Distributed Estimators for Multi-Sensor Systems

Abstract

Consider the following distributed estimation problem. A coordinator must reconstruct the (global) density of a random process, Conditioned on N distributed noise-corrupted observation histories. The coordinator can only access the X (local) conditional probability densities produced by local processing of these distributed observation histories, not the observation histories themselves. The coordinator's models of the distributed observation dynamics can differ from the local processors’ models. By constraining the choice of the local models, the coordinator can recover exactly the centralized conditional density (as if it had access to all the observation histories). This paper extends previous work in nonlinear distributed estimation to include cases where the local models are different from the observed process model. This extension will lessen the local processors’ complexities or computational load without losing the optimality of the coordinator's fusion algorithmWe assume that: the observed random process is a nonlinear (linear) stochastic differential equation driven by a Brownian motion; the observation processes are corrupted with additive Brownian motions that are identically modeled by the coordinator and the local processor; and the sufficient statistics of the local conditional probability densities are transmitted to the coordinator, after every local observation, over noise-free channels