DATA FUSION WITH MINIMAL COMMUNICATION

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