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Antarctic continental shelf waters are poorly sampled, particularly beneath sea ice during winter. Profiling floats could help fill this gap, but floats are unable to surface to obtain a satellite position when ice is present. We deployed Argo profiling floats in a coastal polynya with a novel mission to rest on the sea floor between profiles. "Parking" on the seabed minimized the drift of the floats and allowed year-round, full-depth measurements over multiple winters. Measurements of water depth derived from the floats were used in combination with known bathymetry to constrain the position of profiles collected under ice. Errors were quantified by withholding known positions and comparing them to estimated positions; the bathymetrically constrained algorithm outperformed linear interpolation. A similar approach could potentially be used to geolocate other under-ice oceanographic platforms that measure water depth.