TY  - JOUR
CY  - Cambridge, MA
ID  - publications50339
UR  - http://tse-fr.eu/pub/130263
A1  - Tang, Yukai
A1  - Lasserre, Jean-Bernard
A1  - Yang, Heng
N2  - 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.
VL  - vol. 242
TI  - Uncertainty Quantification of Set-Membership Estimation in Control and Perception : Revisiting the Minimum Enclosing Ellipsoid
AV  - none
EP  - 298
Y1  - 2024///
PB  - JMLR
JF  - Proceedings of Machine Learning Research
KW  - Set-Membership Estimation
KW  - Minimum Enclosing Ellipsoid
KW  - Semidefinite Relaxations
SN  - 2640-3498
SP  - 286
ER  -