Error resilient distributed estimation in wireless sensor networks

We consider distributed parameter estimation using quantized observations in wireless sensor networks (WSN) operating in a noisy channel environment. Due to bandwidth constraints, each sensor quantizes its local observation into one bit of information. Previously, adaptive quantization(AQ) schemes were developed under the assumption of perfect communication links between the sensors and the fusion center (FC). In this paper we propose an adaptive quantization scheme for a WSN with channel links modeled as binary erasure channels. A first-order Hidden Markov Model (HMM) framework is introduced to model the adaptive quantization scheme. The introduction of a HMM framework aids in the systematic design of an estimator. To address the significant problem of bit erasures, we propose an Expectation-Maximization (EM) based estimator. Theoretical closed form solutions for the Cramer-Rao lower bounds are developed for the proposed estimation problem under certain assumptions. We analyze the performance of the proposed quantization scheme and estimator under different criteria. Numerical simulation results are shown for the proposed adaptive quantization and EM parameter estimation scheme under different scenarios. The simulation results indicate that the proposed quantization scheme and estimator are robust and can provide superior performance for erasure rates up to 10%.