Reducing power consumption in a sensor network by information feedback

We study the role of information feedback for the problem of distributed signal tracking/estimation using a sensor network with a fusion center. Assuming that the fusion center has sufficient energy to reliably feed back its intermediate estimates, we show that the sensors can substantially reduce their power consumption by using the feedback information in a manner similar to the stochastic approximation scheme of Robbins-Monro. For the problem of tracking an autoregressive source or estimating an unknown parameter, we quantify the total achievable power saving (as compared to the distributed schemes with no feedback), and provide numerical simulations to confirm the theoretical analysis.