Surface-fitting for improving the resolution of peak estimation on a sparsely sampled two-dimensional surface with high levels of variance, for an acoustic velocity log

Boltryk, Peter J., Hill, Martyn, Keary, Alison C. and White, Paul R. (2004) Surface-fitting for improving the resolution of peak estimation on a sparsely sampled two-dimensional surface with high levels of variance, for an acoustic velocity log. Measurement Science and Technology, 15 (3), 581-591. (doi:10.1088/0957-0233/15/3/010).

Abstract

A correlation velocity log (CVL) is an acoustic navigation aid that estimates the velocity of a maritime vehicle using a transmitter and a receiving array. The CVL discussed here operates by calculating the correlation coefficient between the echoes from a pair of consecutive acoustic pulses transmitted towards the seafloor, across all combinations of receiver pairings in the array. A correlation surface is constructed by plotting the correlation coefficients versus the spatial separation vector of all the receiver pairings. The coordinates of the peak of this surface provide an estimate of the velocity vector of the vessel. However, the correlation coefficient surface exhibits high variance within a modest distance from the peak position, and individual datasets tend to be asymmetric about the peak position. Since each dataset consists of a sparsely sampled set of discrete measurements, the variance makes the task of peak estimation very challenging. This paper outlines the operating principles of CVLs and describes peak-finding techniques that are used to improve the accuracy and precision of the instrument. Three peak estimation techniques are considered, namely the highest point, and fitting of an axisymmetric quadratic model using either least squares or a nonlinear implementation of maximum likelihood estimation. It is shown that the maximum likelihood approach offers some advantages when the peak is controlled to lie near the centre of the receiver array, but the advantages are small compared to the additional computational load required.

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Contributors

Author: Martyn Hill

Author: Paul R. White

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