A system and a method for analyzing the motions of a mechanical structure. The System includes (a) accelerometers provided as standard accelerometers to measurement-points of the mechanical structure, (b) at least three accelerometers provided as reference accelerometers to measurement-points of the mechanical structure, (c) at least one shaker being attached to the mechanical structure for moving the structure periodically within a first frequency range, and at least one data processing system being configured to: (d) receiving measurements from the accelerometers at the measurement-points when periodically moving the structure within the first frequency range by the at least one shaker. To provide accurate and quick calibration the at least one data processing system is further configured to calibrate the accelerometers' positions and orientations by the following steps: (e) determining from the measurements of the at least three reference accelerometers rigid body motions, (f) determining positions and orientations of reference accelerometers from the rigid body motions, and (g) determining positions and orientations of standard accelerometers from the rigid body motions.