  Estimating ocean flow fields in 3D is a critical step in enabling the
reliable operation of underwater gliders and other small, low-powered
autonomous marine vehicles. Existing methods produce depth-averaged 2D layers
arranged at discrete vertical intervals, but this type of estimation can lead
to severe navigation errors. Based on the observation that real-world ocean
currents exhibit relatively low velocity vertical components, we propose an
accurate 3D estimator that extends our previous work in estimating 2D flow
fields as a linear combination of basis flows. The proposed algorithm uses data
from ensemble forecasting to build a set of 3D basis flows, and then
iteratively updates basis coefficients using point measurements of underwater
currents. We report results from experiments using actual ensemble forecasts
and synthetic measurements to compare the performance of our method to the
direct 3D extension of the previous work. These results show that our method
produces estimates with dramatically lower error metrics, with and without
measurement noise.
