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.

翻译：姿态估计是同步定位与建图（SLAM）中的一个关键问题。然而，开发一个鲁棒且一致的状态估计器仍然是一个重大挑战，因为传统的扩展卡尔曼滤波器（EKF）难以处理模型非线性，特别是对于惯性测量单元（IMU）和激光探测与测距（LiDAR）。为了提供一种一致且高效的姿态估计解决方案，我们提出了Eq-LIO，一种基于等变滤波器（EqF）的、用于紧耦合LIO系统的鲁棒状态估计器。与基于$\SE_2(3)$群结构的不变卡尔曼滤波器相比，EqF利用半直积群的对称性来耦合系统状态，包括IMU偏差、导航状态和LiDAR外参标定状态，从而抑制线性化误差，并改善估计器在状态发生意外变化时的性能。所提出的Eq-LIO具有天然的一致性和更高的鲁棒性，这一点通过数学推导在理论上得到了证明，并在公开和私有数据集上进行的一系列测试中得到了实验验证。