On weak points of the ellipsoidal intersection fusion

The Ellipsoidal Intersection algorithm aims at fusing two state estimates under a partial knowledge of the cross-correlation of the estimation errors. However, it has been observed that it does not provide an upper bound of all admissible fused mean square error matrices. This paper provides a mathematical tool for an analysis of the fusion under the considered partial knowledge of correlations. The tool facilitates the visualisation of the improvement gained by the partial knowledge and exposes weak points of the Ellipsoidal Intersection fusion. Finally, strictness of the fusion assumption relative to the Covariance Intersection fusion is demonstrated.