Robust Extended Kalman Filtering for Systems with Measurement Outliers
For practitioners using EKF in nonlinear systems prone to measurement outliers (e.g., sensor errors, cyber attacks), this work provides a computationally efficient method to improve estimation accuracy without requiring measurement redundancy.
This paper proposes a robust extended Kalman filter (EKF) with an innovation saturation mechanism to handle measurement outliers, achieving bounded-error estimation and effectively rejecting outliers of various magnitudes, types, and durations with high computational efficiency.
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.