  We consider the fusion of two aerodynamic data sets originating from
differing fidelity physical or computer experiments. We specifically address
the fusion of: 1) noisy and in-complete fields from wind tunnel measurements
and 2) deterministic but biased fields from numerical simulations. These two
data sources are fused in order to estimate the \emph{true} field that best
matches measured quantities that serves as the ground truth. For example, two
sources of pressure fields about an aircraft are fused based on measured forces
and moments from a wind-tunnel experiment. A fundamental challenge in this
problem is that the true field is unknown and can not be estimated with 100\%
certainty. We employ a Bayesian framework to infer the true fields conditioned
on measured quantities of interest; essentially we perform a \emph{statistical
correction} to the data. The fused data may then be used to construct more
accurate surrogate models suitable for early stages of aerospace design. We
also introduce an extension of the Proper Orthogonal Decomposition with
constraints to solve the same problem. Both methods are demonstrated on fusing
the pressure distributions for flow past the RAE2822 airfoil and the Common
Research Model wing at transonic conditions. Comparison of both methods reveal
that the Bayesian method is more robust when data is scarce while capable of
also accounting for uncertainties in the data. Furthermore, given adequate
data, the POD based and Bayesian approaches lead to \emph{similar} results.
