The Equivalence Between Distributed and Centralized Best Linear Unbiased Estimation Fusion

This paper discusses the equivalence of the performance between the optimal distributed and centralized fusion based on best linear unbiased estimation (BLUE). A necessary and sufficient condition for the optimal distributed BLUE fusion to have identical performance as their centralized counterparts is obtained by setting the difference of two optimal estimates based on the two fusion rules be zero. Furthermore, under some very mild conditions on estimatee and observation error, we provide two theorems when the observations are linear in the estimatee. Specifically, the optimal distributed BLUE fusion is identical to the centralized BLUE fusion if observation errors are uncorrelated across sensors or the observation matrix of each sensor is full row rank. Numerical examples corroborate our analysis.