矢量声场与矢量信号处理理论研究
|
摘要
声传播和信号处理模型是水声系统的两个基础理论,基于矢量水听器的水声系统也是如此。矢量水听器信号处理技术经过十几年快速发展,展示出相比于声压信号处理技术的优点后,它在物理和信号理论方面需要更深入的基础研究,以更明确、更好地挖掘其内在的潜力。本文尝试在这两方面做一些基础性的探索研究。
“智能”水雷声引信、目标低噪声辐射声场测量和港口目标声特性监测等场合均关注近程(2Km以内)声场。因而,本文探讨近程声场的预报方法。
侧面波对近程声场有重要贡献,已发表的公开文献中仅对侧面波声场作近似估计,本文指出这些对侧面波声场的预报误差均较大。本文给出了侧面波声场的精确数值预报方法,从而有可能较精确预报近程声场。
只有在近程声压场精确预报的基础上才能用数值差分法计算振速场,本文的近程声场预报方法符合此要求。
由于矢量传感器正逐步被推广应用,对近程矢量场增加了解是必须的。本文通过数值计算,初步描绘了振速场的物理图像。
本文对比了波动理论、简正波声场和射线模型的声场预报结果,给出了后二种方法的近似程度。仅考虑简正波声场仅适合远程声场预报,它不适合近程声场预报。射线模型适合高频声场的预报,当kh>100时射线模型声场预报有足够高的近似精度。
本文另一部分内容讨论矢量信号处理的基础理论。基于声能流的方法,解决了声压信号处理固有的部分缺陷,提高了处理增益和方位估计精度,试验证明是比较实用的方法。对这种方法作理论建模是必要的,是有实际意义的。
本文推导了矢量水听器频域测量模型和模型参数。该测量模型便于推导互谱、平均声强以及方位估计的概率密度,进而深入分析矢量信号处理方法的性能。
根据频域测量模型,推演得到互谱、平均声强等声能流的概率密度公式,
Sound propagation and signal processing model are the two fundamental theories of underwater acoustic systems, which are the same to that based on vector hydrophone. When vector sensor processing techniques have shown many advantages than pressure after more than ten years of rapid development, it is necessary to do more fundermental researches on physics and signal theory to explore the potential of vector hydrophone more specifically and effectively. We attempt to make probe fundermentally in above two espects in the thesis.Near distance acoustic fields are payed attention in intelligent acoustic mine and the measurement of tranquil targets' radiate field and acoustic feature monitor of targets in the haven, etc. So in the thesis methods of acoustic field prognosis of near distance are discussed.Lateral wave contributes greatly to near distance acoustic field, which is only estimated approximatively in open literature and these have great errors. In this thesis accurate numerical prognosis method for lateral wave field is given, so the near distance acoustic field may be predicted accurately.Only based on accurate prediction of near distance pressure field the particle volicty field can be caculated by numerical differential method. This is satisfied by the near distance acoustic field method studied in this thesis.Since vector hydrophone is being widely applied step by step, it is necessary to comprehend near distance vector field. By numerical analysis physical concepts about the particle velocity field are descripted in the thesis.Results of acoustic field prognosis on wave theory, normal model and ray model are compared, and the approximate degree of the later two models is given. Normal mode is fit to forecast far distance acoustic fields only, but not near distance. Ray model is fit to forecast high frequence acoustic fields. If kh>100, ray model is accurate adequately.In the other part of the thesis the fundamental theories of vector signal processing are studied. Methods based on acoustic energy flow solve some
inherent shortcomings of traditional pressure signal processing methods and increase processing gain and DOA estimation accuracy. Methods based on acoustic energy flow have been verified to be practically useful by trials. And to model those methods is necessary and practically significant.The frequency measurement model and its parameters are deduced in the thesis. Based on this model it's convenient to express the probability densities of cross spectrum and average acoustic intensity and DOA, and to make deep analysis of vector signal processing methods' performance sequentially.Based on the frequency measurement model, probability densities of acoustic energy flows such as cross spectrum and average acoustic intensity are deduced, then ROC (receiver operating characteristic) and vector array's gain are theoretically analysed. In isotropic noise field, acoustic energy flows' ROC is 4dB higher than pressure's. Vector array's gain is higher than that of pressure array. Under the condition of high snr, the vector array's gain based on high orders surpasses that based on acoustic energy flows.Based on frequency measurement model probability densities and Crame-Rao Low Boundary (CRLB) of DOA estimation are deduced. At low snr DOA estimation is bias. If snr is higher than 7dB/Hz, the estimation is an unbiased MLE (Maximum Likelihood Estimation) and its accuracy approaches CRLB.The studies of near distance acoustic field and signal processing theories coincide with simulations and sea (lake) trials rationally.Exordium of the thesis introduces fundamental knowledge about theories and techniques of vector hydrophone, and overviews the corresponding development status at home and abroad, so that readers can have a general acquaintance with them.
“智能”水雷声引信、目标低噪声辐射声场测量和港口目标声特性监测等场合均关注近程(2Km以内)声场。因而,本文探讨近程声场的预报方法。
侧面波对近程声场有重要贡献,已发表的公开文献中仅对侧面波声场作近似估计,本文指出这些对侧面波声场的预报误差均较大。本文给出了侧面波声场的精确数值预报方法,从而有可能较精确预报近程声场。
只有在近程声压场精确预报的基础上才能用数值差分法计算振速场,本文的近程声场预报方法符合此要求。
由于矢量传感器正逐步被推广应用,对近程矢量场增加了解是必须的。本文通过数值计算,初步描绘了振速场的物理图像。
本文对比了波动理论、简正波声场和射线模型的声场预报结果,给出了后二种方法的近似程度。仅考虑简正波声场仅适合远程声场预报,它不适合近程声场预报。射线模型适合高频声场的预报,当kh>100时射线模型声场预报有足够高的近似精度。
本文另一部分内容讨论矢量信号处理的基础理论。基于声能流的方法,解决了声压信号处理固有的部分缺陷,提高了处理增益和方位估计精度,试验证明是比较实用的方法。对这种方法作理论建模是必要的,是有实际意义的。
本文推导了矢量水听器频域测量模型和模型参数。该测量模型便于推导互谱、平均声强以及方位估计的概率密度,进而深入分析矢量信号处理方法的性能。
根据频域测量模型,推演得到互谱、平均声强等声能流的概率密度公式,
Sound propagation and signal processing model are the two fundamental theories of underwater acoustic systems, which are the same to that based on vector hydrophone. When vector sensor processing techniques have shown many advantages than pressure after more than ten years of rapid development, it is necessary to do more fundermental researches on physics and signal theory to explore the potential of vector hydrophone more specifically and effectively. We attempt to make probe fundermentally in above two espects in the thesis.Near distance acoustic fields are payed attention in intelligent acoustic mine and the measurement of tranquil targets' radiate field and acoustic feature monitor of targets in the haven, etc. So in the thesis methods of acoustic field prognosis of near distance are discussed.Lateral wave contributes greatly to near distance acoustic field, which is only estimated approximatively in open literature and these have great errors. In this thesis accurate numerical prognosis method for lateral wave field is given, so the near distance acoustic field may be predicted accurately.Only based on accurate prediction of near distance pressure field the particle volicty field can be caculated by numerical differential method. This is satisfied by the near distance acoustic field method studied in this thesis.Since vector hydrophone is being widely applied step by step, it is necessary to comprehend near distance vector field. By numerical analysis physical concepts about the particle velocity field are descripted in the thesis.Results of acoustic field prognosis on wave theory, normal model and ray model are compared, and the approximate degree of the later two models is given. Normal mode is fit to forecast far distance acoustic fields only, but not near distance. Ray model is fit to forecast high frequence acoustic fields. If kh>100, ray model is accurate adequately.In the other part of the thesis the fundamental theories of vector signal processing are studied. Methods based on acoustic energy flow solve some
inherent shortcomings of traditional pressure signal processing methods and increase processing gain and DOA estimation accuracy. Methods based on acoustic energy flow have been verified to be practically useful by trials. And to model those methods is necessary and practically significant.The frequency measurement model and its parameters are deduced in the thesis. Based on this model it's convenient to express the probability densities of cross spectrum and average acoustic intensity and DOA, and to make deep analysis of vector signal processing methods' performance sequentially.Based on the frequency measurement model, probability densities of acoustic energy flows such as cross spectrum and average acoustic intensity are deduced, then ROC (receiver operating characteristic) and vector array's gain are theoretically analysed. In isotropic noise field, acoustic energy flows' ROC is 4dB higher than pressure's. Vector array's gain is higher than that of pressure array. Under the condition of high snr, the vector array's gain based on high orders surpasses that based on acoustic energy flows.Based on frequency measurement model probability densities and Crame-Rao Low Boundary (CRLB) of DOA estimation are deduced. At low snr DOA estimation is bias. If snr is higher than 7dB/Hz, the estimation is an unbiased MLE (Maximum Likelihood Estimation) and its accuracy approaches CRLB.The studies of near distance acoustic field and signal processing theories coincide with simulations and sea (lake) trials rationally.Exordium of the thesis introduces fundamental knowledge about theories and techniques of vector hydrophone, and overviews the corresponding development status at home and abroad, so that readers can have a general acquaintance with them.
引文
[1] 汪文件,“新世纪中国海洋方向安全分析”,中共中央党校硕士学位论文,北京,2001年
[2] Shchurov V.A., "Modern state and prospects for use of underwater acoustic intensity measurements," Preprint. Vladivostok: Pacific Oceanological Institute FEBRAS, 1998.
[3] Shchurov V.A., "The properties of the vertical and horizontal power flows of the underwater ambient," J. Acoust. Soc. Amer., vol. 90(2), pp. 1002-1004, 1991.
[4] Shchurov V.A., "Coherent and diffusive fields of underwater acoustic ambient noise," J. Acoust. Soc. Am. vol. 90(2), pp. 991-1001, 1991.
[5] Shchurov V.A., "The interaction of energy flows of underwater ambient and a local source," Natural Physical Sources of Underwater Sound. Kluwer Academic Publishers, pp. 93-109, 1993.
[6] Shchurov V.A., "Ambient noise energy motion in the near-surface octan layer," Recent Advances in Underwater Acoustics, Proc.I.O.A. vol. 13, part 3. Weymouth, UK. pp. 250-256, 1991.
[7] Shchurov V.A., Ilyichev V.I., Khvorostov Y.A., "Ambient noise anisotropy in horizontal plane," Proc. ICA-14, El-10. 1992, Beijing, China.
[8] Shchurov V.A. et. al., "The ambient noise energy motion in the near-surface in ocean wake-guide," Journal de Physique Ⅳ, colloque C5, supplement au Journal de Physique Ⅲ. France.1994. Ⅴ. 4. CP.-1273.
[9] Shchurov V.A. et al. "A possible mechanism of dynamic ambient ocean noise horizontal energy flow forming," Proc. I.O.A. Arrays and Beamforming in Sonar. University of Bristol. UK. 1996, P. 121-127.
[10] Shchurov V.A. et al. "Peculiarities of forming underwater combined acoustic receiver noise immunity," Natural Physical Processes Associated with Sea Surface Sound. University of Southampton, UK. 1997. P. 28-35.
[11] Shchurov V.A. "Up-to-Date State and Outlook for the Intensity Measurement Method in Underwater Acoustics," Proc. 16-th Intern. Congr. On Acoust./2aUW21, USA. 1998. P. 989-990.
[12] Ye. L. Gordienko, "Study of the ocean noise field anisotropy," Akusticheskie sredstva i metody osvoyeniya okeana, Vladivostok: DVGU, 1981, pp. 122-126.
[13] V. P. Dzyuba, "Statistical properties of the acoustic noise field," Tez. Dokl. 14-i Vsesoyuz. Shkoly-seminara opstatisticheskoi gidroakustike(SG-14). Nauka, Moscow, 1986, pp. 32-36(in Russian).
[14] V. A. Shchurov, "Investigation of the acoustic noise field in the ocean using the vector-phase techniques," in Utilization of the Vector-Phase Technique in Ocean Acousticss, edited by V. A. Shchurov (DVO AN SSSR, Vladivostok, 1989), pp. 5-47(in Russian).
[15] D'Spain G.L., Hodgriss W.S. and Edmonds G.L. "Energetics of the deep ocean's infrasonic sound field," J. Acoust. Soc. Am. 1991. No. 89(3), pp. 1134-1158.
[16] D'Spain G.L.,The simultaneous measurement of infrasonic acoustic particle velocity and acoustic pressure in ocean by freely drifting swallow floats, J. Oceanic Eng. 1991, vol.16, no.2, pp.195-207.
[17] D'Spain G.L.,Polarization of acoustic particle motion in the ocean and its relation to vector acoustic intensity, The 2nd International Workshop on Acoustical Engineering and Technology, 1999.
[18] J.C.Nickles, G.L.Edmonds,R.A.Harriss, F.H.Fisher, J.Giles, and G.L.D'Spaon. "A vertical array of directional acoustic sensors," Proc. Mast. Oceans thru Tech. (Oceans 92), Newport, RI.Oct. 1992,pp.340-345.
[19] D'Spain G.L., Polarization of acoustic particle motion in the ocean and its relation to vector acoustic intensity, The 2nd International Workshop on Acoustical Engineering and Technology, 1999.
[20] J.Nickles, G. Edmonds, R. Harriss, F. Fisher, W. Hodgkiss, J. Giles, and G. D'Spain,A vertical array of directional acoustic sensors, in Proc.Mast. Oceans thru Tech. (Oceans 92), pp.340-345, Newport, RI, October 1992.
[21] G. L. D'Spain et al., Initial analysis of the data from the vertical DIFAR array, in Proc. Mast. Oceans Tech. (Oceans'92), Newport, RI, Oct. 1992, pp. 346-351.
[22] G.L.D'Spain et al. Initial analysis of the data from the vertical DIFAR array. Proc. Oceans'92. Newport Rhode Island. 1992, P.346-351
[23] 陈湍石,“声强测量及应用”,噪声与振动控制,1987.8。
[24] F. J. Fahy, "Sound intensity", The university, Southampton, UK.
[25] E. G. Richarason, "Technical aspects of sound",中译本。
[26] C. B. Leslie, J. M. Kendall, and J. L. Jones, "Hydrophone for measuring particle velocity," J. Acoust. Soc. Amer., vol. 28, no. 4, pp. 711-715, July 1956.
[27] Boyer G L., "Instrumentation for measuring Underwater acoustic intensity," J. Acoust. Soc. Amer., vol. 32, pp. 1519, 1960.
[28] B. D. Kerler, "Gradient hydropone flow noise," J. Acoust. Soc. Amer., vol. 62, 1972.
[29] C. L. LeBlanc, Handbook of Hydrophone Element Design Technology, NUSC Technical Report 5813(Naval Underwater Systems Center, New London, CT, 1978.
[30] R. D. Marciniak, "Unidirectional underwater sound pressure-gradient transducers," IEEE Trans. Sonics Ultrason. SU-18 920, P.89-95 (April 1971).
[31] Pessy A. Feldman, "Construction of a fiber gradient hydrophone using a nichelion configuration," J. Acoust. Soc. Amer., vol. 80, pp. 700, 1980.
[32] "Fiber optic gradient hydrophones," J. Acoust. Soc. Amer., vol. 77, pp. 2190, 1985.
[33] L. M. Lyamher, "Polarication fiber-optic sound pressure grdient sensor," S. P. A. 36(3)pp. 317.
[34] U. S. Patent 4547870, "Velocity hydrophone".
[35] M. A. Josserand and C. Maerfeld, "PVF2 velocity hydrophones," J. Acoust. Soc. Amer., vol. 3, pp. 861, 1985.
[36] M. Hawkes and A. Nehorai,Acoustic vector-sensor processing in the presence of a reflecting boundary, IEEE Trans. on Signal Processing, Vol. SP-48, pp. 2981-2993, Nov. 2000.
[37] G.L.D'Spain and W.S.Hodgkiss. Array processing with acoustic measurements at a single point in the ocean. J. Acoust. Soc. Am. 1992, 91(4):P. 2364-2365
[38] G.L.D'Spain and W.S.Hodgkiss. Further comments on beamforming with acoustic measurements at a single point in the ocean. J. Acoust. Soc. Am. 1993, 93(4): P.2375-2376
[39] G.L.D'Spain and W.S.Hodgkiss. The polarization of acoustic particle motion in the ocean. J. Acoust. Soc. Am. 1991, 90(4): P.2300-2301
[40] G.L.D'Spain. Relationship of underwater acoustic intensity measurements to beamforming. Canadian Acoust. 1994, 22(3): P. 157-158
[41] G.L.D'Spain. Polarization of acoustic particle motion in the ocean and its relation to vector acoustic intensity. Proc.IWAET-2. Harbin. China. 1999, P.149-164
[42] J.Nickles,et al., A vertical array of directional acoustic sensors, in Proc.Mast.Oceans thru Tech.(Oceans92), pp:340-345, Newport, RI, October 1992.
[43] 贾志富.同振球型声压梯度水听器的研究.应用声学,vol.16(3):20～25页
[44] 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.声学学报,2003,28(1):66-72页
[45] A.D.惠伦.噪声中信号的检测.刘其培等译.第1版.科学出版社.1977
[46] 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
[47] 陈新华.矢量传感器阵列信号处理,哈尔滨工程大学博士学位论文,2004
[48] 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(4):303-307页
[49] Gulin O.E., Yang Desen. On behaviour of scalar and vector power characteristics of a point source acoustical field for various models of shallow sea. In:Sun Hui eds. Proc.of the 3rd IWAET, the 3rd Inte. Workshop on Acou. Engi.& Tech.,Harbin,2002,Harbin: HEU Press,2002:P. 89
[50] Gulin O.E.,Yang Desen. On the Certain Semi-analytical models of low-frequency acoustic fields in terms of Scalar-vector description. CHINESE Journal of acoustics, 2004, vol.23 (1): P. 58～70
[51] Yaroshchuk I.O.,etc. Statistical Modeling of characteristics of scalar-vector sound fields generated in layerly-inhomogeneous shallow sea with fluctuations. In:Sun Hui eds. Proc. of the 3rd IWAET, the 3rd Inte.Workshop on Acou. Engi.& Tech.,Harbin,2002,Harbin:HEU Press,2002:P.439
[52] 布列霍夫斯基赫.分层介质中的波.第二版.北京:科学出版社.1985:211页
[53] 杨士莪.水声传播原理.哈尔滨:哈尔滨工程大学出版社.1994:6页
[54] 汪德昭,尚尔昌.水声学.北京:科学出版社.1981:99页
[55] Pekeris C.L. Theory of propagation of explosive in shallow water. Mem.Geol.Soc. America, 1948; P. 27
[56] Lo E.Y. and Junger M.C. "Signal-to-noise enhancement by underwater intensity measurements," J. Acoust. Soc. Am. 1987, vol. 82, no. 4, pp. 1450-1454.
[57] M. Hawkes and A. Nehorai. Acoustic vector-sensor Correlations in Ambient Noise. in Proc. IEEE. Journal of Oceanic Engineering, vol.26(3)
[58] 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
[59] 孟洪.矢量水听器及联合信号处理研究.哈尔滨工程大学硕士学位论文.2001
[60] 孙岩松.各向异性噪声场对矢量水听器检测性能影响的研究.哈尔滨工程大学硕士学位论文.2003
[61] A.Nehorai,E.Paldi,Acoustic vector sensor array processing,IEEE Trans. Signal Processing,42,P. 2481-2491,1994
[62] M. Hawkes and A. Nehorai,Effects of sensor placement on acoustic vector-sensor array performance,IEEE J. Oceanic Eng., Vol. 24, pp. 33-40,
[63] B. Hochwald and A. Nehorai,Identifiably in array processing models with vector-sensor applications,IEEE Trans. on Signal Processing, Vol. SP-44, pp. 83-95, Jan. 1996.
[64] M. Hawkes and A. Nehorai,Acoustic vector-sensor beamforming and capon direction estimation,IEEE Trans. on Signal Processing, Vol. SP-46, pp. 2291-2304, Sept. 1998
[65] M. Hawkes and A. Nehorai, Surface-mounted acoustic vector-sensor array processing, in Proc. IEEE Intl Conf. On Acoust., Speech, and Sig. Proc.(ICASSP96), pp.3710-3713, Atlanta, GA, May 1996.
[66] A. Nehorai and M. Hawkes, Performance bounds for estimating vector systems, IEEE Trans. on Signal Processing, Vol. SP-48, pp. 1737-1749, June 2000
[67] K. T.Wong and M. D. Zoltowski,Orthogonal-velocity-hydrophone ESPRIT for sonar source localization,in MTS/IEEE Oceans'96 Conf., p. 1307-1312
[68] Kaiman Thomas Wong,Blind beamforming/geolocation for wideband-FFHs with unknown hop-sequences,IEEE trans.on Aerospace and Eletronic system,Vol.37,No. 1, January 2001, p65-76
[69] K. T. Wong and M. D. Zoltowski,ESPRIT-based extended-aperture source localization using velocity-hydrophones,in Proc. MTS/IEEE Oceans Conf., Fort Lauderdate, FL, Sept. 1996, vol. 3, pp. 1427-1432.
[70] Kainam T. Wong,Michael D.Zoltowski,High accuracy 2D estimation with extended aperture vector sensor arrays, IEEE Trans.on Antennas and Propagation,Vol.03,1996,p2789—2792
[71] K.T.Wong and M.D.Zoltowski,Extended-aperture underwater acoustic multisource azimuth/elevation direction-finding using uniformly but sparsely-spaced vector hydrophones,IEEE,J.Oceanic Eng.,vol.22,no.4,oct, 1997,p659-672,
[72] M. D. Zoltowski and K. T. Wong,Extended-aperture spatial diversity and polarizational diversity using a sparse array of electric dipoles or magnetic loops,in IEEE Vehicular Technology Int. Conf., 1997, p1163-1167.
[73] K. T. Wong, M. D. Zoltowski,Closed-Form Direction-Finding with Arbitrarily Spaced Electromagnetic Vector-Sensors at Unknown Locations, IEEE Transactions on Antennas and Propagation, vol. 48, no. 5, May 2000, p671-681
[74] K.T.Wong and M.D.Zoltowski,Self-Initiating MUSIC-Based Direction Finding in Underwater Acoustic Particle Velocity-Field Beamspace,IEEE Intl. Symposium on Circuits & Systems,vol.4,1997,p2553-2556,
[75] Kainam T. Wong,Michael D.Zoltowski,Polarization-Beamspace self-Initiating MUSIC for Azimuth/Elevation angle estimation,IEE Conf.on Radar 97,14-16,October 1997,p328-333
[76] 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.Signal Processing, vol.47. Dec.1999. pp.3250-3260
[77] K.T.Wong and M.D.Zoltowski,Self-Initiating MUSIC-Based Direction Finding in Underwater Acoustic Particle Velocity-Field Beamspace,IEEE J.of Oceanic Engineering,vol.25,no.2, April 2000, p 262-273,
[78] 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
[79] 惠俊英,李春旭,梁国龙,刘宏.声压、振速联合信息处理抗相干干扰.声学学报,2000(5):389-394页
[80] 蔡平,郭龙祥,惠俊英.矢量传感器海底混响仿真模型.声学技术,已录用
[81] 徐海东,梁国龙,惠俊英.解析声能流Capon空间谱估计.声学技术.2004年3期
[82] 陈新华 蔡平,惠俊英等,声矢量阵指向性,声学学报,2003,28(2).-141-144
[83] 王逸林,赵羽,蔡平.矢量阵组合增益仿真分析.声学技术.2004(23):219-221页
[84] 蔡平,赵羽,王逸林.矢量阵恒定束宽波束形成研究.已投稿声学学报
[85] 生雪莉,惠俊英,梁国龙,李维.矢量反转镜时空滤波技术研究.声学学报.已录用
[86] 俞敏.矢量传感器方位估计.哈尔滨工程大学硕士学位论文.2004
[87] 乔刚,基于矢量传感器的水声通信技术研究,哈尔滨工程大学博士学位论文,2004
[88] 刘伯胜,田宝晶.矢量传感器估计目标方位的误差的仿真研究.哈尔滨工程大学学报,vol.24(5):491～494页
[89] 齐娜,田坦,孙大军.确定信号情况下矢量水听器检测及估计性能研究.信号处理(已录用)
[90] 齐娜,田坦,孙大军.一种基于矢量水听器阵的归一化加权Capon波束形成方法.应用声学(已录用)
[91] 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,2004,24(3):295-298页
[92] 田初军.声强水雷引信技术研究.海军工程大学博士学位论文,1997
[93] New R., Eisler T.J. Acoustic Radiation from multipole spheres. J.S.and Vib., 1972;P. 22
[94] 关治,陈景良.数值计算方法.北京:清华大学出版社.1990:P.173
[95] 惠俊英 编著.水下声信道.国防工业出版社,1992
[96] R.J.尤立克.水声原理.洪申译.哈尔滨:哈尔滨船舶工程学院出版社.1990
[97] 布列霍夫斯基赫主编.海洋声学.北京:科学出版社.1983
[98] Finn B.Jensen, William A.Kuperman, etc. Computational Ocean Acoustics. New York, American Institute of Physics, 1995
[99] 赵树杰等.统计信号处理——检测理论、估计和滤波理论及其应用.陕西:西北电讯工程学院出版社.
[100] 项楚骐,田坦.离散估计导论.哈尔滨:哈尔滨船舶工程学院出版社.1989
[101] Baggeroer A B, Kuperman W A, Mikhalersky P N. An overview of matched field methods in ocean acoustics. IEEE Journal of Oceanic Engineering, 1993, 18(4): P. 401～424
[102] B.E.McDonald, Kuperman W A. Time domain formulation for pulse propagation including nonlinear behavior at a caustic. J. Acoustic. Soc. Am. 81, P. 1406～1417
[103] F.R. DiNapoli, R.L. Deavenport. Theoretical and numerical Green's function solution in a plane layered medium. J.A.S.A. 67, P. 92～105
[104] T.W.Dawson, J.A.Fawcett. A boundary integral equation method for acoustic scattering in a waveguide with nonplanar surfaces. J.A.S.A. 87, P. 1110～1120
[105] M.A.Pedersen, D.F. Gordon. Normal-mode and ray theory applied to underwater acoustic conditions of extreme downward refraction. J.A.S.A. 51, P. 323～368
[106] C.T.Tindle, G.E.J.Bold. Improved ray calculations in shallow water. J.A.S.A. 70, P. 813～819
[107] D.C.Stickler. Normal-mode program with both the discrete and branch line contributions. J.A.S.A. 57, P. 856～1861
[108] M.B.Porter, E.L.Reiss. A numerical method for ocean acoustic normal modes. J.A.S.A. 76, P. 244～252
[109] J.S.Perkins, R.N.Baer. An approximation to the three-dimensional parabolic-equation method for acoustic propagation. J.A.S.A.72,P. 515～522
[110] W.L. Siegmann, G.A.Kriegsmann, D.Lee. A wide-angle three-dimensional parabolic wave equation. J.A.S.A. 78, P. 659～664
[111] G.E.Forsythe, W.R.Wasow. Finite Difference Methods for Partial Differential Equations. New York, 1960
[112] G.D.Smith, Numerical Solution of Partial Differential Equations. Oxford University Press, London, 1969
[113] D.Huang. Finite element solution to the parabolic wave equation. J.A.S.A. 84, P. 1405～1413
[114] O.C.Zienkiewicz. The Finite Element Method. London, 1977
[115] T.W.Dawson, J.A.Fawcett. A boundary integral equation method for acoustic scattering in a waveguide with nonplanar surfaces. J.A.S.A. 87, P. 1110～1125
[116] P. Gerstoft, H.Schmidt. A boundary element approach to seismo-acoustic facet reverberation. J.A.S.A. 89, P. 1629～1642
[117] A.N.Guthrie, R.M.Fitzgerald, etc. Long-range low-frequency CW propagation in the deep ocean: Antigua-Newfoundland. J.A.S.A.56,P.58～69
[118] K.E.Hawker. A normal mode theory of acoustic Doppler effects in the oceanic waveguide. J.A.S.A. 65, P. 675～681
[119] M.D.Collins. Applications and time-domain solution of higher-order parabolic equations in underwater acoustics. J.A.S.A. 86, P. 1097～1102
[120] 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
[121] 盛骤,谢式千等.概率论与数理统计.高等教育出版社.1996
[122] 刘式适,刘式达.特殊函数(第二版).气象出版社.2002.3
[123] 李启虎.声呐信号处理引论.海洋出版社.2000
[124] 冯海泓,梁国龙,惠俊英.目标方位的声压、振速联合估计.声学学报,2000,25(6)
[125] 《数学手册》编写组.数学手册.北京:高等教育出版社.1979
[2] Shchurov V.A., "Modern state and prospects for use of underwater acoustic intensity measurements," Preprint. Vladivostok: Pacific Oceanological Institute FEBRAS, 1998.
[3] Shchurov V.A., "The properties of the vertical and horizontal power flows of the underwater ambient," J. Acoust. Soc. Amer., vol. 90(2), pp. 1002-1004, 1991.
[4] Shchurov V.A., "Coherent and diffusive fields of underwater acoustic ambient noise," J. Acoust. Soc. Am. vol. 90(2), pp. 991-1001, 1991.
[5] Shchurov V.A., "The interaction of energy flows of underwater ambient and a local source," Natural Physical Sources of Underwater Sound. Kluwer Academic Publishers, pp. 93-109, 1993.
[6] Shchurov V.A., "Ambient noise energy motion in the near-surface octan layer," Recent Advances in Underwater Acoustics, Proc.I.O.A. vol. 13, part 3. Weymouth, UK. pp. 250-256, 1991.
[7] Shchurov V.A., Ilyichev V.I., Khvorostov Y.A., "Ambient noise anisotropy in horizontal plane," Proc. ICA-14, El-10. 1992, Beijing, China.
[8] Shchurov V.A. et. al., "The ambient noise energy motion in the near-surface in ocean wake-guide," Journal de Physique Ⅳ, colloque C5, supplement au Journal de Physique Ⅲ. France.1994. Ⅴ. 4. CP.-1273.
[9] Shchurov V.A. et al. "A possible mechanism of dynamic ambient ocean noise horizontal energy flow forming," Proc. I.O.A. Arrays and Beamforming in Sonar. University of Bristol. UK. 1996, P. 121-127.
[10] Shchurov V.A. et al. "Peculiarities of forming underwater combined acoustic receiver noise immunity," Natural Physical Processes Associated with Sea Surface Sound. University of Southampton, UK. 1997. P. 28-35.
[11] Shchurov V.A. "Up-to-Date State and Outlook for the Intensity Measurement Method in Underwater Acoustics," Proc. 16-th Intern. Congr. On Acoust./2aUW21, USA. 1998. P. 989-990.
[12] Ye. L. Gordienko, "Study of the ocean noise field anisotropy," Akusticheskie sredstva i metody osvoyeniya okeana, Vladivostok: DVGU, 1981, pp. 122-126.
[13] V. P. Dzyuba, "Statistical properties of the acoustic noise field," Tez. Dokl. 14-i Vsesoyuz. Shkoly-seminara opstatisticheskoi gidroakustike(SG-14). Nauka, Moscow, 1986, pp. 32-36(in Russian).
[14] V. A. Shchurov, "Investigation of the acoustic noise field in the ocean using the vector-phase techniques," in Utilization of the Vector-Phase Technique in Ocean Acousticss, edited by V. A. Shchurov (DVO AN SSSR, Vladivostok, 1989), pp. 5-47(in Russian).
[15] D'Spain G.L., Hodgriss W.S. and Edmonds G.L. "Energetics of the deep ocean's infrasonic sound field," J. Acoust. Soc. Am. 1991. No. 89(3), pp. 1134-1158.
[16] D'Spain G.L.,The simultaneous measurement of infrasonic acoustic particle velocity and acoustic pressure in ocean by freely drifting swallow floats, J. Oceanic Eng. 1991, vol.16, no.2, pp.195-207.
[17] D'Spain G.L.,Polarization of acoustic particle motion in the ocean and its relation to vector acoustic intensity, The 2nd International Workshop on Acoustical Engineering and Technology, 1999.
[18] J.C.Nickles, G.L.Edmonds,R.A.Harriss, F.H.Fisher, J.Giles, and G.L.D'Spaon. "A vertical array of directional acoustic sensors," Proc. Mast. Oceans thru Tech. (Oceans 92), Newport, RI.Oct. 1992,pp.340-345.
[19] D'Spain G.L., Polarization of acoustic particle motion in the ocean and its relation to vector acoustic intensity, The 2nd International Workshop on Acoustical Engineering and Technology, 1999.
[20] J.Nickles, G. Edmonds, R. Harriss, F. Fisher, W. Hodgkiss, J. Giles, and G. D'Spain,A vertical array of directional acoustic sensors, in Proc.Mast. Oceans thru Tech. (Oceans 92), pp.340-345, Newport, RI, October 1992.
[21] G. L. D'Spain et al., Initial analysis of the data from the vertical DIFAR array, in Proc. Mast. Oceans Tech. (Oceans'92), Newport, RI, Oct. 1992, pp. 346-351.
[22] G.L.D'Spain et al. Initial analysis of the data from the vertical DIFAR array. Proc. Oceans'92. Newport Rhode Island. 1992, P.346-351
[23] 陈湍石,“声强测量及应用”,噪声与振动控制,1987.8。
[24] F. J. Fahy, "Sound intensity", The university, Southampton, UK.
[25] E. G. Richarason, "Technical aspects of sound",中译本。
[26] C. B. Leslie, J. M. Kendall, and J. L. Jones, "Hydrophone for measuring particle velocity," J. Acoust. Soc. Amer., vol. 28, no. 4, pp. 711-715, July 1956.
[27] Boyer G L., "Instrumentation for measuring Underwater acoustic intensity," J. Acoust. Soc. Amer., vol. 32, pp. 1519, 1960.
[28] B. D. Kerler, "Gradient hydropone flow noise," J. Acoust. Soc. Amer., vol. 62, 1972.
[29] C. L. LeBlanc, Handbook of Hydrophone Element Design Technology, NUSC Technical Report 5813(Naval Underwater Systems Center, New London, CT, 1978.
[30] R. D. Marciniak, "Unidirectional underwater sound pressure-gradient transducers," IEEE Trans. Sonics Ultrason. SU-18 920, P.89-95 (April 1971).
[31] Pessy A. Feldman, "Construction of a fiber gradient hydrophone using a nichelion configuration," J. Acoust. Soc. Amer., vol. 80, pp. 700, 1980.
[32] "Fiber optic gradient hydrophones," J. Acoust. Soc. Amer., vol. 77, pp. 2190, 1985.
[33] L. M. Lyamher, "Polarication fiber-optic sound pressure grdient sensor," S. P. A. 36(3)pp. 317.
[34] U. S. Patent 4547870, "Velocity hydrophone".
[35] M. A. Josserand and C. Maerfeld, "PVF2 velocity hydrophones," J. Acoust. Soc. Amer., vol. 3, pp. 861, 1985.
[36] M. Hawkes and A. Nehorai,Acoustic vector-sensor processing in the presence of a reflecting boundary, IEEE Trans. on Signal Processing, Vol. SP-48, pp. 2981-2993, Nov. 2000.
[37] G.L.D'Spain and W.S.Hodgkiss. Array processing with acoustic measurements at a single point in the ocean. J. Acoust. Soc. Am. 1992, 91(4):P. 2364-2365
[38] G.L.D'Spain and W.S.Hodgkiss. Further comments on beamforming with acoustic measurements at a single point in the ocean. J. Acoust. Soc. Am. 1993, 93(4): P.2375-2376
[39] G.L.D'Spain and W.S.Hodgkiss. The polarization of acoustic particle motion in the ocean. J. Acoust. Soc. Am. 1991, 90(4): P.2300-2301
[40] G.L.D'Spain. Relationship of underwater acoustic intensity measurements to beamforming. Canadian Acoust. 1994, 22(3): P. 157-158
[41] G.L.D'Spain. Polarization of acoustic particle motion in the ocean and its relation to vector acoustic intensity. Proc.IWAET-2. Harbin. China. 1999, P.149-164
[42] J.Nickles,et al., A vertical array of directional acoustic sensors, in Proc.Mast.Oceans thru Tech.(Oceans92), pp:340-345, Newport, RI, October 1992.
[43] 贾志富.同振球型声压梯度水听器的研究.应用声学,vol.16(3):20～25页
[44] 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.声学学报,2003,28(1):66-72页
[45] A.D.惠伦.噪声中信号的检测.刘其培等译.第1版.科学出版社.1977
[46] 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
[47] 陈新华.矢量传感器阵列信号处理,哈尔滨工程大学博士学位论文,2004
[48] 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(4):303-307页
[49] Gulin O.E., Yang Desen. On behaviour of scalar and vector power characteristics of a point source acoustical field for various models of shallow sea. In:Sun Hui eds. Proc.of the 3rd IWAET, the 3rd Inte. Workshop on Acou. Engi.& Tech.,Harbin,2002,Harbin: HEU Press,2002:P. 89
[50] Gulin O.E.,Yang Desen. On the Certain Semi-analytical models of low-frequency acoustic fields in terms of Scalar-vector description. CHINESE Journal of acoustics, 2004, vol.23 (1): P. 58～70
[51] Yaroshchuk I.O.,etc. Statistical Modeling of characteristics of scalar-vector sound fields generated in layerly-inhomogeneous shallow sea with fluctuations. In:Sun Hui eds. Proc. of the 3rd IWAET, the 3rd Inte.Workshop on Acou. Engi.& Tech.,Harbin,2002,Harbin:HEU Press,2002:P.439
[52] 布列霍夫斯基赫.分层介质中的波.第二版.北京:科学出版社.1985:211页
[53] 杨士莪.水声传播原理.哈尔滨:哈尔滨工程大学出版社.1994:6页
[54] 汪德昭,尚尔昌.水声学.北京:科学出版社.1981:99页
[55] Pekeris C.L. Theory of propagation of explosive in shallow water. Mem.Geol.Soc. America, 1948; P. 27
[56] Lo E.Y. and Junger M.C. "Signal-to-noise enhancement by underwater intensity measurements," J. Acoust. Soc. Am. 1987, vol. 82, no. 4, pp. 1450-1454.
[57] M. Hawkes and A. Nehorai. Acoustic vector-sensor Correlations in Ambient Noise. in Proc. IEEE. Journal of Oceanic Engineering, vol.26(3)
[58] 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
[59] 孟洪.矢量水听器及联合信号处理研究.哈尔滨工程大学硕士学位论文.2001
[60] 孙岩松.各向异性噪声场对矢量水听器检测性能影响的研究.哈尔滨工程大学硕士学位论文.2003
[61] A.Nehorai,E.Paldi,Acoustic vector sensor array processing,IEEE Trans. Signal Processing,42,P. 2481-2491,1994
[62] M. Hawkes and A. Nehorai,Effects of sensor placement on acoustic vector-sensor array performance,IEEE J. Oceanic Eng., Vol. 24, pp. 33-40,
[63] B. Hochwald and A. Nehorai,Identifiably in array processing models with vector-sensor applications,IEEE Trans. on Signal Processing, Vol. SP-44, pp. 83-95, Jan. 1996.
[64] M. Hawkes and A. Nehorai,Acoustic vector-sensor beamforming and capon direction estimation,IEEE Trans. on Signal Processing, Vol. SP-46, pp. 2291-2304, Sept. 1998
[65] M. Hawkes and A. Nehorai, Surface-mounted acoustic vector-sensor array processing, in Proc. IEEE Intl Conf. On Acoust., Speech, and Sig. Proc.(ICASSP96), pp.3710-3713, Atlanta, GA, May 1996.
[66] A. Nehorai and M. Hawkes, Performance bounds for estimating vector systems, IEEE Trans. on Signal Processing, Vol. SP-48, pp. 1737-1749, June 2000
[67] K. T.Wong and M. D. Zoltowski,Orthogonal-velocity-hydrophone ESPRIT for sonar source localization,in MTS/IEEE Oceans'96 Conf., p. 1307-1312
[68] Kaiman Thomas Wong,Blind beamforming/geolocation for wideband-FFHs with unknown hop-sequences,IEEE trans.on Aerospace and Eletronic system,Vol.37,No. 1, January 2001, p65-76
[69] K. T. Wong and M. D. Zoltowski,ESPRIT-based extended-aperture source localization using velocity-hydrophones,in Proc. MTS/IEEE Oceans Conf., Fort Lauderdate, FL, Sept. 1996, vol. 3, pp. 1427-1432.
[70] Kainam T. Wong,Michael D.Zoltowski,High accuracy 2D estimation with extended aperture vector sensor arrays, IEEE Trans.on Antennas and Propagation,Vol.03,1996,p2789—2792
[71] K.T.Wong and M.D.Zoltowski,Extended-aperture underwater acoustic multisource azimuth/elevation direction-finding using uniformly but sparsely-spaced vector hydrophones,IEEE,J.Oceanic Eng.,vol.22,no.4,oct, 1997,p659-672,
[72] M. D. Zoltowski and K. T. Wong,Extended-aperture spatial diversity and polarizational diversity using a sparse array of electric dipoles or magnetic loops,in IEEE Vehicular Technology Int. Conf., 1997, p1163-1167.
[73] K. T. Wong, M. D. Zoltowski,Closed-Form Direction-Finding with Arbitrarily Spaced Electromagnetic Vector-Sensors at Unknown Locations, IEEE Transactions on Antennas and Propagation, vol. 48, no. 5, May 2000, p671-681
[74] K.T.Wong and M.D.Zoltowski,Self-Initiating MUSIC-Based Direction Finding in Underwater Acoustic Particle Velocity-Field Beamspace,IEEE Intl. Symposium on Circuits & Systems,vol.4,1997,p2553-2556,
[75] Kainam T. Wong,Michael D.Zoltowski,Polarization-Beamspace self-Initiating MUSIC for Azimuth/Elevation angle estimation,IEE Conf.on Radar 97,14-16,October 1997,p328-333
[76] 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.Signal Processing, vol.47. Dec.1999. pp.3250-3260
[77] K.T.Wong and M.D.Zoltowski,Self-Initiating MUSIC-Based Direction Finding in Underwater Acoustic Particle Velocity-Field Beamspace,IEEE J.of Oceanic Engineering,vol.25,no.2, April 2000, p 262-273,
[78] 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
[79] 惠俊英,李春旭,梁国龙,刘宏.声压、振速联合信息处理抗相干干扰.声学学报,2000(5):389-394页
[80] 蔡平,郭龙祥,惠俊英.矢量传感器海底混响仿真模型.声学技术,已录用
[81] 徐海东,梁国龙,惠俊英.解析声能流Capon空间谱估计.声学技术.2004年3期
[82] 陈新华 蔡平,惠俊英等,声矢量阵指向性,声学学报,2003,28(2).-141-144
[83] 王逸林,赵羽,蔡平.矢量阵组合增益仿真分析.声学技术.2004(23):219-221页
[84] 蔡平,赵羽,王逸林.矢量阵恒定束宽波束形成研究.已投稿声学学报
[85] 生雪莉,惠俊英,梁国龙,李维.矢量反转镜时空滤波技术研究.声学学报.已录用
[86] 俞敏.矢量传感器方位估计.哈尔滨工程大学硕士学位论文.2004
[87] 乔刚,基于矢量传感器的水声通信技术研究,哈尔滨工程大学博士学位论文,2004
[88] 刘伯胜,田宝晶.矢量传感器估计目标方位的误差的仿真研究.哈尔滨工程大学学报,vol.24(5):491～494页
[89] 齐娜,田坦,孙大军.确定信号情况下矢量水听器检测及估计性能研究.信号处理(已录用)
[90] 齐娜,田坦,孙大军.一种基于矢量水听器阵的归一化加权Capon波束形成方法.应用声学(已录用)
[91] 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,2004,24(3):295-298页
[92] 田初军.声强水雷引信技术研究.海军工程大学博士学位论文,1997
[93] New R., Eisler T.J. Acoustic Radiation from multipole spheres. J.S.and Vib., 1972;P. 22
[94] 关治,陈景良.数值计算方法.北京:清华大学出版社.1990:P.173
[95] 惠俊英 编著.水下声信道.国防工业出版社,1992
[96] R.J.尤立克.水声原理.洪申译.哈尔滨:哈尔滨船舶工程学院出版社.1990
[97] 布列霍夫斯基赫主编.海洋声学.北京:科学出版社.1983
[98] Finn B.Jensen, William A.Kuperman, etc. Computational Ocean Acoustics. New York, American Institute of Physics, 1995
[99] 赵树杰等.统计信号处理——检测理论、估计和滤波理论及其应用.陕西:西北电讯工程学院出版社.
[100] 项楚骐,田坦.离散估计导论.哈尔滨:哈尔滨船舶工程学院出版社.1989
[101] Baggeroer A B, Kuperman W A, Mikhalersky P N. An overview of matched field methods in ocean acoustics. IEEE Journal of Oceanic Engineering, 1993, 18(4): P. 401～424
[102] B.E.McDonald, Kuperman W A. Time domain formulation for pulse propagation including nonlinear behavior at a caustic. J. Acoustic. Soc. Am. 81, P. 1406～1417
[103] F.R. DiNapoli, R.L. Deavenport. Theoretical and numerical Green's function solution in a plane layered medium. J.A.S.A. 67, P. 92～105
[104] T.W.Dawson, J.A.Fawcett. A boundary integral equation method for acoustic scattering in a waveguide with nonplanar surfaces. J.A.S.A. 87, P. 1110～1120
[105] M.A.Pedersen, D.F. Gordon. Normal-mode and ray theory applied to underwater acoustic conditions of extreme downward refraction. J.A.S.A. 51, P. 323～368
[106] C.T.Tindle, G.E.J.Bold. Improved ray calculations in shallow water. J.A.S.A. 70, P. 813～819
[107] D.C.Stickler. Normal-mode program with both the discrete and branch line contributions. J.A.S.A. 57, P. 856～1861
[108] M.B.Porter, E.L.Reiss. A numerical method for ocean acoustic normal modes. J.A.S.A. 76, P. 244～252
[109] J.S.Perkins, R.N.Baer. An approximation to the three-dimensional parabolic-equation method for acoustic propagation. J.A.S.A.72,P. 515～522
[110] W.L. Siegmann, G.A.Kriegsmann, D.Lee. A wide-angle three-dimensional parabolic wave equation. J.A.S.A. 78, P. 659～664
[111] G.E.Forsythe, W.R.Wasow. Finite Difference Methods for Partial Differential Equations. New York, 1960
[112] G.D.Smith, Numerical Solution of Partial Differential Equations. Oxford University Press, London, 1969
[113] D.Huang. Finite element solution to the parabolic wave equation. J.A.S.A. 84, P. 1405～1413
[114] O.C.Zienkiewicz. The Finite Element Method. London, 1977
[115] T.W.Dawson, J.A.Fawcett. A boundary integral equation method for acoustic scattering in a waveguide with nonplanar surfaces. J.A.S.A. 87, P. 1110～1125
[116] P. Gerstoft, H.Schmidt. A boundary element approach to seismo-acoustic facet reverberation. J.A.S.A. 89, P. 1629～1642
[117] A.N.Guthrie, R.M.Fitzgerald, etc. Long-range low-frequency CW propagation in the deep ocean: Antigua-Newfoundland. J.A.S.A.56,P.58～69
[118] K.E.Hawker. A normal mode theory of acoustic Doppler effects in the oceanic waveguide. J.A.S.A. 65, P. 675～681
[119] M.D.Collins. Applications and time-domain solution of higher-order parabolic equations in underwater acoustics. J.A.S.A. 86, P. 1097～1102
[120] 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
[121] 盛骤,谢式千等.概率论与数理统计.高等教育出版社.1996
[122] 刘式适,刘式达.特殊函数(第二版).气象出版社.2002.3
[123] 李启虎.声呐信号处理引论.海洋出版社.2000
[124] 冯海泓,梁国龙,惠俊英.目标方位的声压、振速联合估计.声学学报,2000,25(6)
[125] 《数学手册》编写组.数学手册.北京:高等教育出版社.1979