An Input-Rejection Filter for State Estimation Using Output-Only Measurements
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This work presents a recursive state estimation framework for linear dynamical systems subjected to unknown inputs in the absence of direct feedthrough. The proposed approach is formulated within a minimum-variance unbiased estimation setting and is designed to suppress the influence of unknown inputs during state estimation, rather than explicitly estimating them. By analytically eliminating the unknown input from the state-space equations, closed-form expressions are derived for both the prediction and correction stages, resulting in an efficient and computationally lightweight filtering scheme. Unlike existing methods that rely on joint state–input estimation or constrained optimization of the filter gain, the proposed framework avoids explicit input reconstruction during filtering and does not impose additional constraints on the estimator structure. Theoretical properties of the method are rigorously established, including unbiasedness of the state estimates and explicit propagation of the associated error covariance. To improve numerical robustness in ill-conditioned scenarios, the filter gain is computed using a regularized formulation based on singular value decomposition. Although the primary objective is accurate state estimation under unknown input conditions, an optional post-processing strategy for input reconstruction is also outlined. Extensive numerical simulations and parametric studies demonstrate the robustness, accuracy, and computational efficiency of the proposed approach when compared with representative existing techniques.
