Asymptotically Efficient Estimator for Range-Based Robot Relative Localization

This study investigates the 2-D relative localization problem, which estimates the relative orientation and position between two moving robots using inter-robot range measurements. We propose a novel formulation and a robust weighted semidefinite relaxation solution for the relative localization problem in the presence of range measurement error and robot state transition error. Theoretical analysis and simulations show that the weighted semidefinite relaxation solution achieves Cramér–Rao lower bound performance when the measurement noise and the odometry uncertainty follow Gaussian distributions with moderate noise power. Demonstrations using data from a laboratory environment validate the promising and robust performance of the weighted semidefinite relaxation method. The root-mean-square errors in estimating the orientation and position are
$3.97^\circ$
and 0.22 m with affordable hardware.