For autonomous ground vehicles, global localization with 3D LiDAR is an indispensable part of tasks such as navigation. Usually, global localization using LiDAR is subdivided into two sub-problems, place recognition and global registration. For place recognition, the recent emerging schemes based on deep learning either rely on 3D convolution with high complexity or need to learn features from various forward perspectives. To mitigate this, we propose a model with roll-pitch-yaw invariance that represents point clouds as probabilistic voxels and generates occupancy grids from a bird’s-eye view, fulfilling robust place recognition by learning aggregated embeddings from a fixed perspective. For low-overlap global registration, the traditional handcraft feature-based methods are mostly limited to dense object-level point clouds, while the state-of-the-art learning-based approaches often rely on complex 3D convolution and additional feature association learning. To fill this gap to some extent, we propose to estimate the relative roll-pitch angles and vertical translation by fitting and aligning the ground plane of the point clouds and to determine the horizontal translations and yaw angle by matching their projected occupancy grids. Extensive experiments corroborate the superior recall and generalization ability of our place recognition model, as well as the advanced success rate and accuracy of our 3D registration approach. Especially in the recognition and registration of hard samples, our results far exceed those of our counterparts by large margins. To ensure full reproducibility, the relevant codes and data are made available online at https://cslinzhang.github.io/GLoc/GLoc.html.