Distributed estimation fusion under unknown cross-correlation: An analytic center approach

We develop an analytic center approach to distributed estimation fusion when the cross-correlation of errors between local estimates is unknown. Based on a set-theoretic formulation of the problem, we seek an estimate that maximizes the complementary squared Mahalanobis "distance" between the local and the desired estimates in a logarithmic average form, and the optimal value turns out to be the analytic center. For our problem, we then prove that the analytic center is a convex combination of the local estimates. As such, our proposed analytic center covariance intersection (AC-CI) algorithm could be regarded as the covariance intersection (CI) algorithm with respect to a set-theoretic optimization criteria.