Convergence of consensus filtering under network throughput limitations

Consensus filters (Olfati-Saber and Shamma, 2005) provide a distributed way of computing data aggregates in embedded sensor networks. Prior work has suggested that the rate at which such filters achieve consensus is proportional to the number of neighbors. This conclusion, however, is simplistic because it ignores the intrinsic throughput limitation of multi-hop networks. This paper examines the convergence behavior of consensus filters under such throughput limitations. We consider a time-slotted frequency division multiple access (FDMA) network assuming a regular network. Under these assumptions we show that throughput limits can be modeled as delays. We study the impact these delays have on the time and energy that consensus filters require to achieve epsiv-consensus.