Semidefinite Relaxation for TDOA Localization with Sensor Position Errors in Sensor Networks

In the case of sensor node position errors, this paper proposes a positioning method based on TDOA measurement. Due to the difficulty in obtaining sensor node position errors in practice, the key to this method is that it does not require prior distribution knowledge of sensor node position errors, but only assumes an upper bound of sensor node position errors. Under this assumption, the target localization problem based on TDOA is transformed into a robust least squares (RLS) problem. Due to the non-convex nature of the problem, it is not easy to solve. Therefore, this paper first transforms the non-convex problem into a convex problem through the method of semidefinite relaxation for solution. Secondly, by introducing the S lemma theory, the sensor node position error term is eliminated without introducing penalty factors or penalty terms, achieving target localization. The simulation results show that this scheme can achieve ideal positioning performance.