Equivariant Filter for Tightly Coupled LiDAR-Inertial Odometry

TL;DR

This paper introduces Eq-LIO, a novel equivariant filter-based pose estimator for tightly coupled LiDAR-inertial odometry, improving robustness and consistency over traditional methods by leveraging symmetry properties.

Contribution

The paper proposes a new equivariant filter for LiDAR-inertial odometry that enhances robustness and consistency by exploiting symmetry in the system's group structure.

Findings

Eq-LIO demonstrates higher robustness in experiments.

The method maintains consistency under unexpected state changes.

The approach outperforms traditional EKF-based methods.

Abstract

Pose estimation is a crucial problem in simultaneous localization and mapping (SLAM). However, developing a robust and consistent state estimator remains a significant challenge, as the traditional extended Kalman filter (EKF) struggles to handle the model nonlinearity, especially for inertial measurement unit (IMU) and light detection and ranging (LiDAR). To provide a consistent and efficient solution of pose estimation, we propose Eq-LIO, a robust state estimator for tightly coupled LIO systems based on an equivariant filter (EqF). Compared with the invariant Kalman filter based on the $\SE_2(3)$ group structure, the EqF uses the symmetry of the semi-direct product group to couple the system state including IMU bias, navigation state and LiDAR extrinsic calibration state, thereby suppressing linearization error and improving the behavior of the estimator in the event of unexpected state changes. The proposed Eq-LIO owns natural consistency and higher robustness, which is theoretically proven with mathematical derivation and experimentally verified through a series of tests on both public and private datasets.