Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-12-03T19:06:49.071Z Has data issue: false hasContentIssue false
  • English
  • Français

Determining the probability of correct resolution of the left–right ambiguity in towed array sonar

Published online by Cambridge University Press:  05 December 2016

K. KAOURI  and
D. J. ALLWRIGHT
K. KAOURI
Affiliation:
Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 30 Archbishop Kyprianou Str., Limassol 3036, Cyprus email: [email protected]
D. J. ALLWRIGHT
Affiliation:
Smith Institute for Industrial Mathematics and System Engineering, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road, Oxford, OX2 6GG, UK email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

When a towed sonar array is straight, it has the difficulty that it cannot distinguish a contact on the left from one at the same angle on the right. When the array is not straight and its shape known, we calculate the probability that the left–right ambiguity is resolved correctly, using the Neyman–Pearson hypothesis testing framework, assuming a delay-sum beamformer, a single-frequency contact, and Gaussian noise. We also initially consider the noise field to be uncorrelated and show that the evaluation of the probability of correct resolution reduces to evaluating a one-dimensional integral. We find, as expected, that the probability increases, as the signal-to-noise ratio and the lateral deviation of the array from straight increase. For demonstration purposes, we also evaluate the probability of correct resolution for two representative shapes the array might assume in practice. Finally, we consider a more realistic, correlated noise field and we show that the initial assumption of an uncorrelated noise field provides a good approximation when the lateral deviation of the array is sufficiently large.

Keywords

62F03 (Hypothesis testing)62P30 (applications in engineering and mathematics)94B70 (error probability)74J05 (linear waves)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 5 , October 2017 , pp. 716 - 735
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Abramowitz, M. & Stegun, I. A. (1972) Handbook of Mathematical Functions. Wiley, New York.Google Scholar
[2] Bin, Z. (2010) Effects of sonar shape distortion on time delay estimation method for left/right discrimination. In: 2nd International Conference on Multimedia and Information Technology (MMIT), Vol. 2, IEEE, pp. 78–81.CrossRefGoogle Scholar
[3] Bousnina, I., Stéphenne, A., Affes, S. & Samet, A. (2011) A new low-complexity angular spread estimator in the presence of line-of-sight with angular distribution selection. EURASIP J. Adv. Signal Process. 2011 (1), 1–16.CrossRefGoogle Scholar
[4] Danforth, C. W. (2000) Acoustic applications of phased array technology. Acoust. Bull. 25 (6), 9–15.Google Scholar
[5] Dang, V., Lee, Y. & Lee, S. (2011) Characterizing a moving source in wireless sensor networks from the view of maximum likelihood. In: 2nd International Conference on Next Generation Information Technology (ICNIT), IEEE, pp. 18–22.Google Scholar
[6] Dang, V., Phan, T., Le, B., Lee, Y. & Lee, S. (2011) Clustering based multi-object positioning system. In: International Conference on Advanced Technologies for Communications (ATC), IEEE, pp. 40–44.Google Scholar
[7] Dang, V. (2012) Multiple Object Localization based on Acoustic Signals in Wireless Sensor Networks. PhD thesis, Kyung Hee University, Korea.Google Scholar
[8] Goodman, N. R. (1963) Statistical analysis based on a certain multivariate complex Gaussian distribution (An introduction). Ann. Math. Stat. 34 (1), 152–177.CrossRefGoogle Scholar
[9] Gorbunov, Y. (2003) Pattern Recognition in the Inner Tracking System of HERA-B and Measurement of the V0 Production Cross Section in pN Collisions. PhD thesis, Siegen University, Germany, 2003.Google Scholar
[10] Haralambus, G. & Bardacci, A. (2006) Unambiguous Triplet Array Beamforming and Calibration Algorithms to Facilitate an Environmentally Adaptive Active Sonar Concept. Technical report, NATO Undersea Research Centre, Italy.CrossRefGoogle Scholar
[11] Hodges, R. P. (2011) Underwater Acoustics: Analysis, Design and Performance of Sonar, John Wiley and Sons, New York, USA.Google Scholar
[12] Kaouri, K. (2000) Left-Right Ambiguity Resolution in Towed Array Sonar. Master's thesis, University of Oxford, UK.Google Scholar
[13] Odom, J. L. & Krolik, J. (2013) Heading and hydrophone data fusion for towed array shape estimation. In: Proceedings of Meetings on Acoustics, Vol. 19, Acoustical Society of America, p. 055081.CrossRefGoogle Scholar
[14] Rice, A. C. (1995) Mathematical Statistics and Data Analysis, Duxbury Press, California, USA.Google Scholar
[15] Stiles, Z. H. (2013) Dynamic Towed Array Models and State Estimation for Underwater Target Tracking, PhD thesis, Naval Postgraduate School, Monterey, CA USA.Google Scholar
[16] Urick, R. J. (1975) Principles of Underwater Sound, McGraw-Hill, New York, USA.Google Scholar
[17] Van Trees, H. L. (1968) Detection, Estimation and Modulation Theory-Part I, John Wiley and Sons, New York.Google Scholar