  We present a novel distributed Gauss-Newton method for the non-linear state
estimation (SE) model based on a probabilistic inference method called belief
propagation (BP). The main novelty of our work comes from applying BP
sequentially over a sequence of linear approximations of the SE model, akin to
what is done by the Gauss-Newton method. The resulting iterative Gauss-Newton
belief propagation (GN-BP) algorithm can be interpreted as a distributed
Gauss-Newton method with the same accuracy as the centralized SE, however,
introducing a number of advantages of the BP framework. The paper provides
extensive numerical study of the GN-BP algorithm, provides details on its
convergence behavior, and gives a number of useful insights for its
implementation.
