Optimal linear estimator of origin-destination flows with redundant data

Suppose given a network endowed with a multiflow. We want to estimate some quantities connected with this multiflow, for instance the value of an s‐t flow for one of the sources‐sinks pairs s‐t, but only measures on some arcs are available, at least on one s‐t cocycle (set of arcs having exactly one endpoint in a subset X of vertices with s∈X and t∉X). These measures, supposed to be unbiased, are random variables whose variances are known. How can we combine them optimally in order to get the best estimator of the value of the s‐t flow?