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The relationship between the array invariant-based ranging and the effective range in a weakly range-dependent environment

거리 종속 환경에서의 배열 불변성 기반 거리추정과 상응 거리와의 관계

  • 김동현 (한국해양대학교 수중운동체특화연구센터) ;
  • 변기훈 (한국해양대학교 해양과학기술융합학과) ;
  • 김대환 (한국해양대학교 해양공학과) ;
  • 김재수 (한국해양대학교 해양공학과)
  • Received : 2024.05.08
  • Accepted : 2024.07.22
  • Published : 2024.07.31

Abstract

In shallow water, the array invariant, known as the effective range estimation method, is developed based on the broadband dispersion characteristics in an ideal waveguide, which can be summarized by the waveguide invariant. It is robust enough to estimate both the array tilt and range simultaneously, even in situations where array tilt exists. Recently, it has been extended to fully consider the angle dependence of the waveguide invariant. However, applying the array invariant in range-dependent environments instead of range-independent environments can lead to range estimation errors due to bathymetry mismatch. In this paper, we interpret such range estimation errors by introducing the concept of effective range. Through numerical simulations and experimental data in a weakly range-dependent environment, we demonstrate the relationship between range estimation errors and effective range.

천해역에서 효과적인 거리추정 방법으로 알려진 배열 불변성은 도파관 불변성으로 요약될 수 있는 이상적인 도파관 내에서의 광대역 확산 특징을 기반으로 개발되었으며, 배열 기울기가 존재하는 상황에서도 배열 기울기와 거리를 동시에 추정할 정도로 강인하다. 최근에는 도파관 불변성의 각도 종속성을 완전히 고려할 수 있도록 확장되었다. 하지만, 거리-종속 환경에 대해 거리-독립 환경의 배열 불변성 기법을 적용한다면, 해저 지형 오정합에 의해 거리추정오차가 발생하게 된다. 본 논문에서는 이러한 거리추정 오차를 상응 거리 개념을 도입하여 해석하고자 한다. 거리-종속 환경에서의 수치 시뮬레이션 수행과 해상 실험 데이터를 통해 거리추정의 오차와 상응 거리 사이의 관계를 입증하였다.

Keywords

Acknowledgement

이 논문은 2022학년도 한국해양대학교 신진교수 정착연구지원사업 연구비의 지원을 받아 수행된 연구임.

References

  1. K. A. Sostrand, "Range localization of 10-100 km explosions by means of an endfire array and a waveguide invariant," IEEE J. Ocean. Eng. 30, 207-212 (2005). https://doi.org/10.1109/JOE.2004.834598
  2. S. Lee and N. C. Makris, "The array invariant," J. Acoust. Soc. Am. 119, 336-351 (2006). https://doi.org/10.1121/1.2139074
  3. H. C. Song and G. Byun, "An overview of array invariant for source-range estimation in shallow water," J. Acoust. Soc. Am. 151, 2336-2352 (2022). https://doi.org/10.1121/10.0009828
  4. H. C. Song and C. Cho, "The relation between the waveguide invariant and array invariant," J. Acoust. Soc. Am. 139, 899-903 (2015).
  5. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics (Springer, New York, 2011), pp. 136.
  6. H. C. Song and C. Cho, "Array invariant-based source localization in shallow water using a sparse vertical array," J. Acoust. Soc. Am. 141, 183-188 (2017). https://doi.org/10.1121/1.4973812
  7. H. C. Song, C. Cho, G. Byun, and J. S. Kim, "Cascade of blind deconvolution and array invariant for robust source-range estimation," J. Acoust. Soc. Am. 141, 3270-3273 (2017). https://doi.org/10.1121/1.4983303
  8. C. Cho and H. C. Song, "Impact of array tilt on source-range estimation in shallow water using the array invariant," J. Acoust. Soc. Am. 141, 2849-2856 (2017). https://doi.org/10.1121/1.4981776
  9. G. Byun, J. S. Kim, C. Cho, H. C. Song, and S. Byun, "Array invariant-based ranging of a source of opportunity," J. Acoust. Soc. Am. 142, EL286-EL291 (2017). https://doi.org/10.1121/1.5003327
  10. H. C. Song and G. Byun, "Simultaneous localization of a surface ship and a submerged towed source," J. Acoust. Soc. Am. 144, 2238-2241 (2018). https://doi.org/10.1121/1.5063352
  11. G. Byun, H. C. Song, J. S. Kim, and J. S. Park, "Real-time tracking of a surface ship using a bottom-mounted horizontal array," J. Acoust. Soc. Am. 144, 2375-2382 (2018). https://doi.org/10.1121/1.5064791
  12. G. Byun, H. C. Song, and S. Byun, "Localization of multiple ships using a vertical array in shallow water," J. Acoust. Soc. Am. 145, EL528-EL533 (2019). https://doi.org/10.1121/1.5111773
  13. G. Byun, C. Cho, H. C. Song, J. S. Kim, and S. Byun, "Array invariant-based calibration of array tilt using a source of opportunity," J. Acoust. Soc. Am. 143, 1318-1325 (2018). https://doi.org/10.1121/1.5025844
  14. G. Byun and H. C. Song, "Adaptive array invariant," J. Acoust. Soc. Am. 148, 925-933 (2020). https://doi.org/10.1121/10.0001768
  15. C. Cho, H. C. Song, P. Hursky, and S. M. Jesus, "Iterative range estimation in a sloping-bottom shallow-water waveguide using the generalized array invariant," J. Acoust. Soc. Am. 142, 55-60 (2017). https://doi.org/10.1121/1.4990670
  16. G. Byun, H. C. Song, and C. Cho, "Adaptive array invariant in range-dependent environments with variable bathymetry," J. Acoust. Soc. Am. 149, 1363-1370 (2021). https://doi.org/10.1121/10.0003562
  17. A. B. Baggeroer, W. A. Kuperman, and P. N. Mikhalevsky, "An overview of matched field methods in ocean acoustics," IEEE J. Ocean. Eng. 18, 401-424 (1993). https://doi.org/10.1109/48.262292
  18. A. Tolstoy, Matched Field Processing for Underwater Acoustics(World Scientific, Singapore, 1993), pp. 1-228.
  19. Z. H. Michalopoulou and M. B. Porter, "Matched-field processing for broadband source localization," IEEE J. Ocean. Eng. 21, 384-392 (1996). https://doi.org/10.1109/48.544049
  20. G. J. Orris, M. Nicholas, and J. S. Perkins, "The matched-phase coherent multi-frequency matched field processor," J. Acoust. Soc. Am. 107, 2563-2575 (2000). https://doi.org/10.1121/1.428644
  21. C. Soares and S. M. Jejus, "Broadband matched-field processing: Coherent and incoherent approaches," J. Acoust. Soc. Am. 113, 2587-2598 (2003). https://doi.org/10.1121/1.1564016
  22. C. Debever and W. A. Kuperman, "Robust matched-field processing using a coherent broadband white noise constraint processor," J. Acoust. Soc. Am. 122, 1979-1986 (2007). https://doi.org/10.1121/1.2769830
  23. G. L. D'Spain, J. J. Murray, W. S. Hodgkiss, N. O. Booth, and P. W. Schey, "Mirages in shallow water matched field processing," J. Acoust. Soc. Am. 105, 3245-3265 (1999). https://doi.org/10.1121/1.424653
  24. C. H. Harrison and M. Siderius, "Effective parameters for matched field geoacoustic inversion in range-dependent environments," IEEE J. Ocean. Eng. 28, 432-445 (2003). https://doi.org/10.1109/JOE.2003.816693
  25. G. L. D'Spain and W. A. Kuperman, "Application of waveguide invariants to analysis of spectrograms from shallow water environments that vary in range and azimuth," J. Acoust. Soc. Am. 106, 2454-2468 (1999). https://doi.org/10.1121/1.428124