Robust TOA based localization for wireless sensor networks with anchor position uncertainties

In this paper, we address the problem of sensor network localization based on Time-of-Arrival (TOA) measurements under the presence of anchor location errors. We consider the practically appealing setup where the agents are low-complexity transmit-only nodes whose clocks´ are not synchronized with that of the anchors. The maximum likelihood (ML) solution of the localization problem is formulated and shown to be a non-convex optimization problem. The relaxation of the ML solution to a convex optimization problem based on semi-definite programming (SDP) is proposed. The proposed localization method is compared with the Cramér Rao lower bound (CRLB) and an existing related approach. Simulation results show that the proposed localization method outperforms the existing scheme, notably when the anchor location uncertainties are the dominant source of errors.