Improved robust TOA-based source localization with individual constraint of sensor location uncertainty

Localization of sources like aircraft, ships, speakers, etc. is a very important signal processing task in wireless sensor networks (WSNs). Traditionally, the sensor location uncertainty was characterized by Gaussian distribution noises, which is not always reasonable in practice. In this paper, we propose an improved robust time of arrival (TOA) based source localization method in the presence of sensor location uncertainty, where only the bounded error modulus of the sensor location is assumed. A least-squares problem is formulated and a semidefinite relaxation technique is provided to transform the nonconvex optimization problem into a convex one. Our proposed method individually considered sensor location uncertainty constraint of each sensor rather than further vectorized relaxation, which can improve the source localization accuracy. Furthermore, it is unnecessary to add a penalty term to the objective function of our proposed convex optimization formulation, which can efficiently avoid the costly searching step to the penalty factor of traditional source localization methods. Also, we analyze the effect of the constraint related to the sensor location uncertainty, and unique localizability of our proposed method. The simulation and experimental results show that our proposed method can yield an efficient estimate compared with other robust source localization methods.