On Fusion of Partial Estimates Under Implicit Partial Knowledge of Correlation

Covariance Intersection fusion is bound-optimal under unknown correlations. Partial knowledge can improve the fusion. An implicit constraint on correlation has been introduced in the literature for full-vector estimates. This paper considers fusion of partial estimates. Weak and strong counterparts of the full-vector assumption are proposed. An analysis of admissible ideal fusions reveals that the considered implicit partial knowledge cannot improve the Covariance Intersection fusion of partial estimates. An exception is found for the strong assumption and fusion of one partial and one full-vector estimate. For this case, an improved fusion rule is presented.