Health monitoring is critical for the maintenance and risk management of reinforced concrete (RC) structures. In this paper, a robust adaptive Kalman filter is proposed for an interstory drift estimation problem to show the health condition of RC structures in the case that the statistics or internal dynamics describing the signals and measurements are not known precisely. More precisely, we build an adaptive current Jerk model (ACJM) where the model parameters are updated in each time step to presuppose the statistics characterization of the RC dynamic, while the unknown measurement noise covariance is adapted based on a fixed-lag innovation with respect to measurements. Moreover, a robust adaptive Kalman filter is designed for the modeling mismatch in each time increment by solving a minimax game: one “hostile” player tries to select a worst model far from the proposed ACJM with an exponential decay tolerance, while an optimum filter is designed by minimizing the estimation error according to this worst model. Finally, some simulation and experimental results show the effectiveness of the proposed algorithm.