Safety-Critical Ultra-Wideband 3D Localization With Set-Membership Uncertainty Representation

Existing localization methods frequently focus on offline benchmarking based on datasets and assume that the methods possess the same performance in online applications without ground truth. However, since datasets always provide a limited number of scenarios, the reliability of localization methods in unknown scenarios cannot be inferred from their performance on the datasets. Therefore, the over-reliance on benchmarking results will pose a safety risk to the practical applications of localization methods. Inspired by this challenge, in this letter, we propose a safety-critical localization system that can measure the reliability of the estimated locations online in real time based on the set-membership uncertainty. By considering various system uncertainties and addressing the imbalance issue within the current set-membership filters, we design a dimension-balanced set-membership filter (DB-SMF) for ultra-wideband 3D localization based on the unknown but bounded (UBB) assumption and the dimension-balanced objective functions. Compared with the Gaussian uncertainty, our set-membership uncertainty can cover the unknown ground-truth locations with bounded sets. In safety-critical scenarios, this uncertainty can provide deterministic state bounds for tasks such as motion control and obstacle avoidance, thereby better ensuring the safety of the robot. Real-world experiments show that our DB-SMF can estimate set-membership uncertainties with the ability to cover unknown ground truth in finite spaces from range measurements and in this way ensure the safety of the localization system.