Abstract
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 l 1 -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 l 1 -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.
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