In ice flow modelling, the use of control methods to assimilate the dynamic and geometric state of an ice body has become common practice. These methods have primarily focussed on inverting for one of the two least known properties in glaciology, namely the basal friction coefficient or the ice viscosity parameter. Here, we present an approach to infer both properties simultaneously for the whole of the Antarctic ice sheet. After the assimilation, the root-mean-square deviation between modelled and observed surface velocities attains 8.7 m a−1 for the entire domain, with a slightly higher value of 14.0 m a−1 for the ice shelves. An exception in terms of the velocity mismatch is the Thwaites Glacier Ice Shelf, where the RMS value is almost 70 m a−1. The reason is that the underlying Bedmap2 geometry ignores the presence of an ice rise, which exerts major control on the dynamics of the eastern part of the ice shelf. On these grounds, we suggest an approach to account for pinning points not included in Bedmap2 by locally allowing an optimisation of basal friction during the inversion. In this way, the velocity mismatch on the ice shelf of Thwaites Glacier is more than halved. A characteristic velocity mismatch pattern emerges for unaccounted pinning points close to the marine shelf front. This pattern is exploited to manually identify seven uncharted features around Antarctica that exert significant resistance to the shelf flow. Potential pinning points are detected on Fimbul, West, Shackleton, Nickerson and Venable ice shelves. As pinning points can provide substantial resistance to shelf flow, with considerable consequences if they became ungrounded in the future, the model community is in need of detailed bathymetry there. Our data assimilation points to some of these dynamically important features not present in Bedmap2 and implicitly quantifies their relevance.