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This paper deals with data fusion for the purpose of estimation. Three fusion architectures are considered: centralized, distributed, and hybrid. A unified linear model and general framework for these three architectures are established. Optimal fusion rules in the sense of best linear unbiased estimation (BLUE), weighted least squares (WLS), and their generalized versions are presented for cases with either complete, incomplete, or no prior information. These rules are much more general and flexible than previous results. For example, they are in a unified form that are optimal for all the three fusion architectures with arbitrary correlation of local estimates or observation noises across sensors or across time.. They are also in explicit forms convenient for implementation. The relationships among these rules are also presented.

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