  This letter presents an accurate and robust Lidar Inertial Odometry
framework. We fuse LiDAR scans with IMU data using a tightly-coupled iterative
error state Kalman filter for robust and fast localization. To achieve robust
correspondence matching, we represent the points as a set of Gaussian
distributions and evaluate the divergence in variance for outlier rejection.
Based on the fitted distributions, a new residual metric is proposed for the
filter-based Lidar inertial odometry, which demonstrates an improvement from
merely quantifying distance to incorporating variance disparity, further
enriching the comprehensiveness and accuracy of the residual metric. Due to the
strategic design of the residual metric, we propose a simple yet effective
voxel-solely mapping scheme, which only necessities the maintenance of one
centroid and one covariance matrix for each voxel. Experiments on different
datasets demonstrate the robustness and accuracy of our framework for various
data inputs and environments. To the benefit of the robotics society, we open
source the code at https://github.com/Ji1Xingyu/lio_gvm.
