Accurate Localization of a Rigid Body Using Multiple Sensors and Landmarks

This paper develops estimators for locating a rigid body using the time measurements, and the Doppler as well if it is moving, between the sensors in the rigid body and a few landmarks outside. The challenge of rigid body localization is that in addition to the position, we are also interested in obtaining the rotation parameters of the rigid body that must belong to the special orthogonal group. The proposed estimators are non-iterative and have two steps: preliminary and refinement. The preliminary step provides a coarse estimate and the refinement step improves the first step estimate to yield an accurate solution. When the rigid body is stationary, we are able to locate the body with accuracy higher than the solutions of comparable complexity found in the literature. When the rigid body is moving, we develop an estimator that contains the additional unknowns of angular and translational velocities. Simulations show that the proposed estimators, in both stationary and moving cases, can approach the Cramer-Rao Lower Bound performance under Gaussian noise over the small error region.