A dual Kalman filter approach for state estimation via output-only acceleration measurements

•A novel dual Kalman filter is proposed for output-only state and input estimation.•Sparse pure acceleration measurements and a model of the structure are used.•The unobservability issues attributed to augmented Kalman filter are resolved.•The low frequency drift is properly tackled in an online and autonomous fashion.•The efficiency of the proposed method is verified by numerical simulations.

A dual implementation of the Kalman filter is proposed for estimating the unknown input and states of a linear state-space model by using sparse noisy acceleration measurements. The successive structure of the suggested filter prevents numerical issues attributed to un-observability and rank deficiency of the augmented formulation of the problem. Furthermore, it is shown that the proposed methodology furnishes a tool to avoid the so-called drift in the estimated input and displacements commonly encountered by existing joint input and state estimation filters. It is shown that, by fine-tuning the regulatory parameters of the proposed technique, reasonable estimates of displacements and velocities of structures can be accomplished.