Adaptive Filtering Over Complex Networks in Intricate Environments

In practice, when complex multi-agent networks are used for parameter estimation and tracking, we often face the issue of spatial anisotropy of observing conditions, e.g., different (heterogeneous) noise distributions at different nodes. In this setting, existing cost functions may excel at specialized nodes, and struggle with others, leading to an overall deteriorating performance, sometimes even inferior to the mean square error (MSE) criterion. The aim of the present paper is to propose a robust network-based adaptive filtering algorithm capable of accommodating such intricate environments. Leveraging the inherent versatility of Gaussian mixture model (GMM) to fit any probability distribution, we model the additive noise at each node accordingly. Then a diffusion algorithm founded on recursive maximum log-likelihood function (RMLF) is put forward, denoted as DRMLF. Thanks to the universal adaptability of GMM, the DRMLF can consistently deliver excellent performance across multiple nodes with diverse noise profiles within the complex networks. Simulations undoubtedly demonstrate that the DRMLF outperforms the other commonly used diffusion RLS-type algorithms over complex networks in intricate environments. A thorough analysis of both mean and mean square convergence is also conducted in detail correspondingly.