Reliability-aware coupled-gradient distributed adaptive filtering for heterogeneous networks

Distributed adaptive filtering over heterogeneous networks is challenging due to inconsistent local update directions, varying sensing quality, and unequal reliability across nodes. Conventional diffusion-based adaptive algorithms typically promote cooperation through parameter exchange, which may be insufficient to regulate discrepancies in local learning dynamics under heterogeneous conditions. This paper proposes a reliability-aware coupled-gradient distributed adaptive filtering framework in which cooperation is introduced through two complementary mechanisms: reliability-aware gradient coupling before adaptation and reliability-aware post-update smoothing after intermediate estimation. The proposed approach enables nodes with more reliable observations to exert stronger influence during both adaptation and estimate refinement. A unified network recursion is developed, and the mean as well as mean-square behavior of the resulting algorithm is analyzed using a Lyapunov-based framework. Explicit conditions for stability are established, and the analysis characterizes how gradient coupling and post-update smoothing jointly influence convergence dynamics, disagreement reduction among neighboring update directions, and steady-state estimation accuracy. Simulation results under heterogeneous sensing conditions demonstrate that the proposed strategy improves robustness relative to purely local adaptation and achieves competitive distributed estimation performance compared with conventional diffusion LMS methods. Furthermore, close agreement between theoretical predictions and simulated steady-state behavior validates the developed analytical model.