Patient-specific blood flow simulations are intensively fostered as a way of providing predictive mech- anistic biomarkers for thoracic aneurysms treatment from medical imaging data. Such biomarkers are generally sensitive to the underlying flow model (pure fluid model, fluid-structure interaction, bound- ary conditions, etc.). In the past 20 years, 4D-flow MRI has become a promising image data modality for blood flow model personalization, since it is non-invasive and provides a time-resolved three-dimensional encoding of the blood velocity field. This work is devoted to the state estimation of a fluid-structure interaction (FSI) model of aortic blood flow using 4D-flow MRI data. We propose a state estimation approach which avoids lumped pa- rameter models of boundary conditions through a unique continuation approach coupled to a Luenberger observer. The capabilities of the proposed approach will be assessed in a numerical study involving synthetic and clinical data.