General motion estimation from correlation sonar

The displacement of a sonar array can be estimated accurately using the correlation of bottom reverberation signals, at successive sweeps. This is the principle of the pulsed correlation log. In this paper, the conditions and accuracy of array horizontal translation estimation are analyzed. The case of a three-dimensional array is considered first, to show that in this case arbitrary translation and rotation can be estimated. The case of a plane array is then analyzed and it is shown that such an array allows estimation of horizontal translation. The derivation relies on modeling the space-time correlation function of bottom reverberation, which is assumed isotropic. Both directive and omnidirectional transmissions are considered. Accuracy of displacement estimates are derived, showing the influence of wavelength, grazing angle, bandwidth, number of overlapping hydrophones, and reverberation-to-noise ratio.