Joint Rigid Body and Object Localization via Semidefinite Relaxation Using Bistatic Ranging

This paper investigates the joint rigid body and object localization using bistatic ranging. The rigid body and object localization problem is a complex optimization problem with a large number of nonlinear constraints. To address this issue, the measurement equations are first transformed and formulated in matrix form, then approximated using Constrained Weighted Least Squares (CWLS). Subsequently, the non-convex localization problem is relaxed into a convex semidefinite programming (SDP) form. The solution yields the rotation matrix and displacement vector of the rigid body, as well as the position estimation of the scatterer object. The performance of the proposed method is evaluated through mean square error (MSE) analysis. Simulation results demonstrate that under low noise levels, the performance of the SDP method approaches the Cramér-Rao Lower Bound (CRLB) accuracy. Furthermore, by comparing the CRLBs of different models, we demonstrate that our solution offers higher precision than methods not utilizing bistatic ranging under the same noise levels.