  This work addresses the problem of fusing two random vectors with unknown
cross-correlations. We present a formulation and a numerical method for
computing the optimal estimate in the minimax sense. We extend our formulation
to linear measurement models that depend on two random vectors with unknown
cross-correlations. As an application we consider the problem of decentralized
state estimation for a group of agents. The proposed estimator takes
cross-correlations into account while being less conservative than the widely
used Covariance Intersection. We demonstrate the superiority of the proposed
method compared to Covariance Intersection with numerical examples and
simulations within the specific application of decentralized state estimation
using relative position measurements.
