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The wideband source localization is analysed widely in shallow water. It is pointed out that its performance is poor when the number of array elements is few or the ocean environment is uncertain. A method of estimating the range and depth is studied by using a single hydrophone based on the relationship of the horizontal wavenumber difference between two modes with the waveguide invariant for low frequency underwater acoustic pulse signals in a range-independent shallow water waveguide. This localization method estimates the source range by using the rangedispersion two-dimensional（2D) plane focus phenomenon and also the source depth by matching the modal energy. So it can separately estimate the source range and source depth by single hydrophone. First, the signal received on a single hydrophone can be decomposed into a series of modes within the framework of normal mode theory. In order to obtain a better localization performance, the first few order modal dispersion parameters and waveguide invariant are regarded as the unknown parameters. And then the first few order modal dispersion parameters and waveguide invariant can be estimated by comparing the differences between the modal phase velocity calculated by Eq.(8) and that calculated by the Kraken model. Second, using the estimated dispersion parameters and waveguide invariant for dedispersion transform, the amplitudes of each normal mode can achieve maximum values but only when the range of the received signal after dedispersion transform is equal to the range of source. On range-dispersion 2D plane, there appears the sound pressure focus phenomenon, and this phenomenon can be used to estimate the source range. Simulation results from a shallow water Pekeris waveguide show that the time-frequency distribution represents well the dispersion characteristics of the underwater acoustic pulse signal and the dedisperision transform can eliminate this dispersion at the range of source, so that the source range can be estimated. Besides, the first few order modal signals received are clearly separated in time domain after dedispersion transform, and the first few order modal energy can be calculated accurately. So the source depth can be estimated by matching the modal energy. The errors in range estimation and depth estimation are little in simulation. Finally, the data collected from airgun sources during an experiment in the shallow water are used to verify the presented method, and the experimental results obtained using airgun sources on a straight line are shown. The presented method is very significant for estimating the range and depth in shallow water.
[1] Duan R, Yang K D, Ma Y L 2014 J. Acoust. Soc. Am. 136 EL159
[2] Li K, Fang S L, An L 2013 Acta Phys. Sin. 62 094303(in Chinese)[李焜, 方世良, 安良2013物理学报62 094303]
[3] Qi Y B, Zhou S H, Zhang R H, Ren Y 2015 Acta Phys. Sin. 64 074301(in Chinese)[戚聿波, 周士弘, 张仁和, 任云2015物理学报64 074301]
[4] Bucker H P 1976 J. Acoust. Soc. Am. 59 368
[5] Baggeroer A B, Kuperman W A, Mikhalevsky P N 1993 IEEE J. Ocean. Eng. 18 401
[6] Preisig J C 1994 IEEE Trans. Signal Proces. 42 1305
[7] Thode A M 2000 J. Acoust. Soc. Am. 108 1582
[8] Thode A M, Kuperman W A, D'Spain G L, Hodgkiss W S 2000 J. Acoust. Soc. Am. 107 278
[9] Zhao Z D, Wang N, Gao D Z, Wang H Z 2010 Chin. Phys. Lett. 27 064301
[10] Bonnel J, Gervaise C, Roux P, Nicolas B, Mars J I 2011 J. Acoust. Soc. Am. 130 61
[11] Bonnel J, Gervaise C, Nicolas B, Mars J I 2012 J. Acoust. Soc. Am. 131 119
[12] Bonnel J, Nicolas B, Mars J I, Walker S C 2010 J. Acoust. Soc. Am. 128 719
[13] Gao D Z, Wang N, Wang H Z 2010 J. Comput. Acoust. 18 245
[14] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2000 Computational Ocean Acoustics (Vol. 2)(New York:American Institute of Physics) p67
[15] Brekhovskikh L M, Lysanov Y P 2003 Fundamentals of Ocean Acoustics (Vol. 3)(New York:Springer-Verlag) p101
[16] Grachev G A 1993 Acoust. Phys. 39 33
[17] Wang N, Gao D Z, Wang H Z 201 J. Harbin Eng. Univ. 31 825(in Chinese)[王宁, 高大治, 王好忠201哈尔滨工程大学学报31 825]
[18] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia:SACLANT Undersea Research Center) Technical Report SM-245
[19] Gao D Z, Wang N, Wang H Z 2013 Sci. China G 43 s159(in Chinese)[高大治, 王宁, 王好忠2013中国科学G 43 s159]
[20] Wang H Z, Wang N, Gao D Z 2011 Chin. Phys. Lett. 28 114302
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[1] Duan R, Yang K D, Ma Y L 2014 J. Acoust. Soc. Am. 136 EL159
[2] Li K, Fang S L, An L 2013 Acta Phys. Sin. 62 094303(in Chinese)[李焜, 方世良, 安良2013物理学报62 094303]
[3] Qi Y B, Zhou S H, Zhang R H, Ren Y 2015 Acta Phys. Sin. 64 074301(in Chinese)[戚聿波, 周士弘, 张仁和, 任云2015物理学报64 074301]
[4] Bucker H P 1976 J. Acoust. Soc. Am. 59 368
[5] Baggeroer A B, Kuperman W A, Mikhalevsky P N 1993 IEEE J. Ocean. Eng. 18 401
[6] Preisig J C 1994 IEEE Trans. Signal Proces. 42 1305
[7] Thode A M 2000 J. Acoust. Soc. Am. 108 1582
[8] Thode A M, Kuperman W A, D'Spain G L, Hodgkiss W S 2000 J. Acoust. Soc. Am. 107 278
[9] Zhao Z D, Wang N, Gao D Z, Wang H Z 2010 Chin. Phys. Lett. 27 064301
[10] Bonnel J, Gervaise C, Roux P, Nicolas B, Mars J I 2011 J. Acoust. Soc. Am. 130 61
[11] Bonnel J, Gervaise C, Nicolas B, Mars J I 2012 J. Acoust. Soc. Am. 131 119
[12] Bonnel J, Nicolas B, Mars J I, Walker S C 2010 J. Acoust. Soc. Am. 128 719
[13] Gao D Z, Wang N, Wang H Z 2010 J. Comput. Acoust. 18 245
[14] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2000 Computational Ocean Acoustics (Vol. 2)(New York:American Institute of Physics) p67
[15] Brekhovskikh L M, Lysanov Y P 2003 Fundamentals of Ocean Acoustics (Vol. 3)(New York:Springer-Verlag) p101
[16] Grachev G A 1993 Acoust. Phys. 39 33
[17] Wang N, Gao D Z, Wang H Z 201 J. Harbin Eng. Univ. 31 825(in Chinese)[王宁, 高大治, 王好忠201哈尔滨工程大学学报31 825]
[18] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia:SACLANT Undersea Research Center) Technical Report SM-245
[19] Gao D Z, Wang N, Wang H Z 2013 Sci. China G 43 s159(in Chinese)[高大治, 王宁, 王好忠2013中国科学G 43 s159]
[20] Wang H Z, Wang N, Gao D Z 2011 Chin. Phys. Lett. 28 114302
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