eprintid: 50339 rev_number: 5 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/05/03/39 datestamp: 2025-02-12 14:26:09 lastmod: 2025-02-12 14:26:09 status_changed: 2025-02-12 14:26:09 type: article metadata_visibility: show creators_name: Tang, Yukai creators_name: Lasserre, Jean-Bernard creators_name: Yang, Heng creators_idrefppn: 056782799 creators_halaffid: 1002422;459 title: Uncertainty Quantification of Set-Membership Estimation in Control and Perception : Revisiting the Minimum Enclosing Ellipsoid ispublished: pub subjects: subjects_ECO abstract: Set-membership estimation (SME) outputs a set estimator that guarantees to cover the groundtruth. Such sets are, however, defined by (many) abstract (and potentially nonconvex) constraints and therefore difficult to manipulate. We present tractable algorithms to compute simple and tight overapproximations of SME in the form of minimum enclosing ellipsoids (MEE). We first introduce the hierarchy of enclosing ellipsoids proposed by Nie and Demmel (2005), based on sums-of-squares relaxations, that asymptotically converge to the MEE of a basic semialgebraic set. This framework, however, struggles in modern control and perception problems due to computational challenges. We contribute three computational enhancements to make this framework practical, namely constraints pruning, generalized relaxed Chebyshev center, and handling non-Euclidean geometry. We showcase numerical examples on system identification and object pose estimation. date: 2024 date_type: published publisher: JMLR official_url: http://tse-fr.eu/pub/130263 faculty: tse divisions: tse keywords: Set-Membership Estimation keywords: Minimum Enclosing Ellipsoid keywords: Semidefinite Relaxations language: en has_fulltext: FALSE view_date_year: 2024 full_text_status: none publication: Proceedings of Machine Learning Research volume: vol. 242 place_of_pub: Cambridge, MA pagerange: 286-298 refereed: TRUE issn: 2640-3498 oai_identifier: oai:tse-fr.eu:130263 harvester_local_overwrite: volume harvester_local_overwrite: pending harvester_local_overwrite: keywords harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: title harvester_local_overwrite: creators_halaffid harvester_local_overwrite: pagerange harvester_local_overwrite: publisher harvester_local_overwrite: place_of_pub oai_lastmod: 2025-02-03T07:33:07Z oai_set: tse site: ut1 citation: Tang, Yukai, Lasserre, Jean-Bernard and Yang, Heng (2024) Uncertainty Quantification of Set-Membership Estimation in Control and Perception : Revisiting the Minimum Enclosing Ellipsoid. Proceedings of Machine Learning Research, vol. 242. pp. 286-298.