On Optimal Filtering and Detection of Echoes in Laser-Based Aerial Bathymetric Surveying

There has been a continuous interest in measuring the ocean´s water depth using an airborne laser bathymetric sensor which emits pulses of infra-red and blue-green light towards the ocean surface. The echo-pulses from the surface and the sea bottom are used in order to calculate the depth of the ocean. We are interested in assessing the merits of using matched filtering for pulse detection and depth estimation algorithms. In this paper, we derive a filter matched to the expected shape of the ocean bottom return, which maximizes the signal-to-noise ratio for detection in additive white noise. The shape of the ocean bottom echo-pulses is based on a two dimensional analytical model of the light transmission characteristics of the water medium, where the effects of light propagation are represented geometrically by a cone of propagation. The performance of the matched filter is evaluated in terms of the Receiver Operating Characteristics and is compared with a sub-optimal filter which neglects the attenuation and scattering effects in the water medium. This comparison gives a figure of merit as to the improvement one can achieve using the matched filter, as a function of the ocean bottom´s depth.