Efficient and Consistent Two Key-Frame Visual-Inertial Navigation Using Matrix Lie Groups

This paper presents the design of a two key-frame visual-inertial navigation system (2KF-VINS) using a combined Lie group $SE2(3)$ extended Kalman filter (EKF) design framework. The conventional 2KF-VINS filter is unobservable for translations along all three axes and rotation about the gravity direction. As a result, the filter suffers from estimation inconsistencies related to unobservable transformations of the estimation problem. The proposed combined Lie group $SE2(3)$ framework remedies this issue by implicitly preserving the observability consistency property of the filter. Monte Carlo numerical simulations are used to validate the theoretical performance of the $right−SE2(3)$ 2KF-VINS, along with experimental validation using the EuRoC micro aerial vehicle (MAV) dataset to evaluate the performance in real-world scenarios. Additionally, the proposed algorithm is compared with state-of-the-art MSCKF, RI-MSCKF, $left−SO(3)$⁠, and $right−SO(3)$ 2KF-VINS versions with identical and realistic tuning parameters to validate the performance related to the accuracy, consistency, and computational speed of the method.