# EqVIO: An Equivariant Filter for Visual Inertial Odometry

arXiv: https://arxiv.org/abs/2205.01980 · HTML: https://mlsanity.com/paper/2205.01980/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2022.

## Built on by (most cited first, 3 of 3)

- [Causal Transformer for Fusion and Pose Estimation in Deep Visual Inertial Odometry](https://mlsanity.com/paper/2409.08769/) (2024)
- [PO-MSCKF: An Efficient Visual-Inertial Odometry by Reconstructing the Multi-State Constrained Kalman Filter with the Pose-only Theory](https://mlsanity.com/paper/2407.01888/) (2024)
- [Understanding Sensor Vulnerabilities in Industrial XR Tracking](https://mlsanity.com/paper/2602.14413/) (2026)

## Abstract (arXiv)

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.