  Rigid body localization refers to a problem of estimating the position of a
rigid body along with its orientation using anchors. We consider a setup in
which a few sensors are mounted on a rigid body. The absolute position of the
rigid body is not known, but, the relative position of the sensors or the
topology of the sensors on the rigid body is known. We express the absolute
position of the sensors as an affine function of the Stiefel manifold and
propose a simple least-squares (LS) estimator as well as a constrained total
least-squares (CTLS) estimator to jointly estimate the orientation and the
position of the rigid body. To account for the perturbations of the sensors, we
also propose a constrained total least-squares (CTLS) estimator. Analytical
closed-form solutions for the proposed estimators are provided. Simulations are
used to corroborate and analyze the performance of the proposed estimators.
