摘要
阵列信号处理在很多应用领域具有重要作用。随着传感器和阵列技术的发展，与之相应的阵列信号处理成为近几十年的热点，受到广泛的关注。本文从阵列信号处理的目标检测、方位分辨和估计的角度，对现有算法做出改进，以提高算法性能。
空域匹配滤波是最大信噪比准则下的最优处理器，也是单目标白噪声情况下似然估计的等价处理器。利用最小均方误差准则下的维纳滤波对阵列快拍进行滤波，可以一定程度上抑制噪声。为了在空域进行噪声抵消，利用二阶锥规划实现维纳滤波。对算法进行仿真分析，并在单目标白噪声条件下与最大似然估计(Maximum Likelihood Estlmatlng，MLE)和Bar-tlett波束形成进行比较。空域维纳滤波器的方位估计的信噪比门限要低于MLE，其低信噪比下的检测性能优于Bartlett波束形成，因而是一种良好的波束形成器。
最小方差无畸变响应(Mlnlmum、1arlance[)istortionless Response，MvDR)是波束输出能量最小意义上的最优波束形成。对MvDR的约束条件进行分析，将其转换为二阶锥的形式，通过将，J，范数最小条件改为，J。范数最小条件，提出基于，m范数约束的最小方差无畸变响应(，Jmnorm constlraIntMinimumv1ar。lancei)istortionless Response，，lm．MVDR)波束形成器。，lm．MvDR的权向量波束能更好地抑制干扰，因而，lm．MvDR的方位分辨信噪比门限低于MvDR。对比分析MvDR和，l一．MvDR的稳健性，当阵列存在失配时，MvDR和，lm．MvDR的性能受影响，随着失配的增大，，lm．MvDR比MvDR退化要快，因而，lm．MvDR的分辨能力是以损失对失配的稳健性为代价的。
将宽带导向最小方差波束形成fSteered Mlnlmumv1arlance，sTMv0算法扩展到矢量阵，并与基于声矢量传感器均匀直线阵的：Bai~tlett、非相干最小方差(ncoheren!，Mlnlmum1arlance，IcMv)和空间重采样相干子空间最优(Spatially Resampled Minimumv1arlance，SRMv)波束形成算法进行比较：分析标量阵与矢量阵指向性、抗左右舷模糊、主波束宽度和旁瓣级、空间欠采样，方位分辨力、相关信号源的分辨能力以及强干扰下的弱目标检测能力。最后利用这几种矢量波束形成算法对三次海试数据进行了分析。当目标快速运动时，目标方位的改变会引起互谱密度矩阵的模糊，影响波束形成性能。因而，收敛快的sTMv波束形成与收敛慢的IcMv相比，方位谱主瓣更窄，旁瓣更低。
为了充分发挥线谱信噪比高的特性，提高三维方位历程检测线谱目标的能力，提出了频率方差加权波束形成检测器。首先分析了短时傅里叶变换瞬时频率方差估计，给出了它的理论解，并通过Monte car0仿真验证了其正确性。当线谱的谱级信噪比超过一定门限时瞬时频率方差为零。用频率方差对波束能量进行加权，线谱目标方位波束因输出信号的瞬时频率方差较小得到增强，而其他方位波束被抑制，从而有效提高对线谱目标的检测能力。然后通过仿真频率方差加权常规波束形成(varlance of lnst3mtaneous frequencv．conventional Beaanib~"ruing Beamibrmlng，vIF．cBF)和频率方差加权导向最小方差波束形成(v1arlance of instantaneous frequency．Steered Minimumv1arlance BeamIbianlng，vIF．sTMv)，分析了频率方差加权波束形成抑制无线谱强干扰，增强线谱目标的机理。还比较了倒数加权与指数加权的特性。最后海试数据处理验证了本文提出的vIF．sTMv检测器，处理结果表明，vIF．sTMv检测器可以有效的提高线谱目标的检测能力。
Array signal processing plays a very important role in various applicationfields With the development of sensor and array technology,it has been a populartopic in recent years In this paper,several algorithms are improved to enhancetheir capabilities for target detecting，bearing resolution and DOA estimating
Spatial match filter is the optimal processor under maximum signal to noiseratio(SNR)criterion in mono-source and white noise condition The noise can besuppressed to a certain extend by tilting the array snapshots with Wiener filterwhich is under minimum mean-square error criterion To carry out spatial noisecmaceling，the Wiener filter is constructed through Second-Order ConeProgramming(SOCP)The algorithm is then compared with maximum likelihoodestimating(MLE)and Bartlett beamforming through simulation The SNRthreshold of Spatial filter is lower than maximum likelihood method in DOAestimation，and the detection performance is better at low SNR So it is a excellentprocessor in mono-source mad white noise condition
Minimum Variance Distortionless Response(MVDR)is the optimalprocessor under minimum power of beam output and distortionless responsecriterion Its constraints can be transformed to second-order cone forms L,norlTl constraint Minimum Variance Distortionless Response。-MVDR)isproposed by minimizing L,norlTl instead of L2 norlTl of the power minimizingconstraint in MVDR The weights generated by L,-MVDR repress interferesbetter than MVDR，which is the cause of a better bearing resolution Analyse therobustness of both algorithms comparatively The disturbance of array modelaffects beamformings’behaviors With the increase of the disturbance，L,-MVDR deteriorates more rapidly than MVDR So L,-MVDR sacrifices itsrobustness to gain better resolution ability．
Acoustic vector-sensor array STeered Minimum Variancebeamforming(VSTMV)is propounded A comparative analysis of Bartlett Incoherent Minimum Variance(ICMV)mad Spatially Resmnpled MinimumVariance(SRMV)beamforming algorithms based on vector uniform line aiTa iscarried out Then several aspects are analysis such as directivity,port／staxboarddistinguishing，width of mainlobe，sidelobe levee spatial undersamplingperformance，bearing resolution，resolution of correlated sources mad weak sourcedetecting ability under s~ong interferes Finally sea trial real data is maalysed withthese algorithms comparatively Cross-spe~rM density matrix estimated will notbe accurate with the direction of the target changing caused by its moving，whichleads to beamforming performance’S degenerating So that，STMV with fasterconvergent speed has better performance
Variance of Instantaneous Frequency-Beamforming detector(VIF-BF)isintroduced to improve the detecting ability of targets that radiate line spectrumsignal for three--dimensional time--bearing display,by taking advantage of highSNR prope~y of line spectrum First，the form for the variance of instantaneousfrequency estimating through short-time Fourier Transform(STFT)is derived．and is verified with Monte Carlo simulation The beamforming outputs of thebearings where the targets that radiate line spectrum signal are will bes~enghened，and vice versa Therefore the detecting capacity is enhancedVariance of instantaneous~equency-CBF beamforming detector and variance ofinstantaneous~equency-STMV beamforming detector are simulation as aexample The behavior of multiplicative inverse method and exponentiN weightmethod is also studied Its validity is proved by three sea trial
引文
[1] Arogyaswami Paulraj, Rohit Nabar, Dhananjay Gore. Introduction to Space-Time Wireless Communications. Cambridge University Press. 2003
[2] H Krim, M Viberg. Two Decades of Array Signal Processing Research. IEEE Signal Processing Magazine, 1996.6: 67-94P
[3] E. Brookner, J. M. Howell. Adaptive Array Processing. IEEE Proceedings. 1986, 74(4): 602-604P
[4] B. Ottersten. Array Processing for Wireless Communications. IEEE Proceedings. 1986, 466-473P
[5] S. Haykin, J. P. Reilly. V. Kezys. E. Vertatschitsch. Some Aspects of Array Signal Processing. Radar and Signal Processing. IEE Proceedings F. 1992, 139(1): 1-26P
[6]鲍小琪,徐其昌.凹型弯张换能器的有限元分析.声学学报.1982,4:27-34P
[7]莫喜平.ANSYS软件在模拟分析声学换能器中的应用.声学技术.2007,26(6):1279-1290P
[8]贺西平.稀土超磁致伸缩换能器.科学出版社.2006
[9]曾德平,刘光聪,邹学平.电致伸缩低频换能器的研制.中国声学学会2005青年学术会议.2005,134-137P
[10]李邓化.新型压电复合换能器及其应用.科学出版社.2007
[11]张金铎,栾桂冬.大面积平板PVDF水听器的研制.98全国声学学术会议.1998,43-45P
[12]栾桂冬,王光灿.新型换能器技术的进展.哈尔滨工程大学学报.2004,25(3):1103-1108P
[13]张仁和,倪明.光纤水听器的原理与应用.船舶工程.2004,33(7):503-507P
[14] E. F. Carome. Fiber optic gradient hydrophone and method of using same.United States Patemt 4799752. 1989
[15]杨德森,洪连进.矢量水听器原理及应用引论.科学出版社.2009
[16]贾志富.三维同振球型矢量水听器的特性及其结构设计.应用声学.2001,20(4):124-129P
[17] Articles. Spectra From Various Techniques. IEEE Proceedings, 1981, 69(11): Special Issue
[18] Articles. Time Delay Estimation. IEEE Trans. On Acoustics, Speech and Signal Proc., 1981,29(3): Special issue
[19] Articles. Spectral Estimation. IEEE Proceedings,1982, 70(9): Special Issue
[20] S. P. Applebaum. Adaptive Arrays. IEEE Trans. Antennas and Propagation, 1976, 24(9): 585-598P
[21] J. Capon. High-Resolution Frequency-Wavenumber Spectrum Analysis. Proc. IEEE, 1969, 57(8): 1408-1418P
[22] W. F. Gabriel. Spectral Analysis and Adaptive Array Superresolution Techniques. IEEE Proceedings, 1980, 68(6): 654-666P
[23] J. Burg. Maximum Entropy Spectral Analysis. In 37th Meeting Society Exploration Geophysicists, 1967
[24] O. Strand. Multichannel Complex Maximum Entropy Spectral Analysis. Acoustics, Speech and Signal Processing, IEEE International Conference on ICASSP 77, 2003, 2: 736-741P
[25] A. van den Bos. Alternative Interpretation of Maximum Entropy Spectral Analysis. IEEE Tran. On Information Theory, 1971, 17(4): 493-494P
[26] S. Haykin, B. W. Currie, S. B. Kesler. Maximum-entropy Spectral Analysis of Radar Clutter. Proceedings of the IEEE. 1982, 70(9): 953-962P
[27] T. T. Georgiou. Spectral Analysis Based on The State Covariance: the Maximum Entropy Spectrum and Linear Fractional Parametrization. IEEE Tran. on Automatic Control, 2002, 47(11): 1811-1823P
[28] V. H. MacDonald, P. M. Schultheiss. Optimum Passive Bearing Estimation in a Spatially incoherent Noise Environment. J. Acoust. Soc. Am., 1969,46(1): 37-43P
[29] F. C. Schweppe. Sensor Array Data Processing for Multiple Signal Sources. IEEE Trans. On IT, 1968, IT-14: 294-305P
[30] Hao Zhang. Maximum-likelihood Estimation for Multivariate Spatial Linear coregionalization Models. Environmetrics, 2007, 18: 125-139P
[31] Eulogio Pardo-lguzquiza, K. V. Mardia, Mario Chica-Olmo. MLMATERN: A Computer Program for Maximum Likelihood Inference With the Spatial Matern Covariance Model. Computers & Geosciences, 2009, 35(6): 1139-1150P
[32] Luo Yi, Du Haiwen, Xuan Yongbo, Li Wangxi. Spatial Registration of Different Sensors using Maximum Likelihood Method. Electronics, Optics & Control, 2009, 16(5): 78-80P
[33] Y. I. Abramovich, N. K. Spencer, A. Y. Gorokhov. Bounds on Maximum Likelihood Ratio-part I: Aapplication to Antenna Array Detection-estimation with Perfect Wavefront Coherence. IEEE Trans. on Signal Processing, 2004, 52(6): 1524-1536P
[34] Y. I. Abramovich, N. K. Spencer, A. Y. Gorokhov. Bounds on maximum likelihood ratio-Part II: application to antenna array detection-estimation with imperfect wavefront coherence. IEEE Trans. on Signal Processing, 2005, 53(6): 2046-2058P
[35] Gang Shi, A. Nehorai. A Relationship Between Time-Reversal Imaging and Maximum-Likelihood Scattering Estimation. IEEE Trans. on Signal Processing, 2007, 55(9): 4707-4711P
[36] Hongtu Zhu, Minggao Gu, B. Peterson. Maximum Likelihood from Spatial Random Effects Models via the Stochastic Approximation Expectation Maximization Algorithm. Statistics and Computing, 2007, 17(2): 163-177P
[37] R. Roy, A. Paulraj, T. Kailath. ESPRIT--A SubspaceRotation Approach to Estimation of Parameters of Cisoids in Noise. IEEE Trans. on ASSP, 1986, 34(5): 1340-1342P
[38] P. Stoica, T. Soderstrom. Statistical Aanalysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies. IEEE Trans. on Signal Processing, 1991, 39(8): 1836-1847P
[39] J. S. Goldstein, I. S. Reed. Subspace Selection for Partially Adaptive Sensor Array Processing. IEEE Trans. on Aerospace and Electronic Systems, 1997, 33(2): 539-544P
[40] A. Ferreol, P. Larzabal, M. Viberg. On the Asymptotic Performance Analysis of Subspace DOA Estimation in The Presence of Modeling Errors: Case of MUSIC.
[41] M. L. McCloud, L. L. Scharf. A New Subspace Identification Algorithm for High-resolution DOA Estimation. IEEE Trans. on Antennas and Propagation, 2002, 50(10): 1382-1390P
[42] D. W. Tufts, J. T. Francis. Designing Digital Low-pass Filters: Comparison of Some Methods and Criteria. IEEE Trans. Audio Electroacoust., 1970, AU-18: 487-494P
[43] A. Papoulis, M. S. Bertran. Digital Filtering and Prolate Functions. IEEE Trans. Circuit Theory, 1972, CT-19: 674-681P
[44] D. R. Rhodes. The Optimum Line Source for The Best Mean-square Approximation to a Given Radiation Pattern. IEEE Trans. Antennas Propag., 1963, AP-11: 440-446P
[45] J. F. Kaiser. Nonrecursive Digital Filter Design using the I0-Sinh Window Function. IEEE Proc. Symp. Circuit Syst., 1974, 20-23P
[46] S. A. Schelkunoff. A Mathematical Theory of Linear Arrays. Bell Syst. Tech. J., 1943, 22: 80-107P
[47] P. M. Woodward. A Method for Calculating The Field over A Plane Aperture Required to Produce A Given Polar Diagram. J. IEE, 1946, 93: 1554-1558P
[48] C. L. Dolph. A Current Distribution for Broadside Arrays Which Optimizes The Relationship between Beamwidth And Sidelobe Level.Proc. IRE, 1946, 34: 335-348P
[49] H. J. Riblet. A Current Distribution for Broadside Arrays Which Optimizes The Relationship between Beamwidth and Side-lobe Level. Proc. IRE, 1947, 35: 489-492P
[50] J. D. Kraus. Antennas. McGraw-Hill, New York, 2nd edition, 1988.
[51] T. T. Taylor. One Parameter Family of Line Sources Producing Modified Sin U/U Patterns. Technical Report 324, Hughes Aircraft Co., Culver City, California, 1953
[52] T. T. Taylor. Design of Line-source Antennas for Narrow Beamwidth and Low Sidelobes. IRE Trans. Antennas Propag., 1955, AP-3: 16-28P
[53] H. S. Hersey, D. W. Tufts, J. T. Lewis. Interactive Minimax Design of Linear Phase Nonrecursive Digital Filters Subject to Upper and lLower Function Constraints. IEEE Trans. Audio Elecroacoust., 1972, AU-20: 171-173P
[54] R. A. Mucci, D. W. Tufts, J. T. Lewis. Beam Pattern Synthesis for Line Arrays Subject to Upper and Lower Constraining Bounds. IEEE Trans. Antennas Propag., 1975: 732-734P
[55] T. W. Parks, J. H. McClellan. Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase. IEEE Trans. Circuit Theory, 1972, CT-19: 189-194P
[56] T. W. Parks, J. H. McClellan. A Program for The Design of Linear Phase Finite Impulse Response Digital Filters. IEEE Trans. Audio Electroacoust., 1972, AU-20: 195-199P
[57] H. Steyskal. Synthesis of Antenna Patterns with Prescribed Nulls. IEEE Trans. Antennas Propag., 1982, AP-30; 273-279P
[58]鄢社锋,马远良.二阶锥规划方法对于时空域滤波器的优化设计和验证.中国科学E辑,2006,36(2): 153-171P
[59] J. O. Coleman, D. P. Scholnik, J. J. Brandriss. A Specification Language for The Optimal Design of Exotic FIR Filters with Second-order ConePrograms. Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002, 1(3-6): 341-345P
[60] R. Nitzberg. Effect of Errors in Adaptive Weights. IEEE Trans. Aerosp. Electron. Syst. 1976, AES-12: 369-373P
[61] L. I. Kleinberg. Array Gain for Signals and Noise Having aAmplitude and Phase Fluctuations. J. Acoust. Sot. Am. 1980, 67: 572-576P
[62] R. A. Mucci, R. G. Pridham. Impact of Beam Steering Errors on Shifted Sideband and Phase Shift Beamforming Techniques. J. Acoust. Sot. Am.,1981, 69: 1360-1368P
[63] W. S. Youn, C. K. Un. Robust Adaptive Beamforming Based on The Eigenstructure Method. IEEE Trans. Signal Process, 1994 SP-42: 1543-1547P
[64] B. D. Carlson. Covariance Matrix Estimation Errors and Diagonal Loading in Adaptive Arrays. IEEE Trans. on Aerospace and Electronic Systems, 1988, 24(4): 397–401P
[65] F. Vincent, O. Besson. Steering Vector Errors and Diagonal Loading. IEE Proceedings Radar, Sonar and Navigation, 2004, 151(6): 337-343P
[66] A. B. Gershman. Robust Adaptive Beamforming in Sensor Arrays. AEU-International Journal of Electronics and Communication, 1999, 53(6): 305–314P
[67] B. D. Van Veen. Minimum Variance Beamforming with Soft Response Constraints. IEEE Trans. Signal Process., 1991, SP-39: 1964-1972P
[68] A. Elnashar. S. M. Elnoubi. H. A. El-Mikati. Further Study on Robust Adaptive Beamforming With Optimum Diagonal Loading. IEEE Trans. Antennas and Propagation, 2006, 54(12): 3647-3658P
[69] J. Li. P. Stoica. Z. Wang. On Robust Capon Beamforming and Diagonal Loading. IEEE Transactions on Signal Processing, 2003, 51: 1702–1715P
[70] R. G. Lorenz. S. P. Boyd. Robust minimum variance beamforming. 2005, IEEE Transactions on Signal Processing, 53: 1684–1696P
[71] J. Li. P. Stoica. Z. Wang. Doubly constrained robust Capon beamformer. IEEE Transactions on Signal Processing, 2004, 52: 2407–2423P
[72] M. H. Er. A. Cantoni. An Alternative Formulation for An Optimum Beamformer with Robustness Capability. Proc. IEE, 1985, 132: 447-460P
[73] C. R. Rao. Linear Statistical Inference and Its Applications. Wiley, New York, 1946.
[74] R. A. Fisher. Theory of Statistical Estimation. Proc. Cambridge Phil. Sot., 1925, 22:700P
[75] H. L. Van Trees. Detection, Estimation, and Modulation Theory, Part I. Wiley, New York, 1968
[76] A. J. Weiss. A. S. Willsky. B. C. Levy. Maximum Likelihood Array Processing for Estimation of Superimposed Signals. Proc. IEEE, 1988, 76(2): 203-205P
[77] Y. Bresler. Maximum Likelihood Estimation of A Linearly Structured Covariace with Application to Antenna Array Processing. Proc. 4th ASSP Workshop on Spectrum Estimation and Modeling, Minneapolis, Minnesota, 1988,172-175P
[78] F. Schweppe. Sensor array data processing for multiple signal sources. IEEE Trans. Inf. Theory, 1968, IT-4: 294-305P
[79] S. M. Kay. Modern Spectral Estimation: Theory and Application. Prentice Hall, Englewood Cliffs, New Jersey, 1988
[80] Q. T. Zhang. A Statistical ResolutionTheory of The Beamformer-based Spatial Spectrum for Determining The Directions of Signals in White Noise. IEEE Trans. Signal Process.,1995, SP-43: 1867-1873P
[81] L. VAN TREE. Optimum array processing. New York: John Wiley & Sons INC, 2003: 48P
[82] R. O. Schmidt. Multiple Emitter Location and Signal Parameter Estimation. Proc. RADC Spectrum Estimation Workshop, Griffiths AFB, Rome, New York, 1979, 243-258P
[83] G. Bienvenu. L. Kopp. Adaptivity to Background Noise Spatial Coherence for High Resolution Passive Methods. Proc. ICASSP,1980, 1: 307-310P
[84] R. Kumaresan. D. W. Tufts. Estimating the Angles of Arrival of Multiple Plane Waves. IEEE Trans. AES, 1983, 19(1): 134-139P
[85] A. Paulraj. R. Roy. T. Kailath. A Subspace Rotation Approach to Signal Parameter Estimation. Proc. IEEE, 1986, 1044-1045P
[86] R. Roy. T. Kailath. ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques. IEEE Trans. ASSP, 1989, 37(7): 984-995P
[87] M. Viberg. B. Ottersten. T. Kailath. Detection and Estimation in Sensor Arrays Using Weighted Subspace Fitting. IEEE Trans. SP, 1991, 39(11): 2436-2449P
[88] I. J. Clarke. High Discrimination Target Detection Algorithms and Estimation of Parameters. Underwater Acoustic Data Processing, 1989, 273-277P
[89] H. Akaike. A New Look at the Statistical Model Identification. IEEE Trans. Autom. Control, 1974, 19: 716-723P
[90] G. Schwartz. Estimating the Dimension of A Model. Ann. Stat. 1978, 6: 461-464P
[91] M. Wax. T. Shan. T. Kailath. Spatio-temporal Spectral Analysis by Eigenstructure Methods. IEEE Trans. Acoust, Speech, Signal Processing, 1984, 32: 817-827P
[92] J. Krolik. D. Swingler. The Direction Performance of Coherent WideBand Focusing for a Spatially Resampled Aray. IEEE ICASSP, 1990, 2827-2830P
[93] M. A. Doron. A. J. Weiss. On Focusing Matrices for Wideband Array Processing. IEEE Trans. SP, 1992, 40(6): 1295-2302P
[94] K. M. Buckley. L. J. Griffiths. Broad-band Signal-Subspace Spatial Spectrum (BASS-ALE) Estimation. IEEE Trans. ASSP, 1988, 36(7): 953-964P
[95] Y. Grenier. Wideband Source Location Through Frequency-Dependent Modeling. IEEE Trans. SP, 1994, 42(5): 1087-1096P
[96] G. L. D’Spain. W. S. Hodgkiss. G. L. Edmonds. J. C. Nickles. F. H. Fisher. R. A. Harriss. Initial Analysis of the Data from the Vertical DIFAR Array. Oceans’92, Newport, 1992: 346–351P
[97] G. L. D’Spain. The Simultaneous Measurement of Infrasonic Acoustic Particle Velocity and Acoustic Pressure in Ocean by Freely Drifting Swallow Floats. J. Oceanic Eng., 1991, 16(2):195-207P
[98] V. A. Shchurov. Coherent and Diffusive Fields of Underwater Acoustic Ambient Noise. J. Acoust. Soc. Am., 1991, 90(2):991-1001P
[99] V. A. Shchurov. A Possible Mechanism of Dynamic Ambient Ocean Noise Horizontal Energy Flow Forming. Proc. I.O.A., 1996, 18(5): 154-162P
[100] V. A. Shchurov. The Interaction of Energy Flows of Underwater Ambient Noise and a Local Source. J. Acoust. Soc. Am., 1991, 90(2):1002-1004P
[101]李春旭.声压、振速联合信息处理.哈尔滨工程大学工学博士学位论文,2000
[102]时胜国.矢量水听器及其在平台上的应用研究.哈尔滨工程大学博士学位论文,2007
[103] M. Hawkes, A. Nehorai. Acoustic Vector-sensor Correlations in Ambient Noise. IEEE. Journal of Oceanic Engineering, 2001,26(3): 337- 347P
[104] V. A. Shchurov. Vector Acoustics of The Ocean. Vladivostok: Dalhauka, 2006
[105] M. Hawkes. Issues in Acoustic Vector Sensor Processing. Yale University, 2000
[106] Aryc Nehorai, Eytan Paldi. Acoustic vector-sensor array processing. J. Acoust. Soc. Am., 1994, 42(9):2481-2491P
[107] B. Hochwald, A. Nehorai. Identifiability in array processing models with vector-sensor applications. IEEE Transactions on Signal Processing, 1996, 44:83-95P
[108] M. Hawkes. A. Nehorai. Acoustic Vector-Sensor Processing in the Presence of a Reflecting Boundary. IEEE Trans SP, 2000, 48(11): 2981– 2993P
[109] M. Hawkes. A. Nehorai. Wideband Source Localization Using a Distributed Acoustic Vector-Sensor Array. IEEE Trans SP, 2003, 51(6): 1479-1491P
[110] A. Nehorai. E. Paldi. Acoustic Vector-Sensor Array processing. IEEE Trans SP, 1994, 40(9): 2481-2491P
[111] M. Hawkes. A. Nehorai. Acoustic Vector-sensor Beamforming and Capon Direction Estimation. IEEE Trans SP, 1998, 46(9): 2291-2304P
[112] M. Hawkes. A. Nehorai. Acoustic Vector-Sensor Correlations in Ambient Noise. IEEE Journal Oceanic Engineering, 2001,26(3): 337-347P
[113] K. T. Wong. Novel Techniques of Polarization Diversity & Extended Aperture Spatial Diversity for Sensor-array Direction Fingding in Radar, Sonar, & Wireless communications. Purdue University, 1996
[114] K. T. Wong. M. D. Zoltowski. Closed-Form Underwater Acoustic Direction-Finding with Arbitrarily Spaced Vector Hydrophones at Unknown Locations. IEEE Journal Oceanic Engineering, 1997, 22(4): 566-575P
[115] K. T. Wong. M. D. Zoltowski. Root-MUSIC-Based Azimuth-Elevation Angle-of-Arrival Estimation with Uniformly Spaced but Arbitrarily Oriented Velocity Hydrophones. IEEE Trans. SP, 1999, 47(12): 3250-3260P
[116] K. T. Wong. M. D. Zoltowski. Closed-form Direction-finding with Arbitrarily Spaced Electromagnetic Vector-sensors at Unknown Locations, IEEE Trans AP, 48(5): 671～681P
[117] K. T. Wong. M. D. Zoltowski. Extended-aperture Underwater Acoustic Multisource Azimuth/Elevation Direction-finding Using Uniformly but Sparsely Spaced Vector Hydrophones. IEEE J. Oceanic Eng., 1997,22:659-672P
[118] K. T. Wong. M. D. Zoltowski. Root-MUSIC-based Azimuth-Elevation Angle-Of-Arrival Estimation with Uniformly Spaced but Arbitrarily Oriented Velocity Hydrophones, IEEE Tran SP,1999, 47(12): 3250-3260P
[119] K. T. Wong. M. D. Zoltowski. Self-initiating MUSIC-based Direction Finding in Underwater Acoustic Particle Velocity-Field Beamspace. IEEE J. Oceanic Engi., 2000, 25(2): 262-273P
[120] G. L. D’Spain. J. C. Luby. G. R. Wilson. R. A. Gramann. Vector Sensors and Vector Sensor Line Arrays: Comments on Optimal Array Gain and Eetection. J. Acoust. Soc. Am., 2006, 120(1): 171-185P
[121]惠俊英,李春旭等.声压和振速联合信号处理抗相干干扰.声学学报, 2000, 25(5):389-394P
[122]惠俊英,刘宏等.声压振速联合信息处理及其物理基础初探.声学学报. 2000, 25(4):303-307P
[123]孙贵青,杨德森,张揽月.基于矢量水听器的水下目标低频辐射噪声测量方法研究.声学学报,2002,27(5):429-434P
[124]孙贵青,杨德森,张揽月,时胜国.基于矢量水听器的最大似然比检测和最大似然方位估计,2003, 28(1):66-72P
[125]张揽月,杨德森.基于矢量阵的自初始化MUSIC方位估计算法.哈尔滨工程大学学报,2006,27(2): 248-251P
[126]张揽月,杨德森.矢量水听器扩展孔径线阵方位估计技术.哈尔滨工程大学学报,2004,25(6) :714-718P
[127] J. L?fberg. A Toolbox for Modeling and Optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004
[128]彭建辉.基于凸优化理论的自适应波束形成技术.中国科学技术大学博士论文.2008
[129] Jing Liu. A. B. Gershman. Zhi-Quan Luo. K. M. Wong. Adaptive Beamforming with Sidelobe Control: A Second-Order Cone Programming Approach. IEEE Signal Processing Letters, 2003, 10(11): 331-334P
[130] Kevin Smith. Vincent van Leijen. Steering Vector Sensor Array Elements with Linear Cardioids and Nonlinear Hippioids. J. Acoust. Soc. Am. 2007, 122 (1):370-377P
[131] H. Hung. M. Kaveh. Focusing Matrices for Coherent Signal Subspace Processing. IEEE Trans. ASSP. 1988, 36(8):1272-1281P
[132] J. Krolik, D. Swingler. The Detection Performance of Coherent Wideband Focusing for a Spatially Resampled Array. IEEE International Conference ASSP. 1990, 2(9):2827-2830P
[133] J. Krolik, D. Swingler. The Performance of Minimax Spatial Resampling Filters for Focusing Wide-Band Arrays. IEEE Trans On SP. 1991, 39(8):1899-1903P
[134]陈华伟,赵俊渭.声矢量传感器阵宽带相干信号子空间最优波束形成.声学学报,2005,30(1):76-82P
[135]徐仲,张凯院等.矩阵论简明教程.科学出版社,2001:57-58P
[136] J. Krolik. D. Swingler. Multiple Broadband Source Location Using Steered Covariance Matrices. IEEE Trans. ASSP. 1989, 37(10):1481-1494P
[137]林茂庸,柯有安.雷达分辨理论.北京:国防工业出版社,1984
[138]梁国龙.回波信号瞬时参数序列分析及其应用研究.哈尔滨工程大学博士论文,1997
[139] H. Hung. M. Kaveh. Focussing Matrices for Coherent Signal-subspace Processing. IEEE Trans. ASSP, 1988, 36(8), 1272-1281P
[140]朱华,黄辉宁,李永庆,梅文博.随机信号分析.北京:北京理工大学出版社,1990
[141] A. D. Whalen. Signal Detecting in Noise. Beijing. Science Press, 2006
[142]崔绪生.国外鱼雷技术进展综述.鱼雷技术,2003,11(1):6-11P
[143]刘金山.Wishart分布引论.科学出版社,2005
[144] H. Wang. M. Kaveh. Coherent Signal-Subspace Processing for the Detection and Estimation of Angles of Arrival of Multiple Wideband Source. IEEE Trans. TASSP, 1984, 32: 817-827P