Pınar Oğuz-Ekim, Lambiotte R., Lefebvre E., TDOA based localization and its application to the initialization of LiDAR based autonomous robots, . Robotics and Autonomous Systems, Volume 131, 2020, DOI: 10.1016/j.robot.2020.103590.
This work considers the problem of locating a single robot given a set of squared noisy range difference measurements to a set of points (anchors) whose positions are known. In the sequel, localization problem is solved in the Least-Squares (LS) sense by writing the robot position in polar/spherical coordinates. This representation transforms the original nonconvex/multimodal cost function into the quotient of two quadratic forms, whose constrained maximization is more tractable than the original problem. Simulation results indicate that the proposed method has similar accuracy to state-of-the-art optimization-based localization algorithms in its class, and the simple algorithmic structure and computational efficiency makes it appealing for applications with strong computational constraints. Additionally, location information is used to find the initial orientation of the robot with respect to the previously obtained map in scan matching. Thus, the crucial problem of the autonomous initialization and localization in robotics is solved.