Magnetic Induction-Based Localization in Randomly Deployed Wireless Underground Sensor Networks

Wireless underground sensor networks enable many applications, such as mine and tunnel disaster prevention, oil upstream monitoring, earthquake prediction and landslide detection, and intelligent farming and irrigation among many others. Most applications are location-dependent, so they require precise sensor positions. However, classical localization solutions based on the propagation properties of electromagnetic waves do not function well in underground environments. This paper proposes a magnetic induction (MI)-based localization that accurately and efficiently locates randomly deployed sensors in underground environments by leveraging the multipath fading free nature of MI signals. Specifically, the MI-based localization framework is first proposed based on underground MI channel modeling with additive white Gaussian noise, the designated error function, and semidefinite programming relaxation. Next, this paper proposes a two-step positioning mechanism for obtaining fast and accurate localization results by: first, developing the fast-initial positioning through an alternating direction augmented Lagrangian method for rough sensor locations within a short processing time, and then proposing fine-grained positioning for performing powerful search for optimal location estimations via the conjugate gradient algorithm. Simulations confirm that our solution yields accurate sensor locations with both low and high noise and reveals the fundamental impact of underground environments on the localization performance.