Decentralized Estimation Over Noisy Channels for Bandwidth-Constrained Sensor Networks

Recently proposed decentralized estimation methods do no consider errors occurring during the transmission of binary observations from the sensors to fusion center. In this paper, we extend the decentralized estimation model to the case where imperfect transmission channels are considered. The proposed estimator, which operates on additive channel noise corrupted versions of quantized noisy sensor observations, is approached from maximum likelihood (ML) perspective. The ML estimate unfortunately has no closed-form solution. We analyze the log-likelihood function showing that it is log-concave, thereby indicating that numerical methods, such as Newtons algorithm, can be utilized to obtain the optimal solution. A suboptimal mean estimator that requires minimal information about the channel and sensing environment is also proposed. Simulation results evaluating the variances of the proposed optimal and suboptimal solutions are provided.