Time-Difference-of-Arrival Estimation Based on Cross Recurrence Plots, with Application to Underwater Acoustic Signals

  • Olivier Le Bot
  • Cédric Gervaise
  • Jérôme I. Mars
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 180)


The estimation of the time difference of arrival (TDOA) consists of the determination of the travel-time of a wavefront between two spatially separated receivers, and it is the first step of processing systems dedicated to the identification, localization and tracking of radiating sources. This article presents a TDOA estimator based on cross recurrence plots and on recurrence quantification analysis. Six recurrence quantification analyses measures are considered for this purpose, including two new ones that we propose in this article. Simulated signals are used to study the influence of the parameters of the cross recurrence plot, such as the embedding dimension, the similarity function, and the recurrence threshold, on the reliability and effectiveness of the estimator. Finally, the proposed method is validated on real underwater acoustic data, for which the cross recurrence plot estimates correctly 77.6 % of the TDOAs, whereas the classical cross-correlation estimates correctly only 70.2 % of the TDOAs.


Correct Estimate Recurrence Pattern Simulated Signal Recurrence Plot Recurrence Quantification Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank the DGA for supporting the postdoctoral scholarship of O. Le Bot, the Water Agency of Rhone-Mediterranean-Corsica for supporting the project SEAcoustic during which the acoustic data were recorded, the research team STARESO based in Calvi, and Julie Lossent for technical support during the recording of the data in the Bay of Calvi (France).


  1. 1.
    B.D. Van Veen, K.M. Buckley, Beamforming: a versatile approach to spatial filtering. IEEE ASSP Mag. 5(2), 4–24 (1988)ADSCrossRefGoogle Scholar
  2. 2.
    R.O. Schmidt, A signal subspace approach to multiple emitter location and spectral estimation, Ph.D. Dissertation, Stanford University, Stanford, CA (1981)Google Scholar
  3. 3.
    R. Roy, T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984–995 (1989)CrossRefMATHGoogle Scholar
  4. 4.
    K.T. Wong, M.D. Zoltowski, Uni-vector-sensor ESPRIT for multisource azimuth, elevation, and polarization estimation. IEEE Trans. Antennas Propag. 45(10), 1467–1474 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    P.R. White, T.G. Leighton, D.C. Finfer, C. Powles, O.N. Baumann, Localisation of sperm whales using bottom-mounted sensors. Appl. Acoust. 67(11–12), 1074–90 (2006)Google Scholar
  6. 6.
    P. Giraudet, H. Glotin, Real-time 3D tracking of whales by echo-robust precise TDOA estimates with a widely-spaced hydrophone array. Appl. Acoust. 67(11–12), 1106–1117 (2006)CrossRefGoogle Scholar
  7. 7.
    Y. Simard, N. Roy, Detection and localization of blue and fin whales from large-aperture autonomous hydrophone arrays: a case study from the St. Lawrence estuary. Can. Acoust. 36(1), 104–110 (2008)Google Scholar
  8. 8.
    L. Houégnigan, S. Zaugg, M. van der Schaar, M. André, Space-time and hybrid algorithms for the passive acoustic localisation of sperm whales and vessels. Appl. Acoust. 71(11), 1000–1010 (2010)CrossRefGoogle Scholar
  9. 9.
    C. Knapp, G.G. Carter, The generalized correlation method for estimation of time delay. IEEE Trans. Acoust. Speech Signal Process. 24(4), 320–327 (1976)CrossRefGoogle Scholar
  10. 10.
    J. Chen, J. Benesty, Y. Huang, Time delay estimation in room acoustic environments: an overview. EURASIP J. Appl. Signal Process. 1–19 (2006)Google Scholar
  11. 11.
    W.C. Knight, R.G. Pridham, S.M. Kay, Digital signal processing for sonar. Proc. IEEE 69(11), 1451–1506 (1981)Google Scholar
  12. 12.
    G. Le Touzé, B. Nicolas, J.I. Mars, P. Roux, B. Oudompheng, Double-Capon and double-MUSICAL for arrival separation and observable estimation in an acoustic waveguide. EURASIP J. Adv. Signal Process. 2012(1), 1–13 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    M. Alam, J.H. McClellan, W.R. Scott Jr., Spectrum analysis of seismic surface waves and its applications in seismic landmine detection. J. Acoust. Soc. Am. 121(3), 1499–1509 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    H. Krim, M. Viberg, Two decades of array signal processing research: the parametric approach. IEEE Signal Process. Mag. 13(4), 67–94 (1996)ADSCrossRefGoogle Scholar
  15. 15.
    J.P. Zbilut, A. Giuliani, C.L. Webber, Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification. Phys. Lett. A 246(1–2), 122–128 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    N. Marwan, M. Thiel, N.K. Nowaczyk, Cross recurrence plot based synchronization of time series. Nonlinear Process. Geophys. 9(3–4), 325–331 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    N. Marwan, J. Kurths, Nonlinear analysis of bivariate data with cross recurrence plots. Phys. Lett. A 302(5–6), 299–307 (2002)ADSMathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5), 237–329 (2007)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    N. Marwan, M.H. Trauth, M. Vuille, J. Kurths, Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods. Clim. Dyn. 21(3–4), 317–326 (2003)Google Scholar
  20. 20.
    J.P. Eckmann, S.O. Kamphorst, D. Ruelle, A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples. Europhys. Lett. 4(91), 973–977 (1987)ADSCrossRefGoogle Scholar
  21. 21.
    N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Geometry from a time series. Phys. Rev. Lett. 45(9), 712–716 (1980)ADSCrossRefGoogle Scholar
  22. 22.
    F. Taken, Detecting Strange Attractors in Turbulence. Dynamical Systems and Turbulence, Lecture Notes in Mathematics, vol. 898, pp. 366–381 (1981)Google Scholar
  23. 23.
    O. Le Bot, C. Gervaise, J.I. Mars, Similarity matrix analysis and divergence measures for statistical detection of unknown deterministic signals hidden in additive noise. Phys. Lett. A 379(40–41), 2597–2609 (2015)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    F.M. Birleanu, C. Ioana, C. Gervaise, A. Serbanescu, J. Chanussot, Jocelyn: Caractérisation des signaux transitoires par l’analyse des récurrences de phase. XXIIIème colloque GRETSI (2011)Google Scholar
  25. 25.
    O. Le Bot: Détection, localisation, caractérisation de transitoires acoustiques sous-marins. Thése de l’Université de Grenoble (2014)Google Scholar
  26. 26.
    J.P. Zbilut, C.L. Webber, Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171(3), 199–203 (1992)ADSCrossRefGoogle Scholar
  27. 27.
    C.L. Webber, J.P. Zbilut, Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76(2), 965–973 (1994)Google Scholar
  28. 28.
    N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. Phys. Rev. E 66(2), 026702 (2002)ADSCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Olivier Le Bot
    • 1
    • 2
  • Cédric Gervaise
    • 3
  • Jérôme I. Mars
    • 1
    • 2
  1. 1.GIPSA-LabUniv. Grenoble AlpesGrenobleFrance
  2. 2.GIPSA-LabCNRSGrenobleFrance
  3. 3.Chaire Chorus, Foundation of Grenoble INPGrenoble Cedex 1France

Personalised recommendations