Optimal transport guided GAN with unpaired data for inertial signal enhancement

Low-cost inertial sensors suffer from inherent noise, yet enhancing their signals remains challenging due to the absence of paired high-quality references, which hinders end-to-end supervised training for deep learning models. Therefore, we propose leveraging optimal transport theory to exploit implicit supervision through unpaired data correlations. By establishing the Feature Optimal Transport Theorem, we derive the existence conditions for optimal transport mappings between signal features of different qualities. We also quantify the upper bound of optimal transport error, revealing the impact of feature distribution differences and the compactness radius of feature space on the optimal transport error bound. Guided by this theoretical basis, we design an OTES-GAN, which reduces static noise metrics by over 95%, decreases dynamic displacement prediction error by 83.54%, and improves semantic recognition accuracy by 17.32%, outperforming all comparative methods by a significant margin, offering a new theoretical framework and practical paradigm for unpaired signal translation.