A minimum variance unbiased estimator for ocean surface currents based on multifrequency microwave radar observations

This paper presents a minimum variance unbiased (MVU) estimator for estimating an ocean surface current using the multifrequency microwave radar technique. In this technique the current information is obtained by finding the difference between the measured phase velocities of some specific surface gravity waves and the phase velocities calculated from the dispersion relation for still water. By defining the problem as a linear estimation problem, we develop an unbiased estimator for the current component along the radar look direction, which has a variance that is inversely proportional to the sum of the squared wavenumbers of the gravity waves used in the measurements. We also study the performance of an MVU vector estimator based on radar observations along two directions. Our analysis shows that the confidence region of this estimator has the shape of an elongated ellipse with semi-axes and orientation which are dependent on the angle between the observation directions, but independent on the true current vector. Furthermore, the theoretical models are thoroughly tested using both simulated and real radar data, and these tests show very good agreement with the model predictions.