Algebraic analysis of data fusion with ellipsoidal intersection

For decentralized fusion problems, ellipsoidal intersection has been proposed as an efficient fusion rule that provides less conservative results as compared to the well-know covariance intersection method. Ellipsoidal intersection relies on the computation of a common estimate that is shared by the estimates to be fused. In this paper, an algebraic reformulation of ellipsoidal intersection is discussed that circumvents the computation of the common estimate. It is shown that ellipsoidal intersection corresponds to an internal ellipsoidal approximation of the intersection of covariance ellipsoids. An interesting result is that ellipsoidal intersection can be computed with the aid of the Bar-Shalom/Campo fusion formulae. This is achieved by assuming a specific correlation structure between the estimates to be fused.