Robust Second-order LiDAR Bundle Adjustment Algorithm Using Mean Squared Group Metric

The bundle adjustment (BA) algorithm is a widely used nonlinear optimization technique in the backend of Simultaneous Localization and Mapping (SLAM) systems. By leveraging the co-view relationships of landmarks from multiple perspectives, the BA method constructs a joint estimation model for both poses and landmarks, enabling the system to generate refined maps and reduce front-end localization errors. However, there are unique challenges when applying the BA for LiDAR data, due to the large volume of 3D points. Exploring a robust LiDAR BA estimator and achieving accurate solutions is a very important issue. In this work, firstly we propose a novel mean square group metric (MSGM) to build the optimization objective in the LiDAR BA algorithm. This metric applies mean square transformation to uniformly process the measurement of plane landmarks from one sampling period. The transformed metric ensures scale interpretability, and does not requie a time-consuming point-by-point calculation. Secondly, by integrating a robust kernel function, the metrics involved in the BA algorithm are reweighted, and thus enhancing the robustness of the solution process. Thirdly, based on the proposed robust LiDAR BA model, we derived an explicit second-order estimator (RSO-BA). This estimator employs analytical formulas for Hessian and gradient calculations, ensuring the precision of the BA solution. Finally, we verify the merits of the proposed RSO-BA estimator against existing implicit second-order and explicit approximate second-order estimators using the publicly available datasets. The experimental results demonstrate that the RSO-BA estimator outperforms its counterparts regarding registration accuracy and robustness, particularly in large-scale or complex unstructured environments.