Time and angle of arrival uncertainties in echo-sounding

Estimates of the time of arrival, angle of arrival, and intensity of echoes are the primary quantities obtained with echo-sounders used for underwater remote sensing of targets in the ocean volume, near the sea surface or on the seafloor. Uncertainties in these estimates translate into uncertainties in the location of the detected targets relative to the echo-sounder, which may impact the accuracy of the end product such as a map or an algorithm for autonomous navigation of an underwater vehicle. In addition, uncertainties in these estimates depend on the target detection method used and on sonar parameters such as output signal-to-noise ratio, beamwidth, receiver bandwidth and sampling frequency, and the corresponding spatial sampling geometry. The target detection methods considered here assume that the arrival angle is aligned with the maximum response axis of the beam, which is known a priori. The time of arrival is then estimated based on (1) the echo-amplitude weighted mean time of arrival, or (2) the time of zero phase difference at the output of a split-aperture correlator. Analytical expressions are derived for the uncertainties in time (range) and angle of arrival of echoes given by the variance of the estimated mean of these quantities. These uncertainty expressions are applied to models of sounding uncertainty used in swath bathymetry and compared with such models in current use (e.g. Hammerstad, 1995; Lurton, 2003)).