Diffusion Average-Estimate Bias-Compensated LMS Algorithms over Adaptive Networks Using Noisy Measurements

In this paper, we consider the problem of distributed estimation over adaptive networks in the presence of noisy input, output and communication links. First, a diffusion average-estimate bias-compensated LMS (D-ABC-LMS) algorithm is devised for processing these noisy measurements. Different from the existing diffusion schemes, it consists of three steps: (i) bias-compensated weight update, (ii) average estimation and (iii) weight combination, where the second step utilizes a moving average technique to process imprecise exchange weights caused by communication link noise. Then, we analyze the stability and convergence of the D-ABC-LMS algorithm, and derive closed-form expressions to predict its steady-state mean-square deviation (MSD) and network MSD (NMSD). In addition, by introducing one more step via the adaptive mixture of the noisy exchange weight vectors and their denoised estimates, we propose a diffusion mixed average-estimate bias-compensated LMS (D-MABC-LMS) method for increasing the convergence rate of the D-ABC-LMS scheme. Finally, computer simulation results show the superiority of the proposed algorithms over previously reported techniques using noisy measurements over adaptive networks.