  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. The proposed framework first constructs a linear
Gaussian belief propagation (GaBP) algorithm to estimate the absolute sensor
positions utilizing the range-based received signal model, which is used for
the reconstruction of the RBL transformation model, linearized with a
small-angle approximation. In light of the reformulated system, a second
bivariate GaBP is designed to directly estimate the 3D rotation angles and
translation distances, with an interference cancellation (IC) refinement to
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 position, rotation, and translation estimation performance.
