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.