Sparse Calibration-Based Personalization of Kernel-Based Gait Phase and Speed Estimation Using Wearable IMUs

Kernel-Based Phase and Speed Estimation

The sliding-kernel framework of Posh et al. [ 11 ] jointly estimates locomotion mode and gait phase by selecting the best-matching locomotion-mode kernel and its circular alignment. We adapted this framework to level-ground speed estimation by treating each speed in $\mathcal{V}=\{0.50+0.05r\mid r=0,\ldots,27\}$ m/s as a separate kernel candidate.

Let $x_{s,v,c}(\phi)$ denote the subject-level mean stride trajectory for subject $s$, walking speed $v\in\mathcal{V}$, channel $c$, and normalized gait phase $\phi\in(0,1]$.

Sparse Personalized Kernel Generation

The PCA model was constructed from the open-source Camargo locomotion dataset [ 12 ] . Instead of applying PCA to absolute trajectories, each subject’s baseline averaged all available speeds: where $V(s)$ is the set of valid walking speeds for subject $s$.

The baseline-centered deviation was defined as For each subject–speed pair, the four-channel deviation trajectories were concatenated over 101 phase samples into a 404-dimensional vector $\Delta\mathbf{x}_{s,v}$. PCA was applied to these vectors collected from all valid subject–speed pairs.

Experimental Setup

Methods A–C were evaluated on the 20-subject, 0.50–1.85 m/s dataset using LOSO cross-validation and the fixed calibration speeds above. In each fold, the other 19 subjects defined the population kernel and PCA basis. The quadratic form was held fixed, but its coefficients were re-estimated using the same 19 subjects.

The held-out subject provided only the fixed-speed calibration trajectories and the trajectories used for phase and speed evaluation.

Results

Table 2 shows that Method A reduced mean phase RMSE from 0.0178 to 0.0161 compared with the non-personalized population kernel, corresponding to a 9.55% reduction. The Friedman test showed a significant method effect for offline phase RMSE ($\chi^{2}=15.10$, $p=0.0005$).

In the Holm-corrected Wilcoxon comparisons, Method A and Method B both reduced phase RMSE compared with Method C ($p=0.0005$ and $p=0.0017$, respectively), whereas the difference between Method A and Method B was not significant ($p=0.7285$).

Sources and Demonstrations

Figures are reproduced from Cha et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.