The outer Lowner-John method is widely used in sensor fusion applications to find the smallest ellipsoid that can approximate the intersection of a set of ellipsoids, described by positive definite covariance matrices modeling the quality of each sensor. We propose a distributed algorithm to solve this problem when these matrices are defined over the network's nodes. This is of particular significance as it is the first decentralized algorithm capable of computing the covariance intersection ellipsoid by combining information from the entire network using only local interactions. The solution is based on a reformulation of the centralized problem, leading to a local protocol based on exact dynamic consensus tools. After reaching consensus, the protocol converges to an outer Lowner-John ellipsoid in finite time, and to the global optimum asymptotically. Formal convergence analysis and numerical experiments are provided to validate the proposal's advantages.

翻译：外Löwner-John方法广泛应用于传感器融合领域，旨在寻找能够逼近一组椭球交集的最小椭球，这些椭球由表征各传感器质量的正定协方差矩阵描述。本文提出一种分布式算法，用于解决这些矩阵定义在网络节点上的问题。该工作具有特殊意义，因为它是首个仅利用局部交互即可融合全网络信息并计算协方差交集椭球的去中心化算法。该方案基于对中心化问题的重构，导出了基于精确动态一致性工具的局部协议。在达成一致性后，该协议在有限时间内收敛至外Löwner-John椭球，并渐近收敛至全局最优解。本文通过形式化收敛性分析与数值实验验证了该方案的优越性。