Invariant Extended Kalman Filtering for Robot Localization using IMU and GPS

This paper derives an IMU-GPS-fused inertial navigation observer for a mobile robot using the theory of invariant observer design. One of the main features of invariant observers for invariant systems on Lie groups is that the estimation error is autonomous, hence the observable state variables can be rendered convergent within a domain of attraction that is independent of the system’s trajectory. The Invariant Extended Kalman Filter (In-EKF) which is an extension of the Extended Kalman Filter (EKF) is supposed to be more efficient given that the system converges to constant values on a larger set of trajectories as opposed to the equilibrium points that an EKF is based on. This paper explores the implementation of the In-EKF for robot localization and is compared against an implementation of the EKF. The localization is performed on the University of Michigan north campus long-term vision and LIDAR dataset.