Optimization Based Self-localization for IoT Wireless Sensor Networks

In this paper we propose an embedded optimization framework for the simultaneous self-localization of all sensors in wireless sensor networks making use of range measurements from ultra-wideband (UWB) signals. Low-power UWB radios, which provide time-of-arrival measurements with decimeter accuracy over large distances, have been increasingly envisioned for realtime localization of IoT devices in GPS-denied environments and large sensor networks. In this work, we therefore explore different non-linear least-squares optimization problems to formulate the localization task based on UWB range measurements. We solve the resulting optimization problems directly using non-linear-programming algorithms that guarantee convergence to locally optimal solutions. This optimization framework allows the consistent comparison of different optimization methods for sensor localization. We propose and demonstrate the best optimization approach for the self-localization of sensors equipped with off-the-shelf microcontrollers using state-of-the-art code generation techniques for the plug-and-play deployment of the optimal localization algorithm. Numerical results indicate that the proposed approach improves localization accuracy and decreases computation times relative to existing iterative methods

Distributed Maximum Likelihood Sensor Network Localization

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks