AbstractA displacement estimation method for a nonlinear single-degree-of-freedom (SDOF) system under seismic excitation is proposed based on an extended Kalman filter (EKF). This method first identifies time intervals where a system experiences significant nonlinearity. For a time period when the system is in an elastic phase, available observations for EKF are acceleration, displacement from numerical integration, and residual displacement. During a time period with significant nonlinearity, acceleration and virtual displacement measurements are employed as observations. Two EKF schemes are applied in this part. In the first scheme, displacement is estimated along with time-varying stiffness using an augmented state vector. In the second scheme, a bilinear hysteresis model with optimized system parameters is employed. The results are further smoothed by extended Kalman smoother (EKS). The proposed displacement estimation method is numerically studied on a bilinear SDOF system and applied to various hysteresis models and earthquake excitations. Data obtained in shaking table experiments on a full-scale bridge pier and a 4-story building are analyzed to validate the method. The displacements are estimated with high accuracies.