LOG-LIO2: A LiDAR-Inertial Odometry with Efficient Uncertainty Analysis

TL;DR

This work tackles the critical problem of uncertainty in LiDAR-based LiDAR-Inertial Odometry by introducing a comprehensive point uncertainty model that accounts for range, bearing, incident angle, and surface roughness. It presents a fast Local Uncertainty Fast Approximation (LUFA) framework that incrementally updates the center, covariance, and the Jacobians of eigenvalues/eigenvectors, reducing uncertainty propagation from linear in the number of points to effectively constant time per new point. The authors integrate these components into the LOG-LIO2 system, leveraging adaptive voxel maps and uncertainty-weighted point-to-plane residuals to achieve higher accuracy and real-time performance on public datasets, outperforming several state-of-the-art LIO methods. The approach is supported by theoretical proofs in the appendices and validated through simulations and real-world experiments, with code released publicly for reproducibility and broader use.

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 https://github.com/tiev-tongji/LOG-LIO2.

Figures (7)

• Figure 1: Illustrations of geometric relationship for the point uncertainty model.
• Figure 2: An illustration of geometric relationship for the $\mathbf{m}_{k-1}$ local frame.
• Figure 3: System overview of LOG-LIO2 with enhancements marked in red.
• Figure 4: Illustration of the simulation environment.
• Figure 5: Comparison of covariance calculated by LUFA and BALM.