Generalized diffusion adaptation for energy-constrained distributed estimation

We propose a generalized diffusion adaptation strategy for distributed estimation under local and network-wide energy constraints. In our generalized diffusion strategy, at each iteration, each node can optimally combine intermediate parameter estimates from nodes other than its physical neighbors. The nodes whose intermediate estimates are relayed via a multi-hop path to a particular node, and fused there, are called the information neighbors of that node. This generalizes the physical neighborhood of nodes used in traditional diffusion strategies. We propose a method to determine the optimal information neighborhood, and combination weights for the information neighbors, subject to each node's energy budget, and an overall energy budget on the whole network for each iteration. By varying the energy budgets, our strategy covers the whole spectrum of strategies ranging from the centralized estimation method where all information is available at a single node, to the non-cooperative approach where each node performs its own local estimation. Numerical results suggest that our proposed method is able to achieve the same mean-square deviation as the adapt-then-combine diffusion algorithm with a lower energy budget.