# GNSS Positioning using Cost Function Regulated Multilateration and Graph Neural Networks

arXiv: https://arxiv.org/abs/2402.18630 · HTML: https://mlsanity.com/paper/2402.18630/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Improving GNSS Positioning using Neural Network-based Corrections](https://mlsanity.com/paper/2110.09581/) (2021)

## Built on by (most cited first, 1 of 1)

- [Neural Augmented Kalman Filters for Road Network assisted GNSS positioning](https://mlsanity.com/paper/2507.00654/) (2025)

## Abstract (arXiv)

In urban environments, where line-of-sight signals from GNSS satellites are frequently blocked by high-rise objects, GNSS receivers are subject to large errors in measuring satellite ranges. Heuristic methods are commonly used to estimate these errors and reduce the impact of noisy measurements on localization accuracy. In our work, we replace these error estimation heuristics with a deep learning model based on Graph Neural Networks. Additionally, by analyzing the cost function of the multilateration process, we derive an optimal method to utilize the estimated errors. Our approach guarantees that the multilateration converges to the receiver's location as the error estimation accuracy increases. We evaluate our solution on a real-world dataset containing more than 100k GNSS epochs, collected from multiple cities with diverse characteristics. The empirical results show improvements from 40% to 80% in the horizontal localization error against recent deep learning baselines as well as classical localization approaches.