Globally Optimal Data-Association-Free Landmark-Based Localization Using Semidefinite Relaxations

--This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally optimal fashion. Relative position measurements to a fixed set of known landmarks are used, but the data association is unknown in that the robot does not know which landmark each measurement is generated from. The relaxation is shown to be tight in a majority of cases for moderate noise levels. The proposed algorithm is compared to local Gauss-Newton baselines initialized at the dead-reckoned trajectory, and is shown to significantly improve convergence to the problem's global optimum in simulation and experiment. STIMA TING the state of a robot from noisy and incomplete sensor data is a central task associated with autonomy. In the landmark-based localization task, the robot infers its position and orientation from measurements from landmarks with known positions. State estimation methods for localization can be split into filtering methods and batch optimization methods [1].