A Computational Geometry Approach for Localization and Tracking in GPS-denied Environments

Localization and tracking of vehicles is still an important issue in GPS-denied environments (both indoors and outdoors), where accurate motion is required. In this work, a localization system based on the random disposition of LiDAR sensors (which share a partially common field of view) and on the use of the Hausdorff distance is addressed. The proposed system uses the Hausdorff distance to estimate both the position of the LiDAR sensors and the pose of the vehicle as it drives within the environment. Our approach is not restricted to the number of LiDAR sensors (the estimation procedure is asynchronous), the number of vehicles (it is a multidimensional approach), or the nature of the environment. However, it is implemented in open spaces, limited by the range of the LiDAR sensors and the geometry of the vehicle. An empirical analysis of the presented approach is also included here, showing that the error in the localization estimation remains bounded in approximately 50 cm. Real-time experimentation as validation of the proposed localization and tracking techniques as well as the pros and cons of our proposal are also shown in this work.