Distributed Estimation Fusion with Unavailable Cross-Correlation

The problem of distributed fusion for estimation when the cross-correlation of errors of local estimates is unavailable is addressed. We discuss a general estimation fusion approach for this problem-generalized convex combination (GCC) - and classify various GCC fusion approaches in three categories. We develop three GCC fusion algorithms for the problem under consideration. First, based on a set-theoretic formulation of the problem, we propose a relaxed Chebyshev center covariance intersection (RCC-CI) algorithm to fuse the local estimates. Second, based on an information-theoretic criterion, we develop a fast covariance intersection (IT-FCI) algorithm with weights in a closed form. The proposed RCC-CI and IT-FCI algorithms are characterized by both the local estimates and the mean-square error (MSE) matrices being taken into account. Third, to fuse incoherent local estimates, we propose a fault-tolerant GCC fusion algorithm by introducing an adaptive parameter, which can obtain robust fusion and the degree of robustness varies with that of incoherency between estimates to be fused.