I am attempting to understand the theory behind combining correlated estimates which have unequal variances. All the estimates are unbiased estimates of one true mean.

I've been reading the paper "Almost linearly-optimum combination of unbiased estimates" by Max Halperin. (If my description of the problem isn't clear, Halperin's abstract may make more sense.) While it has the equations I need, I'm a little confused about how he got to that point.

Can anyone suggest a textbook that presents the solution to this problem at an introductory-to-intermediate statistics level? I am a graduate student in engineering, and I have what probably amounts to an introductory-level statistics course worth of statistics knowledge.

Thanks for any suggestions.