# Uncertainty Quantification of Set-Membership Estimation in Control and Perception: Revisiting the Minimum Enclosing Ellipsoid

arXiv: https://arxiv.org/abs/2311.15962 · HTML: https://mlsanity.com/paper/2311.15962/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2023.

## Built on by (most cited first, 3 of 3)

- [On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets](https://mlsanity.com/paper/2406.00574/) (2024)
- [Swap Regret Minimization Through Response-Based Approachability](https://mlsanity.com/paper/2602.06264/) (2026)
- [Uncertainty Quantification for Visual Object Pose Estimation: S-Lemma Ellipsoidal Bounds](https://mlsanity.com/paper/2511.21666/) (2025)

## Abstract (arXiv)

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.