# PC-DeepNet: A GNSS Positioning Error Minimization Framework Using Permutation-Invariant Deep Neural Network

arXiv: https://arxiv.org/abs/2504.13990 · HTML: https://mlsanity.com/paper/2504.13990/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [Improving GNSS Positioning using Neural Network-based Corrections](https://mlsanity.com/paper/2110.09581/) (2021)
- [It is time for Factor Graph Optimization for GNSS/INS Integration: Comparison between FGO and EKF](https://mlsanity.com/paper/2004.10572/) (2020)

## Abstract (arXiv)

Global navigation satellite systems (GNSS) face significant challenges in urban and sub-urban areas due to non-line-of-sight (NLOS) propagation, multipath effects, and low received power levels, resulting in highly non-linear and non-Gaussian measurement error distributions. In light of this, conventional model-based positioning approaches, which rely on Gaussian error approximations, struggle to achieve precise localization under these conditions. To overcome these challenges, we put forth a novel learning-based framework, PC-DeepNet, that employs a permutation-invariant (PI) deep neural network (DNN) to estimate position corrections (PC). This approach is designed to ensure robustness against changes in the number and/or order of visible satellite measurements, a common issue in GNSS systems, while leveraging NLOS and multipath indicators as features to enhance positioning accuracy in challenging urban and sub-urban environments. To validate the performance of the proposed framework, we compare the positioning error with state-of-the-art model-based and learning-based positioning methods using two publicly available datasets. The results confirm that proposed PC-DeepNet achieves superior accuracy than existing model-based and learning-based methods while exhibiting lower computational complexity compared to previous learning-based approaches.