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.