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-ofsquares 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：集员估计（SME）输出保证包含真实值的集合估计量。然而，这类集合由（大量）抽象且可能非凸的约束定义，因此难以处理。我们提出了可行算法，以最小包络椭球（MEE）形式计算SME的简单且紧致的过逼近。首先引入Nie和Demmel（2005）提出的基于平方和松弛的包络椭球层级结构，该结构渐近收敛于基本半代数集的最小包络椭球。然而，由于计算挑战，该框架在现代控制与感知问题中难以应用。我们贡献了三种计算增强方法使该框架实用化，即约束剪枝、广义松弛切比雪夫中心以及非欧几里得几何处理。通过系统辨识和目标位姿估计的数值示例进行验证。