Knowledge of the cross-correlation of errors of local estimates is needed for many distributed fusion algorithms. However, in a fully distributed system or decentralized network, the calculation of crosscorrelation between local estimates is quite involved and may be impractical. The Covariance Intersection (CI) algorithm has been proposed under unknown correlation. But the CI algorithm has high computational complexity because it requires optimization of a nonlinear cost function. This paper presents a fast CI algorithm, and an alternative optimization criterion with a closed form solution. Based on this criterion, a fast and fault-tolerant convex combination fusion algorithm is presented by introducing an adaptive parameter, which can obtain robust estimate when estimates to be fused are inconsistent with each other, and the degree of robustness of fusion result varies with that of inconsistency between estimates to be fused.