Optimization-Based Single Anchor UWB Positioning System for Mobile Robots

In recent years, ultra-wideband (UWB) technology has found extensive applications in indoor positioning systems (IPS). However, a significant challenge for achieving low-cost positioning solutions is the requirement of three or more anchors in most existing UWB positioning methods. In this article, we propose a method that achieves mobile robot localization using only a single anchor. To solve for the initial positioning of the robot, we construct a factor graph composed of multiple sets of odometry position and UWB distance measurements, which is then solved through graph optimization. The robot's tracking problem can be transformed into solving a system of equations with inequality constraints. We propose an adaptive trust region algorithm for solving a system of equations jointly composed of preprocessed UWB distance measurements, odometry increments, and kinematic constraints. The trust region radius is adaptively adjusted according to the robot's motion model, leading to the iterative determination of the robot's optimal position. Experimental results demonstrate that this system achieves a high level of localization accuracy.