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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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