Distributed sparse signal estimation in sensor networks using H∞-consensus filtering

This paper is concerned with the sparse signal recovery problem in sensor networks, and the main purpose is to design a filter for each sensor node to estimate a sparse signal sequence using the measurements distributed over the whole network. A so-called ℓ₁-regularized H_∞ filter is established at first by introducing a pseudo-measurement equation, and the necessary and sufficient condition for existence of this filter is derived by means of Krein space Kalman filtering. By embedding a high-pass consensus filter into ℓ₁-regularized H_∞ filter in information form, a distributed filtering algorithm is developed, which ensures that all node filters can reach a consensus on the estimates of sparse signals asymptotically and satisfy the prescribed H_∞ performance constraint. Finally, a numerical example is provided to demonstrate effectiveness and applicability of the proposed method.