Decentralized sparsity-based multi-source association and state tracking

The problem of tracking multiple sources using observations acquired at spatially scattered sensors is considered here. Two different sensing architectures are studied: (i) a fusion-center based topology where sensors have a limited power budget; and (ii) an ad hoc architecture where sensors collaborate with neighboring nodes enabling in-network processing. A novel source-to-sensor association scheme and tracking is introduced by enhancing the standard Kalman filtering minimization formulation with norm-one regularization terms. In the fusion-based topology a pertinent transmission power constraint is introduced, while coordinate descent techniques are employed to recover the unknown sparse observation matrix, select pertinent sensors and subsequently track the source states. In the ad hoc topology, the centralized minimization problem is written in a separable way and the alternating direction method of multipliers is utilized to construct an in-network algorithmic tracking and association framework. Numerical tests demonstrate that the resulting schemes are capable to associate sources with sensors, and track the unknown sources while adhering to any imposed power constraints.