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

**2016-02-02**

1602.01128 | cs.SY

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.

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