Rectification of Partitioned Covariance Intersection

Linear combination of two estimates is a cornerstone of decentralised estimation/fusion. Under unknown or partially known correlation of estimation errors, a conservative fusion constructs upper bounds of mean square error (MSE) matrices of the fused estimate. This paper points out a defect in the Partitioned Covariance Intersection fusion rule. By explicitly parametrising the admissible MSE matrices, their tight upper bounds are found. The new bounds are used to rectify the existing fusion rule. A virtue and interpretation of the new fusion rule are discussed and an illustrative example is presented.