Spectral estimate in ADCP

An acoustic Doppler current profiler (ADCP) measures the backscattering wave in a moving medium, which is a non-stationary stochastic process. The authors´ research shows that, due to the contribution of motion, there exists a Doppler frequency shift, widening, asymmetry and splitting of spectral peaks in the spectra of the echo. In engineering, the backscattering wave is often assumed to be time-stationary and space-homogeneous, and this is the case of the narrow-band ADCP (NBADCP). The echo´s covariance function of hundreds of transmissions in the same layer is calculated to estimate the Doppler frequency shift. This method is called the independent-pulse-pair covariance technique (IPPC), in which it considers that there exist merely the Doppler frequency shift and the widening in the echo´s spectra. When the flow is complicated or the vessel moves at a high speed, the above hypotheses no longer hold, but the authors still consider that there exist merely the Doppler frequency shift and the widening in the echo´s spectra. Under these conditions, it is required to calculate the Doppler frequency shift in the time of one transmission, and this method is called the correlated-pulse-pair covariance technique (CPPC), which the broadband ADCP (BBADCP) adopts. When the movement of the medium is more complicated, the contribution of the movement to the echo´s spectra exists in four aspects, recursive least square (RLS) adaptive spectral estimate technique is required, by which the authors estimate the entire spectra of the echoes of a few transmissions, not just the Doppler frequency shift. Both the signal and the noise are supposed to be independent colored Guassian processes, then the standard deviation of the Doppler frequency shift estimate by IPPC increases monotonically with Δfτ, where Δf and τ are the signal´s bandwidth and time delay respectively. No minimum exists. This contradicts the conclusion made by Miller, K.S. and Rochwarger, M.M. in (1992). Under the same hypotheses, the authors also obtain the standard deviation formula for the Doppler frequency shift estimate by CPPC. It is closely related to S/N, while in the paper of Brumley, B. (1990), it has nothing to do with S/N. All the above conclusions are consistent with experimental results