Belief Propagation-Based Rotation and Translation Estimation for Rigid Body Localization

We propose a novel solution to the rigid body localization (RBL) problem, in which the three-dimensional (3D) rotation and translation is estimated by only utilizing the range measurements between the wireless sensors on the rigid body and the anchor sensors. Given the prior knowledge of the absolute sensor positions, by leveraging a linearized RBL transformation model with small-angle approximations, the proposed bivariate Gaussian belief propagation (GaBP) is designed to directly estimate the 3D rotation angles and translation distances, with an interference cancellation (IC) refinement step to further improve the angle estimation performance. The effectiveness of the proposed method is verified via numerical simulations, highlighting the superior performance of the proposed method against the state-of-the-art (SotA) techniques for the rotation and translation estimation performance.