  This paper introduces a new conservative fusion method to exploit the
correlated components within the estimation errors. Fusion is the process of
combining multiple estimates of a given state to produce a new estimate with a
smaller MSE. To perform the optimal linear fusion, the (centralized) covariance
associated with the errors of all estimates is required. If it is partially
unknown, the optimal fusion cannot be computed. Instead, a solution is to
perform a conservative fusion. A conservative fusion provides a gain and a
bound on the resulting MSE matrix which guarantees that the error is not
underestimated. A well-known conservative fusion is the Covariance Intersection
fusion. It has been modified to exploit the uncorrelated components within the
errors. In this paper, it is further extended to exploit the correlated
components as well. The resulting fusion is integrated into standard
distributed algorithms where it allows exploiting the process noise observed by
all agents. The improvement is confirmed by simulations.
