Consensus based distributed estimation with local-accuracy exchange in dense wireless systems

For a connected network, consensus based algorithms guarantee that local estimates are iteratively shared and refined among neighbors to reach the same weighted average on all nodes. Parameter estimation for linear models are common problems where average consensus are routinely adopted to mimic a centralized approach without the need of any fusion center. Convergence speed, accuracy and the amount of signalling involved in consensus iterations are all relevant for practical usage (e.g., spectrum sensing in cognitive radios). In this paper we propose to exchange at initialization stage of consensus the covariance of each local estimate in form of long-term information on regressors, so that consensus steps are weighted accordingly. In spite of the simplicity, the preliminary exchange of the reliability among neighbors improves MSE performance close to the Cramér Rao bound for centralized approach, with a reduced convergence time. In time-varying settings, the balance between estimate refinements from consensus steps and reliability updates are also discussed.