Scaling Results for Robust Distributed Estimation in Sensor Networks Using Order Statistics

Robust modeling of estimation error in a distributed sensor network under random sensing environment is a challenging problem. In this paper, we propose a novel methodology based on order statistics to statistically model scaling behavior of the mean-squared error (MSE) for distributed estimation in a wireless sensor network. In particular, by leveraging order statistics of the random signal-to-noise ratios (SNRs) over the entire network, we derive and compute cumulative distribution functions of average MSE for distributed estimation. In addition, we develop a novel approach of expressing the scaling of the maximum of independent and identically distributed (i.i.d.) sensors’ random SNRs by deriving the distribution function of the estimation error. Simulation results validate the close gap between the proposed method and the empirically obtained result.