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  • Research Article
  • Open Access

Underwater Noise Modeling and Direction-Finding Based on Heteroscedastic Time Series

EURASIP Journal on Advances in Signal Processing20062007:071528

  • Received: 8 November 2005
  • Accepted: 29 June 2006
  • Published:


We propose a new method for practical non-Gaussian and nonstationary underwater noise modeling. This model is very useful for passive sonar in shallow waters. In this application, measurement of additive noise in natural environment and exhibits shows that noise can sometimes be significantly non-Gaussian and a time-varying feature especially in the variance. Therefore, signal processing algorithms such as direction-finding that is optimized for Gaussian noise may degrade significantly in this environment. Generalized autoregressive conditional heteroscedasticity (GARCH) models are suitable for heavy tailed PDFs and time-varying variances of stochastic process. We use a more realistic GARCH-based noise model in the maximum-likelihood approach for the estimation of direction-of-arrivals (DOAs) of impinging sources onto a linear array, and demonstrate using measured noise that this approach is feasible for the additive noise and direction finding in an underwater environment.


  • Time Series
  • Shallow Water
  • Gaussian Noise
  • Quantum Information
  • Sonar

Authors’ Affiliations

Department of Electrical Engineering, Amirkabir University of Technology, P.O. Box 15914, Tehran, Iran
Department of Electrical and Computer Engineering, University of Tehran, P.O. Box 14395-515, Tehran, Iran


  1. Van Trees HL: Optimum Array Processing. John Wiley & Sons, New York, NY, USA; 2002.View ArticleGoogle Scholar
  2. Krim H, Viberg M: Two decades of array signal processing research: the parametric approach. IEEE Signal Processing Magazine 1996,13(4):67–94. 10.1109/79.526899View ArticleGoogle Scholar
  3. Brockett PL, Hinich M, Wilson GR: Nonlinear and non-Gaussian ocean noise. The Journal of the Acoustical Society of America 1987,82(4):1386–1394. 10.1121/1.395273View ArticleGoogle Scholar
  4. Middleton D: Channel modeling and threshold signal processing in underwater acoustics: an analytical overview. IEEE Journal of Oceanic Engineering 1987,12(1):4–28. 10.1109/JOE.1987.1145225MathSciNetView ArticleGoogle Scholar
  5. Wegman E, Schwartz S, Thomas J (Eds): Topics in Non-Gaussian Signal Processing. Springer, New York, NY, USA; 1989.MATHGoogle Scholar
  6. Engle RF: Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 1982,50(4):987–1007. 10.2307/1912773MathSciNetView ArticleGoogle Scholar
  7. Bullerslev T: Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 1986, 31: 307–327. 10.1016/0304-4076(86)90063-1MathSciNetView ArticleGoogle Scholar
  8. Amiri H, Amindavar H, Kirlin RL: Array signal processing using GARCH noise modeling. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 2: 105–108.Google Scholar
  9. Webster RJ: Ambient noise statistics. IEEE Transactions on Signal Processing 1993,41(6):2249–2253. 10.1109/78.218152View ArticleGoogle Scholar
  10. Zhou Y, Yip PC: DOA estimation by ARMA modelling and pole decomposition. IEE Proceedings: Radar, Sonar and Navigation 1995,142(3):115–122. 10.1049/ip-rsn:19951876Google Scholar
  11. Nielson RO: Sonar Signal Processing. Artech House, Boston, Mass, USA; 1990.Google Scholar
  12. Cheung Y-M, Xu L: Dual multivariate auto-regressive modeling in state space for temporal signal separation. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics 2003,33(3):386–398.View ArticleGoogle Scholar
  13. Li WK, Ling S, Wong H: Estimation for partially nonstationary multivariate autoregressive models with conditional heteroscedasticity. Biometrika 2001,88(4):1135–1152. 10.1093/biomet/88.4.1135MathSciNetView ArticleGoogle Scholar
  14. Hamilton JD: Time Series Analysis. Princeton University Press, Princeton, NJ, USA; 1994.MATHGoogle Scholar
  15. Box GEP, Jenkins GM, Reinsel GC: Time Series Analysis: Forecasting and Control. 3rd edition. Prentice Hall, Englewood Clifs, NJ, USA; 1994.MATHGoogle Scholar
  16. Catipovic JA: Performance limitations in underwater acoustic telemetry. IEEE Journal of Oceanic Engineering 1990,15(3):205–216. 10.1109/48.107149View ArticleGoogle Scholar
  17. Stojanovic M: Recent advances in high-speed underwater acoustic communications. IEEE Journal of Oceanic Engineering 1996,21(2):125–136. 10.1109/48.486787View ArticleGoogle Scholar
  18. El Gamal H, Geraniotis E: Iterative channel estimation and decoding for convolutionally coded anti-jam FH signals. IEEE Transactions on Communications 2002,50(2):321–331. 10.1109/26.983327View ArticleGoogle Scholar
  19. Haykin S, Barker R, Currie BW: Uncovering nonlinear dynamics—the case study of sea clutter. Proceedings of the IEEE 2002,90(5):860–881. 10.1109/JPROC.2002.1015011View ArticleGoogle Scholar
  20. Zabin SM, Poor HV: Parameter estimation for Middleton class A interference processes. IEEE Transactions on Communications 1989,37(10):1042–1051. 10.1109/26.41159View ArticleGoogle Scholar
  21. Delaney PA: Signal detection in multivariate class-A interference. IEEE Transactions on Communications 1995,43(2–4):365–373.View ArticleGoogle Scholar
  22. Pesavento M, Gershman AB: Maximum-likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise. IEEE Transactions on Signal Processing 2001,49(7):1310–1324. 10.1109/78.928686View ArticleGoogle Scholar
  23. Chiu K-C, Xu L: Arbitrage pricing theory-based Gaussian temporal factor analysis for adaptive portfolio management. Decision Support Systems 2004,37(4):485–500. 10.1016/S0167-9236(03)00082-4View ArticleGoogle Scholar
  24. Stoica P, Nehorai A: Performance study of conditional and unconditional direction-of-arrival estimation. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990,38(10):1783–1795. 10.1109/29.60109View ArticleGoogle Scholar
  25. Rajagopal R, Rao PR: Generalised algorithm for DOA estimation in a passive sonar. IEE Proceedings. F, Radar and Signal Processing 1993,140(1):12–20. 10.1049/ip-f-2.1993.0002View ArticleGoogle Scholar


© Amiri et al. 2007