In our recent paper, the sensitivity of infrasound to the upper atmosphere is investigated using impulsive signals from the Tungurahua volcano in Ecuador. We reported on the coherent variability of thermospheric travel times, with periods equal to those of the tidal harmonics. Moreover, it was shown that the error in predicted thermospheric travel time is in accord with typical uncertainties in the upper atmospheric wind speed models. Given the observed response of the infrasound celerities to upper atmospheric tidal variability, it was suggested that infrasound observations may be used to reduce uncertainty in the knowledge of the atmospheric specifications in the upper atmosphere. In this paper, we discuss the estimation of upper atmospheric wind model updates from the infrasound data described in the aforementioned paper. The parameterization of the model space by empirical orthogonal functions is described; it is found that the wind model in the upper mesosphere and lower thermosphere can be described by a four-parameter model. Due to the small dimensionality of the model space, a grid search method can be used to solve the inverse problem. A Bayesian method is used to assess the uncertainty in the inverse solution given the a priori uncertainty in the data and model spaces and the nonlinearity of the inverse problem at hand. We believe that this is the first study in which such methods are applied to real infrasound data, allowing for a rigorous analysis of this inverse problem. It is found that the complexity of the a posteriori model distribution increases for a larger dimensional model space and larger uncertainties in the data. A case study is presented in which the nonlinear propagation from source to receiver is simulated using an updated wind model and nonlinear ray theory. As nonlinear propagation effects further constrain the propagation path, this is a way to check the physical self-consistency of the travel time inversion approach. We obtain excellent agreement between the simulated and observed waveforms.