## 4 Results
The root-mean-square-error (RMSE) between the KF implementation and the ground-truth GVV (\(RMSE_{KF}\)) and the RMSE between the standard IBIF and the ground-truth GVV (\(RMSE_{IBIF}\)) were calculated for each subject with voiced frames from the Rainbow Passage.The percentage of the error difference \(\Delta=(RMSE_{KF}-RMSE_{IBIF})/RMSE_{IBIF}\) are shown in Table 4 as the median and interquartile range for each PVH and healthy group for all the glottal features. The results indicate an improvement on the median of ACFL for both healthy and pathological using the KF implementation compared to the standard IBIF. Other features show medians indicating IBIF provides a better estimate of the ground-truth signal. However, it is worth to notice that there is a large dispersion of \(\Delta\)'s for all subjects, indicating that some subjects estimates have a large improvement by using KF as well. Moreover, ACFL estimated from the neck-surface acceleration signal is a key measure able to discriminate between PVH subjects from healthy controls [29] in steady vowels, and which the KF implementation can provide better estimates. We can observe some differences between the IBIF and its KF implementation when estimating the peak-to-peak amplitude (e.g., ACFL). Figure 11 shows a voiced segment of the Rainbow passage from a vocally healthy female. The KF method (green line) estimates a reasonably good fit to the GVV waveform from the SNF method (\(RMSE=24.9\) mL/s). However, the IBIF method does not follow the same ground truth signal (\(RMSE=42.7\) mL/s). The peak-to-peak amplitude is smaller, and the close phase contains a large resonance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **ACFL** & **MFDR** & **H1-H2** & **NAQ** \\ \hline Healthy & \(-9.28\) (41.6) & 14.2 (27.5) & 1.13 (22.2) & 5.17 (18.4) \\ \hline PVH & \(-9.95\) (39.9) & 7.73 (37.5) & 2.45 (27.2) & 0.76 (18.2) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Median (interquartile range) of RMSE \(\Delta\)s in percentage (%) of the modified Kalman filter with respect to the standard IBIF. Figure 10: Distribution of average measures from the Rainbow passage for 50 vocally-healthy subjects (left panel in each subplot) and 50 PVH subjects (right panel in each subplot): (**a**) ACFL, (**b**) MFDR, (**c**) H1-H2, and (**d**) NAQ  
However, the KF method improves the estimation of the peak-to-peak amplitude for the same segment. There is some phase distortion in the closed and opening phase, but overall, the waveform has a closer match to the SNF method than IBIF. The errors to IBIF could be attributed to the production of vowels whose spectra are substantially different to a steady /a/ vowel, which in some cases could affect estimated glottal features up to 50% in error [60]. Figure 12 shows a voiced segment from a PVH female subject. In this case, the IBIF methods overestimates the peak-to-peak values from the SNF method (\(RMSE=229.4\) mL/s). Also, the opening phase is faster compared to ground truth. The KF method compensates the large amplitude of the IBIF output waveform, while at the same time it gets closer to the ground truth signal in the opening and close phase (\(RMSE=76.3\) mL/s). As previously stated, the IBIF and, therefore, the model used by the Kalman filter, are both calibrated using a procedure based on fitting the vowel /a/. In these cases, the method based on Kalman follows the reference signal a bit closer than IBIF. Even though the Kalman filter is an alternative implementation of the IBIF filter, the adaptive filtering nature of Kalman allows to track better the ground truth signal than IBIF. Similar trends were found in different subjects and tokens. Figure 11: Section from the Rainbow passage (healthy female) with estimations of GVV: Kalman filter (solid and dot green), IBIF (dashed red), and single notch filter (solid blue). The estimation of GVV using Kalman filter includes \(\pm 2\sigma\) (standard deviation) on the green shaded region.