Synthetic Multi-Delay NLMS for Single-Channel PPG: Motion Artifact Removal and rHRI-Based Heart Rate Estimation

Accurate heart rate estimation from single-channel photoplethysmography (PPG) remains challenging in wearable settings because motion artifacts corrupt the pulsatile waveform. Multi-sensor fusion and deep learning approaches mitigate these artifacts but impose additional hardware cost or computational burden unsuitable for resource-constrained edge devices. This paper proposes SMD-NLMS, a lightweight, model-free, sensor-less framework for single-channel PPG-based heart rate estimation during ambulatory motion. A motion-related noise reference is synthesized directly from the input PPG by aggregating delayed replicas using a root-sum-of-squares (RSS) operation, and this intrinsic reference drives a normalized least mean squares (NLMS) adaptive filter to suppress artifacts without auxiliary inertial sensors, and substituting a physical tri-axial accelerometer for it changes the primary-set error by less than 0.3 bpm. Heart rate tracking is stabilized by a maximal rate of heart rate increase (rHRI)-derived bounded search corridor (±18 bpm) integrated into spectral peak selection, enforcing physiological plausibility without post-smoothing latency. On the IEEE Signal Processing Cup 2015 dataset (22 subjects), SMD-NLMS achieves a mean absolute error (MAE) of 2.43 beats per minute on the 20-subject primary evaluation set—with the full 22-subject MAE of 3.35 bpm also reported for transparency—using approximately 130 multiply-accumulate operations per sample and a sub-kilobyte memory footprint, establishing an accuracy baseline for model-free, sensor-less single-channel PPG estimation while offering substantially lower computational cost and hardware complexity compared with multi-sensor and deep learning alternatives. Transferred without re-tuning to PPG-DaLiA’s daily-living recordings, the same configuration yields 16.55 bpm, bounding the validated envelope to structured, quasi-periodic exercise.