Human Activity Recognition via a Categorical Kalman Filter Using Inertial Sensors

Human Activity Recognition (HAR) has gained significant attention due to its applications in healthcare, sports, and surveillance systems. While many existing models demonstrate good performance, they often lack interpretability and struggle with nonstationary data distributions common in sensor-based applications. This paper proposes a novel Categorical Kalman Filter (CatKF) for classifying human activities using inertial measurement unit (IMU) data. The CatKF extends the traditional Kalman filter framework to handle classification tasks by modeling class probabilities through a softmax function with time-varying parameters that evolve according to dynamic linear models. The approach enables online processing, adapts to distributional shifts, and maintains computational efficiency through sequential parameter updates. We evaluate the proposed method on three standard HAR datasets (PAMAP2, DSA, and USC-HAD) using leave-one-subject-out cross-validation. Experimental results demonstrate that the CatKF with learned hyperparameters achieves competitive performance compared to classical machine learning methods, matching multilayer perceptrons while being outperformed only by ensemble methods like Random Forest and XGBoost. A complementary online classification experiment further demonstrates fast adaptation and robustness under nonstationary data streams. We also analyze the temporal evolution of the model’s predictive parameters, highlighting how it adapts to new information and how its uncertainty changes over time. The Random-Walk Categorical Kalman Filter (RWCatKF) variant requires only three hyperparameters and operates without matrix inversions, making it particularly suitable for resource-constrained wearable devices. The proposed approach offers a transparent, interpretable alternative for HAR applications where model explainability is essential.