Optimization-based UWB positioning with multiple tags for estimating position and rotation simultaneously

Currently, the ultra-wideband (UWB) positioning scheme is widely applied to indoor robot positioning and has achieved high positioning accuracy. However, in some narrow and complex environments, its accuracy is still significantly degraded by the multipath effect or non-line-of-sight situations. In addition, the current single tag-based pure UWB positioning methods only estimate the tag position and ignore the rotation estimation of the robot. Therefore, in this paper, we propose a multiple tags-based UWB positioning method to estimate the position and rotation simultaneously, and further improve the position estimation accuracy. To be specific, we first install four fixed tags on the robot. Then, based on the ranging measurements, anchor positions and geometric relationships between each tag, we design five different geometric constraints and smooth constraints to build a whole optimization function. With this optimization function, both the rotations and positions at each time step can be estimated by the iterative optimization algorithm, and the results of tag positions can be improved. Both simulation and real-world experiments are conducted to evaluate the proposed method. Furthermore, we also explore the effect of relative distances between multiple tags on the rotations in the experiments. The experimental results suggest that the proposed method can effectively improve the position estimation performance, while the large relative distances between multiple tags benefit the rotation estimation.