RT Journal Article
SR 00
A1 Tang, Yukai
A1 Lasserre, Jean-Bernard
A1 Yang, Heng
T1 Uncertainty Quantification of Set-Membership Estimation in Control and Perception : Revisiting the Minimum Enclosing Ellipsoid
JF Proceedings of Machine Learning Research
YR 2024
FD 2024
VO vol. 242
SP 286
OP 298
K1 Set-Membership Estimation
K1 Minimum Enclosing Ellipsoid
K1 Semidefinite Relaxations
AB 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.
PB JMLR
SN 2640-3498
LK https://publications.ut-capitole.fr/id/eprint/50339/
UL http://tse-fr.eu/pub/130263