Distributed estimation: constraints on the choice of the local models

The following estimation problem is considered: a coordinator must reconstruct the (global) probability density of a nonlinear random process, conditioned on the noise-corrupted observation history. The coordinator can only access the (local) probability density produced by local processing of the observation history using a (local) model different from the process model. It is shown that if the local model satisfies an algebraic constraint, the coordinator can reconstruct the same conditional density of the state process as the one obtained if the observations were processed using the coordinator (process) model. It is assumed that the random process is a nonlinear stochastic differential equation driven by a Brownian motion, and the observation process is corrupted by additive Brownian motion, which is identically modeled by the coordinator and the local processor