Impact of Heterogeneous UWB Sensor Noise on the Optimality and Sensitivity of Mobile Positioning Systems

In this paper, we propose a theoretical framework for designing a multi-robot formation equipped with Ultra-wideband (UWB) sensors to localize a target robot. In the presence of noisy range measurements, the accuracy of the target robot’s pose estimation is highly dependent on the chosen formation geometry. Different from existing works, we account for the heterogeneous standard deviations of range measurements across different UWB transmitter-receiver pairs. We establish new optimality conditions for formation geometries and conduct a sensitivity analysis of optimal formations under robot positioning errors. In a 2D setting, we derive necessary and sufficient conditions for both optimality and robustness to robot positioning uncertainty. Experimental results confirm the heterogeneous standard deviations of UWB range measurements and validate the target robot’s confidence ellipse model. An experimental comparison of formation geometries, optimized with and without considering heterogeneous noise, emphasizes the importance of accounting for the heterogeneous standard deviations of range measurements. In addition, we experimentally demonstrate that robust formation geometries improve the target robot’s confidence ellipse in the presence of positioning errors.