This research investigates simultaneous input-state estimation for stochastic linear systems in the presence of unknown input or disturbance. When prior knowledge of the unknown input is not available, an input-state estimator with a white Gaussian input model is proposed. Furthermore, delayed measurements are utilized to improve estimator performance. When some prior knowledge of the unknown input is available (such as maximum magnitude, statistical properties or frequency bandwidth), an input-state estimator with an exogenous input model is proposed to utilize such prior information. A unifying minimum-mean-square-error (MMSE) framework is presented for a comprehensive characterization and direct comparison among the proposed estimators and the conventional approaches. These include the augmented Kalman filter with a Gaussian random walk model and the weighted least squares approach. The proposed recursive estimators can not only estimate inputs with fixed locations, but also estimate moving inputs with time-varying locations. The performance of the estimators is validated and compared in both structural dynamics simulation and field tests. Besides numerical examples, the first field validation is performed on a full-scale concrete frame under hydraulic shaker excitation, where the shaker force input for the full-scale frame is estimated using measured structural acceleration responses. The second field validation is performed on an in-service highway bridge under traffic excitation, where the moving vehicle loads are estimated using a set of heterogeneous sensor measurements obtained from a wireless sensing system instrumented on the bridge.
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