Fast and Convergent Method for Large-Scale Sensor Network Localization With Anchor Uncertainty

The localization of sensor networks involves determining the spatial coordinates of each sensor in a deployed network. This task is accomplished by utilizing noisy distance measurements between neighboring sensors and a limited number of anchor sensors, which are sensors with known approximate locations. In this study, we present a unified maximum-likelihood formulation to address the sensor network localization problem. Our formulation incorporates anchor uncertainty by employing a truncated normal multivariate distribution. This unified approach generalizes previous formulations as it is applicable to various network architectures and noise levels, and various anchor certainty or uncertainty scenarios. Additionally, we introduce a novel algorithm that is simple, fast, fully distributed, and parallel. This algorithm converges to critical points of the non-convex, non-smooth, and constrained unified maximum-likelihood formulation. Notably, the algorithm is suitable for both centralized and distributed network architectures, making it well-suited for very large-scale networks comprising even thousands of sensors.