Consistent Rigid Body Localization from Range Measurements with Anchor Position Uncertainty

Rigid Body Localization (RBL) using range measurements has recently attracted much attention. In some large and complicated scenarios, we may not obtain the accurate positions for anchors deployed in the environment. However, few works have considered the anchor position uncertainty. In this paper, we formulate the Maximum Likelihood (ML) RBL problem with anchor position uncertainty and find that the ML estimate is not necessarily consistent. As an alternative, we propose a two-step estimator MGN-CULS, which is both consistent and computationally efficient. In the first step, we develop a closed-form initial estimate with consistency using bias-eliminating techniques. In the second step, we design a modified Gauss-Newton iteration to refine the initial estimate without destabilizing the consistency. Simulation results demonstrate the stable and accurate performance of our proposed algorithm.