Invariant-EKF Design for a Unicycle Robot under Linear Disturbances

Abstract

We consider a nonlinear estimation problem where a unicycle vehicle moves with unknown disturbances generated from linear time-invariant systems. The vehicle measures its position to estimate its state and disturbance information simultaneously. We show that this system is invariant under the action of a Lie group and design an Invariant Extended Kalman Filter (IEKF). We propose a first-order approximation of the noise covariance in the invariant frame. Through Monte-Carlo simulations, we demonstrate that the first-order approximation improves the performance of the IEKF and that the IEKF yields superior transient performance over the standard EKF.