The Mathematical Institute, University of Oxford, Eprints Archive

Left-right ambiguity resolution of a towed array sonar

Kaouri, K. (2000) Left-right ambiguity resolution of a towed array sonar. Masters thesis, University of Oxford.

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Abstract

In this work, a method is proposed for resolving the Left-Right Ambiguity in Passive Sonar Systems with towed arrays. This problem arises in source localization when the array is straight. In practice, the array is not straight and a statistical analysis within the Neyman-Pearson framework is developed for a monochromatic signal in the presence of random noise, assuming that the exact array shape is known. For any given array shape, an expression for the Probability of Correct Resolution (PCR) is derived as a function of two parameters; the signal to noise ratio (SNR) and an array-lateral-displacement parameter. SNR measures the strength of the signal relative to the noise and the second parameter the curvature of the array relative to the acoustic wavelength. The PCR is calculated numerically for a variety of array shapes of practical importance. The model results are found to agree with intuition; the PCR is 0.5 when the array is straight and is increasing as the signal is becoming louder and the array more curved. It is explained why the method is useful in practice and the effects of correlation between beams are discussed.

Furthermore, we look at the acoustical Sharpness Methods; these methods have originated from optical imaging, where they were used successfully to correct atmospherically degraded optical images of telescopes. The method entails that an appropriate function, called `Sharpness Function' is supposed to be maximised when the shape of the towed array, used to construct the beamformer image, is the true one. Reviewing carefully previous literature, which indicated that the method has good chances of producing a very good estimate of the array shape, we prove that the proposed Sharpness Function is in fact not maximised and we deduce that the Sharpness Method does not seem appropriate in the sonar context. Therefore, we conclude that, with the proposed Sharpness function, the Sharpness Method does not work, unlike what has been suggested in the literature. We prove however that, most crucially, Optical Imaging is the same as Beamforming. This opens avenues for further exploration of the sharpness analogy between optics and acoustics imaging.

Item Type:Thesis (Masters)
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:11
Deposited By:Eprints Administrator
Deposited On:03 Mar 2004
Last Modified:20 Jul 2009 14:12

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