In this paper, a subspace fitting method is proposed to update, in the time domain, thefinite element model of a rotating machine. The procedure is achieved by minimizing anerror norm, leading to the comparison between experimental and theoretical observabilitymatrices. Experimental observability matrix is obtained through a MOESP subspaceidentification algorithm, by projecting the output signal onto some appropriate subspaces,resulting in a cancellation of input excitations and noises. The theoretical observabilitymatrix is obtained from modal parameters of a finite element model of the structure. Theminimization procedure is carried out through a Gauss-Newton algorithm. The method isapplied to determine the foundation stiffness of an experimental rotating machine subjectto a random noise.