Reconstruction of time-varying fields in wireless sensor networks using shift-invariant spaces: Iterative algorithms and impact of sensor localization errors

Based on the concept of hybrid shift-invariant spaces, we develop a distributed protocol for the reconstruction of time-varying physical fields in wireless sensor networks. The localized nature of these spaces allows for a clustered network architecture that leads to low communication overhead. Capitalizing on the sparsity of the reconstruction matrix, we propose an iterative reconstruction algorithm whose complexity per time-slot is linear in the number of sensors. We furthermore analyse the impact of sensor localization errors on the mean square error of the reconstructed field and provide numerical simulations illustrating our results.