In this work, we describe a new self-calibration algorithm in the case of 3D cone-beam geometry with sources on a plane parallel to the detector plane. This algorithm is hybrid, so it combines data consistency conditions (DCCs) and the partial knowledge on the pattern of the calibration cage. We explain how we build this algorithm with the modelling of calibration markers by Diracs and the generalization of existing DCCs for this geometry to distributions. This new method can work with truncated projections if the marker projections are not truncated. With this hybrid approach, we build an analytical self-calibration algorithm based on DCCs, robust to projection truncations. We show numerical experiments.