  Underwater robots are subject to position drift due to the effect of ocean
currents and the lack of accurate localisation while submerged. We are
interested in exploiting such position drift to estimate the ocean current in
the surrounding area, thereby assisting navigation and planning. We present a
Gaussian process~(GP)-based expectation-maximisation~(EM) algorithm that
estimates the underlying ocean current using sparse GPS data obtained on the
surface and dead-reckoned position estimates. We first develop a specialised GP
regression scheme that exploits the incompressibility of ocean currents to
counteract the underdetermined nature of the problem. We then use the proposed
regression scheme in an EM algorithm that estimates the best-fitting ocean
current in between each GPS fix. The proposed algorithm is validated in
simulation and on a real dataset, and is shown to be capable of reconstructing
the underlying ocean current field. We expect to use this algorithm to close
the loop between planning and estimation for underwater navigation in unknown
ocean currents.
