As the next generation of turbomachinery components becomes more sensitive to instrumentation intrusiveness, a reduction of the number of measurement devices required for the evaluation of performance is a possible and cost-effective way to mitigate the arising of non-mastered experimental errors. A first approach to a data assimilation methodology based on Bayesian inference is developed with the aim of reducing the instrumentation effort. A numerical model is employed to provide an initial belief of the flow, that is then updated based on experimental observations, using an ensemble Kalman filter algorithm for inverse problems. Validation of the algorithm is achieved with the usage of experimental measurements not used in the data assimilation process. The methodology is tested for a low aspect ratio axial compressor stage, showing a good prediction of the corrected compressor map, as well as a promising prediction of the inter-row radial pressure distribution and 2D flow field.