Summary Real‐time input/state estimation by means of the observed response has drawn considerable attention in the structural, dynamic, and control systems. In this line, a minimum‐variance unbiased (MVU) estimator has been utilized to develop three‐step filters that sometimes experience instability and divergence, especially for the input estimation in structural dynamics. To solve this challenge, this study is aimed at to estimate both the input and state simultaneously for a linear system. A Bayesian framework is developed, in which the prior information of the unknown input in terms of the a priori probability density function is incorporated in estimation process. Formulation of the estimation is presented in the state‐space representation in presence and absence of the direct feedthrough. Three‐step filters including input estimation, state prediction, and the updating are developed for the system having model uncertainty and noisy observed data. In addition to the estimation, another novel feature of this study is to predict the steady states of the filters in the closed‐form representation. We also establish sufficient conditions for convergence and stability of the proposed filters. At the end, the efficiency, robustness, and advantage of the approach is verified through numerical studies for different systems. Results for the input and state estimation are compared with real values according to the MVU estimator for the observed noisy data sets.

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