Optimal quantizers for distributed Bayesian estimation

In this paper, we consider the problem of quantizer design for distributed estimation under the Bayesian criterion. We derive general optimality conditions under the assumption of conditionally independent observations at the local sensors and show that for a conditionally unbiased and efficient estimator at the Fusion Center, identical quantizers are optimal when local observations have identical distributions. This results in an N-fold reduction in complexity where N is the number of sensors. We illustrate our approach by applying it to the location parameter estimation problem.