Decentralised estimation aims at providing the best combination of multiple estimates. Since the exact solutions are expensive in terms of computation and communication requirements, the mean square error optimality is traded for the bound optimality. Fusion under unknown correlations has been inspected for two decades and the research now focuses on a partial knowledge of the correlations. This paper focuses on the assumption that the estimates to be fused were obtained by the optimal processing of local data with independent measurement errors. A generalisation of a recent solution to such a problem is proposed. In particular, non-uniqueness of the optimal fusion weights is discovered. The relation of the generalised and existing solutions is discussed and illustrative examples are given. (C) 2018 Elsevier Ltd. All rights reserved.