Distributed consensus algorithms in sensor networks with communication channel noise and random link failures (2007)
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| Venue: | in Proc. 41st Asilomar Conf. Signals, Systems, Computers |
| Citations: | 149 - 21 self |
BibTeX
@INPROCEEDINGS{Kar07distributedconsensus,
author = {Soummya Kar and José M. F. Moura},
title = {Distributed consensus algorithms in sensor networks with communication channel noise and random link failures},
booktitle = {in Proc. 41st Asilomar Conf. Signals, Systems, Computers},
year = {2007}
}
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Abstract
Abstract—The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma—running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero;) and the algorithm where the weights are constant but consensus is run for a fixed number of iterations, then it is restarted and rerun for a total of runs, and at the end averages the final states of the runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of to a finite consensus limit and compute explicitly the mean square error (mse) (variance) of the consensus limit. We show that represents the best of both worlds—zero bias and low variance—at the cost of a slow convergence rate; rescaling the weights balances the variance versus the rate of bias reduction (convergence rate). In contrast, , because of its constant weights, converges fast but presents a different bias-variance tradeoff. For the same number of iterations, shorter runs (smaller) lead to high bias but smaller variance (larger number of runs to average over.) For a static nonrandom network with Gaussian noise, we compute the optimal gain for to reach in the shortest number of iterations, with high probability (1), ()-consensus ( residual bias). Our results hold under fairly general assumptions on the random link failures and communication noise. Index Terms—Additive noise, consensus, sensor networks, stochastic approximation, random topology. I.
Keyphrases
sensor network random link failure communication channel noise consensus algorithm random topology slow convergence rate final average estimate conventional consensus convergence rate consensus limit persistence condition high probability constant weight intermittent link monte carlo general assumption low variance finite consensus limit gaussian noise noisy channel fixed number paper study static nonrandom network different bias-variance tradeoff communication noise final state markov process long reduces stochastic approximation argument sure convergence high bias bias reduction residual bias bias-variance dilemma different compromise index term additive noise mean square error optimal gain stochastic approximation
