Max Consensus in Sensor Networks: Non-linear Bounded Transmission and Additive Noise

TL;DR

This paper introduces a novel distributed consensus algorithm for sensor networks to estimate the maximum initial measurement value accurately despite communication noise, using non-linear bounded transmission and soft-max approximation techniques.

Contribution

It proposes a new non-linear consensus method with a soft-max approximation and analyzes the trade-off between error and convergence speed, including prior knowledge utilization for faster convergence.

Findings

The algorithm effectively estimates maximum values under noisy conditions.

Trade-off analysis guides parameter selection for accuracy and speed.

Simulation results validate theoretical insights.

Abstract

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.