Maximum A posteriori velocity estimation for multi-frequency coherent doppler sonar

Abstract

Pulse-to-pulse coherent Doppler sonar is a promising tool for measuring near-bed turbulence and sediment transport in energetic environments such as the bottom boundary layer. However, turbulence measurements are limited by measurement noise caused by pulse-to-pulse backscatter decorrelation, and by the requirement to resolve velocity ambiguity in the presence of measurement noise. Existing methods address these limitations separately. This thesis presents an algorithm for velocity estimation that optimally fuses multi-frequency and multi-transducer measurements to simultaneously suppress noise and resolve velocity ambiguity. Data fusion is achieved using a probabilistic approach, whereby measurements are combined numerically to derive a velocity likelihood function evaluated on a discrete grid. Maximum A Posteriori (MAP) estimation is used to produce a velocity time series in which measurement noise is suppressed while high frequency turbulent fluctuations are retained. The algorithm is validated with numerical simulations of a multi-frequency coherent Doppler sonar. Results are presented from a turbulent round jet and a towing tank grid turbulence experiment where both velocity ambiguity and backscatter decorrelation were present. Time series and spectra from MAP velocity estimation are compared to those obtained with conventional Doppler signal processing. In addition to robustly resolving velocity ambiguity, the MAP velocity estimator is shown to lower the noise floor in measured turbulence spectra.