Can Sleep Heart Rate Be Estimated from Wrist Accelerometry Without Optical Sensors?

Cardiac signal already sits in existing wrist data

Large longitudinal cohorts such as the U.K. Biobank collected week-long wrist accelerometry from roughly 100,000 participants, but often without a continuous optical heart-rate channel. The paper's motivation is that recovering heart rate from motion signals already recorded during sleep could add a physiological signal to future retrospective analyses, provided the reconstruction is first validated against a cardiac reference.

The physical basis is the ballistocardiogram: the mechanical recoil of each heartbeat produces a vibration measurable by accelerometers. At the wrist this signal is easily overwhelmed by voluntary motion, so sleep, with its longer low-movement periods, is the operating regime the study targets. All inference-time features in SeqSmoother come from wrist accelerometry; ECG is used only to build reference heart-rate labels and training-label quality weights.

SeqSmoother refines a Nightbeat anchor with temporal context

SeqSmoother is a transformer-based temporal corrector, not a replacement pipeline. For each 60-second window it builds a 26-dimensional feature vector combining an intermediate Nightbeat-derived frequency anchor, spectral descriptors, a sub-harmonic descriptor, and temporal change information. If the intermediate anchor is unavailable, a spectral fallback estimate is used and the feature representation records that fallback state.

The model uses two pre-layer-normalized transformer encoder layers with four attention heads, feed-forward dimension 256, and dropout 0.15, over a 40-window sequence, totaling 106,625 trainable parameters. Each token is projected to 64 dimensions and combined with a learned positional embedding. All positions are supervised during training, but the final token supplies the primary out-of-fold test prediction.

Training uses AdamW with learning rate 3e-4, weight decay 1e-3, batch size 128, five warm-up epochs, and cosine decay to 1e-6, capped at 120 epochs with early stopping patience of 30 epochs on validation MAE. The loss combines a Huber term, an extra tail penalty for errors above 3 bpm, ECG-reference-quality weighting, and a Pearson-correlation term. The ECG-derived quality score q is used only during training and is never required at deployment.

Nightbeat wins on retained intervals, SeqSmoother covers more

The formal analysis uses 13 participant-disjoint held-out folds, with the participant as the independent statistical unit. Across all out-of-fold predictions, SeqSmoother achieved a participant-macro MAE of 1.60 bpm. The official ETH-SIPLAB Nightbeat implementation was re-evaluated under a matched 60-second window and 15-second step protocol, with final estimates aligned to SeqSmoother endpoints within 0.11 seconds.

On Nightbeat-retained matched intervals, Nightbeat achieved lower absolute error than SeqSmoother: 0.615 versus 1.091 bpm, a paired difference of +0.475 bpm favoring Nightbeat. Nightbeat achieved lower matched MAE for 12 of the 13 held-out participants. This is why the authors state SeqSmoother should not be read as a replacement for the engineered signal-processing pipeline.

The comparison instead exposes an accuracy-availability trade-off. Nightbeat produced final estimates for 72.85% of the SeqSmoother-eligible out-of-fold grid; conditional on timestamp alignment, 77.76% of Nightbeat candidates were retained. SeqSmoother continues to predict in regions where final Nightbeat abstains, and those rejected regions are substantially harder: SeqSmoother's MAE there rises to 2.656 bpm. A pooled descriptive correlation of r = 0.815 suggests those intervals may still carry temporal heart-rate information, though this value is not used for participant-level inference.

A half-anchor ratio flags harmonic lock-on

A common frequency-tracking failure occurs when the estimated frequency locks near twice the true cardiac fundamental. The conventional second-harmonic ratio does not directly test for energy at one-half of a potentially locked anchor, so the authors define a sub-harmonic ratio eta_1/2 that compares spectral power at the half-anchor frequency with power at the current anchor.

The mechanism is direct: if the anchor is near twice the true heart rate, the half-anchor frequency falls near the true cardiac fundamental, so elevated relative power there is a physically interpretable cue for harmonic lock-on. A companion half-HR candidate provides an explicit alternative estimate.

The proposed sub-harmonic ratio achieved an AUROC of 0.972 for identifying reference-defined harmonic lock-on candidates, across 337 candidate lock-on windows from 7 held-out participants. Because windows overlap and SeqSmoother jointly uses spectral, anchor, and temporal information, the authors do not attribute a specific portion of total regression improvement uniquely to this feature.

NightbeatDB supports at-home sleep, not clinical cohorts

The study uses NightbeatDB, full-night at-home recordings from 42 participants. Each wore a wrist-mounted triaxial accelerometer (Axivity AX3, 100 Hz) on the dominant wrist and an ECG chest belt (movisens EcgMove 4, 1,024 Hz) as the cardiac reference. After synchronization, 38 of the 42 recordings yielded usable aligned accelerometer-ECG data.

The finalized windowing, Welch-feature extraction, and intermediate Nightbeat-anchor pipeline ran across all 38 usable recordings as a descriptive applicability check, but this pass is a preprocessing consistency check only and does not increase the inferential sample size. Formal model-performance inference rests on the 13 participant-disjoint held-out folds, and all splits are at the participant level so windows from a held-out participant never appear in training or validation.

The official Nightbeat comparison uses the official algorithm under the unified 60-second/15-second protocol rather than reproducing every detail behind the published 0.88 bpm result. Strict paired analysis excludes non-aligned endpoints, so absolute error must be interpreted jointly with prediction availability.

Window-level sleep HR is not beat-to-beat or clinical

NightbeatDB is dominated by typical sleeping heart rates in a limited physiological range. The study does not establish performance for arrhythmia, markedly elevated nocturnal heart rate, cardiovascular disease cohorts, or other clinical sleep populations not adequately represented in the dataset.

The model estimates window-level heart rate rather than beat-to-beat RR or NN intervals, so conventional heart-rate variability, sleep-stage classification, disease prediction, clinical decision-making, and population-cohort outcome analysis remain outside the validated scope. The evaluation is also retrospective and does not establish prospective real-time deployment performance.

The sub-harmonic result is a pooled mechanistic diagnostic across overlapping windows from seven positive-event participants; the AUROC of 0.972 is not participant-level inference. Large accelerometer-only cohorts are therefore a future application domain rather than a demonstrated deployment setting, and the authors call for prospective and external validation before clinical or population-level claims.

Preserve confident Nightbeat estimates, learn the rejected regions

The paper's own priority follows from the split between the two result sets. On intervals Nightbeat retains, its matched participant-macro MAE of 0.615 bpm beats SeqSmoother's 1.091 bpm, so the engineered pipeline remains the accuracy reference where it commits. The complementary value sits in the 27.15% of the SeqSmoother-eligible out-of-fold grid where Nightbeat produces no final estimate, and where SeqSmoother's error rises to 2.656 bpm but its pooled correlation of r = 0.815 suggests residual temporal information.

That is the concrete decision threshold this study offers: use the quality-gated signal-processing estimate when it is available, and treat learned temporal correction as a way to extend coverage into abstained regions rather than to replace the anchor. The sub-harmonic ratio at AUROC 0.972 adds a separate diagnostic for the frequency-doubling failure mode that produces some of those abstentions, giving a physics-informed way to flag when a tracker has locked onto twice the true cardiac fundamental.

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