Max Consensus in Sensor Networks: Non-linear Bounded Transmission and Additive Noise
This work addresses the problem of robust max consensus in noisy sensor networks, which is important for applications like distributed decision-making and environmental monitoring.
The paper proposes a distributed consensus algorithm for estimating the maximum value of initial measurements in sensor networks under additive communication noise, using a soft-max approximation and non-linear bounded transmission. The algorithm controls the trade-off between soft-max error and convergence speed, and an optimal step size is derived for faster convergence when prior knowledge is available.
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 trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives a guideline towards 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.