Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach
Estimating the system state is a non-trivial task given a large set of measurements, fuelling the ongoing research attempts to find efficient, scalable and fast state estimation (SE) algorithms. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (i.e., subsystems) and distributing the computation across clusters, solves the constraints of a centralised based approach. In such scenarios, using distributed SE methods brings many advantages over the centralised approaches. In this paper, we propose a novel distributed method to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed method is based on the factor graph operating without a central coordinator, where subsystems exchange only “beliefs”, thus preserving the privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solutions upon arrival of new information to the subsystem. Finally, the proposed algorithm reaches the accuracy of the centralised WLS solution in a few iterations and outperforms the vanilla GBP algorithm with respect to its convergence properties.