  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.
