  We consider the problem of maximum likelihood estimation in linear models
represented by factor graphs and solved via the Gaussian belief propagation
algorithm. Motivated by massive internet of things (IoT) networks and edge
computing, we set the above problem in a clustered scenario, where the factor
graph is divided into clusters and assigned for processing in a distributed
fashion across a number of edge computing nodes. For these scenarios, we show
that an alternating Gaussian belief propagation (AGBP) algorithm that
alternates between inter- and intra-cluster iterations, demonstrates superior
performance in terms of convergence properties compared to the existing
solutions in the literature. We present a comprehensive framework and introduce
appropriate metrics to analyse AGBP algorithm across a wide range of linear
models characterised by symmetric and non-symmetric, square, and rectangular
matrices. We extend the analysis to the case of dynamic linear models by
introducing dynamic arrival of new data over time. Using a combination of
analytical and extensive numerical results, we show the efficiency and
scalability of AGBP algorithm, making it a suitable solution for large-scale
inference in massive IoT networks.
