The Effective Cooperative Diffusion Strategies With Adaptation Ability by Learning Across Adaptive Network-Wide Systems

In this paper, we consider the nonlinear least squares (NLLSs) problems in adaptive networks, where a collection of nodes with adaptation ability by learning are required to estimate a global vector parameter by minimizing the specified convex cost function. Although the global Gauss–Newton (GN) method is an excellent candidate for solving such problems, many challenges need to be addressed for practical realization due to its natures of centralization and noncooperation. Without specialized design for routing, we motivate and propose new diffusion GN methods with cooperative strategy among local neighborhoods. The good performances of diffusion cooperation schemes have been proved in different literatures, such as distribution, robustness, and easy implementation. The proposed cooperative diffusion strategies are named as aggregation-then-update (ATU) and update-then-aggregation (UTA), which reach fully information diffusion across network and consist of two steps in a reversible way including aggregation of local estimates and local GN update. Although all implementations are local, the cooperation between nodes is network wide. Based on the steady-state equilibria theory in the nonlinear discrete dynamical system, the convergence analysis of proposed algorithms is provided. The results show that the global convergence can be achieved when the sufficient conditions are satisfied. We also provide performance comparisons and analysis together with simulation to confirm the applicability and effectiveness of proposed diffusion GN algorithms.