Automatic tuning of a velocity estimator for pulse-to-pulse coherent Doppler sonar

Abstract

Pulse-to-pulse coherent Doppler sonar is capable of measuring simultaneous profiles of veloctiy and sediment concentration in turbulent suspensions. However, the presence of measurement noise introduces biases when turbulence statistics are calculated from the fluctuating component of velocity. In order to further develop coherent Doppler sonar as a tool for turbulence measurement, a velocity estimator based on Maximum A Posteriori (MAP) estimation has been developed. The estimator optimally combines measurements from multiple acoustic carrier frequencies and multiple transducers. Data fusion is achieved using a probabilistic approach, whereby measurements are combined numerically to derive a velocity likelihood function. The only parameter which must be chosen by the user is a smoothing factor that describes the diffusion of velocity (in a probabilistic sense) from sample to sample in time. A method is presented for automatically determining the smoothing parameter from examination of the spectrum of a representative segment of the measurement time series. Results are presented from a laboratory turbulent jet in which velocity was measured simultaneously with multi-frequency coherent Doppler sonar and particle image velocimetry (PIV). Time series and turbulence spectra from PIV are compared to those obtained with conventional Doppler signal processing and MAP velocity estimation. It is shown that automatic tuning of the estimator results in a velocity time series where measurement noise is suppressed while high frequency turbulent fluctuations are retained.