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Wavelet Dynamic Selection Network for Inertial Sensor Signal Enhancement

Yifeng Wang, Yi Zhao

TL;DR

This work tackles noisy inertial sensor signals by dynamically selecting wavelet bases for signal enhancement. The proposed WDSNet combines a 1D-ResNet feature extractor with a wavelet-category classifier, enabling adaptive wavelet thresholding, while CRM encodes wavelet categories as informative, near-orthogonal vectors and FSM directly supervises feature learning. Weakly-supervised guidance tasks—attitude and displacement prediction—drive high-quality wavelet selection without frame-level labels. Empirical results on a smartphone IMU dataset show state-of-the-art performance in Allan variance metrics and four downstream tasks, including accurate trajectory reconstruction, highlighting practical impact for robust, interpretable inertial sensing. The approach marries model-driven interpretability with data-driven adaptability, offering a universal wavelet-selection mechanism for dynamic sensing environments.

Abstract

As attitude and motion sensing components, inertial sensors are widely used in various portable devices. But the severe errors of inertial sensors restrain their function, especially the trajectory recovery and semantic recognition. As a mainstream signal processing method, wavelet is hailed as the mathematical microscope of signal due to the plentiful and 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 dynamic selection network (WDSNet), which intelligently selects the appropriate wavelet basis for variable inertial signals. In addition, existing deep learning architectures excel at extracting features from input data but neglect to learn the characteristics of target categories, which is essential to enhance the category awareness capability, thereby improving the selection of wavelet basis. Therefore, we propose a category representation mechanism (CRM), which enables the network to extract and represent category features without increasing trainable parameters. Furthermore, CRM transforms the common fully connected network into category representations, which provide closer supervision to the feature extractor than the far and trivial one-hot classification labels. We call this process of imposing interpretability on a network and using it to supervise the feature extractor the feature supervision mechanism, and its effectiveness is demonstrated experimentally and theoretically in this paper. The enhanced inertial signal can perform impracticable tasks with regard to the original signal, such as trajectory reconstruction. Both quantitative and visual results show that WDSNet outperforms the existing methods. Remarkably, WDSNet, as a weakly-supervised method, achieves the state-of-the-art performance of all the compared fully-supervised methods.

Wavelet Dynamic Selection Network for Inertial Sensor Signal Enhancement

TL;DR

This work tackles noisy inertial sensor signals by dynamically selecting wavelet bases for signal enhancement. The proposed WDSNet combines a 1D-ResNet feature extractor with a wavelet-category classifier, enabling adaptive wavelet thresholding, while CRM encodes wavelet categories as informative, near-orthogonal vectors and FSM directly supervises feature learning. Weakly-supervised guidance tasks—attitude and displacement prediction—drive high-quality wavelet selection without frame-level labels. Empirical results on a smartphone IMU dataset show state-of-the-art performance in Allan variance metrics and four downstream tasks, including accurate trajectory reconstruction, highlighting practical impact for robust, interpretable inertial sensing. The approach marries model-driven interpretability with data-driven adaptability, offering a universal wavelet-selection mechanism for dynamic sensing environments.

Abstract

As attitude and motion sensing components, inertial sensors are widely used in various portable devices. But the severe errors of inertial sensors restrain their function, especially the trajectory recovery and semantic recognition. As a mainstream signal processing method, wavelet is hailed as the mathematical microscope of signal due to the plentiful and 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 dynamic selection network (WDSNet), which intelligently selects the appropriate wavelet basis for variable inertial signals. In addition, existing deep learning architectures excel at extracting features from input data but neglect to learn the characteristics of target categories, which is essential to enhance the category awareness capability, thereby improving the selection of wavelet basis. Therefore, we propose a category representation mechanism (CRM), which enables the network to extract and represent category features without increasing trainable parameters. Furthermore, CRM transforms the common fully connected network into category representations, which provide closer supervision to the feature extractor than the far and trivial one-hot classification labels. We call this process of imposing interpretability on a network and using it to supervise the feature extractor the feature supervision mechanism, and its effectiveness is demonstrated experimentally and theoretically in this paper. The enhanced inertial signal can perform impracticable tasks with regard to the original signal, such as trajectory reconstruction. Both quantitative and visual results show that WDSNet outperforms the existing methods. Remarkably, WDSNet, as a weakly-supervised method, achieves the state-of-the-art performance of all the compared fully-supervised methods.
Paper Structure (17 sections, 5 equations, 4 figures, 4 tables)

This paper contains 17 sections, 5 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Model-Driven Methods for IMU Signal Denoising
  4. Data-Driven Methods for IMU Signal Denoising
  5. Methodology
  6. Framework Overview
  7. Category Representation Mechanism
  8. Feature Supervision Mechanism
  9. Weakly-Supervised Guidance Tasks
  10. Experiments and Results
  11. Experiment Dataset
  12. Comparative Results
  13. Static Evaluation
  14. Dynamic Evaluation
  15. Ablation Study
  16. ...and 2 more sections

Figures (4)

  • Figure 1: An overview of the WDSNet framework. The input data is fed into a 1D-ResNet for feature extraction, and an FC layer serves as a classifier that performs wavelet selection based on the extracted features. Then the selected wavelet is used to perform wavelet thresholding denoising on the original signal. The enhanced signal is input into another 1D-ResNet for attitude prediction and displacement prediction, which supervises the wavelet selection through the backpropagation of task losses.
  • Figure 2: Illustration of feature supervision mechanism. Pentagrams represent category features, and small blocks represent data features. Under the supervision of category features, data features exhibit category characteristics and become more discriminative.
  • Figure 3: Trajectory reconstruction visualization for ablation study. The dashed lines in each panel indicate the projection of a reconstructed trajectory in the XY, XZ, and YZ planes.
  • Figure 4: Effect visualization of with (right panel) and without (left panel) FSM. Each point represents the feature of a sample, and 16 colors correspond to the 16 wavelets. The data features are clustered according to wavelet categories under category feature supervision.