Dynamic accurate heart-rate (HR) estimation using a photoplethysmogram (PPG) during intense physical activities is always challenging due to corruption by motion artifacts (MAs). It is difficult to reconstruct a clean signal and extract HR from contaminated PPG. This paper proposes a robust HR-estimation algorithm framework that uses one-channel PPG and tri-axis acceleration data to reconstruct the PPG and calculate the HR based on features of the PPG and spectral analysis. Firstly, the signal is judged by the presence of MAs. Then, the spectral peaks corresponding to acceleration data are filtered from the periodogram of the PPG when MAs exist. Different signal-processing methods are applied based on the amount of remaining PPG spectral peaks. The main MA-removal algorithm (NFEEMD) includes the repeated single-notch filter and ensemble empirical mode decomposition. Finally, HR calibration is designed to ensure the accuracy of HR tracking. The NFEEMD algorithm was performed on the 23 datasets from the 2015 IEEE Signal Processing Cup Database. The average estimation errors were 1.12 BPM (12 training datasets), 2.63 BPM (10 testing datasets) and 1.87 BPM (all 23 datasets), respectively. The Pearson correlation was 0.992. The experiment results illustrate that the proposed algorithm is not only suitable for HR estimation during continuous activities, like slow running (13 training datasets), but also for intense physical activities with acceleration, like arm exercise (10 testing datasets).