Convergence analysis of the information matrix in Gaussian belief propagation
This addresses a foundational issue for distributed estimation in large-scale networks like smart grids, though it is incremental as it builds on existing Gaussian BP methods.
The paper tackles the open problem of convergence in Gaussian belief propagation by analytically proving that the information matrix converges for any positive semidefinite initial value, with its distance to a unique positive definite limit decreasing exponentially fast.
Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local measurements/observations are scattered over a wide geographical area. However, the convergence of Gaus- sian BP is still an open issue. In this paper, we consider the convergence of Gaussian BP, focusing in particular on the convergence of the information matrix. We show analytically that the exchanged message information matrix converges for arbitrary positive semidefinite initial value, and its dis- tance to the unique positive definite limit matrix decreases exponentially fast.