Bayesian Cramér-Rao bound for distributed estimation of correlated data with non-linear observation model

In this paper we study the problem of distributed estimation of a random vector in wireless sensor networks (WSNs) with non-linear observation model. Sensors transmit their binary modulated quantized observations over orthogonal erroneous wireless channels (subject to fading and noise) to a fusion center, which is tasked with estimating the unknown vector. We derive the Bayesian Cramer-Rao Bound (CRB) matrix and study the behavior of its trace (through analysis and simulations), with respect to the observation and communication channel signal-to-noise ratios (SNRs). The derived CRB serves as a benchmark for performance comparison of different Bayesian estimators, including linear MMSE estimator.