Decentralized Estimation with Dependent Gaussian Observations

This paper considers decentralized estimation with correlated noises under the Bayesian framework. For a tandem network with correlated additive Gaussian noises, we establish that threshold quantizers on local observations are optimal in the sense of maximizing Fisher information at the fusion center; this is true despite the fact that subsequent estimators may differ at the fusion center, depending on the statistical distribution of the parameter to be estimated. In addition, it is always beneficial to have the better sensor, i.e., the one with higher signal-To-noise ratio, serve as the fusion center in a tandem network. Finally, we identify different correlation regimes in terms of their impact on the estimation performance. These include the well-known case where negatively correlated noise benefits estimation performance as it facilitates noise cancellation, as well as two distinct regimes with positively correlated noises.