GNSS Positioning using Cost Function Regulated Multilateration and Graph Neural Networks

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.