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This work presents an application of the Kalman filter with a recursive estimator to determine the excitation forces of linear dynamic systems. The forces were estimated from the measured dynamic responses through an inverse method. The estimator employed a least squares algorithm to compute the magnitudes and, therefore, the onset time histories of the forces. The practicability and accuracy of the proposed method were verified with laboratory tests from which the input forces of a cantilever beam were estimated from the measured dynamic responses. In the experimental study, the beam was subjected to periodic forces and random forces. The estimation results of the input forces are qualitatively and quantitatively good in all cases tested.

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