Multistatic Localization With Unknown Transmitter Position and Signal Propagation Speed

In this letter, we address the multistatic object localization problem when the transmitter position and signal propagation speed are not known. By transforming the time delay measurement model, we first formulate a non-convex weighted least squares problem, which is then relaxed into a convex semidefinite programming (SDP) problem by applying semidefinite relaxation. It turns out that the relaxed SDP problem is too loose and fails to achieve the Cramer-Rao lower bound (CRLB) performance. To address this problem, we propose to tighten the relaxed SDP problem by adding a second-order cone constraint to reach better solutions. Simulation results show that the proposed method is able to achieve the CRLB.