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This paper proposes a method that estimates the parameters of a seismically excited building. The acceleration measurements of the ground and of each floor are used for identification purposes. It is assumed that these measurements have offsets and noise. The proposed scheme is based on the Least Squares algorithm with forgetting factor and a parametrization of the structure using high-pass filters and integrals over finite time intervals. These filters pass the typical frequency bandwidth of structures undergoing earthquake excitation, eliminate the offsets and attenuate the measurement noise. To confirm the effectiveness of the proposed method a simulation of a two-story building is presented. The results show that the estimated parameters converge to the true parameters in a short time.