  The objective of this study is improving the location estimate of a mobile
robot capable of motion on a plane and mounted with a conventional 2D LIDAR
sensor, given an initial guess for its location on a 2D map of its
surroundings. Documented herein is the theoretical reasoning behind solving a
matching problem between two homoriented 2D scans, one derived from the robot's
physical sensor and one derived by simulating its operation within the map, in
a manner that does not require the establishing of correspondences between
their constituting rays. Two results are proved and subsequently shown through
experiments. The first is that the true position of the sensor can be recovered
with arbitrary precision when the physical sensor reports faultless
measurements and there is no discrepancy between the environment the robot
operates in and its perception of it by the robot. The second is that when
either is affected by disturbance, the location estimate is bound in a
neighbourhood of the true location whose radius is proportional to the
affecting disturbance.
