Robust Extended Kalman Filtering for Systems With Measurement Outliers

Outliers can be caused by sensor errors, model uncertainties, changes in the ambient environment, data loss, or malicious cyberattacks to contaminate the measurement process of many nonlinear dynamic systems. When the extended Kalman filter (EKF) is applied to such systems for state estimation, the outliers can seriously reduce the estimation accuracy. This brief proposes an innovation saturation mechanism to make the EKF robust against outliers. This mechanism applies a saturation function to the innovation process that the EKF leverages to correct the state estimation. As such, when outliers occur, the distorted innovation is saturated, so as not to undermine the state estimation. The mechanism features an adaptive adjustment of the saturation bounds. The design leads to the development of robust EKF approaches for both continuous- and discrete-time systems. The stability of the proposed approaches when applied to linear systems is characterized, showing that they are capable of performing bounded-error estimation in the presence of bounded outlier disturbances in this case. A simulation study about mobile robot localization is presented to illustrate 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 additional measurement redundancy.