  LiDAR-based global localization is a fundamental problem for mobile robots.
It consists of two stages, place recognition and pose estimation, which yields
the current orientation and translation, using only the current scan as query
and a database of map scans. Inspired by the definition of a recognized place,
we consider that a good global localization solution should keep the pose
estimation accuracy with a lower place density. Following this idea, we propose
a novel framework towards sparse place-based global localization, which
utilizes a unified and learning-free representation, Radon sinogram (RING), for
all sub-tasks. Based on the theoretical derivation, a translation invariant
descriptor and an orientation invariant metric are proposed for place
recognition, achieving certifiable robustness against arbitrary orientation and
large translation between query and map scan. In addition, we also utilize the
property of RING to propose a global convergent solver for both orientation and
translation estimation, arriving at global localization. Evaluation of the
proposed RING based framework validates the feasibility and demonstrates a
superior performance even under a lower place density.
