Distributed Gauss-Newton Method for State Estimation Using Belief Propagation

TL;DR

This paper introduces a distributed Gauss-Newton algorithm based on belief propagation for non-linear state estimation, achieving centralized accuracy with distributed computation advantages.

Contribution

It develops a novel iterative GN-BP algorithm that applies belief propagation over linear approximations, combining distributed processing with centralized accuracy.

Findings

GN-BP achieves accuracy comparable to centralized SE.

The algorithm demonstrates good convergence properties.

Extensive numerical studies validate the approach.

Abstract

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.