State Estimation for Stochastic Time Varying Systems with Disturbance Rejection

Structural health monitoring with non-linear sensor measurements robust to unknown non-stationary input forcing

“…With an intent to generalize earlier works of IPKF [42] for non-linear systems with an added robustness against unknown external disturbances, PF has been coupled with EnKF. While the authors' previous works [38] approached this input robustness through an explicit estimation of inputs online, the present article rejects the effect of input variability through output injection for a modified state transition equation following [43].…”

“…Following the ideas of [43], the proposed approach ensures robustness against the unknown input S g k by rejecting its effect from the system dynamics by means of an output injection, as demonstrated in the following.…”

“…Recently, for LTV systems with known system matrices, instead of estimating the input time histories [12,29,38], or its statistics [34], [43] developed a robust and stable linear state estimator unaffected by unknown inputs. This unknown input rejection approach is used in Kalman filter environment with linear measurements.…”

“…Rejection of unknown inputs is usually addressed by unknown input observers, with a rich literature on this topic (see [43] and references therein). While most unknown input observers are limited to linear systems, they do not consider parameter estimation in addition to state estimation.…”

“…It should be noted here, that stability of state estimation algorithms with unknown input rejection is studied in the literature of unknown input observers for LTI systems and for some affine parameter varying systems. To our knowledge, the only stability analysis of such algorithms for general LTV systems has been proposed in [43]. The generalization of this analysis to EnKF with output injection, applied in this paper to address non-linearities, is certainly an important and difficult task clearly outside of the scope of this paper.…”