  Location-aware networks will introduce innovative services and applications
for modern convenience, applied ocean sciences, and public safety. In this
paper, we establish a hybrid method for model-based and data-driven inference.
We consider a cooperative localization (CL) scenario where the mobile agents in
a wireless network aim to localize themselves by performing pairwise
observations with other agents and by exchanging location information. A
traditional method for distributed CL in large agent networks is belief
propagation (BP) which is completely model-based and is known to suffer from
providing inconsistent (overconfident) estimates. The proposed approach
addresses these limitations by complementing BP with learned information
provided by a graph neural network (GNN). We demonstrate numerically that our
method can improve estimation accuracy and avoid overconfident beliefs, while
its computational complexity remains comparable to BP. Notably, more consistent
beliefs are obtained by not explicitly addressing overconfidence in the loss
function used for training of the GNN.

Machine Learning;Multiagent Systems;Robotics;Signal Processing