  Visual Inertial Odometry (VIO) is the problem of estimating a robot's
trajectory by combining information from an inertial measurement unit (IMU) and
a camera, and is of great interest to the robotics community. This paper
develops a novel Lie group symmetry for the VIO problem and applies the
recently proposed equivariant filter. The symmetry is shown to be compatible
with the invariance of the VIO reference frame, lead to exact linearisation of
bias-free IMU dynamics, and provide equivariance of the visual measurement
function. As a result, the equivariant filter (EqF) based on this Lie group is
a consistent estimator for VIO with lower linearisation error in the
propagation of state dynamics and a higher order equivariant output
approximation than standard formulations. Experimental results on the popular
EuRoC and UZH FPV datasets demonstrate that the proposed system outperforms
other state-of-the-art VIO algorithms in terms of both speed and accuracy.
