Abstract
Uncertainty in LiDAR measurements, stemming from factors such as range sensing, is crucial for LIO (LiDAR-Inertial Odometry) systems as it affects the accurate weighting in the loss function. While recent LIO systems address uncertainty related to range sensing, the impact of incident angle on uncertainty is often overlooked by the community. Moreover, the existing uncertainty propagation methods suffer from computational inefficiency. This paper proposes a comprehensive point uncertainty model that accounts for both the uncertainties from LiDAR measurements and surface characteristics, along with an efficient local uncertainty analytical method for LiDAR-based state estimation problem. We employ a projection operator that separates the uncertainty into the ray direction and its orthogonal plane. Then, we derive incremental Jacobian matrices of eigenvalues and eigenvectors w.r.t. points, which enables a fast approximation of uncertainty propagation. This approach eliminates the requirement for redundant traversal of points, significantly reducing the time complexity of uncertainty propagation from $\mathcal{O} (n)$ to $\mathcal{O} (1)$ when a new point is added. Simulations and experiments on public datasets are conducted to validate the accuracy and efficiency of our formulations. The proposed methods have been integrated into a LIO system, which is available at this https URL.
Abstract (translated)
来自因素如测距感知的LiDAR测量的不确定性对LIO（LiDAR-Inertial Odometry）系统至关重要，因为它会影响损失函数的准确加权。虽然最近的一些LIO系统解决了与测距感有关的不确定性，但通常忽视了入射角对不确定性的影响。此外，现有的不确定性传播方法存在计算效率低下的问题。本文提出了一种全面的点不确定性模型，考虑了来自测距感的不确定性和表面特征，以及用于LiDAR基于状态估计问题的有效局部不确定性分析方法。我们采用一个投影操作将不确定性分解为光线方向和其垂直平面。然后，我们求解关于点的增量雅可比矩阵，使得不确定性传播变得更加快速。这种方法消除了冗余的点遍历，从而显著减少了不确定传播的时间复杂度从$\mathcal{O}(n)$到$\mathcal{O}(1)$，当添加新点时。在公开数据集上进行模拟和实验验证了我们的公式的准确性和效率。所提出的方法已集成到LIO系统中，该系统可用于此链接：https://。
URL
https://arxiv.org/abs/2405.01316
