Decentralized Estimation for Bandwidth Constrained Sensor Networks in Clustered Environments

This paper extends the homogeneous wireless sensor network (WSN) model to possess (possibly) varying levels of noise that represent environment clusters in a WSN. The estimation of the source parameter is approached from maximum likelihood (ML) perspective. The Cramer Rao lower bound (CRLB) for any unbiased estimator operating in a clustered WSN environment is derived. Noting that the ML estimate cannot be found in closed-from, we resort to a numerical search. Although numerically determined, the ML estimate is guaranteed to converge to the optimal solution since it is shown here that the log-likelihood function is concave. Also considered is the estimation of a random parameter with a priori information, which is approached from maximum a posteriori (MAP) perspective. Finally, the proposed MAP and ML optimal are validated and compared to theoretical bounds with illustrative numerical examples.