Two-Layer Diffusion Adaptive Filters Over Directed Markovian Switching Networks

We consider the problem of distributed adaptive filtering in this letter, where a set of nodes in the network is required to estimate an unknown parameter of interest from noisy measurements cooperatively. Based on normalized least mean squares (NLMS) adaptive filters, we focus on a two-layer diffusion strategy to diffuse data more thoroughly. We propose and analyze the two-layer diffusion NLMS algorithm, where the communications between nodes in the network are described by directed Markovian switching graphs. The directed graphs are not only used for the combination of local estimates but also used for the adaptation step in the two-layer strategy. The stability results of the proposed two-layer diffusion adaptive filters are established under a general cooperative information assumption, without independence and stationarity signal conditions which were widely used in the literature. Moreover, the stability result indicates that even if any node cannot estimate the unknown parameter individually, the whole network can still fulfill the estimation task through communications. Simulation results also show that the proposed two-layer diffusion NLMS algorithm has better performance compared with the consensus one.