Equivariant Filter for Tightly Coupled LiDAR-Inertial Odometry

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.

SuperVINS: A visual-inertial SLAM framework integrated deep learning features

In this article, we propose enhancements to VINS-Fusion by incorporating deep learning features and deep learning matching methods. We implemented the training of deep learning feature bag of words and utilized these features for loop closure detection. Additionally, we introduce the RANSAC algorithm in the deep learning feature matching module to optimize matching. SuperVINS, an improved version of VINS-Fusion, outperforms it in terms of positioning accuracy, robustness, and more. Particularly in challenging scenarios like low illumination and rapid jitter, traditional geometric features fail to fully exploit image information, whereas deep learning features excel at capturing image features.To validate our proposed improvement scheme, we conducted experiments using open source datasets. We performed a comprehensive analysis of the experimental results from both qualitative and quantitative perspectives. The results demonstrate the feasibility and effectiveness of this deep learning-based approach for SLAM systems.To foster knowledge exchange in this field, we have made the code for this article publicly available. You can find the code at this link: https://github.com/luohongk/SuperVINS.

The Unified Mathematical Framework for IMU Preintegration in Inertial-Aided Navigation System

This paper proposes a unified mathematical framework for inertial measurement unit (IMU) preintegration in inertial-aided navigation system in different frames under different motion condition. The navigation state is precisely discretized as three part: local increment, global state, and global increment. The global increment can be calculated in different frames such as local geodetic navigation frame and earth-centered-earth-fixed frame. The local increment which is referred as the IMU preintegration can be calculated under different assumptions according to the motion of the agent and the grade of the IMU. Thus, it more accurate and more convenient for online state estimation of inertial-integrated navigation system under different environment.

Equivariant Filtering Framework for Inertial-Integrated Navigation

This paper proposes a equivariant filtering (EqF) framework for the inertial-integrated state estimation problem. As the kinematic system of the inertial-integrated navigation can be naturally modeling on the matrix Lie group $SE_2(3)$, the symmetry of the Lie group can be exploited to design a equivariant filter which extends the invariant extended Kalman filtering on the group affine system. Furthermore, details of the analytic state transition matrices for left invariant error and right invariant error are given.

$SE_2$ based Extended Kalman Filtering and Smoothing Framework for Inertial-Integrated Navigation

This paper proposes an $SE_2(3)$ based extended Kalman filtering (EKF) framework for the inertial-integrated state estimation problem. The error representation using the straight difference of two vectors in the inertial navigation system may not be reasonable as it does not take the direction difference into consideration. Therefore, we choose to use the $SE_2(3)$ matrix Lie group to represent the state of the inertial-integrated navigation system which consequently leads to the common frame error representation. With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down (NED) navigation frame and the earth-centered earth-fixed (ECEF) frame, respectively, the corresponding EKF, terms as $SE_2(3)$ based EKF has also been derived. It provides a new perspective on the geometric EKF with a more sophisticated formula for the inertial-integrated navigation system. Furthermore, we design two new modified error dynamics on the NED frame and the ECEF frame respectively by introducing new auxiliary vectors. Finally the equivalence of the left-invariant EKF and left $SE_2(3)$ based EKF have been shown in navigation frame and ECEF frame.

The Geometry and Kinematics of the Matrix Lie Group $SE_K$

Currently state estimation is very important for the robotics, and the uncertainty representation based Lie group is natural for the state estimation problem. It is necessary to exploit the geometry and kinematic of matrix Lie group sufficiently. Therefore, this note gives a detailed derivation of the recently proposed matrix Lie group $SE_K(3)$ for the first time, our results extend the results in Barfoot \cite{barfoot2017state}. Then we describe the situations where this group is suitable for state representation. We also have developed code based on Matlab framework for quickly implementing and testing.