During their lifetime, structures are usually subjected to some mechanical shocks that generate high levels of vibration that can damage the structure itself as well as the embedded devices. However, the characteristics of these shocks (location, time history, maximum intensity,. . .) are often unknown due to the inaccessibility of the excitation region for direct force measurements or the inability to instrument the system. Therefore, inverse methods have been developed to quantify these complex excitations. Recently, a Bayesian formulation of the input-state estimation problem for linear systems has been proposed by the authors, which unifies most of the state-of-the-art