Background Heart rate (HR) is widely used to guide exercise intensity because it is non-invasive and easy to measure. However, outdoor recordings often contain artifacts and gaps, which can bias downstream metrics if not reconstructed accurately. Common reconstruction methods (e.g. linear interpolation) perform well in short gaps but ignore HR kinetics and changing external load, which is problematic in trail running with frequent intensity changes. The present study presents a HR reconstruction approach that leverages GNSS data and a model of HR dynamics. Methods 12 recreational trail runners completed a total of 53 trail bouts, of which 37 were included in the final analysis (1 Hz GNSS, 130 Hz chest-strap ECG). Gaps of 1-800 consecutive heart beats were simulated at four phases representative of trail running: onset, uphill, switch (uphill-to-downhill), and downhill. Energy expenditure was estimated from GNSS data and mapped to heart rate using a first-order differential equation, with individualized parameters. The end of the reconstructed gap was aligned with post-gap measurements via a linear drift correction. HR model based reconstructions without (HRM) and with drift correction (HRMD) were compared against baseline linear interpolation (LI). Reconstruction accuracy was assessed via RMSE and a linear mixed-effects model, and bias was summarized using mean error (ME) and limits of agreement (LoA). Results Overall, HRMD and LI had a similar low median RMSE (approx. 2 bpm), both outperforming HRM (approx. 3 bpm). However, significant interaction effects indicated condition-dependent performance. HRMD was significantly better than LI for non-steady exercise intensities at longer gaps (onset and switch for 200 missing beats or more). LI slightly outperformed HRMD during steady uphill (200 missing beats or more). Bias and dispersion favored HRMD: ME remained near zero with LoA less than 10 bpm across all conditions. LI showed large, length-dependent bias at onset (ME up to 14.6 bpm; LoA up to 20.3 bpm). This indicates that HRMD provides an absolute reduction of mean error of up to 14 bpm (at onset for 800 missing beats). Conclusions LI is adequate for short gaps and steady intensity, but errors grow and become biased during long, non-steady gaps. Integrating GNSS-derived energy expenditure with individualized HR dynamics and drift correction (HRMD) reduces error and bias in these challenging conditions. Practical implementation of this reconstruction approach is accessible since wearables facilitate synchronous HR and GNSS recordings. However, it remains uncertain how the results generalize to different demographics and other running disciplines.

Modeling heart rate (HR) dynamics to reconstruct missing HR data in trail running

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2026年5月7日

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Tjorven Schnack,
Raimundo Sanchez,
Arnold Baca

摘要

Background

Heart rate (HR) is widely used to guide exercise intensity because it is non-invasive and easy to measure. However, outdoor recordings often contain artifacts and gaps, which can bias downstream metrics if not reconstructed accurately. Common reconstruction methods (e.g. linear interpolation) perform well in short gaps but ignore HR kinetics and changing external load, which is problematic in trail running with frequent intensity changes. The present study presents a HR reconstruction approach that leverages GNSS data and a model of HR dynamics.

Methods

12 recreational trail runners completed a total of 53 trail bouts, of which 37 were included in the final analysis (1 Hz GNSS, 130 Hz chest-strap ECG). Gaps of 1-800 consecutive heart beats were simulated at four phases representative of trail running: onset, uphill, switch (uphill-to-downhill), and downhill. Energy expenditure was estimated from GNSS data and mapped to heart rate using a first-order differential equation, with individualized parameters. The end of the reconstructed gap was aligned with post-gap measurements via a linear drift correction. HR model based reconstructions without (HRM) and with drift correction (HRMD) were compared against baseline linear interpolation (LI). Reconstruction accuracy was assessed via RMSE and a linear mixed-effects model, and bias was summarized using mean error (ME) and limits of agreement (LoA).

Results

Overall, HRMD and LI had a similar low median RMSE (approx. 2 bpm), both outperforming HRM (approx. 3 bpm). However, significant interaction effects indicated condition-dependent performance. HRMD was significantly better than LI for non-steady exercise intensities at longer gaps (onset and switch for 200 missing beats or more). LI slightly outperformed HRMD during steady uphill (200 missing beats or more). Bias and dispersion favored HRMD: ME remained near zero with LoA less than 10 bpm across all conditions. LI showed large, length-dependent bias at onset (ME up to 14.6 bpm; LoA up to 20.3 bpm). This indicates that HRMD provides an absolute reduction of mean error of up to 14 bpm (at onset for 800 missing beats).

Conclusions

LI is adequate for short gaps and steady intensity, but errors grow and become biased during long, non-steady gaps. Integrating GNSS-derived energy expenditure with individualized HR dynamics and drift correction (HRMD) reduces error and bias in these challenging conditions. Practical implementation of this reconstruction approach is accessible since wearables facilitate synchronous HR and GNSS recordings. However, it remains uncertain how the results generalize to different demographics and other running disciplines.