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The Argo project deploys thousands of floats throughout the world's oceans. Carried only by the current, these floats take measurements such as temperature and salinity at depths of up to two kilometers. These measurements are critical for scientific tasks such as modeling climate change, estimating temperature and salinity fields, and tracking the global hydrological cycle. In the Southern Ocean, Argo floats frequently drift under ice cover which prevents tracking via GPS. Managing this missing location data is an important scientific challenge for the Argo project. To predict the floats' trajectories under ice and quantify their uncertainty, we introduce a probabilistic state-space model (SSM) called ArgoSSM. ArgoSSM infers the posterior distribution of a float's position and velocity at each time based on all available data, which includes GPS measurements, ice cover, and potential vorticity. This inference is achieved via an efficient particle filtering scheme, which is effective despite the high signal-to0noise ratio in the GPS data. Compared to existing interpolation approaches in oceanography, ArgoSSM more accurately predicts held-out GPS measurements. Moreover, because uncertainty estimates are well-calibrated in the posterior distribution, ArgoSSM enables more robust and accurate temperature, salinity, and circulation estimates.