TY - JOUR
T1 - Max Consensus in Sensor Networks
T2 - Non-Linear Bounded Transmission and Additive Noise
AU - Zhang, Sai
AU - Tepedelenlioglu, Cihan
AU - Banavar, Mahesh K.
AU - Spanias, Andreas
N1 - Funding Information:
The work of S. Zhang, C. Tepedelenlio?lu, and A. Spanias was supported in part by NSF under Award ECCS-1307982 and in part by the SenSIP Center, School of ECEE, Arizona State University. The work of M. K. Banavar was supported by NSF CRII under Award 1464222.
PY - 2016/12/15
Y1 - 2016/12/15
N2 - A distributed consensus algorithm for estimating the maximum value of the initial measurements in a sensor network with communication noise is proposed. In the absence of communication noise, max estimation can be done by updating the state value with the largest received measurements in every iteration at each sensor. In the presence of communication noise, however, the maximum estimate will incorrectly drift and the estimate at each sensor will diverge. As a result, a soft-max approximation together with a non-linear consensus algorithm is introduced herein. A design parameter controls the tradeoff between the soft-max error and convergence speed. An analysis of this tradeoff gives a guideline toward how to choose the design parameter for the max estimate. We also show that if some prior knowledge of the initial measurements is available, the consensus process can converge faster by using an optimal step size in the iterative algorithm. A shifted non-linear bounded transmit function is also introduced for faster convergence when sensor nodes have some prior knowledge of the initial measurements. Simulation results corroborating the theory are also provided.
AB - A distributed consensus algorithm for estimating the maximum value of the initial measurements in a sensor network with communication noise is proposed. In the absence of communication noise, max estimation can be done by updating the state value with the largest received measurements in every iteration at each sensor. In the presence of communication noise, however, the maximum estimate will incorrectly drift and the estimate at each sensor will diverge. As a result, a soft-max approximation together with a non-linear consensus algorithm is introduced herein. A design parameter controls the tradeoff between the soft-max error and convergence speed. An analysis of this tradeoff gives a guideline toward how to choose the design parameter for the max estimate. We also show that if some prior knowledge of the initial measurements is available, the consensus process can converge faster by using an optimal step size in the iterative algorithm. A shifted non-linear bounded transmit function is also introduced for faster convergence when sensor nodes have some prior knowledge of the initial measurements. Simulation results corroborating the theory are also provided.
KW - Max consensus
KW - adaptive step size
KW - asymptotic covariance
KW - bounded transmissions
KW - soft-max
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U2 - 10.1109/JSEN.2016.2612642
DO - 10.1109/JSEN.2016.2612642
M3 - Article
AN - SCOPUS:85026996841
VL - 16
SP - 9089
EP - 9098
JO - IEEE Sensors Journal
JF - IEEE Sensors Journal
SN - 1530-437X
IS - 24
ER -