Wavelet Encoding Network for Inertial Signal Enhancement via Feature Supervision

Inertial sensors, as motion-sensing components, are widely used in inertial navigation, aerospace, and consumer electronics. Their wide applications and severe errors form a sharp contradiction, which attracts considerable attention. Wavelet is hailed as the mathematical signal microscope due to the diverse wavelet basis functions. However, complicated noise types and application scenarios of inertial sensors make selecting wavelet basis perplexing. To this end, we propose a wavelet encoding network (WENet), which intelligently selects the appropriate wavelet for variable inertial signals by representing wavelet characteristics through the devised category representation mechanism (CRM). Furthermore, CRM introduces a feature supervision effect, which imposes interpretability on a black-box network and forces it to provide direct supervision for other network structures. This supervision strategy is closer and more effective than the supervision provided by the output end, which is far and needs to go through backpropagation. The proposed WENet has the reliability of the model-driven method and the flexibility of the data-driven method. As a weakly supervised method, the WENet achieves the best performance among all signal improvement methods, including fully supervised ones. After being enhanced by WENet, the low-cost sensor signal can perform accurate spatial trajectory reconstruction, which was once considered an impossible task.