Some aspects of fusion in estimation theory

The problem of fusing or combining various estimates to obtain a single good estimate is investigated. The problem of fusion in estimation theory is addressed, and several examples using common distributions in which virtually any method of fusion would be useless in approximating the random variable of interest are presented. A theorem which, for a very general situation, shows that fusion resulting in an almost surely exact approximation is always possible is presented. In particular, this result addresses the situation in which the data consists of the random variable of interest corrupted by additive Gaussian noise and the random variable of interest could be any second-order random variable. Finally, an example which illustrates the utility of this result is presented