Computational models for speech production and analysis have been of research interest since the 1960s. Most models assume the vocal tract (VT) to be a segmented straight tube, but when pronouncing nasals like /m/ and /n/ or nasalized vowels the nasal part of the vocal tract plays an important part and a single tube model is not feasible anymore. Thus, it is necessary to consider a branched tube model that includes an additional tube model for the nasal tract. For these branched models, the estimation of the cross section area of each segments from a given signal is highly non trivial and in general requires the solution of a non-linear system of equations.
The problem is overdetermined, and we have to add additional restrictions to our solution, for example restrictions on upper and lower bounds of the area functions or smoothness assumption about the vocal tract. To that end we introduced e.g. probabilistic methods (variational Bayes) into our model estimation.