Comparison and Improvement of 3D-Multilateration for Solving Simultaneous Localization of Drones and UWB Anchors

Drone fleets have attracted a lot of attention from the research community in recent years. One of the biggest challenges in deploying such systems is localization. While GNSS localization systems can only be effective in open outdoor environments, new solutions based on radio sensors (e.g., ultra-wideband) are increasingly being used for localization in various situations and environments. However, self-localization without prior knowledge of anchor positions remains an open problem, which, for example, makes it impossible to track a moving target. In this article, we provide a comparison of different variants of gradient descent-based algorithms, with a new improved variant, for solving the localization problem using relative distance measurements and multilateration. Extensive simulation results are provided, varying the number of neighboring nodes for multilateration, algorithm initialization, and cost functions, in addition to accounting for node positioning errors and ultra-wideband sensor noise. They help set the adequate rate for fixed step descent when used and produce a damping effect in the variable step rate, which will otherwise diverge. In particular, we consider three scenarios: (i) self-localization of anchors; (ii) tracking moving targets using ultra-wideband range sensors; and (iii) simultaneously estimating unknown positions of ultra-wideband anchors and mobile agents (drones). The latter shows a great improvement in localization accuracy.