# Learning-based NLOS Detection and Uncertainty Prediction of GNSS Observations with Transformer-Enhanced LSTM Network

arXiv: https://arxiv.org/abs/2309.00480 · HTML: https://mlsanity.com/paper/2309.00480/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [EA-LSTM: Evolutionary Attention-based LSTM for Time Series Prediction](https://mlsanity.com/paper/1811.03760/) (2018)
- [GNSS Outlier Mitigation Via Graduated Non-Convexity Factor Graph Optimization](https://mlsanity.com/paper/2109.00667/) (2021)
- [onlineFGO: Online Continuous-Time Factor Graph Optimization with Time-Centric Multi-Sensor Fusion for Robust Localization in Large-Scale Environments](https://mlsanity.com/paper/2211.05400/) (2022)
- [3D LiDAR Aided GNSS NLOS Mitigation for Reliable GNSS-RTK Positioning in Urban Canyons](https://mlsanity.com/paper/2212.05477/) (2022)

## Built on by (most cited first, 4 of 4)

- [pyrtklib: An open-source package for tightly coupled deep learning and GNSS integration for positioning in urban canyons](https://mlsanity.com/paper/2409.12996/) (2024)
- [Learning-based GNSS Uncertainty Quantification using Continuous-Time Factor Graph Optimization](https://mlsanity.com/paper/2503.04933/) (2025)
- [An End-to-End Learning-Based Multi-Sensor Fusion for Autonomous Vehicle Localization](https://mlsanity.com/paper/2503.05088/) (2025)
- [Diff-GNSS: Diffusion-based Pseudorange Error Estimation](https://mlsanity.com/paper/2509.17397/) (2025)

## Abstract (arXiv)

The global navigation satellite systems (GNSS) play a vital role in transport systems for accurate and consistent vehicle localization. However, GNSS observations can be distorted due to multipath effects and non-line-of-sight (NLOS) receptions in challenging environments such as urban canyons. In such cases, traditional methods to classify and exclude faulty GNSS observations may fail, leading to unreliable state estimation and unsafe system operations. This work proposes a deep-learning-based method to detect NLOS receptions and predict GNSS pseudorange errors by analyzing GNSS observations as a spatio-temporal modeling problem. Compared to previous works, we construct a transformer-like attention mechanism to enhance the long short-term memory (LSTM) networks, improving model performance and generalization. For the training and evaluation of the proposed network, we used labeled datasets from the cities of Hong Kong and Aachen. We also introduce a dataset generation process to label the GNSS observations using lidar maps. In experimental studies, we compare the proposed network with a deep-learning-based model and classical machine-learning models. Furthermore, we conduct ablation studies of our network components and integrate the NLOS detection with data out-of-distribution in a state estimator. As a result, our network presents improved precision and recall ratios compared to other models. Additionally, we show that the proposed method avoids trajectory divergence in real-world vehicle localization by classifying and excluding NLOS observations.