  Pose estimation is important for robotic perception, path planning, etc.
Robot poses can be modeled on matrix Lie groups and are usually estimated via
filter-based methods. In this paper, we establish the closed-form formula for
the error propagation for the Invariant extended Kalman filter (IEKF) in the
presence of random noises and apply it to vision-aided inertial navigation. We
evaluate our algorithm via numerical simulations and experiments on the
OPENVINS platform. Both simulations and the experiments performed on the public
EuRoC MAV datasets demonstrate that our algorithm outperforms some state-of-art
filter-based methods such as the quaternion-based EKF, first estimates Jacobian
EKF, etc.
