Linear fusion of estimates under the condition of no knowledge of correlation of estimation errors has reached maturity. On the other hand, various cases of partial knowledge are still active research areas. A frequent motivation is to deal with "common information" or "common noise", whatever it means. A fusion rule for a strict meaning of the former expression has already been elaborated. Despite the dual relationship, a strict meaning of the latter one has not been considered so far. The paper focuses on this area. The assumption of unknown "common noise" is formulated first, analysis of theoretical properties and illustrations follow. Although the results are disappointing from the perspective of a single upper bound of mean square error matrices, the partial knowledge demonstrates improvement over no knowledge in suboptimal cases and from the perspective of families of upper bounds.