A geometrical perspective on fusion under unknown correlations based on Minkowski sums

In decentralised estimation, locally measured data are processed locally and the local filters are unaware of the other ones. Due to the lack of the global knowledge, the fusion of the local estimates cannot utilise the correlations of the local estimate errors in the computation of the fused mean square error matrix. For this reason, algorithms of fusion under unknown correlations have been designed to provide upper bounds of these matrices. This paper reveals a fundamental relation between the upper bounds and Minkowski sums of ellipsoids. The obtained insight improves the comprehension of the fusion algorithms. Application of the ellipsoidal calculus is illustrated using elemental examples.