Robust multiple sensor localization via semidefinite relaxation in wireless sensor networks with anchor position uncertainty

Sensor localization is an important step of wireless sensor network (WSN) before conducting a common surveillance task. We propose a robust multiple sensor cooperative localization method against the uncertainty of anchor position estimate based on Time of Flight (TOF) measurements. A key feature is that it makes no statistic assumption on the anchor position uncertainties, which are often difficult to obtain, and only assumes that the error modulus of anchor position is upper bounded. The Maximum likelihood (ML) problem is formulated, where both the TOF measurements between anchors and sensors and the measurements among sensors are utilized in a cooperative way. The semidefinite relaxation technique is provided to transform the nonconvex ML problem into a convex one. The Cramer–Rao lower bounds with and without anchor position uncertainties are also derived. The simulation and experimental results show that our method can yield a good estimate compared to other localization methods.