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 proposed symmetry is compatible with the invariance of the VIO reference frame, leading to improved filter consistency. The bias-free IMU dynamics are group-affine, ensuring that filter linearisation errors depend only on the bias estimation error and measurement noise. Furthermore, visual measurements are equivariant with respect to the symmetry, enabling the application of the higher-order equivariant output approximation to reduce approximation error in the filter update equation. 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.

翻译：视觉惯性里程计（VIO）是通过结合惯性测量单元（IMU）和相机的信息来估计机器人轨迹的问题，在机器人学界备受关注。本文为VIO问题提出了一种新颖的李群对称性，并应用了近期提出的等变滤波器。所提出的对称性与VIO参考系的不变性兼容，从而提高了滤波器的一致性。无偏置的IMU动力学是群仿射的，这确保了滤波器线性化误差仅取决于偏置估计误差和测量噪声。此外，视觉测量相对于该对称性是等变的，这使得能够应用高阶等变输出近似来减少滤波器更新方程中的近似误差。因此，基于此李群的等变滤波器（EqF）是VIO的一致估计器，其在状态动力学传播中具有比标准公式更低的线性化误差和更高阶的等变输出近似。在流行的EuRoC和UZH FPV数据集上的实验结果表明，所提出的系统在速度和精度方面均优于其他最先进的VIO算法。