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给出了海洋波导中位置未知简谐声源的广义似然比检测器及其理论检测性能. 通过对检测器中模态相关矩阵进行特征值分解，将该检测器分解为与各阶特征值相对应的谱成分. 推导了各阶谱成分的统计特性并以此获得了谱成分对输入信号的空间处理增益，该增益与谱成分对应的特征值成正比. 当模态信息采样不完备时，模态相关矩阵存在部分接近于0的小特征值，相应的谱成分对输入信号的空间处理增益与其余谱成分相比非常小. 通过舍去这部分谱成分，提出了有效谱检测器. 该检测器在保持其输出中目标信号成分与广义似然比检测器相同的基础上，有效减少了其中的噪声成分，因此，具有比广义似然比检测器更好的检测性能. 在典型的浅海环境下进行仿真实验，仿真结果验证了理论分析、推导以及有效谱检测器的有效性，并且表明非完备采样程度越严重，有效谱检测器相对于广义似然比检测器的检测性能提高越显著. 此外，有效谱检测器具有比广义似然比检测器更好的数值计算稳健性.The generalized likelihood ratio test (GLRT) detector and its theoretical detection performance for an underwater narrowband source with an unknown position are both given in this paper. Via the eigenvalue decomposition of the mode correlation matrix (MCM), the GLRT detector is decomposed into different spectrum components corresponding to the eigenvalues of the MCM. Based on the derived statistical property of each component, the spatial processing gain of each spectrum component with respect to the input signal is obtained, which is proportional to the corresponding eigenvalue. As there are several eigenvalues of the MCM approaching to zero when the modal information is incompletely sampled, the components corresponding to these small eigenvalues contribute much less spatial processing gain to the input signal than other components. By discarding the components corresponding to these small eigenvalues, the effective spectrum detector (ESD) is proposed, of which the target signal component in the output is approximately identical to that of the GLRT detector, and the noise in the ESD output is much less. Therefore, a much more robust detection performance is obtained by ESD than by the GLRT detector. Numerical simulations in a typical shallow water environment demonstrate that 1) the theoretical analyses, derivations and the effectiveness of the proposed ESD are verified; 2) the more incomplete the modal information sampling is, the more significant performance improvement of ESD over the GLRT detector can be acquired; 3) the numerical stability of the ESD is better than that of the GLRT detector.
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Keywords:
- spatial processing gain /
- small eigenvalues /
- effective spectrum detector /
- incomplete modal information sampling
[1] Jensen F B, Kuperman W A, Portor M B, Schmidt H 2000 Computational Ocean Acoustics (New York: Springer) pp258-261
[2] Wang N, Liu J Z 2002 Chin. Phys. 11 456
[3] [4] Shang E C 1985 J. Acoust. Soc. Am. 77 1413
[5] [6] [7] Shang E C, Clay C S, Wang Y Y 1985 J. Acoust. Soc. Am 78 172
[8] Wilson G R, Koch R A, Vidmar P J 1988 J. Acoust. Soc. Am. 84 310
[9] [10] [11] Buck J R, Preisig J C, Wage K E 1998 J. Acoust. Soc. Am. 103 1813
[12] Yang T C 1987 J. Acoust. Soc. Am. 82 1736
[13] [14] Collison N E, Dosso S E 2000 J. Acoust. Soc. Am. 107 3089
[15] [16] [17] Yi F, Sun C 2013 Acta Acust. 38 35 (in Chinese) [易锋, 孙超 2013 声学学报 38 35]
[18] [19] Sha L, Nolte L W 2005 J. Acoust. Soc. Am. 117 1942
[20] [21] Liu Z W, Sun C, Du J Y 2013 Acta Phys. Sin. 62 064303 (in Chinese) [刘宗伟, 孙超, 杜金燕 2013 62 064303]
[22] Liu Z W 2013 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [刘宗伟 2013 博士学位论文 (西安: 西北工业大学) ]
[23] [24] [25] Baggeroer A B, Kuperman W A, Mikhalevsky P N 1993 IEEE J. Ocean. Eng. 18 401
[26] [27] Wang Z J 2003 Ph. D. Dissertation (Beijing: Graduate University of Chinese Academy of Sciences) (in Chinese) [王振杰 2003博士学位论文 (北京: 中国科学院研究生院)]
[28] Ou J K 2004 Acta Geodaet. Cartograph. Sin. 33 283 (in Chinese) [欧吉坤 2004 测绘学报 33 283]
[29] [30] Yang W C 1989 Geophysical Inversion and Seismic Tomography (Beijing: Geology Press) pp78-112 (in Chinese) [杨文采 1989 地球物理反演和地震层析成像 (北京: 地质出版社) 第78112页]
[31] [32] [33] Xu P L 1998 Geophys. J. Int. 135 505
[34] Kay S M 1998 Fundamentals of Statistical Signal Processing Volume II: Detection Theory (New Jersey: Prentice Hall) pp499-501
[35] [36] [37] Neilsen T B, Westwood E K 2002 J. Acoust. Soc. Am. 111 748
[38] [39] Kay S M 2013 IEEE Sign. Process. Lett. 20 619
[40] Zhang X D 2004 Matrix Analysis and Applications (Beijing: Tsinghua University Press) p453 (in Chinese) [张贤达 2004 矩阵分析与应用 (北京: 清华大学出版社) 第453页]
[41] [42] [43] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia. Italy: SACLANT Undersea Research Centre)
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[1] Jensen F B, Kuperman W A, Portor M B, Schmidt H 2000 Computational Ocean Acoustics (New York: Springer) pp258-261
[2] Wang N, Liu J Z 2002 Chin. Phys. 11 456
[3] [4] Shang E C 1985 J. Acoust. Soc. Am. 77 1413
[5] [6] [7] Shang E C, Clay C S, Wang Y Y 1985 J. Acoust. Soc. Am 78 172
[8] Wilson G R, Koch R A, Vidmar P J 1988 J. Acoust. Soc. Am. 84 310
[9] [10] [11] Buck J R, Preisig J C, Wage K E 1998 J. Acoust. Soc. Am. 103 1813
[12] Yang T C 1987 J. Acoust. Soc. Am. 82 1736
[13] [14] Collison N E, Dosso S E 2000 J. Acoust. Soc. Am. 107 3089
[15] [16] [17] Yi F, Sun C 2013 Acta Acust. 38 35 (in Chinese) [易锋, 孙超 2013 声学学报 38 35]
[18] [19] Sha L, Nolte L W 2005 J. Acoust. Soc. Am. 117 1942
[20] [21] Liu Z W, Sun C, Du J Y 2013 Acta Phys. Sin. 62 064303 (in Chinese) [刘宗伟, 孙超, 杜金燕 2013 62 064303]
[22] Liu Z W 2013 Ph. D. Dissertation (Xi'an: Northwestern Polytechnical University) (in Chinese) [刘宗伟 2013 博士学位论文 (西安: 西北工业大学) ]
[23] [24] [25] Baggeroer A B, Kuperman W A, Mikhalevsky P N 1993 IEEE J. Ocean. Eng. 18 401
[26] [27] Wang Z J 2003 Ph. D. Dissertation (Beijing: Graduate University of Chinese Academy of Sciences) (in Chinese) [王振杰 2003博士学位论文 (北京: 中国科学院研究生院)]
[28] Ou J K 2004 Acta Geodaet. Cartograph. Sin. 33 283 (in Chinese) [欧吉坤 2004 测绘学报 33 283]
[29] [30] Yang W C 1989 Geophysical Inversion and Seismic Tomography (Beijing: Geology Press) pp78-112 (in Chinese) [杨文采 1989 地球物理反演和地震层析成像 (北京: 地质出版社) 第78112页]
[31] [32] [33] Xu P L 1998 Geophys. J. Int. 135 505
[34] Kay S M 1998 Fundamentals of Statistical Signal Processing Volume II: Detection Theory (New Jersey: Prentice Hall) pp499-501
[35] [36] [37] Neilsen T B, Westwood E K 2002 J. Acoust. Soc. Am. 111 748
[38] [39] Kay S M 2013 IEEE Sign. Process. Lett. 20 619
[40] Zhang X D 2004 Matrix Analysis and Applications (Beijing: Tsinghua University Press) p453 (in Chinese) [张贤达 2004 矩阵分析与应用 (北京: 清华大学出版社) 第453页]
[41] [42] [43] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia. Italy: SACLANT Undersea Research Centre)
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