@article{Liu2026, 
author = {Siqi Liu and Penghao Zhao and Lei Dong and Na Dong and Liyuan Ding and Guangshi Pei},
title = {GNTI: Gaussian noise-based trajectory imputation via self-supervised learning},
year = {2026},
journal = {Journal of Highway and Transportation Research and Development (English Edition)},
volume = {20},
number = {1},
pages = {28-34},
keywords = {Transportation engineering, ITS, trajectory imputation, Gaussian noise, self-supervised learning, GPS noise, transformer},
url = {https://www.sciopen.com/article/10.26599/HTRD.2026.9480088},
doi = {10.26599/HTRD.2026.9480088},
abstract = {Trajectory imputation aims to reconstruct complete movement sequences from noisy or incomplete GPS data, crucial for intelligent transportation systems (ITS). This study proposes GNTI (Gaussian Noise-based Trajectory Imputation), a self-supervised learning framework that introduces Gaussian noise during model training to simulate real-world GPS errors. By perturbing the input trajectories with probabilistic Gaussian noise, GNTI enables the model to learn robust trajectory representations without relying on labeled datasets. A transformer-based BERT encoder is employed to capture complex spatial-temporal dependencies, while a simple multilayer perceptron (MLP) decoder predicts corrected trajectory points based on contextualized embeddings. Extensive experiments were conducted on two large-scale real-world datasets, Chengdu and Porto. Comparative results show that GNTI outperforms traditional Seq2Seq-based models (gated recurrent unit (GRU), long short-term memory (LSTM)) and recent transformer-based models (Transformer, ST-BerImp), achieving the highest Micro-F1 scores across all settings. Specifically, GNTI improves Micro-F1 scores by 3%–5% over ST-BerImp. Ablation studies demonstrate that Gaussian noise augmentation improves model robustness by approximately 5% compared to models trained without augmentation. GNTI offers a practical and scalable solution for trajectory imputation tasks, enhancing robustness to GPS inaccuracies and reducing the need for complex multi-task objectives. Future work may explore extending the method to denser urban environments and optimizing it for real-time deployment.}
}