A Robust Recursive State Estimation Method for Uncertain Linear Discrete-Time Systems

This study presents a robust estimation approach for linear discrete-time systems subject to parametric uncertainties. To address model mismatch, the proposed method enhances the MHE framework, thereby improving estimation accuracy. Based on this framework, the estimator is derived by minimizing the expected estimation error. A detailed derivation is provided, along with a novel recursive formulation for the pseudo-covariance of the estimation error. The resulting estimator maintains structural similarity to the Kalman filter and supports recursive implementation. Theoretical analysis establishes convergence to a stable system, with guaranteed boundedness and asymptotic unbiasedness of the estimation error. Simulation results demonstrate that the proposed strategy maintains high effectiveness and robustness under different uncertain conditions.