Continuous HRV Estimation from PPG via State-Space Modeling

Official implementation for Continuous Heart Rate Variability Estimation From PPG via State-Space Modeling by Berken Utku Demirel and Christian Holz.

The method estimates ECG-aligned inter-beat intervals (IBIs) from wearable photoplethysmography (PPG), then refines the estimates with a causal, learnable state-space model (SSM). Motion (IMU) and temperature are used as auxiliary signals when available. The result is a continuous IBI sequence from which standard HRV measures, including SDNN, RMSSD, and LF/HF power, are computed.

Highlights

• Two-stage model: a 1-D UNet predicts IBI mean and uncertainty; a learnable AR(2) state-space model refines the sequence.
• Multimodal support for PPG, 3-axis IMU, and temperature; a PPG-only path is used for BIDMC.
• Subject-level cross-validation on PPG-DaLiA, WildPPG, and BIDMC.
• Reproducible evaluation outputs for IBI accuracy, time-domain HRV (SDNN/RMSSD), and frequency-domain HRV (LF/HF Bland–Altman statistics).
• Traditional foot-to-foot and optional NeuroKit2 peak-detection baselines, plus a CNN–LSTM (DCL) learning baseline.

Paper results at a glance

The following are the reported IBI results (mean ± standard deviation across subjects/folds, in ms). r is Pearson correlation with ECG-derived IBI.

Dataset	Method	MAE ↓	RMSE ↓	r ↑
DaLiA	Ours	60.0 ± 7.3	83.8 ± 8.4	0.81 ± 0.11
WildPPG	Ours	89.4 ± 17.1	113.5 ± 25.6	0.60 ± 0.11
BIDMC	Ours	8.65 ± 3.12	13.2 ± 10.4	0.91 ± 0.10

For full SDNN, RMSSD, and frequency-domain results, see the manuscript. Example experiment artifacts—checkpoints, per-subject arrays, and fold summaries—are in results/.

Repository layout

Path	Purpose
main.py	Main training/evaluation entry point. Runs all cross-validation folds for the selected dataset.
trainer.py	Model construction, two-stage training, inference, quality gating, and HRV evaluation.
models/models_nc.py	UNet and DCL model definitions.
models/SSM.py	Learnable AR(2) state-space head and causal-Transformer ablation head.
data_preprocess/	Dataset loaders and subject-level split logic.
one_time_wild.py	One-off converter from a WildPPG MATLAB segment file to per-subject NPZ shards.
trad_eval.py	Traditional signal-processing baseline (foot-to-foot or NeuroKit2 peaks).
results/aggregate_folds.py	Aggregates per-fold CSV files into overall summaries.
Figures/to_plot.py	Produces per-subject correlation and Bland–Altman SVG plots.
results/	Included checkpoints and evaluation artifacts.

Setup

The training entry point is designed for Linux with an NVIDIA GPU and a CUDA-enabled PyTorch installation. It uses torchrun even for one GPU because distributed initialization is part of main.py.

Create an environment (Python 3.8+), install the CUDA-enabled PyTorch build appropriate for your system from pytorch.org, then install the remaining packages:

python -m pip install numpy scipy pandas matplotlib seaborn scikit-learn fitlog mat73

neurokit2 is only needed for the optional Elgendi/NeuroKit peak-detection baseline:

python -m pip install neurokit2

Run commands from the repository root. A quick environment check is:

python -c "import torch; print(torch.__version__, torch.cuda.is_available())"

Data preparation

The datasets are not included in this repository. Please download and use them according to their respective licenses:

• PPG-DaLiA
• WildPPG
• BIDMC PPG and Respiration Dataset

The loaders consume pre-segmented seg_*.npz files, not the raw dataset downloads. All signals are represented as overlapping 8-second windows with a 2-second hop; PPG/IMU windows are sampled at 128 Hz in the experiment pipeline.

NPZ schema

For DaLiA and WildPPG, each subject shard must contain:

ppg         (n_windows, 1024)      PPG windows
imu         (n_windows, 1024, 3)   accelerometer windows
temp        (n_windows,) object    per-window temperature arrays
ibi_ecg_ms  (n_windows,) object    per-window ECG IBI arrays, in milliseconds

For BIDMC, the loader requires only:

ppg         (n_windows, 1024)      PPG windows
ibi_ecg_ms  (n_windows,) object    per-window ECG IBI arrays, in milliseconds

The supplied one_time_wild.py converts a MATLAB file containing segs with these fields into WildPPG NPZ shards. Before running it, set SRC and OUT_DIR at the top of the file.

Point the loaders at your files

Update the hard-coded NPZ_DIR near the top of these files:

data_preprocess/data_prep_dalia.py
data_preprocess/data_prep_wildppg.py

For BIDMC, provide the directory without modifying source code:

export BIDMC_NPZ_DIR=/path/to/bidmc_npz

Each directory must contain files named seg_*.npz. The DaLiA/WildPPG fold map in the current loaders uses five held-out subject groups: 0–2, 3–5, 6–8, 9–11, and 12–14; therefore keep the sort order of your shards consistent with this indexing.

Train and evaluate

Every main.py run trains and evaluates all folds: five folds for DaLiA/WildPPG and ten for BIDMC. Results are written below results/<model_tag>/fold_<k>/ratio_<keep_ratio>/.

Proposed UNet + SSM model

# WildPPG
torchrun --standalone --nproc_per_node=1 main.py \
  --dataset wildppg --backbone unet --batch_size 128 --lr 5e-4 \
  --n_epoch 60 --keep_ratio 0.80

# PPG-DaLiA
torchrun --standalone --nproc_per_node=1 main.py \
  --dataset dalia --backbone unet --batch_size 128 --lr 5e-4 \
  --n_epoch 60 --keep_ratio 0.80

# BIDMC
BIDMC_NPZ_DIR=/path/to/bidmc_npz \
torchrun --standalone --nproc_per_node=1 main.py \
  --dataset bidmc --backbone unet --batch_size 128 --lr 5e-4 \
  --n_epoch 60 --keep_ratio 0.80

The UNet is trained first; its weights are then frozen while the SSM head is trained for 15 epochs. For the multimodal datasets the default sequential chunk length is eight 2-second updates. --keep_ratio 0.80 retains the highest-quality 80% of intervals at evaluation, matching the paper setting.

Ablations and baselines

# Stage-1 UNet only (no state-space refinement)
torchrun --standalone --nproc_per_node=1 main.py \
  --dataset dalia --backbone unet --batch_size 128 --no_ssm

# Causal Transformer sequence-head ablation
torchrun --standalone --nproc_per_node=1 main.py \
  --dataset wildppg --backbone unet --batch_size 128 --stage2_head ctf

# CNN–LSTM (DCL) baseline, evaluated without the SSM
torchrun --standalone --nproc_per_node=1 main.py \
  --dataset wildppg --backbone DCL --batch_size 128 --no_ssm

To run on multiple GPUs, change --nproc_per_node to the number of local GPUs. Make sure the per-GPU batch size and worker count fit available memory.

Traditional PPG baseline

trad_eval.py implements 0.5–8 Hz filtering, PPG event detection, IBI cleaning, and top-SNR window selection. It currently reads NPZ_DIR at the top of the script; update that path before use.

# Foot-to-foot baseline (default)
python trad_eval.py --out_dir results/traditional_bidmc --detector scipy_feet

# NeuroKit2 peak detector
python trad_eval.py --out_dir results/traditional_bidmc_neurokit --detector nk_peaks

Summarize and visualize results

Aggregate a full cross-validation experiment:

python results/aggregate_folds.py \
  --root results/unet_dalia_cuda0_bs128_sw1024 \
  --keep_ratio 0.80

This creates fold_summary.csv and overall_summary.csv in the corresponding ratio_0.80/ directory.

Generate per-subject IBI correlation and Bland–Altman plots from a fold directory:

python Figures/to_plot.py \
  --results_dir results/unet_dalia_cuda0_bs128_sw1024/fold_0/ratio_0.80 \
  --out_dir Figures/Dalia/fold_0/ratio_0.80

The plotting script can optionally trim residual outliers for display only; use --outlier_mode none to plot all valid points.

Output files

For each fold and quality ratio:

• subject_<id>.npz: estimated and ECG IBI sequences, masks, and per-subject metrics.
• summary_fold<k>_r<ratio>.csv: one-row-per-subject metrics.
• fold_summary.csv / overall_summary.csv: aggregate reports created by aggregate_folds.py.
• <model_tag>.pt: first-stage model checkpoint; <model_tag>_ssm_last.pt: final SSM head checkpoint.

Citation

If you use this code, please cite:

@ARTICLE{11456553,
  author={Demirel, Berken Utku and Holz, Christian},
  journal={IEEE Transactions on Biomedical Engineering}, 
  title={Continuous Heart Rate Variability Estimation From PPG via State-Space Modeling}, 
  year={2026},
  volume={},
  number={},
  pages={1-8},
  doi={10.1109/TBME.2026.3678004}}

License and data use

No repository license file is currently included. The individual datasets are distributed separately and remain subject to their original terms and licenses.