障板条件下矢量水听器应用研究
|
摘要
矢量水听器的出现，突破了声纳设备获取水下声信号长期依靠标量声压水听器的限制，为我国声纳技术的发展开辟了新的途径。矢量水听器可以空间共点同步拾取声场一点处的声压和质点振速矢量，利用获取的声压和质点振速可在全空间对声源进行无模糊定向，且获得等价于四元声压阵声纳系统的检测性能，这种水声传感器的紧凑型配置方式为解决水下小尺度平台湿端布置空间受限的问题提供了很好的解决方案。矢量水听器还具有不依赖于声波频率的空间指向性，这个优点在水声系统低频化发展的趋势下显得尤为突出，能够使得基于矢量水听器的声纳系统具有更好的低频适应性。当利用多个矢量水听器组成声纳基阵时，能够将矢量水听器的抗噪能力和阵列系统的空间分辨能力有机结合起来，进一步提高声纳系统的性能，获得比相同数目的声压阵更好的性能；或者在相同的性能指标要求下，能够显著的减小阵元数目。矢量水听器的诸多优势使得这项技术已经成功应用于低噪声测量系统、海上浮标声纳、拖曳阵声纳等水声设备中。但是上述应用都是假设矢量水听器处于自由场条件下，当矢量水听器安装于水面船舶和水下航行器等载体时，由于载体障板声学散射的影响，会导致矢量水听器性能发挥受到极大影响。如何在水面和水下载体声障板条件下应用，并且使得矢量水听器可以取得海上声纳浮标设备那样的良好效果，成为急需解决的一个难题。本文以船舶上三型典型声纳设备声障板——矩形、圆柱形和球形障板为模型，研究上述三种障板声散射近场矢量特性以及相应障板条件下矢量信号处理方法。
针对矩形障板，以工程实际中使用的弹性矩形空气腔障板为研究对象，探讨了弹性矩形空气腔障板水下声散射，将弹性矩形空气腔障板建模为无限大刚硬平幕中，镶嵌一块可以振动的板，板的两侧流体分别为水和空气，板的边缘满足简支边界条件。给出弹性矩形空气腔障板水下声散射声场的解析解，并且验证了该模型的合理性以及推导公式的正确性，在此基础上研究了弹性矩形空气腔障板水下声散射近场矢量特性。由于矩形空气腔障板声散射的声压场和质点振速场的表达式比较复杂，不利于后续的信号处理，将散射声场表示为反射系数刻画的简洁的模型，这样，就建立起反射系数所表征的矩形空气腔障板条件下矢量线阵的测量模型。基于该测量模型研究了矩形障板条件下矢量线阵阵列信号处理方法，在直接阵元域实现了声压和振速的相干信号处理。与相同阵型的声压阵相互比较的结果表明，矩形障板条件下矢量线阵仍然能够充分发挥矢量水听器的优点。
针对圆柱形障板，考虑工程实际，采用密闭的圆柱形空气腔壳体作为圆柱形基阵的反声障板。首先研究有限长圆柱壳体水下声散射，在前人研究的基础上，采用弹性力学中的薄壳理论（Donnell方程）表述圆柱壳体运动，并在一定的近似假设下给出有限长圆柱空气腔壳体表面水下声散射声场的解析解，在此基础上研究了有限长圆柱空气腔壳体水下声散射近场矢量特性。在此基础上将传统的障板条件下标量圆弧阵的相位模态域信号处理方法引入圆柱形障板条件下的矢量圆阵，对远场平面波激起的圆柱形障板附近声场，将复杂的近场干涉图案分解为规则的相位模态域图案，提出了矢量圆阵声压振速相位模态域阵列信号处理方法，在相位模态域实现了声压和振速的相干处理，将矢量水听器的抗噪能力与圆阵阵列系统的分辨能力有机结合起来，同时将子空间类DOA(direction of arrival)估计算法和相位模态域阵列信号处理技术有机结合起来，从而将矢量水听器的适用范围扩展至圆柱形障板条件。
本文还研究了球形障板条件下矢量水听器的应用。首先采用薄壳理论和分离变量法研究球形空气腔壳体水下声散射，重点研究空气腔球壳水下声散射近场矢量特性，在此基础上从球形障板条件下声矢量圆阵阵元域信号的表达式出发，利用声场分解理论，将阵元域信号表示为若干阶正交的相位模态，然后给出声压、径向振速和切向振速的预处理矩阵，利用预处理矩阵将声矢量圆阵阵元域信号变换到相位模态域，在相位模态域给出了协方差矩阵的生成方法，然后进行方位估计，实现了球形障板条件下声压和振速的相干处理，将矢量水听器的适用范围扩展至球形障板条件。
本文设计了矩形空气腔障板三元矢量线阵和圆柱形空气腔障板八元矢量圆阵水声试验系统，开展了外场试验研究，试验结果和仿真结果符合得较好，验证了本文理论的正确性。为矩形空气腔障板和圆柱形空气腔障板条件下矢量水听器的工程应用提供了试验基础。
The emergence of acoustic vector sensor, broke through the restrictions that measuringthe underwater acoustic signal for the sonar equipment has long relied on scalar pressuresensor, opens up a new way for the development of sonar technology. The acoustic vectorsensor is combined by omnidirectional pressure sensor and dipole particle velocity sensor,which co-locating and simultaneously measures acoustic pressure and all the three orthogonalcompotents of particle velocity in acoustic field. Using that information, it can obtain theintensity and direction of sources, and can have equivalent performance of a four elementssonar system with omnidirectional pressure sensor. This compact configuration of theacoustic sensors provides a very good solution to solve the problem of limited of the layoutspace of the small scale underwater platform. The directivity of acoustic vector sensor is notdependent on the frequency of sound. This advantage is particularly prominent in thelow-frequency trend of development of sonar systems. And it can make the sonar systemswhich base on the acoustic vector sensor have better low-frequency adaptability. The vectorsensor provides more information than a pressure sensor as it contains three dipole channelsin addition to a monopole channel. Hence, an array of N vector sensors can achieve betterperformance than a conventional array of N pressure sensors. Likewise, a given level ofperformance may be attained with fewer vector sensors. Due to these attractive characteristics,the acoustic vector sensor has been successfully applied to low-noise measurement system,marine sonar buoys, towed array sonar and other acoustic devices. These works have onlyconsidered the acoustic vector sensors in free space; however, when the acoustic vectorsensors are mounted on a ship, due to the scattering of the acoustic baffle, it will result in asignificant decline in the performance of the vector sensor. Therefore, how to use the acousticvector sensor in the presence of an acoustic baffle and obtain good performance as the marinesonar buoys have become urgent problems. In this paper, the three typical sonar baffles--rectangular, cylindrical and spherical baffle are taken as research objects, acoustic vectorcharacteristics of near fields scattered by the three typical sonar baffles as well as thecorresponding vector signal processing methods are studied.
For the rectangular baffle, an elastic rectangular air chamber baffle which is usedcommonly in practical engineering is taked as research object. The elastic rectangular airchamber baffle is modeled as a baffled, simply supported plate. The both sides of the plate arewater and air respectively. The analytical expressions for the scattered pressure and particle velocity are derived. Then the rationality of the model and the correctness of the formula areverified. Calculations are presented for the scattered near fields of the pressure, the particlevelocity and the intensity. Because the expression of sound pressure field and particle velocityis quite complex, is not conducive to the signal processing, the scattering field were simplymodeled based on the reflection coefficient. In this way, we can establish a measurementmodel of vector sensor linear array with rectangular air chamber baffle based on the reflectioncoefficient. Based on this measurement model, vector signal processing methods for thevector sensor linear array with rectangular air chamber baffle is studied. Coherent signalprocessing of pressure and particle velocity is achieved in the direct element space.Simulation and experimental results show that the vector sensor linear array with rectangularair chamber baffle still can take full advantage of the vector sensor.
Considering the engineering practice, a closed finite length cylindrical air chamber shellis used as a cylindrical baffle. Firstly, the acoustic scaterring from finite length cylindricalshell is studied. On the basis of previous studies, we use the elastic thin shell theory (Donnellequation) describe the motion of cylindrical shell, and under some approximation assumptionsanalytical expressions are derived for the total acoustic pressure field and the total particlevelocity field scattering from the cylindrical shell. The acoustic vector characteristics ofspatial distribution are discussed based on the analytical expressions. Phase modal domainsignal processing method for a traditional scalar circular array is introduced into the acousticvector sensor circular array mounted around a cylindrical baffle. The complex interferencepattern near the surface of cylindrical baffle, which is provoked by the far-field plane wave,can be decomposed into regular phase modal patterns. Then the modal vector-sensor arraysignal processing algorithm, which is based on the wavefield decomposition techniques, forthe acoustic vector sensor circular array mounted around the cylindrical baffle is proposed.Coherent signal processing of pressure and particle velocity is achieved in phase modal space.It is concluded that the vector sensor can be used under the condition of the cylindrical baffleand that the acoustic vector sensor circular array mounted around the cylindrical baffle canalso combine subspace DOA (direction of arrival) estimation algorithm with phase modalspace array signal processing technology. The scope of application of vector hydrophone isextended to the cylindrical baffle condition.
The article also studied applications of vector sensor under the conditions of sphericalbaffle. Firstly, the analytic expressions for the scattered pressure and particle velocity arederived using the elastic thin shell theory. Calculations are presented for the scattered nearfields of the pressure, the particle velocity and the intensity. Based on the Wavefield decomposition techniques, the element domain signal were represented for some orderquadrature phase modes, and then gives the preconditioning matrix of the pressure, the radialvelocity and tangential velocity. The array signals are converted from element space to phasemodal space using the preconditioning matrix, and then estimate direction of arrival in phasemodal space. The algorithm is based on the principle of coherency between pressure andparticle velocity, which can suppress interference in isotropic noise field. The scope ofapplication of vector hydrophone is extended to the spherical baffle condition.
Two experimental sonar systems, the three elements linear acoustic vector-sensor arraywith a rectangular air chamber baffle and the eight elements circular acoustic vector-sensorarray with cylindrical air chamber baffle, were designed to carry out the Songhua Lakeexperiment. The test results and the simulation results were in good agreement, to verify thecorrectness of the theory in this paper and provide the experimental basis for the engineeringapplication of acoustic vector-sensor with acoustic baffle.
针对矩形障板，以工程实际中使用的弹性矩形空气腔障板为研究对象，探讨了弹性矩形空气腔障板水下声散射，将弹性矩形空气腔障板建模为无限大刚硬平幕中，镶嵌一块可以振动的板，板的两侧流体分别为水和空气，板的边缘满足简支边界条件。给出弹性矩形空气腔障板水下声散射声场的解析解，并且验证了该模型的合理性以及推导公式的正确性，在此基础上研究了弹性矩形空气腔障板水下声散射近场矢量特性。由于矩形空气腔障板声散射的声压场和质点振速场的表达式比较复杂，不利于后续的信号处理，将散射声场表示为反射系数刻画的简洁的模型，这样，就建立起反射系数所表征的矩形空气腔障板条件下矢量线阵的测量模型。基于该测量模型研究了矩形障板条件下矢量线阵阵列信号处理方法，在直接阵元域实现了声压和振速的相干信号处理。与相同阵型的声压阵相互比较的结果表明，矩形障板条件下矢量线阵仍然能够充分发挥矢量水听器的优点。
针对圆柱形障板，考虑工程实际，采用密闭的圆柱形空气腔壳体作为圆柱形基阵的反声障板。首先研究有限长圆柱壳体水下声散射，在前人研究的基础上，采用弹性力学中的薄壳理论（Donnell方程）表述圆柱壳体运动，并在一定的近似假设下给出有限长圆柱空气腔壳体表面水下声散射声场的解析解，在此基础上研究了有限长圆柱空气腔壳体水下声散射近场矢量特性。在此基础上将传统的障板条件下标量圆弧阵的相位模态域信号处理方法引入圆柱形障板条件下的矢量圆阵，对远场平面波激起的圆柱形障板附近声场，将复杂的近场干涉图案分解为规则的相位模态域图案，提出了矢量圆阵声压振速相位模态域阵列信号处理方法，在相位模态域实现了声压和振速的相干处理，将矢量水听器的抗噪能力与圆阵阵列系统的分辨能力有机结合起来，同时将子空间类DOA(direction of arrival)估计算法和相位模态域阵列信号处理技术有机结合起来，从而将矢量水听器的适用范围扩展至圆柱形障板条件。
本文还研究了球形障板条件下矢量水听器的应用。首先采用薄壳理论和分离变量法研究球形空气腔壳体水下声散射，重点研究空气腔球壳水下声散射近场矢量特性，在此基础上从球形障板条件下声矢量圆阵阵元域信号的表达式出发，利用声场分解理论，将阵元域信号表示为若干阶正交的相位模态，然后给出声压、径向振速和切向振速的预处理矩阵，利用预处理矩阵将声矢量圆阵阵元域信号变换到相位模态域，在相位模态域给出了协方差矩阵的生成方法，然后进行方位估计，实现了球形障板条件下声压和振速的相干处理，将矢量水听器的适用范围扩展至球形障板条件。
本文设计了矩形空气腔障板三元矢量线阵和圆柱形空气腔障板八元矢量圆阵水声试验系统，开展了外场试验研究，试验结果和仿真结果符合得较好，验证了本文理论的正确性。为矩形空气腔障板和圆柱形空气腔障板条件下矢量水听器的工程应用提供了试验基础。
The emergence of acoustic vector sensor, broke through the restrictions that measuringthe underwater acoustic signal for the sonar equipment has long relied on scalar pressuresensor, opens up a new way for the development of sonar technology. The acoustic vectorsensor is combined by omnidirectional pressure sensor and dipole particle velocity sensor,which co-locating and simultaneously measures acoustic pressure and all the three orthogonalcompotents of particle velocity in acoustic field. Using that information, it can obtain theintensity and direction of sources, and can have equivalent performance of a four elementssonar system with omnidirectional pressure sensor. This compact configuration of theacoustic sensors provides a very good solution to solve the problem of limited of the layoutspace of the small scale underwater platform. The directivity of acoustic vector sensor is notdependent on the frequency of sound. This advantage is particularly prominent in thelow-frequency trend of development of sonar systems. And it can make the sonar systemswhich base on the acoustic vector sensor have better low-frequency adaptability. The vectorsensor provides more information than a pressure sensor as it contains three dipole channelsin addition to a monopole channel. Hence, an array of N vector sensors can achieve betterperformance than a conventional array of N pressure sensors. Likewise, a given level ofperformance may be attained with fewer vector sensors. Due to these attractive characteristics,the acoustic vector sensor has been successfully applied to low-noise measurement system,marine sonar buoys, towed array sonar and other acoustic devices. These works have onlyconsidered the acoustic vector sensors in free space; however, when the acoustic vectorsensors are mounted on a ship, due to the scattering of the acoustic baffle, it will result in asignificant decline in the performance of the vector sensor. Therefore, how to use the acousticvector sensor in the presence of an acoustic baffle and obtain good performance as the marinesonar buoys have become urgent problems. In this paper, the three typical sonar baffles--rectangular, cylindrical and spherical baffle are taken as research objects, acoustic vectorcharacteristics of near fields scattered by the three typical sonar baffles as well as thecorresponding vector signal processing methods are studied.
For the rectangular baffle, an elastic rectangular air chamber baffle which is usedcommonly in practical engineering is taked as research object. The elastic rectangular airchamber baffle is modeled as a baffled, simply supported plate. The both sides of the plate arewater and air respectively. The analytical expressions for the scattered pressure and particle velocity are derived. Then the rationality of the model and the correctness of the formula areverified. Calculations are presented for the scattered near fields of the pressure, the particlevelocity and the intensity. Because the expression of sound pressure field and particle velocityis quite complex, is not conducive to the signal processing, the scattering field were simplymodeled based on the reflection coefficient. In this way, we can establish a measurementmodel of vector sensor linear array with rectangular air chamber baffle based on the reflectioncoefficient. Based on this measurement model, vector signal processing methods for thevector sensor linear array with rectangular air chamber baffle is studied. Coherent signalprocessing of pressure and particle velocity is achieved in the direct element space.Simulation and experimental results show that the vector sensor linear array with rectangularair chamber baffle still can take full advantage of the vector sensor.
Considering the engineering practice, a closed finite length cylindrical air chamber shellis used as a cylindrical baffle. Firstly, the acoustic scaterring from finite length cylindricalshell is studied. On the basis of previous studies, we use the elastic thin shell theory (Donnellequation) describe the motion of cylindrical shell, and under some approximation assumptionsanalytical expressions are derived for the total acoustic pressure field and the total particlevelocity field scattering from the cylindrical shell. The acoustic vector characteristics ofspatial distribution are discussed based on the analytical expressions. Phase modal domainsignal processing method for a traditional scalar circular array is introduced into the acousticvector sensor circular array mounted around a cylindrical baffle. The complex interferencepattern near the surface of cylindrical baffle, which is provoked by the far-field plane wave,can be decomposed into regular phase modal patterns. Then the modal vector-sensor arraysignal processing algorithm, which is based on the wavefield decomposition techniques, forthe acoustic vector sensor circular array mounted around the cylindrical baffle is proposed.Coherent signal processing of pressure and particle velocity is achieved in phase modal space.It is concluded that the vector sensor can be used under the condition of the cylindrical baffleand that the acoustic vector sensor circular array mounted around the cylindrical baffle canalso combine subspace DOA (direction of arrival) estimation algorithm with phase modalspace array signal processing technology. The scope of application of vector hydrophone isextended to the cylindrical baffle condition.
The article also studied applications of vector sensor under the conditions of sphericalbaffle. Firstly, the analytic expressions for the scattered pressure and particle velocity arederived using the elastic thin shell theory. Calculations are presented for the scattered nearfields of the pressure, the particle velocity and the intensity. Based on the Wavefield decomposition techniques, the element domain signal were represented for some orderquadrature phase modes, and then gives the preconditioning matrix of the pressure, the radialvelocity and tangential velocity. The array signals are converted from element space to phasemodal space using the preconditioning matrix, and then estimate direction of arrival in phasemodal space. The algorithm is based on the principle of coherency between pressure andparticle velocity, which can suppress interference in isotropic noise field. The scope ofapplication of vector hydrophone is extended to the spherical baffle condition.
Two experimental sonar systems, the three elements linear acoustic vector-sensor arraywith a rectangular air chamber baffle and the eight elements circular acoustic vector-sensorarray with cylindrical air chamber baffle, were designed to carry out the Songhua Lakeexperiment. The test results and the simulation results were in good agreement, to verify thecorrectness of the theory in this paper and provide the experimental basis for the engineeringapplication of acoustic vector-sensor with acoustic baffle.
引文
[1]惠俊英，刘宏，余华兵，范敏毅．声压振速联合信息处理及其物理基础初探．声学学报，2000，25(5)：389-394页
[2]孙贵青，杨德森等．基于矢量水听器的声压和质点振速的空间相关系数[J]．声学学报，2004，29(6):481-490．
[3]孙贵青．矢量水听器检测技术研究．哈尔滨工程大学博士学位论文，2001．
[4]孙贵青，杨德森等．基于矢量水听器的最大似然比检测和最大似然方位估计[J]．声学学报，2003，28(1):66-72
[5] V. A. Shchurov,“Coherent and diffusive fields of underwater acoustic ambientnoise,” J. Acoust. Soc. Am.90,991-1001(1991).
[6] G. L. D’Spain,“Energetics of the deep ocean’s infrasonic sound field,” J. Acoust.Soc. Am.89,1134-1158(1991)
[7] A. Thode, J. Skinner, P. Scott and J. Rosewell,“Tracking sperm whales with a towedacoustic vector sensor,” J. Acoust. Soc. Am.128,2681-2694(2010)
[8] R．J．尤立克（美）著洪申译．水声原理．哈尔滨船舶工程学院出版社．1990．
[9]刘孟庵，连立民．水声工程．浙江科学技术出版社，2002．
[10]申杰罗夫著何祚镛译．水声学波动问题．国防工业出版社，1983
[11]何祚镛．结构振动与声辐射．哈尔滨工程大学出版社,2001．
[12]汤渭霖．用物理声学方法计算非硬表面的声散射．声学学报,1993,18(1):45-53．
[13]汤渭霖．用物理声学方法计算界面附近目标的回波．声学学报,1999,24(1):1-5．
[14]汤渭霖，范军．水中弹性结构声散射和声辐射机理——结构和水的声-振耦合作用．声学学报,2004,29(5):385-392．
[15] Morser P J. Uberall H, Yuan J R. Sound scattering from a finite cylinder with ribs. J.Acoust. Soc. Am.94(6):3342-3351(1993).
[16]汤渭霖．声呐目标回波的亮点模型．声学学报,1994,19(2):92-100．
[17]汤渭霖．奇异点展开法_SEM_与共振散射理论_RST_之间的联系．声学学报,1991,16(3):199-208．
[18]汤渭霖．可分离变量的水下弹性体的纯弹性共振散射．声学学报,1995,20(6):456-465．
[19]汤渭霖,范军．水中弹性球壳的共振声辐射理论．声学学报,2000,25(4):308-312．
[20]刘涛,范军,汤渭霖．水中弹性圆柱壳的共振声辐射．声学学报,2002,27(1):62-66．
[21]朱韬．水中目标低频声散射特性研究．上海交通大学硕士学位论文,2008
[22] Michael H. Davis. Target strength estimation using Finite Element Analysis.DSTO-TN-0395. Australia.2001.9
[23]姚振汉，王海涛．边界元法，高等教育出版社，2010
[24]卓琳凯，范军，汤渭霖． FEM-BEM耦合方法分析弹性体目标的声散射问题，上海交通大学学报，2009:43(8):1258-1262．
[25]杨德森等．矢量水听器湖试报告．中国国防科学技术报告．哈尔滨工程大学水声研究所．1998．10
[26]杨德森等．矢量水听器海试报告．中国国防科学技术报告．哈尔滨工程大学水声研究所．2000．9
[27]惠俊英，李春旭，梁国龙等．声压和振速联合信息信号处理抗相干干扰．声学学报．2000，25（5）：389-394页
[28]余华兵，刘宏等．小尺度声传感器的指向性锐化技术研究．声学学报．2000，25(4)：319-322页
[29]何心怡，蒋兴舟，李启虎．矢量水听器线阵的被动合成孔径技术．武汉理工大学学报，2003，27(6)：799-801页
[30]何心怡，蒋兴舟，李启虎等．拖线阵的阵形畸变与左右舷分辨．声学学报，2004，29(5)：409-413页
[31] Gordienko V A et al. Basic rules of vector-phase structure formation of the oceannoise field. Acoust. Phys.,1993;39(3):237-242
[32] Arye Nehorai, Eytan Paldi. Acoustic vector-sensor array processing. IEEE Trans.Signal Processing,1994,42(9):2481-2491.
[33] A．Nheora，E．Paldi．Acoustic vector sensor array processing．IEEE Trans．SignalProeessing，1994，42(9)：2481-249lP
[34] B．Hochwald and A．Nehorai．Identifiability in array processing models withvector-sensor applications．IEEE Trans．Signal Processing．1996，44：83-95P
[35] A．Nehorai and E．Paldi. Vector-sensor array processing for electromagnetic sourcelocalization．IEEE Trans．on Signal Processing，1994，42：376-398P
[36] M． Hawkes and A． Nehorai． Surface-mounted acoustic vector-sensor arrayproeessing．Proc，Inil Conf．on Acous．，Speech and Sig．Proc (ICASSP96)，Atlanta，GA．1996：3170-3173P
[37] M．Hawkes and A．Nehorai．Effects of sensor placement on acoustic vector-sensorarray performance．IEEE J．Oceanic Eng．1999，24：33-40P
[38] M．Hawkes and A． Nehorai．Acoustic vector-sensor correlations in ambientnoise．IEEE J．Oceanic Eng．2001，26(3)：337-347P
[39] M．Hawkes and A．Nehorai．Wideband source localization using a distributedacoustic vector-sensor array．IEEE Trans．Signal Processing．2003，51：1479-149lP
[40] K．T．Wong，M．D．Zoltowski. Self-initiating MUSIC-based direction finding inunderwater acoustic particle velocity-field beamspace. IEEE J. Oceanic Eng.,2000,25(2):262-273
[41] K．T．Wong，M．D．Zoltowski．Closed-Form Underwater Acoustic Direction Findingwith Arbitrarily Spaced Vector Hydrophones at Unknown Locations．IEEE Journal ofOcean Engineering．1997，22(3)：566-575P
[42] K．T．Wong，M．D．Zoltowski．Extended aperture underwater acoustic multisourceazimuth/elevation direction-finding using uniformly but sparsely-spaced vectorhydrophones．IEEE，J．Ocean Eng．1997，22(4)：659-672P
[43] K． T． Wong and M． D． Zoltowski． Root-MUSIC-based azimuth-elevationangle-of-arrival estimation with uniformly spaced but arbitrarily oriented velocityhydrophones. IEEE Trans. Signal Processing．1999,47(12):3250-3260P
[44] M．D．Zoltowski and K．T．Wong．ESPRIT-based2-D direction finding with a sparseuniform array of electromagnetic vector sensors． IEEE Trans． SignalProcessing．2000，48(8)：2195-2204P
[45] K．T．Wong and Ho．Chi．Beam patterns of an underwater acoustic vectorhydrophone located away from any reflecting boundary．IEEE J．Oceanic Eng．2002，27(3)：628-637P
[46] K．T．Wong and M．D．Zoltowski．Uni-Vector-Sensor ESPRIT for multisourceazimuth，elevation，and Polarization estimation．IEEE Trans．on Antennas anPropagation．1997，45(10)：1467-1474P
[47] K．T．Wong，M．D．Zoltowski．Uni-Vector-Sensor ESPRIT for multisourceazimuth-elevation angle estimation． IEEE AntennasPropagate．Soc．Int．Symp．1996：1368-137lP
[48]孙贵青．声矢量传感器均匀直线阵列研究．中国科学院声学所博士后研究工作报告．2003
[49]陈新华，蔡平，惠俊英．声矢量阵指向性．声学学报．2004，28(2)：141-144页
[50] H．W．Chen，J．W．Zhao．Widebnad MVDR beamforming for acoustic vector sensorlinear array．IEEE Proc．Radar Sonar Navig，2004，151(3)：158-162P
[51] H．W．Chen，J．W．Zhao．Coherent signal-subspace processing of acoustic vectorsensor array for DOA estimation of wideband sources．Signal Processing，2005，85(l)：837-847P
[52]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)：76-82页
[53]齐娜．基于确定脉冲信号的矢量传感器的目标方位估计研究.哈尔滨工程大学博士学位论文．2004
[54]吕钱浩．矢量阵处理技术研究．哈尔滨工程大学博士学位论文．2004
[55]吕钱浩，杨士莪等．矢量传感器阵列高分辨率方位估计技术研究．哈尔滨工程大学学报，2004，25(4)：440-445页
[56]张揽月，杨德森．基于MUSIC算法的矢量水听器阵源方位估计．哈尔滨工程大学学报，2004，25(l)：30-33页
[57]喻敏．声矢量传感器的Capon方位估计．哈尔滨工程大学硕士学位论文．2004
[58]田坦，齐娜，孙大军．矢量水听器阵波束域MVDR方法研究．哈尔滨工程大学学报，2004，25(3)：295-298页
[59]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)：714-718页
[60]江南，黄建国，冯西安，管静．矢量传感器阵列的空间谱估计及定向性能分析．昆明理工大学学报，2003，28(2)：77-82页
[61]张揽月，杨德森．矢量水听器高分辨率波束形成．声学技术增刊．2002，21：437-438页
[62]张揽月．矢量水听器阵列处理技术研究．哈尔滨工程大学博士学位论文，2005
[63]肖卫国，高翔．基于AR谱的声矢量传感器阵方位估计．声学技术增刊，2004，23：250-252页
[64]白兴宇．基于联合信息处理的声矢量阵测向技术．哈尔滨工程大学博士生论文．2006
[65]白兴宇，杨德森，赵春晖．基于声压振速联合信息处理的声矢量阵相干信号子空间方法[J]．声学学报，2006;31(5):410-417．
[66]白兴宇，姜煜，赵春晖．基于声压振速联合处理的声矢量阵信源数检测与方位估计[J]．声学学报，2008;33(1):56-61．
[67]何祚镛．水声作用下矩形弹性-粘弹性复合板的振动和散射声近场（II）矩形弹性-粘弹性复合板散射声近场研究[J]．声学学报，1986;11(1):1-19．
[68]何祚镛．水声作用下矩形弹性-粘弹性复合板的振动和散射声近场（I）矩形复合板的振动分析[J]．声学学报，1983;10(6):344-357．
[69]唐海清，繆荣兴．接收阵声障板的性能评价和理论计算．声学与电子工程，2000，57:28-34．
[70]徐俊华，兰军．具有反声障板的圆柱（弧）基阵水平指向性的研究．声学学报，1985，10(3)：149-160页
[71]张广荣，周福洪，王育生．对镶在圆柱障板上单块有限复合板散射声场的研究．声学学报，1989，14(1)：36-44页
[72]陈景德，王育生．三叠层宽带散射矩形反声障板的设计．应用声学，1992，3：20-25页
[73]王育生，刘振江，陈景德．离散障板稀疏圆柱基阵．声学学报，1995，20(1)：49-59页
[74]耿成德．宽带稀疏圆柱阵的实验研究．声学技术，1990，9(2)：26-31页
[75]兰军．平面障板对水声换能器指向性的影响．应用声学，1984，3(1)：14-19页
[76]耿成德．带障板圆柱阵指向性研究．声学与电子工程，1990，18:1-8．
[77]何祚镛．带障板的水声相控接收阵的研究．水声通讯，1983，3：48-65．
[78]耿成德．耐压反声障板的反声特性及其对水听器指向性的影响．声学与电子工程，1989，2:7-10．
[79]傅临泰．关于反声障板．水声通讯，1984，1：59-68．
[80] R.J.Bobber.Underwater electroacoustic measurements.Washington D.C.: NavalResearch Laboratory，1956
[81]郑士杰，袁文俊．水声计量测试技术．哈尔滨:哈尔滨工程大学出版社，1995
[82] R.A. Kosobrodov, V N. Nekrasov. Effect of the diffraction of sound by the carrier ofhydroacoustic equipment on the results of measurements. Acoust. Phys.2001,47(3):323-328
[83] Barton J P, Nicholas L W, Zhang H F, et al. Near-field calculations for a rigidspheroid with an arbitrary incident acoustic field. J Acoust Soc Am,2003,113(3):1216-1222.
[84] Rapids B R, Lauchle G C. Vector intensity field scattered by a rigid prolate spheroid.J Acoust Soc Am,2006,120(1):38-48.
[85] Hawkes M, Nehorai A. Acoustic Vector-Sensor Processing in the Presence of aReflecting Boundary. IEEE Trans. Sign. Process,2000;48:2981-2993.
[86] Javad Ahmadi-Shokouh,Hengameh Keshavarz.A Vector-Hydrophone’s MinimalComposition for Finite Estimation-Variance in Direction-Finding Near/Without aReflecting Boundary.IEEE Transactions on SignalProcessing,Vol.55,No.6,June,2007,2785-2794
[87]生雪莉，郭龙翔，梁国龙．球形软障板矢量传感器指向性研究，中国声学学会全国声学学术会议论文集，2002
[88]时胜国，杨德森．弹性球壳声散射对矢量水听器测向影响研究，声学技术，Vol.27,No.5,Oct.,2008,642-648
[89]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，2006
[90]侯玉敏，毛卫宁．刚性曲面障板散射对多模球形水听器测向的影响．声学技术，2005;24(2):94-97．
[91]陈亚林，杨博，马远良．复杂边界条件下矢量传感器的指向性分析和实验研究．声学技术，2006;25(4):381-386．
[92]刘宏伟．一类界面刚性目标的声散射及障板声特性的研究．北京：中国科学院声学研究所，2000．
[93]布列霍夫斯基著杨训仁译．分层介质中的波（第二版）．北京：科学出版社，1985．
[94]何祚镛，赵玉芳．声学理论基础，国防工业出版社，1992
[95] W. L. LI， H. J. GIBELING．Determination of the mutual radiation resistances of arectangular plate and their impact on the radiated sound power. Journal of Sound andVibration,2000,229(5):1213-1233.
[96]孙超．水下多传感器阵列信号处理．西北工业大学出版社，2007
[97]王永良等．空间谱估计理论与算法．清华大学出版社，2005
[98]惠俊英等．矢量信号处理基础．国防工业出版社，2009
[99] Tran-Van-Nhieu M. Scattering from a ribbed finite cylindrical shell. J Acoust SocAm,2001,110(6):2858-2866
[100] Tran-Van-Nhieu M. Scattering from a ribbed finite cylindrical shell with internalaxisymmetric oscillators. J Acoust Soc Am,2002,112(2):402-410
[101] Moyer J, Elko G. A highly scalable spherical microphone array based on anorthonormal decomposition of the sound field[J]. In: Proc. ICASSP,2002(2):1781-1784
[102] Rafaely B. Plane-wave decomposition of the sound field on a sphere by sphericalconvolution[J]. J Acoust Soc Am,2004,116(4):2149-2157
[103] Rafaely B. Phase-mode versus delay-and-sum spherical microphpne arrayprocessing[J]. IEEE Signal process. Lett.,2005,12(10):713-716
[104] Rafaely B. Analysis and design of spherical microphone arrays[J]. IEEE Trans.Speech Audio Process.,2005,13(1):135-143
[105] Rafaely B, Weiss B, Bachmat E. Spatial aliasing in spherical microphone arrays[J].IEEE Trans. Signal process.,2007,55(3):1003-1010
[106] Rafaely B, Balmages I, Eger L. High-resolution plane-wave decomposition in anauditorium using a dual-radius scanning spherical microphone array[J]. J Acoust SocAm,2007,122(5):2661-2668
[107] Rafaely B, Kleider M. Spherical microphone array beam steering using Wigner-Dweighting[J]. IEEE Signal process. Lett.,2008,15:417-420
[108] Li Z Y,Duraiswami R. Flexible and optimal design of spherical microphone arraysfor beamforming[J]. IEEE Trans. Audio Speech Lang. Process.,2007,15(2):702-714
[109]鄢社锋，侯朝焕，马晓川．从阵元域到模态域阵列信号处理[J]．声学学报，2011;36(5):461-468．
[110]钱琛，杨益新，郭国强．球体表面圆环阵模态域稳健高增益波束形成方法研究[J]．声学学报，2010;35(6):623-633
[111]张成，陈克安，杨志兴．刚性圆柱体上圆阵波束形成性能分析[J]．声学学报，2010，35(1):68-75．
[112]谢树艺．矢量分析与场论．北京：高等教育出版社1985．
[113] L.Hopf（德）著杜树槐译物理学微分方程引论。北京：人民教育出版社，1981.
[114] Williams. Fourier Acoustics: Sound Radiation and Nearfield Acoustic Holography.London: Academic Press,1999
[115] Teutsch H. Acoustic source detection and localition based on wavefielddecomposition using circular microphone arrays. J Acoust Soc Am,2006,120(5):2724-2736
[116]郑国垠，汤渭霖，范军．充水有限长圆柱薄壳声散射I：理论．声学学报，2009，34(6):490-497．
[117]郑国垠，汤渭霖，范军．充水有限长圆柱薄壳声散射II：实验．声学学报，2010，35(1):31-37．
[118]吴崇试．数学物理方法，北京大学出版社，2003
[119]郭敦仁．数学物理方法，高等教育出版社，1991
[120]王竹溪，郭敦仁．特殊函数概论，北京大学出版社，2000
[121] G. C. Gaunaurd, and M. F. Werby. Sound scattering by resonantly excited,fluid-loaded, elastic spherical shells. J Acoust Soc Am,2002,112(2):2536-2550
[122] H. Uberall, A. C. Ahyi and P. K. Raju. Circumferential-wave phase velocities forempty, fluid-immersed spherical metal shells. J Acoust Soc Am,2002,112(2):2536-2550
[123] B. T. Hefner and P. L. Marston. Backscattering enhancements associated withsubsonic Rayleigh waves on polymer spheres in water: Observation and modeling foracrylic spheres J Acoust Soc Am,2000,107(4):1930-1936
[124] M. F. Werby, and H. Uberall. A systematic study of water-filled submerged elasticspherical shells and the resolution of elastic-and water-included resonances. J AcoustSoc Am,2002,112(3):896-905
[125] H. Uberall. Acoustic of Shells. Acoust. Physics,2002,48(3),309-320
[126] M. C. Junger. Sound Scattering by thin Elastic Shells. J Acoust Soc Am,1952,24(4):366-374
[127] R. R. Goodman and R. Stern. Reflection and Transmission of Sound by ElasticSpherical Shells. J Acoust Soc Am,1962,34(3):338-344.
[128] J. D. Murphy, J. George, A. Nagl, and H. Uberall. Isolation of the ResonantComponent in Acoustic Scattering From Fluid-loaded Elastic Spherical Shells. JAcoust Soc Am,1979,65(2):368-373.
[129]时胜国，杨德森，王三德．弹性球壳声衍射对矢量传感器测量影响．哈尔滨工程大学学报，2006，27(1)：84-89页
[2]孙贵青，杨德森等．基于矢量水听器的声压和质点振速的空间相关系数[J]．声学学报，2004，29(6):481-490．
[3]孙贵青．矢量水听器检测技术研究．哈尔滨工程大学博士学位论文，2001．
[4]孙贵青，杨德森等．基于矢量水听器的最大似然比检测和最大似然方位估计[J]．声学学报，2003，28(1):66-72
[5] V. A. Shchurov,“Coherent and diffusive fields of underwater acoustic ambientnoise,” J. Acoust. Soc. Am.90,991-1001(1991).
[6] G. L. D’Spain,“Energetics of the deep ocean’s infrasonic sound field,” J. Acoust.Soc. Am.89,1134-1158(1991)
[7] A. Thode, J. Skinner, P. Scott and J. Rosewell,“Tracking sperm whales with a towedacoustic vector sensor,” J. Acoust. Soc. Am.128,2681-2694(2010)
[8] R．J．尤立克（美）著洪申译．水声原理．哈尔滨船舶工程学院出版社．1990．
[9]刘孟庵，连立民．水声工程．浙江科学技术出版社，2002．
[10]申杰罗夫著何祚镛译．水声学波动问题．国防工业出版社，1983
[11]何祚镛．结构振动与声辐射．哈尔滨工程大学出版社,2001．
[12]汤渭霖．用物理声学方法计算非硬表面的声散射．声学学报,1993,18(1):45-53．
[13]汤渭霖．用物理声学方法计算界面附近目标的回波．声学学报,1999,24(1):1-5．
[14]汤渭霖，范军．水中弹性结构声散射和声辐射机理——结构和水的声-振耦合作用．声学学报,2004,29(5):385-392．
[15] Morser P J. Uberall H, Yuan J R. Sound scattering from a finite cylinder with ribs. J.Acoust. Soc. Am.94(6):3342-3351(1993).
[16]汤渭霖．声呐目标回波的亮点模型．声学学报,1994,19(2):92-100．
[17]汤渭霖．奇异点展开法_SEM_与共振散射理论_RST_之间的联系．声学学报,1991,16(3):199-208．
[18]汤渭霖．可分离变量的水下弹性体的纯弹性共振散射．声学学报,1995,20(6):456-465．
[19]汤渭霖,范军．水中弹性球壳的共振声辐射理论．声学学报,2000,25(4):308-312．
[20]刘涛,范军,汤渭霖．水中弹性圆柱壳的共振声辐射．声学学报,2002,27(1):62-66．
[21]朱韬．水中目标低频声散射特性研究．上海交通大学硕士学位论文,2008
[22] Michael H. Davis. Target strength estimation using Finite Element Analysis.DSTO-TN-0395. Australia.2001.9
[23]姚振汉，王海涛．边界元法，高等教育出版社，2010
[24]卓琳凯，范军，汤渭霖． FEM-BEM耦合方法分析弹性体目标的声散射问题，上海交通大学学报，2009:43(8):1258-1262．
[25]杨德森等．矢量水听器湖试报告．中国国防科学技术报告．哈尔滨工程大学水声研究所．1998．10
[26]杨德森等．矢量水听器海试报告．中国国防科学技术报告．哈尔滨工程大学水声研究所．2000．9
[27]惠俊英，李春旭，梁国龙等．声压和振速联合信息信号处理抗相干干扰．声学学报．2000，25（5）：389-394页
[28]余华兵，刘宏等．小尺度声传感器的指向性锐化技术研究．声学学报．2000，25(4)：319-322页
[29]何心怡，蒋兴舟，李启虎．矢量水听器线阵的被动合成孔径技术．武汉理工大学学报，2003，27(6)：799-801页
[30]何心怡，蒋兴舟，李启虎等．拖线阵的阵形畸变与左右舷分辨．声学学报，2004，29(5)：409-413页
[31] Gordienko V A et al. Basic rules of vector-phase structure formation of the oceannoise field. Acoust. Phys.,1993;39(3):237-242
[32] Arye Nehorai, Eytan Paldi. Acoustic vector-sensor array processing. IEEE Trans.Signal Processing,1994,42(9):2481-2491.
[33] A．Nheora，E．Paldi．Acoustic vector sensor array processing．IEEE Trans．SignalProeessing，1994，42(9)：2481-249lP
[34] B．Hochwald and A．Nehorai．Identifiability in array processing models withvector-sensor applications．IEEE Trans．Signal Processing．1996，44：83-95P
[35] A．Nehorai and E．Paldi. Vector-sensor array processing for electromagnetic sourcelocalization．IEEE Trans．on Signal Processing，1994，42：376-398P
[36] M． Hawkes and A． Nehorai． Surface-mounted acoustic vector-sensor arrayproeessing．Proc，Inil Conf．on Acous．，Speech and Sig．Proc (ICASSP96)，Atlanta，GA．1996：3170-3173P
[37] M．Hawkes and A．Nehorai．Effects of sensor placement on acoustic vector-sensorarray performance．IEEE J．Oceanic Eng．1999，24：33-40P
[38] M．Hawkes and A． Nehorai．Acoustic vector-sensor correlations in ambientnoise．IEEE J．Oceanic Eng．2001，26(3)：337-347P
[39] M．Hawkes and A．Nehorai．Wideband source localization using a distributedacoustic vector-sensor array．IEEE Trans．Signal Processing．2003，51：1479-149lP
[40] K．T．Wong，M．D．Zoltowski. Self-initiating MUSIC-based direction finding inunderwater acoustic particle velocity-field beamspace. IEEE J. Oceanic Eng.,2000,25(2):262-273
[41] K．T．Wong，M．D．Zoltowski．Closed-Form Underwater Acoustic Direction Findingwith Arbitrarily Spaced Vector Hydrophones at Unknown Locations．IEEE Journal ofOcean Engineering．1997，22(3)：566-575P
[42] K．T．Wong，M．D．Zoltowski．Extended aperture underwater acoustic multisourceazimuth/elevation direction-finding using uniformly but sparsely-spaced vectorhydrophones．IEEE，J．Ocean Eng．1997，22(4)：659-672P
[43] K． T． Wong and M． D． Zoltowski． Root-MUSIC-based azimuth-elevationangle-of-arrival estimation with uniformly spaced but arbitrarily oriented velocityhydrophones. IEEE Trans. Signal Processing．1999,47(12):3250-3260P
[44] M．D．Zoltowski and K．T．Wong．ESPRIT-based2-D direction finding with a sparseuniform array of electromagnetic vector sensors． IEEE Trans． SignalProcessing．2000，48(8)：2195-2204P
[45] K．T．Wong and Ho．Chi．Beam patterns of an underwater acoustic vectorhydrophone located away from any reflecting boundary．IEEE J．Oceanic Eng．2002，27(3)：628-637P
[46] K．T．Wong and M．D．Zoltowski．Uni-Vector-Sensor ESPRIT for multisourceazimuth，elevation，and Polarization estimation．IEEE Trans．on Antennas anPropagation．1997，45(10)：1467-1474P
[47] K．T．Wong，M．D．Zoltowski．Uni-Vector-Sensor ESPRIT for multisourceazimuth-elevation angle estimation． IEEE AntennasPropagate．Soc．Int．Symp．1996：1368-137lP
[48]孙贵青．声矢量传感器均匀直线阵列研究．中国科学院声学所博士后研究工作报告．2003
[49]陈新华，蔡平，惠俊英．声矢量阵指向性．声学学报．2004，28(2)：141-144页
[50] H．W．Chen，J．W．Zhao．Widebnad MVDR beamforming for acoustic vector sensorlinear array．IEEE Proc．Radar Sonar Navig，2004，151(3)：158-162P
[51] H．W．Chen，J．W．Zhao．Coherent signal-subspace processing of acoustic vectorsensor array for DOA estimation of wideband sources．Signal Processing，2005，85(l)：837-847P
[52]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)：76-82页
[53]齐娜．基于确定脉冲信号的矢量传感器的目标方位估计研究.哈尔滨工程大学博士学位论文．2004
[54]吕钱浩．矢量阵处理技术研究．哈尔滨工程大学博士学位论文．2004
[55]吕钱浩，杨士莪等．矢量传感器阵列高分辨率方位估计技术研究．哈尔滨工程大学学报，2004，25(4)：440-445页
[56]张揽月，杨德森．基于MUSIC算法的矢量水听器阵源方位估计．哈尔滨工程大学学报，2004，25(l)：30-33页
[57]喻敏．声矢量传感器的Capon方位估计．哈尔滨工程大学硕士学位论文．2004
[58]田坦，齐娜，孙大军．矢量水听器阵波束域MVDR方法研究．哈尔滨工程大学学报，2004，25(3)：295-298页
[59]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)：714-718页
[60]江南，黄建国，冯西安，管静．矢量传感器阵列的空间谱估计及定向性能分析．昆明理工大学学报，2003，28(2)：77-82页
[61]张揽月，杨德森．矢量水听器高分辨率波束形成．声学技术增刊．2002，21：437-438页
[62]张揽月．矢量水听器阵列处理技术研究．哈尔滨工程大学博士学位论文，2005
[63]肖卫国，高翔．基于AR谱的声矢量传感器阵方位估计．声学技术增刊，2004，23：250-252页
[64]白兴宇．基于联合信息处理的声矢量阵测向技术．哈尔滨工程大学博士生论文．2006
[65]白兴宇，杨德森，赵春晖．基于声压振速联合信息处理的声矢量阵相干信号子空间方法[J]．声学学报，2006;31(5):410-417．
[66]白兴宇，姜煜，赵春晖．基于声压振速联合处理的声矢量阵信源数检测与方位估计[J]．声学学报，2008;33(1):56-61．
[67]何祚镛．水声作用下矩形弹性-粘弹性复合板的振动和散射声近场（II）矩形弹性-粘弹性复合板散射声近场研究[J]．声学学报，1986;11(1):1-19．
[68]何祚镛．水声作用下矩形弹性-粘弹性复合板的振动和散射声近场（I）矩形复合板的振动分析[J]．声学学报，1983;10(6):344-357．
[69]唐海清，繆荣兴．接收阵声障板的性能评价和理论计算．声学与电子工程，2000，57:28-34．
[70]徐俊华，兰军．具有反声障板的圆柱（弧）基阵水平指向性的研究．声学学报，1985，10(3)：149-160页
[71]张广荣，周福洪，王育生．对镶在圆柱障板上单块有限复合板散射声场的研究．声学学报，1989，14(1)：36-44页
[72]陈景德，王育生．三叠层宽带散射矩形反声障板的设计．应用声学，1992，3：20-25页
[73]王育生，刘振江，陈景德．离散障板稀疏圆柱基阵．声学学报，1995，20(1)：49-59页
[74]耿成德．宽带稀疏圆柱阵的实验研究．声学技术，1990，9(2)：26-31页
[75]兰军．平面障板对水声换能器指向性的影响．应用声学，1984，3(1)：14-19页
[76]耿成德．带障板圆柱阵指向性研究．声学与电子工程，1990，18:1-8．
[77]何祚镛．带障板的水声相控接收阵的研究．水声通讯，1983，3：48-65．
[78]耿成德．耐压反声障板的反声特性及其对水听器指向性的影响．声学与电子工程，1989，2:7-10．
[79]傅临泰．关于反声障板．水声通讯，1984，1：59-68．
[80] R.J.Bobber.Underwater electroacoustic measurements.Washington D.C.: NavalResearch Laboratory，1956
[81]郑士杰，袁文俊．水声计量测试技术．哈尔滨:哈尔滨工程大学出版社，1995
[82] R.A. Kosobrodov, V N. Nekrasov. Effect of the diffraction of sound by the carrier ofhydroacoustic equipment on the results of measurements. Acoust. Phys.2001,47(3):323-328
[83] Barton J P, Nicholas L W, Zhang H F, et al. Near-field calculations for a rigidspheroid with an arbitrary incident acoustic field. J Acoust Soc Am,2003,113(3):1216-1222.
[84] Rapids B R, Lauchle G C. Vector intensity field scattered by a rigid prolate spheroid.J Acoust Soc Am,2006,120(1):38-48.
[85] Hawkes M, Nehorai A. Acoustic Vector-Sensor Processing in the Presence of aReflecting Boundary. IEEE Trans. Sign. Process,2000;48:2981-2993.
[86] Javad Ahmadi-Shokouh,Hengameh Keshavarz.A Vector-Hydrophone’s MinimalComposition for Finite Estimation-Variance in Direction-Finding Near/Without aReflecting Boundary.IEEE Transactions on SignalProcessing,Vol.55,No.6,June,2007,2785-2794
[87]生雪莉，郭龙翔，梁国龙．球形软障板矢量传感器指向性研究，中国声学学会全国声学学术会议论文集，2002
[88]时胜国，杨德森．弹性球壳声散射对矢量水听器测向影响研究，声学技术，Vol.27,No.5,Oct.,2008,642-648
[89]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，2006
[90]侯玉敏，毛卫宁．刚性曲面障板散射对多模球形水听器测向的影响．声学技术，2005;24(2):94-97．
[91]陈亚林，杨博，马远良．复杂边界条件下矢量传感器的指向性分析和实验研究．声学技术，2006;25(4):381-386．
[92]刘宏伟．一类界面刚性目标的声散射及障板声特性的研究．北京：中国科学院声学研究所，2000．
[93]布列霍夫斯基著杨训仁译．分层介质中的波（第二版）．北京：科学出版社，1985．
[94]何祚镛，赵玉芳．声学理论基础，国防工业出版社，1992
[95] W. L. LI， H. J. GIBELING．Determination of the mutual radiation resistances of arectangular plate and their impact on the radiated sound power. Journal of Sound andVibration,2000,229(5):1213-1233.
[96]孙超．水下多传感器阵列信号处理．西北工业大学出版社，2007
[97]王永良等．空间谱估计理论与算法．清华大学出版社，2005
[98]惠俊英等．矢量信号处理基础．国防工业出版社，2009
[99] Tran-Van-Nhieu M. Scattering from a ribbed finite cylindrical shell. J Acoust SocAm,2001,110(6):2858-2866
[100] Tran-Van-Nhieu M. Scattering from a ribbed finite cylindrical shell with internalaxisymmetric oscillators. J Acoust Soc Am,2002,112(2):402-410
[101] Moyer J, Elko G. A highly scalable spherical microphone array based on anorthonormal decomposition of the sound field[J]. In: Proc. ICASSP,2002(2):1781-1784
[102] Rafaely B. Plane-wave decomposition of the sound field on a sphere by sphericalconvolution[J]. J Acoust Soc Am,2004,116(4):2149-2157
[103] Rafaely B. Phase-mode versus delay-and-sum spherical microphpne arrayprocessing[J]. IEEE Signal process. Lett.,2005,12(10):713-716
[104] Rafaely B. Analysis and design of spherical microphone arrays[J]. IEEE Trans.Speech Audio Process.,2005,13(1):135-143
[105] Rafaely B, Weiss B, Bachmat E. Spatial aliasing in spherical microphone arrays[J].IEEE Trans. Signal process.,2007,55(3):1003-1010
[106] Rafaely B, Balmages I, Eger L. High-resolution plane-wave decomposition in anauditorium using a dual-radius scanning spherical microphone array[J]. J Acoust SocAm,2007,122(5):2661-2668
[107] Rafaely B, Kleider M. Spherical microphone array beam steering using Wigner-Dweighting[J]. IEEE Signal process. Lett.,2008,15:417-420
[108] Li Z Y,Duraiswami R. Flexible and optimal design of spherical microphone arraysfor beamforming[J]. IEEE Trans. Audio Speech Lang. Process.,2007,15(2):702-714
[109]鄢社锋，侯朝焕，马晓川．从阵元域到模态域阵列信号处理[J]．声学学报，2011;36(5):461-468．
[110]钱琛，杨益新，郭国强．球体表面圆环阵模态域稳健高增益波束形成方法研究[J]．声学学报，2010;35(6):623-633
[111]张成，陈克安，杨志兴．刚性圆柱体上圆阵波束形成性能分析[J]．声学学报，2010，35(1):68-75．
[112]谢树艺．矢量分析与场论．北京：高等教育出版社1985．
[113] L.Hopf（德）著杜树槐译物理学微分方程引论。北京：人民教育出版社，1981.
[114] Williams. Fourier Acoustics: Sound Radiation and Nearfield Acoustic Holography.London: Academic Press,1999
[115] Teutsch H. Acoustic source detection and localition based on wavefielddecomposition using circular microphone arrays. J Acoust Soc Am,2006,120(5):2724-2736
[116]郑国垠，汤渭霖，范军．充水有限长圆柱薄壳声散射I：理论．声学学报，2009，34(6):490-497．
[117]郑国垠，汤渭霖，范军．充水有限长圆柱薄壳声散射II：实验．声学学报，2010，35(1):31-37．
[118]吴崇试．数学物理方法，北京大学出版社，2003
[119]郭敦仁．数学物理方法，高等教育出版社，1991
[120]王竹溪，郭敦仁．特殊函数概论，北京大学出版社，2000
[121] G. C. Gaunaurd, and M. F. Werby. Sound scattering by resonantly excited,fluid-loaded, elastic spherical shells. J Acoust Soc Am,2002,112(2):2536-2550
[122] H. Uberall, A. C. Ahyi and P. K. Raju. Circumferential-wave phase velocities forempty, fluid-immersed spherical metal shells. J Acoust Soc Am,2002,112(2):2536-2550
[123] B. T. Hefner and P. L. Marston. Backscattering enhancements associated withsubsonic Rayleigh waves on polymer spheres in water: Observation and modeling foracrylic spheres J Acoust Soc Am,2000,107(4):1930-1936
[124] M. F. Werby, and H. Uberall. A systematic study of water-filled submerged elasticspherical shells and the resolution of elastic-and water-included resonances. J AcoustSoc Am,2002,112(3):896-905
[125] H. Uberall. Acoustic of Shells. Acoust. Physics,2002,48(3),309-320
[126] M. C. Junger. Sound Scattering by thin Elastic Shells. J Acoust Soc Am,1952,24(4):366-374
[127] R. R. Goodman and R. Stern. Reflection and Transmission of Sound by ElasticSpherical Shells. J Acoust Soc Am,1962,34(3):338-344.
[128] J. D. Murphy, J. George, A. Nagl, and H. Uberall. Isolation of the ResonantComponent in Acoustic Scattering From Fluid-loaded Elastic Spherical Shells. JAcoust Soc Am,1979,65(2):368-373.
[129]时胜国，杨德森，王三德．弹性球壳声衍射对矢量传感器测量影响．哈尔滨工程大学学报，2006，27(1)：84-89页
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |