Linear Fusion with Element-Wise Knowledge

The process of combining data and estimates is inherent in estimation problems. This paper focuses on the linear fusion under the assumption that only some elements of the cross-correlation matrix of the estimation errors are known. Configurations of the knowledge are discussed individually for up to five estimates. For an arbitrary number of estimates, a general construction of upper bounds of the joint mean square error matrix is proposed. Last, the relation with the Split Covariance Intersection fusion is discussed.