∥2006 Fourth IEEE Workshop on Sensor Array and Multichannel Processing. Waltham, MA: 2006: 70~73.
    [29] Mukhopadhyay M, Sarkar B K, Chakraborty A. Augmentation of Anti-jam GPS System using Smart Antenna with a Simple DOA Estimation Algorithm [J]. Progress in Electromagnetics Research, 2007, 67: 231~249.
    [30] Mao W L, Liu D P, Tsao H W, et al. design of relaxed look-ahead pipelined adaptive canceller in anti-jamming GPS Receiver [C]∥ION NTM 2005. San Diego, CA: 2005: 306-309.
    [31]王瑛.卫星导航天线阵抗干扰技术研究[D].长沙:国防科技大学研究生院, 2008: 9~14.
    [32] Falcone K. Small Affordable Anti-Jam GPS Antenna (SAAGA) Development [C]∥ION GPS 1999. Nashville, TN, USA: 1999, 1149~1156.
    [33] Brown A, Reynolds D, Tseng H W. Miniaturized GPS Antenna Array Technology [C]∥ION 55th AM. Cambridge: 1999: 243~252.
    [34] Manry C W, et al. Advanced Mini Array Antenna Design Using High Fidelity Computer Modeling and Simulation [C]∥ION GPS 2000. Salt Lake City, Utah: 2000: 2485~2490.
    [35] Brown A, Morley D. Test Results of a 7-Element Small Controlled Reception Pattern Antenna [C]∥ION GPS 2001. Salt Lake City, Utah: 2001: 2022~2029.
    [36] Ly H, et al. Design, Simulation, and Testing of a Miniaturized GPSDual-Frequency (L1/L2) Antenna Array [C]∥ION GPS 2002. Portland, Dregon: 2002: 2111~2119.
    [37] Brown A K, Mathews B. GPS Multipath Mitigation Using a Three Dimensional Phased Array [C]∥ION GNSS 2005. Long Beach, CA: 2005: 659~666.
    [38] Brown A, Silva R, Zhang G. Test Results of a High Gain Advanced GPS Receiver [C]∥ION 55th AM. Cambridge: 1999: 557~566.
    [39] Brown A. High Accuracy GPS and Antijam Protection Using a P(Y) Code Digital Beamsteering Receiver [C]∥ION GPS 2001, Salt Lake City, Utah: 2001: 1245~1254.
    [40] Brown A. Performance and Jamming Test Results of a Digital Beamforming GPS Receiver [C]∥Joint Navigation Conference 2002, Orlando, Florida: 2002: 1-11.
    [41] Sharawi M S, Aloi D N. Comparative Analysis via Simulation of Two Null-steering Approaches for the Multipath Limiting Antenna for LAAS [C]∥ION NTM 2006. Monterey, CA: 2006: 935~948.
    [42] Dickman J, Bartone C, Zhang Y J. Characterization and Performance of a Prototype Wideband Airport Pseudolite Multipath Limiting Antenna for the Local Area Augmentation System [C]∥ION NTM 2003. Anaheim, CA: 2003: 783~793.
    [43] Graas F V, Bartone C, Arthur T. GPS Antenna Phase and Group Delay Corrections [C]∥ION NTM 2004. San Diego, CA: 2004: 399-408.
    [44] Brown A. High Accuracy GPS Performance using a Digital Adaptive Antenna Array [C]∥ION NTM 2001. Long Beach, CA: 2001: 335~343.
    [45] Gold K, Brown A, Stolk K. Bistatic Sensing and Multipath Mitigation with a 109-Element GPS Antenna Array and Digital Beam Steering Receiver [C]∥ION NTM 2005. San Diego, CA: 2005: 849~857.
    [46] Gold K, Brown A. An Array of Digital Antenna Elements for Mitigation of Multipath for Carrier Landings [C]∥ION NTM 2005. San Diego, CA: 2005: 190~196.
    [47] Thornberg D B, Dickinson M. LAAS Multipath Limiting Antenna Performance Testing and Annlysis [C]∥ION NTM 2005. San Diego, CA: 2005: 140~152.
    [48] Ung S K. Mitigation of Signal Biases Introduced by Controlled Reception Pattern Antennas in a High Integrity Carrier Phase Differential GPS System [D]. USA: Stanford University, 2007: 14~22.
    [49]金荣洪,耿军平,范瑜.无线通信中的智能天线[M].北京:北京邮电大学出版社, 2006: 202~203,208,221.
    [50] Liu J, Huang J T, Zhou Y Y. Azimuth and Elevation Estimation for Noncircular Signals [J]. Electronics Letters, 2007, 43(20): 1~2.
    [51] Tayem N, Kwon H M. L-Shape Two-Dimensional Arrival Angle Estimation with Propagator Method”[J]. IEEE Trans. Antennas and Propagation, 2005, 53(5): 1622~1630.
    [52] Shu T, Liu X Z, Lu J H. Comments on“L-Shape Two-Dimensional Arrival Angle Estimation with Propagator Method”[J]. IEEE Trans. Antennas and Propagation, 2008, 56(5): 1502~1503.
    [53] Gu J F, Wei P, Tai H M. 2-D Direction-of-arrival Estimation of Coherent Signals using Cross-correlation Matrix [J]. Elsevier Signal Processing, 2008, 88: 75~85.
    [54] Liu F L, Wang J K, Du R Y, et al. Space-time Matrix Method for 2-DDirection-of-arrival Estimation [J]. Elsevier Signal Processing, 2007, 87: 101~106.
    [55] Lee J, Song I, Kwon H, et al. Low-complexity estimation of 2D DOA for coherently distributed sources [J]. Elsevier Signal Processing, 2003, 83: 1789~1802.
    [56] Roemer F, Haardt M. Efficient 1-D and 2-D DOA Estimation for Non-circular Sources with Hexagonal Shaped Espar Arrays [C]∥2006 International Coference on Acoustics, Speech and Signal Processig. Toulouse, France: 2006: 881~884.
    [57] Strobach P. Total Least Squares Phased Averaging and 3-D ESPRIT for Joint Azimuth-elevation-carrier Estimation [J]. IEEE Trans. Signal Processing, 2001, 49(1): 54~62.
    [58] See C M S, Nehorai A. Distributed Electromagnetic Component Sensor Array Processing [C]∥7th Workshop on Adaptive Sensor Array Proceedings. Lexington MA: Lincoln Laboratory MIT, 1999: 75~79.
    [59] Nehorai A, Tichavsky P. Cross-Product Algorithms for Source Tracking using an EM Vector Sensor [J]. IEEE Trans. Signal Processing, 1999, 47(10): 2863~2867.
    [60] Tan K C, Ho K C, Nehorai A. Linear Independence of Steering Vectors of an Electromagnetic Vector Sensor [J]. IEEE Trans. Signal Processing, 1996, 44(12): 3099~3107.
    [61] Hochwald B, Nehorai A. Identifiability in Array Processing Models with Vector-Sensor Applications [J]. IEEE Trans. Signal Processing, 1996, 44(1): 83~95.
    [62] Nehorai A, Ho K C, Tan B T G. Minimum-Noise-Variance Beamformer with an Electromagnetic Vector Sensor [J]. IEEE Trans. Signal Processing, 1999, 47(3): 601~618.
    [63] Ho K C, Nehorai A. Separation and Tracking of Multiple Broadband Sources with One Electromagnetic Vector Sensor [J]. IEEE Trans. Aerospace and Electronic Systems, 2002, 38(3): 1109~1116.
    [64] See C M S, Nehorai A. Source Localization with Partially Calibrated Distributed Electromagnetic Component Sensor Array [C]∥12th International Workshop on Statistical Signal Processing Procccedings. St. Louis, MI: 2003: 441~444.
    [65] Elnour B, Monte L L, Hurtado M, et al. Experiments to Measure the Direction of Arrival (DOA) using a Vector Antenna [C]∥2006 IEEE AP-S International Symposuim and USNC/URSI National Radio Science Meeting. Albuquerque, NM, USA: 2006.
    [66] Ho K C, Tan K C, Nehorai A. Estimating Directions of Arrival of Completely and Incompletely Polarized Signals with Electromagnetic Vector Sensors [J]. IEEE Trans. Signal Processing, 1999, 47(10): 2845~2852.
    [67] Wong K T, Zoltowski M D. Uni-Vector-Sensor ESPRIT for Multi-Source Azimuth-Elevation Angle-Estimation [C]∥IEEE International Symposium Antennas and Propagation Society. Baltimore, MD, USA: 1996: 1368~1371.
    [68] Wong K T, Zoltowski M D. Uni-vector-sensor ESPRIT for Multisource Azimuth, Elevation, and Polarization Estimation [J]. IEEE Trans. Antennas and Propagation, 1997, 45(10): 1467~1474.
    [69] Wong K T, Zoltowski M D. Diversely Polarized Root-MUSIC for Azimuth-Elevation Angle-of-Arrival Estimation [C]∥IEEE International Symposium Antennas and Propagation Society. Baltimore, MD, USA: 1996:1352~1355.
    [70] Wong K T, Zoltowski M D. High Accuracy 2D Angle Estimation with Extended Aperture Vector Sensor Arrays [C]∥1996 International Coference on Acoustics, Speech and Signal Processig. Atlanta, GA, USA: 1996: 2789~2792.
    [71] Zoltowski M D, Wong K T. ESPRIT-Based 2-D Direction Finding with a Sparse Uniform Array of Electromagnetic Vector Sensors [J]. IEEE Trans. Signal Processing, 2000, 48(8): 2195~2204.
    [72] Zoltowski M D, Wong K T. Closed-Form Eigenstructure-Based Direction Finding using Arbitrary but Identical Subarrays on a Sparse Uniform Cartesian Array Grid [J]. IEEE Trans. Signal Processing, 2000, 48(8): 2205~2210.
    [73] Wong K T, Zoltowski M D. Self-Initiating Velocity-Field Beamspace MUSIC for Underwater Acoustic Direction-Finding with Irregularly Spaced Vector-Hydrophones [C]∥IEEE International Symposium on Circuits and Systems. Hong Kong: 1996: 1352~1355.
    [74] Wong K T, Zoltowski M D. Closed-Form Underwater Acoustic Direction-Finding with Arbitrarily Spaced Vector Hydrophones at Unknown Locations [J]. IEEE Journal of Oceanic Engineering, 1997, 22(3): 566~575.
    [75] Wong K T, Zoltowski M D. Closed-Form Direction-Finding with Arbitrarily Spaced Electromagnetic Vector-Sensors at Unknown Locations [C]∥Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing. Seattle, WA, USA: 1998: 1949~1952.
    [76] Wong K T, Zoltowski M D. Closed-Form Direction Finding and Polarization Estimation with Arbitrarily Spaced Electromagnetic Vector-Sensors at Unknown Locations [J]. IEEE Trans. Antennas and Propagation, 2000, 48(5): 671~681.
    [77] Wong K T, Zoltowski M D. Self-Initiating MUSIC-Based Direction Finding and Polarization Estimation in Spatio-Polarizational Beamspace [J]. IEEE Trans. Antennas and Propagation, 2000, 48(8): 1235~1245.
    [78] Monte L L, Elnour B, Erricolo, D. Distributed 6D Vector Antenna Design for Direction of Arrival Applications [C]∥International Conference on Electromagnetic in Advanced Applications. Torino, Italy: 2007: 431~434.
    [79] Monte L L, Elnour B, Erricolo D, et al. Design and Realization of a Distributed Vector Sensor for Polarization Diversity Applications [C]∥2007 Waveform Diversity & Design. Pisa, Italy: 2007: 358~361.
    [80] Hurtado M, Nehorai A. Performance Analysis of Passive Low-Grazing-Angle Source Localization in Maritime Environments using Vector Sensors [J]. IEEE Trans. Aerospace and Electronic Systems, 2007, 43(2): 780~789.
    [81] Wong K T. Direction Finding Polarization Estimation dipole and or loop triads [J]. IEEE Trans. Aerospace and Electronic Systems, 2001, 37(2): 679~684.
    [82] Tabrikian J S, Rahamim D R. An Efficient Vector Sensor Configuration for Source Localization [J]. IEEE Signal Processing Letters, 2004, 11(8): 690~693.
    [83] Huang Y K, Nehorai A, Friedman G. Mutual Coupling of Two Collocated Orthogonally Oriented Circular Thin-Wire Loops [J]. IEEE Trans. Antennas and Propagation, 2003, 51(6): 1307~1314.
    [84] Appadwedula S, Keller C M. Direction-Finding Results for a Vector Sensor Antenna on a Small UAV [C]∥2006 Fourth IEEE Workshop on Sensor Array and Multichannel Processing. Waltham, MA: 2006: 74~78.
    [85] Mir H S, Sahr J D, Keller C M. Source Localization of Airborne Vector Sensors[C]∥International Coference on Acoustics, Speech and Signal Processig. Philadelphia,USA: 2005: 1033~1036.
    [86] Mir H S, Sahr J D. Passive Direction Finding using Airborne Vector Sensors in the Presence of Manifold Perturbations [J]. IEEE Trans. Signal Processing, 2007, 55(1): 156~164.
    [87] Zhao T, Hurtado M, Nehorai A. Adaptive Polarized Waveform Design for Target Tracking using Electromagnetic Vector Sensors [C]∥IEEE International Conf. on Acoustics, Speech, Signal Processing. Honolulu, HI: 2007: 1117~1120.
    [88] Balanis C A. Antenna theory analysis and design [M]. John Wiley & Sons. Arizona State University, 1982: Appendix.
    [89]许福永,赵克玉.电磁场与电磁波[M].北京:科学出版社, 2005: 348~355.
    [90] Kraus J D, Marhefka R J,张文勋.天线[M].北京:电子工业出版社, 2006: 132.
    [91] Sun L, Li C H, Lu Y L, Ou G. Distributed Vector Sensor Cross-product added with MUSIC for Direction of Arrival Estimation [C]∥2010 Asia-Pacific International Symposium on Electromagnetic Compatibility. Beijing, China: 2010: 1354~1357.
    [92]桑怀胜.卫星定位接收机全局最优空时抗干扰技术研究[D].长沙:国防科技大学研究生院, 2003.
    [93] Compton R T. The Power-Inversion Adaptive Array: Concept and Performance [J]. IEEE Trans. Aerospace and Electronic Systems, 1979, 15(6): 803-814.
    [94] Frost O L. An Algorithm for Linearly Constrained Adaptive Array Processing [J]. Proceedings of the IEEE, 1962, 60(8): 926-935.
    [95] Nguyen H N. Robust Steering Vector Mismatch Techniques for Reduced Rank Adaptive Array Signal Processing [D]. The Virginia Polytechnic Institute and State University, 2002.
    [96] Chen H W, Qin X J, Zhao J W. Two-dimensional Wideband Direction of Arrival Estimation with Acoustic Vector-sensor Array [J]. Chinese Journal of Acoustics, 2006, 25(1): 36~44, 202~240.
    [97]吴晓进,邱致和等. GPS理论与应用第1卷下[M].西安:西安导航技术研究所, 1999: 111~127.
    [98]孙莉,周力,李柏渝,欧钢.卫星导航定位多径信号极化状态分析[C].第一届中国卫星导航学术年会.北京:2010:1~6.
    [99]毛钧杰,刘荧,朱建清.电磁场与微波工程基础[M].北京:电子工业出版社,2004:142~164.
    [100] Lopez A R. LAAS/GBAS Ground Reference Antenna with Enhanced Mitigation of Ground Multipath [C]∥ION NTM 2008. San Diego, CA: 2008.
    [101] Counselman C C. Multipath-Rejecting GPS Antennas [J]. Proceedings of the IEEE, 1999, 87(1): 86~91.
    [102] Shan T J, Wax M, Kailath T. On Spatial Smoothing for Direction-of-arrival Estimation of Coherent Signals [J]. IEEE Trans. Acoustics Speech and Signal Processing, 1985, 33(4): 806~811.
    [103] Williams R T, Prasad S, Mahalanabis A K, et al. An Improved Spatial Smoothing Technique for Bearing Estimation in a Multipath Environment [J]. IEEE Trans. Acoustics Speech and Signal Processing, 1988, 36(4): 425~432.
    [104]张贤达.现代信号处理[M].北京:清华大学出版社, 2002: 136.
    [105]张辉,葛临东,李蒙等.多径环境中二维波达方向估计的子空间平滑算法[J].电子学报, 2005, 33(6): 1077~1080.
    [106]许驰,康晓涛,刘志军等.基于L型阵的二维相干源信号的DOA估计[J].长春理工大学学报, 2009, 32(2): 245~238.
    [107] Yeh C C, Lee J H, Chen Y M. Estimating Two-dimensional Angles of Arrival in Coherent Source Environment [J]. IEEE Trans. Acoustics Speech and Signal Processing, 1989, 37(1): 153~155.
    [108] Chen Y M. On Spatial Smoothing for Two Dimensional Direction of Arrival Estimation of Coherent Signals [J]. IEEE Trans. Signal Processing, 1997, 45(7): 1689~1696.
    [109]魏小丽,陈建,林琳.基于空间平滑算法的二维相干源DOA估计[J].吉林大学学报, 2008, 38(5): 1160~1164.
    [110] IEEE Standard 145-1993, IEEE Standard Definition of Terms for Antennas [S].
    [111]孙莉.卫星接收机中小型化宽波束微带天线研究及应用[D].长沙:国防科技大学研究生院, 2006: 25~35.
    [112]李柏渝.通道非理想特性对导航接收机伪码测距零值的影响分析技术报告[R].长沙:国防科技大学, 2011: 2~3.