A hierarchical state bounding estimation method is presented for a nonlinear dynamic system where different sensors offer several potentially faulty measurements of the same state vector, each of which is subject to unknown but bounded disturbances and is equipped with a local processor. The proposed algorithm works at two levels : at each sampling time, each local processor computes the state estimate and its outer-bounding ellipsoid according to the local measurements given by the corresponding sensor. These ellipsoids are transmitted simultaneously from all local processors to the fusion center which synthesizes them to compute the global state estimate bounding ellipsoid, rejecting, if necessary, the faulty measurements through a judicious choice of some weighting parameters. Then it feeds these data back to all the local processors. This feedback allows the local processors to adjust their results by taking into account the measurements of all the other sensors.