Sensor Network Event Localization via Nonconvex Nonsmooth ADMM and Augmented Lagrangian Methods

Event localization plays a fundamental role in many wireless-sensor network applications, such as environmental monitoring, homeland security, medical treatment, and health care, and it is essentially a nonconvex and nonsmooth problem. In this paper, we address such a problem in a completely decentralized way based on augmented Lagrangian methods and alternating direction method of multipliers (ADMM). A decentralized algorithm is proposed to solve the nonsmooth and nonconvex event localization problem directly, rather than using conventional convex relaxation techniques. The avoidance of convex relaxation is significant in that convex relaxation-based methods generally suffer from high computational complexity. The convergence properties are also evaluated and substantiated using numerical simulations, which show that the proposed algorithm achieves better localization accuracy than existing projection-based approaches when the target is within the convex hull of localization sensors. When the target is outside the convex hull, numerical simulations show that the proposed approach has a higher probability to converge to the target event location than existing projection-based approaches. Numerical simulation results show that our approach is also robust to network topology changes.