## 2 Materials and Methods  
### Standard IBIF Implementation  
The IBIF scheme is described in the frequency domain, where the glottal airflow (also referred to as glottal volume velocity, GVV) and the acceleration signal are related by  
\[\dot{U}_{skin}(\omega)=T_{skin}(\omega)\cdot U_{sub}(\omega) \tag{1}\]  
where \(\dot{U}_{skin}(\omega)\) is the acceleration signal, \(U_{sub}(\omega)\) is the inverted GVV (assuming source is a dipole, that is, two equal and opposite volume velocity sources [37]), and \(T_{skin}(\omega)\) is the neck-skin frequency response. In what follows, we remove the frequency dependency \(\omega\) in the expressions for the sake of clarity. \(T_{skin}\) can be modeled by:  
\[T_{skin}=\frac{\dot{U}_{skin}}{U_{sub}}=\frac{H_{sub1}\cdot Z_{sub2}\cdot H_{ d}}{Z_{sub2}+Z_{skin}}, \tag{2}\]  
where \(H_{sub1}\) is the frequency response of the subglottal section from the glottis to the accelerometer location, and \(H_{d}=j\omega\) is a derivative filter (similar to the lip radiation effect, except that in this case is the acceleration in free field). \(Z_{sub2}\) is a frequency-dependent driving-point impedance corresponding to the subglottal section [38] below the accelerometer position. \(Z_{skin}\) is the neck-skin impedance modeled as a mechanical analog of a resistor-inductor-capacitor circuit in series:  
\[Z_{skin}=R_{m}+j\bigg{(}\omega M_{m}-\frac{K_{m}}{\omega}\bigg{)}+\frac{j \omega M_{acc}}{A_{acc}}, \tag{3}\]  
where \(R_{m}\), \(M_{m}\), and \(K_{m}\) are the per-unit-area resistance, inertance, and stiffness of the skin, respectively. The radiation impedance due to the accelerometer loading is modeled as a derivative term \(j\omega\) times the mass \(M_{acc}\) divided by the surface \(A_{acc}\) (per-unit-area) of the accelerometer and the coating or mounting disk attached to it [39]. These parameters are subject specific, and therefore involve calibration factors that can be fitted per subject using a reference GVV signal and an optimization method. The calibration factors \(\mathbf{Q}=\{Q_{i}\}_{i=1,...,5}\) are defined as:  
\[\mathbf{Q} =\{Q_{1},Q_{2},Q_{3},Q_{4},Q_{5}\} \tag{4}\] \[R_{m} =2320\cdot Q_{1} [\text{g}\cdot\text{s}^{-1}\cdot\text{cm}^{-2}],\] (5) \[M_{m} =2.4\cdot Q_{2} [\text{g}\cdot\text{cm}^{-2}],\] (6) \[K_{m} =491,000\cdot Q_{3} [\text{dyn}\cdot\text{cm}^{-3}],\] (7) \[L_{\text{t}rachea} =10\cdot Q_{4} [\text{cm}],\] (8) \[L_{\text{s}ubl} =5\cdot Q_{5} [\text{cm}], \tag{9}\]where \(L_{trachea}\) (related to the length of the trachea) and \(L_{sub1}\) (related to sensor position on the neck-surface) are embedded in \(Z_{sub2}\) and \(H_{sub1}\), respectively. The derivation of these terms is beyond the scope of this paper and details can be found in [33; 40]. Given the \(\mathbf{Q}\) factors above, the impulse response of neck-skin \(h(n)\) in the time domain is obtained by first taking the fast Fourier transform (FFT) of \(T_{skin}(\omega)\) with \(N\) points, which becomes \(\hat{T}_{skin}(k)\) with \(k=0,1,\ldots,N-1\), where \(N\) is the number of FFT frequency points. Then, after forcing \(\hat{T}_{skin}(k)\) to be conjugate symmetric (\(\hat{T}_{skin}(k)=\hat{T}_{skin}^{*}(N-k)\)), we take the inverse FFT to obtain a real impulse response \(h(n)\). In this way, the resulting IBIF filter is implemented as a deterministic finite impulse response filter (FIR) of length \(N\). Therefore, in the time domain, the IBIF scheme assumes that the GVV signal \(x(n)\) is convolved with the impulse response \(h(n)\) to produce an output signal \(y(n)\), which corresponds to the neck-surface acceleration. Since we are interested in estimating \(x(n)\), the discrete frequency response \(\hat{T}_{skin}(k)\) is inverted to yield \(\hat{T}_{skin}(k)=1/\hat{T}_{skin}(k)\) and, as with \(\hat{T}_{skin}(k)\), it is also forced to be conjugate symmetric, so when taking the IFFT the sequence \(\hat{\mathrm{R}}(n)\) is obtained, which is the impulse response of \(\hat{\mathrm{T}}_{skin}(k)\).