TY - JOUR
T1 - Analysis and design of robust max consensus for wireless sensor networks
AU - Muniraju, Gowtham
AU - Tepedelenlioglu, Cihan
AU - Spanias, Andreas
N1 - Funding Information:
Manuscript received February 19, 2019; revised July 3, 2019 and August 28, 2019; accepted September 8, 2019. Date of publication October 3, 2019; date of current version October 22, 2019. The work of the authors from Arizona State University was supported in part by the National Science Foundation under Grants ECSS 1307982 and CPS 1646542, and in part by the SenSIP Center, School of Electrical, Computer and Energy Engineering, Arizona State University. This article was presented in part at the 2018 Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, October 28–31, 2018 [1]. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Waheed U. Bajwa. (Corresponding author: Gowtham Muniraju.) The authors are with the School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 USA (e-mail: gmuniraj@ asu.edu; cihan@asu.edu; spanias@asu.edu). Digital Object Identifier 10.1109/TSIPN.2019.2945639
Publisher Copyright:
© 2015 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.
AB - A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.
KW - Max consensus
KW - max-plus algebra
KW - spectral radius
KW - wireless sensor networks
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U2 - 10.1109/TSIPN.2019.2945639
DO - 10.1109/TSIPN.2019.2945639
M3 - Article
AN - SCOPUS:85073152728
SN - 2373-776X
VL - 5
SP - 779
EP - 791
JO - IEEE Transactions on Signal and Information Processing over Networks
JF - IEEE Transactions on Signal and Information Processing over Networks
IS - 4
M1 - 8859263
ER -