Joint Distributed Estimation and Random Gain Channel Estimation With Beta Prior

In this letter, we propose a joint distributed estimation and channel estimation algorithm for wireless sensor networks (WSNs). We assume a random gain channel model with a Beta prior, where the channel gain is an attenuation factor ranging between zero and one. To estimate the augmented unknown vector, which includes both the unknown vector and the channel gain vector, we employ Maximum A Posteriori (MAP) estimation. This is achieved through an iterative steepest-descent method to find the MAP estimators for both the unknown vector and the channel gain vector. We mathematically derive the optimum combination coefficients that minimize disturbance. Additionally, we propose a separate approach for channel gain estimation using Least Squares (LS) and provide the convexity analysis of the cost function along with the sufficient conditions for the convergence of the iterative channel gain estimator. Simulation results demonstrate the effectiveness of the proposed algorithm compared to some other algorithms in the literature, specially when channel gains are modeled with a Beta prior.