Asymptotic noise analysis of high dimensional consensus

The paper studies the effect of noise on the asymptotic properties of high dimensional consensus (HDC). HDC offers a unified framework to study a broad class of distributed algorithms with applications to average consensus, leader-follower dynamics in multi-agent networks and distributed sensor localization. We show that under a broad range of perturbations, including inter-sensor communication noise, random data packet dropouts and algorithmic parameter uncertainty, a modified version of the HDC converges almost surely (a.s.) We characterize the asymptotic mean squared error (m.s.e.) from the desired agreement state of the sensors (which, in general, vary from sensor to sensor) and show broad conditions on the noise leading to zero asymptotic m.s.e. The convergence proof of the modified HDC algorithm is based on stochastic approximation arguments and offers a general framework to study the convergence properties of distributed algorithms in the presence of noise.