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.
We consider the potential for making current measurements from gliders, and present data from a deployment in early 2007 of 1000 m Slocum electric gliders in the North West Mediterranean Sea. Three types of current measurement are considered. First, by comparing the difference between successive GPS positions, obtained when the glider surfaces, and dead-reckoned displacements when the glider is submerged, it is possible to estimate depth averaged horizontal currents and also surface drift. Second, our gliders were equipped with Conductivity Temperature Depth sensors, which provided data used to calculate geostrophic horizontal velocity. Third, from the measured rate of change of pressure it is possible to quantify the vertical water velocity as the difference between the measurement and the expected vertical motion. The latter two both require a model of the glider motion, which we outline. Horizontal currents of the order of 30 cm s were measured in the westward flowing Northern Current off the south coast of France, with a width and transport comparable with previous observations using different technologies. The accuracy of the depth-averaged currents in magnitude and direction was limited by the accuracy of the measured heading of the glider. Measurements of vertical velocity were made during a time of active convection when the magnitude of the vertical motion was up to 10 cm s. We estimate that the accuracy of the calculated velocity was of the order of 1 cm s.