This paper proposes online input, state, and response estimation based on Augmented Kalman filter for systems without direct feedthrough, such as earthquake-excited building structures with absolute floor acceleration measurements. Measurement noise, modelling error, and incomplete absolute acceleration measurement are considered. The system model in this case lacks direct feedthrough, resulting in weak observability of system input, for which a small uncertainty in the model and measurement data would lead to a drastic change in the estimation. The augmented state Kalman filter for system without direct feedthrough is proposed for earthquake-excited building structures, in which the input with known variance is augmented with states in order to estimate them together. Compared with unbiased minimum-variance input and state estimation methods that make no assumption of input, the proposed online approach is able to perform robust estimation of states, input, and responses at unmeasured locations successfully using only a limited number of absolute acceleration measurements.
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