# Neural Enhanced Belief Propagation for Cooperative Localization

arXiv: https://arxiv.org/abs/2105.12903 · HTML: https://mlsanity.com/paper/2105.12903/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Inference in Probabilistic Graphical Models by Graph Neural Networks](https://mlsanity.com/paper/1803.07710/) (2018)
- [Sigma Point Belief Propagation](https://mlsanity.com/paper/1309.0363/) (2013)
- [Distributed Estimation with Information-Seeking Control in Agent Network](https://mlsanity.com/paper/1408.3732/) (2014)

## Built on by (most cited first, 5 of 5)

- [Neural Enhanced Belief Propagation for Multiobject Tracking](https://mlsanity.com/paper/2212.08340/) (2022)
- [Neural Enhanced Belief Propagation for Data Association in Multiobject Tracking](https://mlsanity.com/paper/2203.09948/) (2022)
- [Message Passing Meets Graph Neural Networks: A New Paradigm for Massive MIMO Systems](https://mlsanity.com/paper/2302.06896/) (2023)
- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [Classification-Aided Robust Multiple Target Tracking Using Neural Enhanced Message Passing](https://mlsanity.com/paper/2310.12407/) (2023)

## Abstract (arXiv)

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.