An optimal filtering and detection of echoes in laser-based aerial bathymetric surveying

A filter matched to the expected shape of the ocean bottom return is derived. It 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 suboptimal 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.