To design a hypersonic vehicle, it is necessary to accurately predict the heat flows at the wall. These flows are strongly constrained by the nature of the boundary layer (laminar/transitional/turbulent). The mechanisms behind the laminar-turbulent transition are complex and still poorly understood. What's more, transitional phenomena are highly dependent on fluctuations in the free flow around the model in the case of wind tunnel testing, or around the craft in the case of flight. These fluctuations are very difficult to measure precisely, which makes the comparison between calculation and testing very complex. To carry out a detailed analysis of flow physics during testing, we need to turn to the results of high-fidelity calculations. It is therefore crucial to be able to reproduce numerically the upstream disturbances encountered. During the course of the thesis, we will be looking to develop data assimilation methods, based on high-fidelity simulation, to invert, i.e. determine fluctuations in the light of observations. The focus will be on assembly techniques based on Bayesian inference. Emphasis will be placed on integrating a priori knowledge of fluctuations. In addition, we will try to reduce the computational cost and quantify the uncertainties on the solution obtained. In particular, the approach will be applied to a flow around the CCF12 (cone-cylinder-flare) geometry realised in the R2Ch wind tunnel at ONERA.