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.

翻译：集合成员估计（SME）输出一个保证覆盖真实值的集合估计器。然而，此类集合由（众多）抽象（且可能非凸）的约束所定义，因而难以处理。我们提出了可计算的算法，以最小包围椭球（MEE）的形式计算SME的简单且紧致的过近似。我们首先介绍了Nie与Demmel（2005）基于平方和松弛提出的包围椭球层次结构，该结构渐近收敛于基本半代数集的最小包围椭球。然而，该框架在现代控制与感知问题中因计算挑战而难以应用。我们提出了三项计算增强以使该框架实用化，即约束剪枝、广义松弛切比雪夫中心以及处理非欧几里得几何。我们在系统辨识和物体位姿估计问题上展示了数值算例。