Bayesian hypothesis testing detector for one bit diffusion LMS with blind missing samples

This paper proposes a sparse distributed estimation algorithm when missing data occurs in the measurements over adaptive networks. Two classes of measurement models are considered. First, the traditional linear regression model is investigated and second the sign of the linear regression model is studied. The latter is referred to as one-bit model. We utilize the diffusion LMS strategy, in the proposed methods, where a set of nodes cooperates with each other to estimate a vector model parameter. In both models, it is shown that replacing the missing sample with a simple estimate is equivalent to removing the missing sample from the distributed diffusion algorithm. We consider two cases, where in the first case the positions of missing samples are known (non-blind) and in the second case the positions of missing samples are unknown (blind). In the linear regression model scenario, a Bayesian hypothesis testing (BHT) is used for detection of the missing samples. In the one-bit model, in addition to BHT detector, a simple heuristic detector, based on mean square error (MSE), is also suggested. Simulation results show the effectiveness of the proposed detector-assisted distributed algorithms.