Data fusion with minimal communication

Two sensors obtain data vectors x and y, respectively, and transmit real vectors m&oarr;₁(x) and m&oarr;₂(y), respectively, to a fusion center. The authors obtain tight lower bounds on the number of messages (the sum of the dimensions of m&oarr;₁ and m&oarr;₂) that have to be transmitted for the fusion center to be able to evaluate a given function f&oarr;(x,y). When the function f&oarr; is linear, they show that these bounds are effectively computable. Certain decentralized estimation problems can be cast in the framework and are discussed in some detail. In particular, the authors consider the case where x and y are random variables representing noisy measurements and f&oarr;(x,y)=E[z|x,y], where z is a random variable to be estimated. Furthermore, it is established that a standard method for combining decentralized estimates of Gaussian random variables has nearly optimal communication requirements