Robust Max Consensus Algorithm for Wireless Sensor Networks
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Solution Overview
Problem
Existing max consensus algorithms fail to converge in wireless sensor networks due to additive noise, causing nodes to diverge from the true maximum value, as they update state values based on noisy measurements.
Innovation Solution
The proposed solution involves using max-plus algebra and large deviation theory to estimate and compensate for the growth rate of state values, implementing a two-run algorithm to locally estimate and correct for noise-induced drift, and deriving upper and lower bounds on the growth rate to ensure consensus on the true maximum value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If max consensus algorithms update state values based on noisy measurements, then nodes can communicate and reach consensus, but the additive noise causes nodes to diverge from the true maximum value
Solution Approach 1:
The patent applies large deviation theory to characterize the noise-induced drift and converts the harmful additive noise into a quantifiable growth rate that can be compensated. By analyzing the noise statistics and deriving the growth rate of state values, the algorithm transforms the unpredictable noise effect into a predictable drift that can be corrected through subtraction, thereby converting the harmful noise into a manageable parameter for compensation.
Solution Approach 2:
The patent implements a feedback mechanism where nodes continuously monitor their state value growth and compensate for the noise-induced drift by subtracting the estimated growth rate. This feedback loop allows the system to adapt to the noisy environment and maintain convergence to the true maximum value despite the presence of additive noise in wireless communications.
2Ease of operation
If existing max consensus algorithms are used in wireless sensor networks, then implementation is simple, but convergence fails due to noise-induced divergence
Solution Approach 1:
The patent modifies the standard max consensus algorithm by introducing a compensation term that subtracts the noise-induced growth rate from the state value updates. This parameter change transforms the algorithm from one that diverges under noise to one that converges reliably, while maintaining the distributed and iterative nature of the original approach suitable for wireless sensor networks.
3Reliability
If compensation for noise-induced drift is implemented, then convergence to true maximum is achieved, but algorithm complexity increases
Solution Approach 1:
The patent performs preliminary analysis using large deviation theory to derive the growth rate caused by additive noise before implementing the consensus algorithm. By pre-characterizing the noise effects and calculating the expected drift, the compensation mechanism becomes a straightforward subtraction operation rather than a complex iterative correction, reducing the actual runtime complexity while ensuring reliable convergence.
Data Source
AI summary
Various embodiments of systems and methods for robust max consensus for wireless sensor networks in the presence of additive noise by determining and removing a growth rate estimate from state values of each node in a wireless sensor network are disclosed.