Robust extended Kalman filtering for non-linear systems with unknown input: a UBB model approach

This study presents an unknown-but-bounded (UBB) model approach to robust extended Kalman filtering (REKF) problem for the simultaneous input and state estimation of non-linear systems with parametric uncertainties. An augmented non-linear state-space model is suggested to estimate the unknown input concurrently with the state variables without any delay. Due to more satisfactory physical assumptions and interpretations, the initial state vector and the disturbances are considered as UBB white processes, rather than the conventional stochastic white processes. Hence, they are modelled as ellipsoidal sets, and a recursive UBB-REKF is developed. The suggested algorithm aims to guarantee an optimal upper bound for the estimation error covariance considering the parametric uncertainties and the linearisation errors. Finally, the effectiveness and remarkable estimation accuracy of the proposed UBB-REKF is illustrated in a manoeuvring target tracking problem.