Distributed Averaging Using Compensation

In a sensor network of n nodes, each node i is assigned with a time-dependent scalar state x_i(t) and is able to exchange information with a certain number of other nodes called its neighbor nodes. The distributed averaging algorithm is to drive each x_i(t), 1≤ i≤ n, to converge to 1/nΣ_i=1ⁿ x_i(0), the average of the initial state values of all nodes, only by communication between each node and its neighbor nodes. This paper proposes a new request-based distributed averaging protocol using the idea of compensation, in which at each time t each node i first updates its state to a weighted average of its own current state x_i(t) and the current states of some neighbor nodes and then compensates its updated value by the change in the sums, before and after the update, of the states of all the nodes involved. It is proved that the proposed protocol drives all the x_i(t) to converge to 1/nΣ_i=1ⁿ x_i(0). Simulations on random networks are also provided to show that this new protocol converges much faster and consumes less energy than the deterministic gossiping protocol in [1].