Accurate Rigid Body Localization via Semidefinite Relaxation Using Range Measurements

In this letter, we propose a method to improve the localization accuracy of a rigid body using the range measurements between the anchors and several sensors mounted on the body. Rigid body localization aims to estimate the rotation matrix and position vector of the sensor array on the body and it is a nonlinear and challenging problem to solve. Through the application of semidefinite relaxation to the original maximum likelihood formulation, we can obtain a coarse estimate of the rotation matrix and position vector that is robust to measurement noise. We next apply orthogonalization and refinement to the estimate and gain back the performance loss from relaxation and approximation. Simulation results show that the proposed method can reach the Cramér–Rao lower bound performance even at high noise levels where existing estimators cannot.