Controlling the formation of several mobile robots allows for the connection of these robots to a larger virtual unit. This enables the group of mobile robots to carry out tasks that a single robot could not perform. In order to control all robots like a unit, a formation controller is required, the accuracy of which determines the performance of the group. As shown in various publications and our previous work, the accuracy and control performance of this controller depends heavily on the quality of the localization of the individual robots in the formation, which itself depends on the ability of the robots to locate themselves within a map. Other errors are caused by inaccuracies in the map. To avoid any errors related to the map or external sensors, we plan to calculate the relative positions and velocities directly from the LiDAR data. To do this, we designed an algorithm which uses the LiDAR data to detect the outline of individual robots. Based on this detection, we estimate the robots pose and combine this estimate with the odometry to improve the accuracy. Lastly, we perform a qualitative evaluation of the algorithm using a Faro laser tracker in a realistic indoor environment, showing benefits in localization accuracy for environments with a low density of landmarks.