  Outliers can contaminate the measurement process of many nonlinear systems,
which can be caused by sensor errors, model uncertainties, change in ambient
environment, data loss or malicious cyber attacks. When the extended Kalman
filter (EKF) is applied to such systems for state estimation, the outliers can
seriously reduce the estimation accuracy. This paper proposes an innovation
saturation mechanism to modify the EKF toward building robustness against
outliers. This mechanism applies a saturation function to the innovation
process that the EKF leverages to correct the state estimation. As such, when
an outlier occurs, the distorting innovation is saturated and thus prevented
from damaging the state estimation. The mechanism features an adaptive
adjustment of the saturation bound. The design leads to the development robust
EKF approaches for continuous- and discrete-time systems. They are proven to be
capable of generating bounded-error estimation in the presence of bounded
outlier disturbances. An application study about mobile robot localization is
presented, with the numerical simulation showing the efficacy of the proposed
design. Compared to existing methods, the proposed approaches can effectively
reject outliers of various magnitudes, types and durations, at significant
computational efficiency and without requiring measurement redundancy.
