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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: katerina.kaouri@cut.ac.cy
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: david.allwright@smithinst.co.uk
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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 

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