Estimating core body temperature from heart rate using a residual-compensated adaptive Kalman filter

• A hybrid model is proposed that combines a Kalman filter with an LSTM to learn and correct observation residuals. • Using only heart rate, core temperature estimation (RMSE=0.31 °C) significantly outperforms five baseline models. • High sensitivity in detecting elevated temperatures supports its use in real-time, wearable safety monitoring systems. Accurate, real-time estimation of core body temperature is critical for preventing heat-related illness. While existing Kalman filter-based methods offer interpretable, single-input (heart rate) solutions, they are limited by fixed observation models that fail to capture the complex, non-linear, state-dependent dynamics of physiological signals. To address this, we propose the Residual-Compensated Adaptive Kalman Filter (RCAKF), a novel hybrid framework. The RCAKF integrates a long short-term memory (LSTM) network to learn and correct structured, state-dependent errors in the observation model, alongside an adaptive noise estimator that dynamically adjusts for measurement uncertainty. This architecture enhances the classic Kalman filter with data-driven flexibility while maintaining its recursive structure and interpretability. Evaluation was conducted on a controlled experimental dataset with 22 participants performing exercise and recovery under varied thermal conditions. Compared to five baseline models: extended Kalman filter (EKF: RMSE = 0.39 °C), the improved ECTemp model with a sigmoid observation function (ECTemp-S: RMSE = 0.40 °C), biphasic Kalman filter-based model (BKFB: RMSE = 0.48 °C), moving-average Kalman filter (MAKF: RMSE = 0.38 °C), and a standalone LSTM network (RMSE = 0.46 °C), RCAKF achieved the best accuracy with an RMSE of 0.31 °C. By augmenting the Kalman filter with a learned residual correction and adaptive uncertainty, the RCAKF framework significantly enhances core temperature tracking from a single heart rate signal. Its accuracy and reliance on a single, common sensor make it a practical and promising solution for real-time deployment on wearable devices for safety monitoring.