Statistical Characterization of Jerk Magnitude for Human Activity Recognition Using Wearable Sensors

Abstract

Human Activity Recognition (HAR) focuses on measuring human activities from inertial sensor signals acquired through wearable devices. While machine learning and deep learning approaches achieve high classification performance, they often suffer from limited interpretability, high computational cost, and reduced generalization across users. From a measurement perspective, there is therefore increasing interest in identifying simple, physically meaningful descriptors that can be reliably derived from sensor data. In this work, we investigate jerk magnitude, defined as the time derivative of acceleration, as a standalone kinematic measurand for activity discrimination. Triaxial acceleration data were acquired using an Empatica EmbracePlus smartwatch from 20 subjects performing five Activities of Daily Living (ADLs) with different intensity levels. The jerk magnitude was computed through a signal processing pipeline and summarized over short temporal windows using basic statistical features, with particular focus on the mean jerk. To evaluate the discriminative capability of this descriptor, a fully non-parametric statistical framework was adopted, combining the Kruskal–Wallis test for global analysis and Dunn's post-hoc test with Bonferroni correction for pairwise comparisons. The results show that mean jerk magnitude exhibits statistically significant differences across all activity classes $(p<0.001$), enabling clear discrimination between static, low-intensity, and highly dynamic movements. Pairwise analysis confirms strong separability for most activity combinations, while highlighting limitations in distinguishing tasks with similar motion smoothness but different spatial orientation. These findings demonstrate that a single, computationally lightweight and physically interpretable measurand can provide robust activity discrimination without relying on complex models. The proposed approach establishes a reproducible baseline for HAR and highlights the potential of measurement-driven, physics-based descriptors for low-power wearable applications.