Distributed Estimation by Two Agents with Different Feature Spaces

We consider the problem of estimation of a function by two agents (and a fusion center) given local data. Data comprises of samples of an independent variable and the corresponding value of a dependent variable. The agents are given a set of features using which they construct suitable function spaces to formulate and solve the estimation problem. The estimated functions are to be uploaded to a fusion space where they are fused to obtain the system estimate of the mapping and then downloaded by the agents to gather knowledge about the other agents estimate of the function. To this end, we present the following: a systematic construction of fusion space given the features of the agents; the derivation of an uploading operator for the agents to upload their estimated functions to a fusion space; an optimization problem in the fusion space to fuse the functions uploaded; the derivation of a downloading operator for the fused function to be downloaded. Through an example on least squares regression, we demonstrate the distributed estimation architecture that has been developed.