  A key challenge in Bayesian decentralized data fusion is the `rumor
propagation' or `double counting' phenomenon, where previously sent data
circulates back to its sender. It is often addressed by approximate methods
like covariance intersection (CI) which takes a weighted average of the
estimates to compute the bound. The problem is that this bound is not tight,
i.e. the estimate is often over-conservative. In this paper, we show that by
exploiting the probabilistic independence structure in multi-agent
decentralized fusion problems a tighter bound can be found using (i) an
expansion to the CI algorithm that uses multiple (non-monolithic) weighting
factors instead of one (monolithic) factor in the original CI and (ii) a
general optimization scheme that is able to compute optimal bounds and fully
exploit an arbitrary dependency structure. We compare our methods and show that
on a simple problem, they converge to the same solution. We then test our new
non-monolithic CI algorithm on a large-scale target tracking simulation and
show that it achieves a tighter bound and a more accurate estimate compared to
the original monolithic CI.
