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In this paper, we propose a novel framework called rigid body localizationfor joint position and orientation estimation of a rigid body. We consider asetup in which a few sensors are mounted on a rigid body. The absolute positionof the sensors on the rigid body, or the absolute position of the rigid bodyitself is not known. However, we know how the sensors are mounted on the rigidbody, i.e., the sensor topology is known. Using range-only measurements betweenthe sensors and a few anchors (nodes with known absolute positions), andwithout using any inertial measurements (e.g., accelerometers), we estimate theposition and orientation of the rigid body. For this purpose, the absoluteposition of the sensors is expressed as an affine function of the Stiefelmanifold. In other words, we represent the orientation as a rotation matrix,and absolute position as a translation vector. We propose a least-squares (LS),simplified unitarily constrained LS (SUC-LS), and optimal unitarily constrainedleast-squares (OUC-LS) estimator, where the latter is based on Newton's method.As a benchmark, we derive a unitarily constrained Cram\'er-Rao bound (UC-CRB).The known topology of the sensors can sometimes be perturbed duringfabrication. To take these perturbations into account, a simplified unitarilyconstrained total-least-squares (SUC-TLS), and an optimal unitarily constrainedtotal-least-squares (OUC-TLS) estimator are also proposed.

Rigid Body Localization Using Sensor Networks: Position and Orientation Estimation