Hierarchical Bayesian Kalman filters for wireless sensor networks

We are interested in reconstructing signals sensed by wireless sensor networks over large areas with a great number of nodes. Numerous constraints usually exist regarding power consumption, communication bandwidth, computational capacity and data volume. By assuming that the sensed signal is sparse in some transform domain we are able to exploit structures in the signal towards achieving coarser and easier-to-deploy sensing grids. By tracking the statistics of the sensed signal it is possible to achieve better performance. Unfortunately traditional approaches like the Kalman filter are known to fail when the signal is sparse. We propose the employment of a hierarchical Bayesian model in the tracking process which succeeds in modelling sparsity. It is then possible to achieve further reduction in the number of active sensors by exploiting the temporal correlation of consecutive samples. The theoretical analysis provided solidifies the proposed approach regarding convergence and also provides the conditions under which all sparse signals are recovered exactly. Simulations for synthetic and real-life scenarios show that the proposed method succeeds in recovering time-varying sparse signals with greater accuracy than traditional approaches.