An Investigation and Solution of Angle Based Rigid Body Localization

This paper investigates the problem of rigid body localization using angle measurements between the sensors on the body, and some anchors. Rigid body localization consists of the estimation of the rotation, and position of the rigid body, where the sensor positions are known locally to the body. We have shown that a minimum of one sensor is sufficient for the rigid body to self-localize itself with respect to its own local coordinate system. On the other hand, as little as one anchor can locate the rigid body with respect to the global coordinate system. This is in contrast to the previous studies for range based rigid body localization where multiple sensors, and anchors are needed. The respective numbers of anchors, and sensors needed for the two cases are also deduced. A formulation is proposed to solve this non-linear constrained optimization problem by transforming the measurement equations. Perturbation analysis shows the formulation leads to an estimator that achieves the Cramèr-Rao Lower Bound performance for Gaussian measurement noise over the small error region. A semidefinite relaxation method is developed to solve the rigid body localization problem from the proposed formulation. Simulation validates the theoretical studies, and the performance of the proposed solution.