On the Equivalence of the General Covariance Union (GCU) and Minimum Enclosing Ellipsoid (MEE) Problems

TL;DR

This paper proves the surprising equivalence between the General Covariance Union and Minimum Enclosing Ellipsoid problems, linking covariance-based filtering methods with geometric data fusion approaches.

Contribution

It establishes the theoretical equivalence between GCU and MEE, bridging statistical and geometric interpretations in data fusion.

Findings

GCU and MEE solutions are mathematically equivalent.

The result connects covariance-based and geometric data fusion methods.

This equivalence has implications for filtering and data fusion techniques.

Abstract

In this paper we describe General Covariance Union (GCU) and show that solutions to GCU and the Minimum Enclosing Ellipsoid (MEE) problems are equivalent. This is a surprising result because GCU is defined over positive semidefinite (PSD) matrices with statistical interpretations while MEE involves PSD matrices with geometric interpretations. Their equivalence establishes an intersection between the seemingly disparate methodologies of covariance-based (e.g., Kalman) filtering and bounded region approaches to data fusion.