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

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

2010-12-21

arxiv.org/abs/1012.4795v1

Mathematics

Optimization and Control

Scientific paper

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.

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