PM-EKF: A Physiological Model-Based Extended Kalman Filter for Daily-Life Physical Activity Energy Expenditure Estimation

Monitoring physical activity energy expenditure (PAEE) in daily life is essential for characterizing individual health and metabolic status. Although indirect calorimetry provides gold-standard PAEE measurements, it is impractical for continuous daily-life monitoring. Consequently, wearable sensing approaches using inertial measurement units (IMUs) and heart rate (HR) sensors have attracted substantial interest. However, most existing IMU- and HR-based methods are purely data-driven and offer limited physiological interpretability. In this work, we propose a simplified physiological model that explicitly links body movement during activities of daily living to the underlying metabolic gas-exchange processes governing PAEE. The model is formulated as a nonlinear state-space system and embedded within an Extended Kalman Filter (EKF), enabling principled handling of measurement noise, model uncertainty, and system nonlinearities. The proposed framework provides personalized, interpretable PAEE estimates without employing black-box models. Our model was validated using a dataset, including 9 subjects with around 50 minutes of measurements per subject, collected in our lab simulating a free-living condition. Using the respiratory data measured by COSMED K5 as reference and explained variance (R^2) as evaluation metric, our model's predicted PAEE yielded median (min-max) R^2 = 0.72 (0.60--0.87), using three IMUs (pelvis and two thighs) for capturing the body-center-of-mass motion and measured HR for the time-varying cardiac output. Our model outperformed a linear regression (LR) model (R^2 = 0.52 (0.23--0.92)) and CNN-LSTM model (R^2 = 0.65 (0.46--0.78)) on the same dataset. Notably, excluding the sensory HR measurement did not significantly degrade PAEE estimation of all three models, indicating that IMU-captured mechanical workload dominated PAEE estimation performance in our protocol.