Distributed estimation with dependent observations in wireless sensor networks

A wireless sensor network with a fusion center is considered to study the effects of dependent observations on the parameter estimation problem. The sensor observations are corrupted by Gaussian noise with geometric spatial correlation. From an energy point of view, sending all the local data to the fusion center is the most costly, but leads to optimum performance results since all the dependencies are taken into account. From an estimation accuracy point of view, sending only parameter estimates is the least accurate, but is the most parsimonious in terms of communication costs. Hence, this tradeoff between the energy efficiency and the estimation accuracy is explored by comparing the performance of maximum likelihood estimator (MLE) and the sample average estimator (SAE) under various topologies and communication protocols. We start by reviewing the results from the one-dimensional case and continue by extending those results to various two-dimensional topologies. Surprisingly, we discover a class of regular polygon topologies where the MLE under spatial correlation reduces to the SAE.