Local Average Consensus in Distributed Measurement of Spatial-Temporal Varying Parameters: 1D Case

TL;DR

This paper introduces local average consensus algorithms for distributed measurement of spatial-temporal varying parameters in sensor networks, balancing local information retention and noise mitigation, with analysis of frequency responses and tradeoffs.

Contribution

It proposes novel distributed algorithms for local average consensus in 1D spatial settings, addressing both spatial and temporal variations, and analyzes their frequency response and noise characteristics.

Findings

Algorithms effectively estimate local parameters with spatial-temporal variations.

Tradeoffs include increased memory and noise degradation compared to global consensus.

Analysis covers arbitrary weights and sensor spacing, enhancing robustness.

Abstract

We study a new variant of consensus problems, termed `local average consensus', in networks of agents. We consider the task of using sensor networks to perform distributed measurement of a parameter which has both spatial (in this paper 1D) and temporal variations. Our idea is to maintain potentially useful local information regarding spatial variation, as contrasted with reaching a single, global consensus, as well as to mitigate the effect of measurement errors. We employ two schemes for computation of local average consensus: exponential weighting and uniform finite window. In both schemes, we design local average consensus algorithms to address first the case where the measured parameter has spatial variation but is constant in time, and then the case where the measured parameter has both spatial and temporal variations. Our designed algorithms are distributed, in that information is exchanged only among neighbors. Moreover, we analyze both spatial and temporal frequency responses and noise propagation associated with the algorithms. The tradeoffs of using local consensus, as compared to standard global consensus, include higher memory requirement and degraded noise performance. Arbitrary updating weights and random spacing between sensors are analyzed in the proposed algorithms.