In this paper, we consider the problem of distributed parameter estimation in imperfect environments for wireless sensor networks (WSNs). By imperfect environments, we refer to distortions that can be caused by sensor noise, quantization noise and channel effect. A novel statistical model is proposed to quantify these errors in WSNs. The first and second order statistics are derived analytically. The estimator is then probability density function unaware.

An analytical bound of the mean square error (MSE) performance at the fusion center is also derived. We further apply the proposed method to the power scheduling problem of WSNs. By formulating it as a convex optimization problem, an analytical solution is obtained. Simulation results show that the proposed approach outperforms the conventional distributed estimation methods. For the power scheduling application, the proposed method is shown to have an improved power saving compared to a classic method in the literature.