Sparse Bayesian consensus-based distributed field estimation

We present a fully decentralized algorithm that is inspired by sparse Bayesian learning (SBL) and can be used for non-parametric sparse estimation of unknown spatial functions - spatial fields - with wireless sensor networks (WSNs). It is assumed that a spatial field is represented as a linear combination of weighted fixed basis functions. By exploiting the similarity between the topology of a WSN and the proposed probabilistic graphical model for distributed SBL, a combination of variational inference and loopy belief propagation (LBP) is used to obtain the weights and the sparse subset of relevant basis functions. The algorithm requires only transmission between neighboring sensors and no multi-hop communication is needed. Furthermore, it does not rely on a fixed network structure and no information about the total number of sensors in the network is necessary. Due to consensus in the weight parameters between neighboring sensors, it is demonstrated that also the sparsity patterns of relevant basis functions generally agree. The effectiveness of the proposed algorithm is demonstrated with synthetic data.