## 5 Discussion  
The proposed method based on the modified MA framework and the Kalman filter algorithm is an adaptive implementation of the IBIF scheme. Therefore, it has some differences with the original IBIF design, namely a forward prediction of the accelerometer signal (i.e., no filter is inverted) and a truncation of the finite impulse response required to reduce the computational burden. Despite these differences, in this paper we have shown that the Kalman filter implementation allows for enhancing the glottal airflow estimates, as it optimally adapts its latent states to better predict the accelerometer signal, thus resulting in a closer estimation of the glottal airflow from a Rothenberg mask in benchmark experiments. It is important to note that there are still differences between the Kalman filter glottal airflow estimates and the reference signal from the Rothenberg mask, due to supraglottal inverse filtering errors and measurement uncertainty of the oral airflow signal [61]. Small, but significant, differences between the mean values of ACFL and MFDR from PVH subjects can be observed using the IBIF and Kalman method, respectively. These are difficult to assess, particularly, for high-pitched female pathological voices [62]. For example, the method of closed phase covariance requires several samples in the closed phase of the glottal flow, which are difficult to obtain for high-pitched subjects [63]. The signal deviations between the Kalman filter and the original (time invariant) FIR IBIF glottal airflow estimates are relatively small, although the former better estimates the amplitude, or peak-to-peak flow, compared to IBIF. These differences can be relevant in some cases, depending on the application. In the case of ACFL, there is an improvement on its estimation using KF from running speech, which adds value in a clinical setting, where ACFL has proven to be a key discriminant measure between health subjects and subjects with PVH only for steady vowels [29]. When assessing the relevance of these differences in the context of a classification task to discriminate between vocal fold nodules patients and control subjects using ambulatory accelerometer data, no significant variations in the classification were found, even when comparing frames with low and high error (or deviation) [64]. Thus, the classification task for long periods of time seems to be fairly insensitive to the uncertainty of the airflow estimates from IBIF model parameters, sensor positioning, and other effects. This supports the use of the original FIR version of the IBIF scheme for such classification tasks, which indicates that factors affecting the classification performance in [16] were not degraded by the airflow estimates. However, other applications more sensitive to signal quality (for instance, the estimation of glottal biomechanics and assessment of tissue-flow-acoustic interaction [65]) can further benefit from the enhancement offered by the proposed Kalman implementation to estimate more accurate glottal airflow in running speech and/or ambulatory scenarios. The main differences between the Kalman filter and SNF approach can be observed in H1-H2 and NAQ measures, which are related to low-frequency content and closed quotient, respectively. The IBIF method shows similar differences as well. In order to better estimate these measures, it is necessary to correctly detect the upward and downward slope of the glottal cycle, as well as the closed phase portion. Undue modelled rapid changes in the signal trajectory might induce errors in the Kalman approach which affect the detection of those landmarks in the glottal cycle. In addition, for some subjects, errors in the parameters from IBIF due to calibration could carry through to the Kalman implementation since the latter is built upon the IBIF scheme.