This paper describes and analyzes a hierarchical gossip algorithm for solving
the distributed average consensus problem in wireless sensor networks. The
network is recursively partitioned into subnetworks. Initially, nodes at the
finest scale gossip to compute local averages. Then, using geographic routing
to enable gossip between nodes that are not directly connected, these local
averages are progressively fused up the hierarchy until the global average is
computed.
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area.
In this paper, we demonstrate, both theoretically and by numerical examples,
that adding a local prediction component to the update rule can significantly
improve the convergence rate of distributed averaging algorithms. We focus on
the case where the local predictor is a linear combination of the node's two
previous values (i.e., two memory taps), and our update rule computes a
combination of the predictor and the usual weighted linear combination of
values received from neighbouring nodes.