Nonlinear data fusion

Consider the following estimation problem: The state trajectory of a random process is observed by K distinct observers, using noise-corrupted observations. Each observer processes his own observation history, to obtain the local conditional distribution of the state, as a function of time. Assume that sufficient statistics representing each local conditional distribution are communicated to a coordinator at a central location at each point in time. The coordinators´s estimation problem consists of constructing the overall conditional distribution of the state, conditioned on knowing all of the observations, while using only the sufficient statistics communicated to him.