## 4 Experiments and Results  
To validate the effectiveness of the proposed heart rate estimation method, we conducted experiments involving 20 adult participants aged between 30 and 40 years (14 males, 6 females). This age range was selected to minimize variability due to age-related physiological differences, ensuring a relatively homogeneous autonomic response across the cohort. Participants were fitted with the six-axis HRSD on the crown of the head and a TP320 PPG sensor on the index finger (Figure 6). Figure 6a shows the front view of the participant, while Figure 6b presents the rear view. For comparative analysis, optical-based PPG signals were utilized to measure changes in blood flow within the body, considering both reflection and transmission characteristics [20]. Frequency domain analysis of PPG signals allows for the evaluation of autonomic nervous system responses that correspond to the normal heart rate range in adults (60-120 bpm). This enables a deeper exploration of physiological information related to heart rate variability. In this study, PPG data was collected using the TP320 sensor (LAX-THA Inc., Daejeon, South Korea). The TP320 SpO\({}_{2}\) sensor utilizes a photoplethysmography (PPG) principle, employing dual-wavelength light sources (infrared and red LEDs) and a photodiode. Variations in light absorption caused by pulsatile blood flow are captured to derive heart rate and SpO\({}_{2}\) measurements (see Figure 7). Figure 6: HR signal acquisition using a six-axis sensing unit and a PPG sensor. Figure 7: Internal structure of the TP320 SpO\({}_{2}\) oxygen saturation pulse sensor. The TP320 device demonstrated high validity for heart rate measurement, with a Pearson correlation coefficient of 0.96 and a mean absolute error of 2.4 bpm when compared to ECG. Furthermore, test-retest reliability analyses yielded an ICC of 0.92, indicating strong measurement consistency. These results suggest that TP320 is both a valid and reliable tool for wearable cardiac monitoring in clinical and daily settings [23]. After preprocessing (high-pass filtering, downsampling, and RMS calculation), [PERSON]'s method was employed to compute the Power Spectral Density (PSD) from the six-axis and PPG signals. By reducing variance in the spectral estimate, this method enabled a more robust identification of the dominant frequency within the 0.8-2.0 Hz range. Heart rate (HR) was then calculated by converting this peak frequency to beats per minute (bpm). To determine the optimal analysis window size, various time windows (4 s, 8 s, 20 s, and 30 s) were applied, and the corresponding HR estimation accuracy was compared using Mean Absolute Error (MAE) against the PPG reference. As shown in Figure 8, a 4 s analysis window achieved the lowest mean absolute error (MAE) of 4.75 bpm, demonstrating the best performance for short-term heart rate (HR) estimation. Additionally, the application of Welch-based spectral analysis reduced the MAE from 5.3 bpm to 4.75 bpm compared to the conventional FFT-based approach, indicating improved robustness and accuracy in frequency-domain HR detection. Although a 4 s window theoretically limits frequency resolution to 0.25 Hz, the use of [PERSON]'s method--with 50% overlap and Hanning windowing--compensates for this limitation by increasing the robustness of spectral peak detection. This allows reliable heart rate estimation even with short time signals. Additionally, Bland-Altman analysis was performed to evaluate agreement between the HR values derived from the six-axis sensing method and the reference PPG data. As depicted in Figure 9, the majority of the heart rate differences fell within the \(\pm\)5 bpm limits of agreement, and as indicated by the blue dashed line, the mean difference was only 0.6 bpm.