Positioning Uncertainty Estimation of LiDAR SLAM Based on Multifault Hypothesis Solution Separation and Lie Group Theory

Estimating the positioning uncertainty is important for location-based applications, such as autonomous driving and robotics, since they are safety-critical and acquire reliable positions whose uncertainty should be provided. Existing SLAM frameworks focus on how to improve positioning accuracy and pay less attention to the uncertainty of vehicle positioning. In this paper, we applied the multi-fault hypothesis solution separation (MHSS) theory in GNSS integrity monitoring, using it for an approximate estimate of the uncertainty of newly updated state in every new scan. The estimated uncertainty in new scan is used to propagate the covariance of the vehicle's position in Lie group to obtain the position distribution circle of current scan. At the same time, we consider the geometric distribution of LiDAR measurements, proposing a low computational burden MHSS calculation method. Our approach considers both the front end and back end of SLAM framework. Both KITTI dataset and actual measured data verification experiments are conducted. The experimental results show that the spatial covariance propagated has good similarity with the actual vehicle positioning error in horizontal and vertical direction and the efficient calculation model reduces the computational burden of the system by more than 50%.