提出新型等变滤波器，提升激光惯性里程计的精度与鲁棒性
Equivariant Filter for Tightly Coupled LiDAR-Inertial Odometry
- 基于半直积群对称性设计等变滤波器，耦合状态变量抑制线性化误差
- 在多个公开与私有数据集上验证，相比传统方法姿态估计更一致
- 适合需要高精度、强鲁棒性的实时定位系统开发者使用
位姿估算是同时定位与地图构建（SLAM）中的关键问题。然而，开发鲁棒且一致的状态估计算法仍具挑战性，传统扩展卡尔曼滤波器（EKF）难以处理惯性测量单元（IMU）和激光雷达（LiDAR）模型的非线性。为此，我们提出 Eq-LIO，一种基于等变滤波器（EqF）的紧耦合激光惯性里程计（LIO）鲁棒状态估计算法。相较于基于 $\ ext{SE}_2(3)$ 群结构的不变卡尔曼滤波器，该方法利用半直积群的对称性，将惯性偏差、导航状态及激光外参联合建模，有效降低线性化误差，增强在状态突变下的估计性能。理论推导证明其天然一致性，实验在多个公共与私有数据集上验证了其优越性。
原文摘要 · Abstract (English)
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.
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