Hankel Dynamic Mode Decomposition for Radar-Based Respiratory Sensing and Tracking

Non-contact respiratory monitoring in uncontrolled environments is a critical unmet need for applications ranging from remote healthcare to search and rescue. While low-power radar is a promising sensing modality, its effectiveness is severely limited by environmental clutter and signal non-stationarity, which cause traditional signal processing pipelines to fail. We present a novel framework for respiratory sensing and tracking that overcomes these limitations by leveraging Hankel Dynamic Mode Decomposition (HDMD) with temporal tracking. Our approach treats the noisy time-series data as the output of a dynamical system and decomposes it into a set of coherent oscillatory modes, enabling the robust isolation of the respiratory signal without requiring extensive hyperparameter tuning. We evaluate our method on a dataset of 24 subjects recorded with a compact pulsed radar in diverse indoor and outdoor conditions. The proposed HDMD pipeline significantly outperforms established decomposition baselines, achieving an NRMSE of 6.00% indoors and 1.33% outdoors, substantially reducing the Root Mean Square Error (RMSE) compared to the next-best methods. These results establish HDMD as the first modal decomposition method to extend radar-based respiratory rate estimation and variability analysis into outdoor, mobile contexts, advancing the feasibility of privacy-preserving and low-power physiological sensing.