Robust Extended Kalman Filtering for Systems with Measurement Outliers

TL;DR

This paper introduces a robust extended Kalman filter with an innovation saturation mechanism that effectively rejects measurement outliers, improving state estimation accuracy in nonlinear systems affected by sensor errors, cyber attacks, or environmental changes.

Contribution

It proposes a novel adaptive saturation-based modification to the EKF that enhances robustness against outliers without measurement redundancy, applicable to both continuous and discrete systems.

Findings

Successfully rejects outliers of various types and magnitudes

Maintains bounded estimation errors under bounded outlier disturbances

Demonstrates effectiveness in mobile robot localization simulations

Abstract

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.