A Unified Bayesian Framework for Topology Inference, Blind System Identification, and Source Localization in Edge-Cloud LAWNs

Distributed data analysis tasks-including topology inference, blind system identification, and source localization-are critical for Low-Altitude Wireless Networks (LAWNs) architected on an edge-cloud paradigm. While recent efforts have explored joint estimation, they often infer deterministic graphs, overlooking the inherent stochasticity of wireless links, or are limited to specific sub-tasks, lacking a unified, end-to-end formulation. To overcome these limitations, we propose a unified Bayesian framework that cohesively addresses these interconnected challenges. We formulate a single hierarchical generative model integrating a probabilistic graph structure, a composite signal prior for smoothness and sparsity, a generalized graph operator, and observation noise. Building on this model, we derive a versatile and distributed variational inference framework, termed UBIG, which features a dual-scheme posterior approximation to efficiently handle different inference objectives. The UBIG framework is systematically instantiated to solve the three core tasks, and is naturally suited for edge-cloud architectures. Through extensive experiments simulating LAWNs, we demonstrate that our framework achieves superior accuracy and robustness compared to state-of-the-art methods, while providing principled uncertainty quantification.