Compressive Diffusion Bias-Compensated Bayesian Adaptation Over Networks With Noisy Data

This paper considers the scenario of noisy inputs and compressive diffusion (for reducing communication load) with noisy links over sensor networks. We first study the implementation of diffusion bias-compensated Bayesian adaptation (DBCBA) for noisy inputs, which outperforms the existing solution. Next, an average-estimate step is applied to lessen the impact of link noise in the full diffusion case, yielding a diffusion average-estimate bias-compensated Bayesian adaptation (DABCBA) algorithm. A Bayes-based adaptation construction step is then presented to reconstruct the compressed diffusion information in the presence of link noise, resulting in a compressive DBCBA (CDBCBA) algorithm whose mean and mean-square behaviors are analyzed and the closed-form expression of the steady-state mean-square deviation is derived. In addition, estimators are devised for the input and output noise variances. The excellent performance of our algorithms is demonstrated via numerical examples while the theoretical calculation aligns closely with the simulation results.