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First, to attack the correlation and outliers, a correlated robust Kalman filtering (coR<jats:sup>2<\/jats:sup>KF) scheme with weighted matrices on innovation sequences is introduced as local estimator. It is shown that the proposed coR<jats:sup>2<\/jats:sup>KF takes both conventional Kalman filter and robust Kalman filter as a special case. Then, a novel version of our internal ellipsoid approximation fusion (IEAF) is used in the fusion center to handle the unknown cross-correlation of local estimates. The explicit solution to both fusion estimate and corresponding covariance is given. 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