Open Access

Cumulant-Based Coherent Signal Subspace Method for Bearing and Range Estimation

EURASIP Journal on Advances in Signal Processing20062007:084576

https://doi.org/10.1155/2007/84576

Received: 27 July 2005

Accepted: 11 June 2006

Published: 13 September 2006

Abstract

A new method for simultaneous range and bearing estimation for buried objects in the presence of an unknown Gaussian noise is proposed. This method uses the MUSIC algorithm with noise subspace estimated by using the slice fourth-order cumulant matrix of the received data. The higher-order statistics aim at the removal of the additive unknown Gaussian noise. The bilinear focusing operator is used to decorrelate the received signals and to estimate the coherent signal subspace. A new source steering vector is proposed including the acoustic scattering model at each sensor. Range and bearing of the objects at each sensor are expressed as a function of those at the first sensor. This leads to the improvement of object localization anywhere, in the near-field or in the far-field zone of the sensor array. Finally, the performances of the proposed method are validated on data recorded during experiments in a water tank.

Keywords

Information TechnologyReceive SignalQuantum InformationWater TankSensor Array

[12345678910111213141516171819202122232425262728293031323334]

Authors’ Affiliations

(1)
EA 3634, Institut de Recherche de École Navale (IRENav), École Navale, Brest-Armées, France
(2)
Institut Fresnel, UMR CNRS 6133, Université Paul Cézanne Aix-Marseille III, EGIM, DU de Saint Jérôme, Marseille Cedex, France

References

  1. Nicq G, Brussieux M: A time-frequency method for classifying objects at low frequencies. Proceedings of the IEEE Oceans Conference, September-October 1998, Nice, France 1: 148-152.Google Scholar
  2. Guillermin R, Lasaygues P, Sessarego J, Wirgin A: Characterization of buried objects by a discretized domain integral equation inversion method using born approximation. Proceedings of the 5th European Conference on Underwater Acoustics (ECUA '00), July 2000, Lyon, France 2: 863-868.MATHGoogle Scholar
  3. Hetet A, Amate M, Zerr B, et al.: SAS processing results for the detection of buried objects with a ship-mounted sonar. Proceedings of the 7th European Conference on Underwater Acoustics (ECUA '04), July 2004, Delft, The Netherlands 1127-1132.Google Scholar
  4. Roux P, Fink M: Time reversal in a waveguide: study of the temporal and spatial focusing. The Journal of the Acoustical Society of America 2000,107(5):2418-2429. 10.1121/1.428628View ArticleGoogle Scholar
  5. Derode A, Tourin A, Fink M: Limits of time-reversal focusing through multiple scattering: long-range correlation. The Journal of the Acoustical Society of America 2000,107(6):2987-2998. 10.1121/1.429328View ArticleGoogle Scholar
  6. Gonen E, Mendel JM: Applications of cumulants to array processing—Part III: blind beamforming for coherent signals. IEEE Transactions on Signal Processing 1997,45(9):2252-2264. 10.1109/78.622948View ArticleGoogle Scholar
  7. Mendel JM: Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications. Proceedings of the IEEE 1991,79(3):278-305. 10.1109/5.75086View ArticleGoogle Scholar
  8. Valaee S, Kabal P: Wideband array processing using a two-sided correlation transformation. IEEE Transactions on Signal Processing 1995,43(1):160-172. 10.1109/78.365295View ArticleGoogle Scholar
  9. Wang H, Kaveh M: Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(4):823-831. 10.1109/TASSP.1985.1164667View ArticleGoogle Scholar
  10. Fawcett JA, Fox WLJ, Maguer A: Modeling of scattering by objects on the seabed. The Journal of the Acoustical Society of America 1998,104(6):3296-3304. 10.1121/1.423969View ArticleGoogle Scholar
  11. Junger MC: Sound scattering by thin elastic shells. The Journal of the Acoustical Society of America 1952,24(4):366-373. 10.1121/1.1906905MathSciNetView ArticleGoogle Scholar
  12. Doolittle RD, Überall H: Sound scattering by elastic cylindrical shells. The Journal of the Acoustical Society of America 1966,39(2):272-275. 10.1121/1.1909886View ArticleMATHGoogle Scholar
  13. Goodman R, Stern R: Reflection and transmission of sound by elastic spherical shells. The Journal of the Acoustical Society of America 1962,34(3):338-344. 10.1121/1.1928120MathSciNetView ArticleGoogle Scholar
  14. Prada C, Fink M: Separation of interfering acoustic scattered signals using the invariants of the time-reversal operator. Application to Lamb waves characterization. The Journal of the Acoustical Society of America 1998,104(2):801-807. 10.1121/1.423354View ArticleGoogle Scholar
  15. Ye Z: Recent developments in underwater Acoustics: acoustic scattering from single and multiple bodies. Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering 2001,25(3):137-150.Google Scholar
  16. Lim R, Lopes JL, Hackman RH, Todoroff DG: Scattering by objects buried in underwater sediments: theory and experiment. The Journal of the Acoustical Society of America 1993,93(4):1762-1783. 10.1121/1.406719View ArticleGoogle Scholar
  17. Tesei A, Maguer A, Fox WLJ, Lim R, Schmidt H: Measurements and modeling of acoustic scattering from partially and completely buried spherical shells. The Journal of the Acoustical Society of America 2002,112(5):1817-1830. 10.1121/1.1509425View ArticleGoogle Scholar
  18. Bendjama A, Bourennane S, Frikel M: Direction finding after blind identification of source steering vectors. Proceedings of the IASTED International Conference on Signal and Image Processing (SIP '98), October 1998, Las Vegas, Nev, USA 491-494.Google Scholar
  19. Yuen N, Friedlander B: DOA estimation in multipath: an approach using fourth-order cumulants. IEEE Transactions on Signal Processing 1997,45(5):1253-1263. 10.1109/78.575698View ArticleGoogle Scholar
  20. Bourennane S, Frikel M, Bendjama A: Fast wideband source separation based on higher-order statistics. Proceedings of the IEEE Signal Processing Workshop on Higher Order Statistics (HOS '97), July 1997, Banff, Canada 354-358.View ArticleGoogle Scholar
  21. Pillai SU, Kwon BUH: Forward/backward spatial smoothing techniques for coherent signal identification. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(1):8-15. 10.1109/29.17496View ArticleMATHGoogle Scholar
  22. Maze G, Decultot D, Lecroq F, Ripoche J, Bao X-L, Uberall H: Resonance identifications of a solid axisymmetric finite length target. The Journal of the Acoustical Society of America 1994,96(2):944-950. 10.1121/1.410268View ArticleGoogle Scholar
  23. Rumerman ML: Contribution of membrane wave reradiation to scattering from finite cylindrical steel shells in water. The Journal of the Acoustical Society of America 1993,93(1):55-65. 10.1121/1.405636View ArticleGoogle Scholar
  24. Veksler NK: Resonance Acoustic Spectroscopy. Springer, New York, NY, USA; 1993.View ArticleGoogle Scholar
  25. Bao X-L: Echoes and helical surface waves on a finite elastic cylinder excited by sound pulses in water. The Journal of the Acoustical Society of America 1993,94(3):1461-1466. 10.1121/1.408148View ArticleGoogle Scholar
  26. Frikel M, Bourennane S: Fast algorithm for the wideband array processing using twosided correlation transformation. Proceedings of the 8th European Signal Processing Conference (EUSIPCO '96), September 1996, Trieste, Italy 2: 959-962.Google Scholar
  27. Reddy KM, Reddy VU: Further results in spatial smoothing. Signal Processing 1996,48(3):217-224. 10.1016/0165-1684(95)00137-9View ArticleMATHGoogle Scholar
  28. Hung H, Kaveh M: Focussing matrices for coherent signal-subspace processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 1988,36(8):1272-1281. 10.1109/29.1655View ArticleMATHGoogle Scholar
  29. Wax M, Kailath T: Detection of signals by information theoretic criteria. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(2):387-392. 10.1109/TASSP.1985.1164557MathSciNetView ArticleGoogle Scholar
  30. Stanton TK: Sound scattering by cylinders of finite length. II. Elastic cylinders. The Journal of the Acoustical Society of America 1988,83(1):64-67. 10.1121/1.396185View ArticleGoogle Scholar
  31. Fawcett JA: Scattering from a partially fluid-filled, elastic-shelled sphere. The Journal of the Acoustical Society of America 2001,109(2):508-513. 10.1121/1.1339827View ArticleGoogle Scholar
  32. Fawcett JA, Lim R: Evaluation of the integrals of target/seabed scattering using the method of complex images. The Journal of the Acoustical Society of America 2003,114(3):1406-1415. 10.1121/1.1600726View ArticleGoogle Scholar
  33. Lim R, Williams KL, Thorsos EI: Acoustic scattering by a three-dimensional elastic object near a rough surface. The Journal of the Acoustical Society of America 2000,107(3):1246-1262. 10.1121/1.428414View ArticleGoogle Scholar
  34. Lim R: Acoustic scattering by a partially buried three-dimensional elastic obstacle. The Journal of the Acoustical Society of America 1998,104(2):769-782. 10.1121/1.423352View ArticleGoogle Scholar

Copyright

© Saidi and Bourennane 2007

Advertisement