We present a non-parametric inference of impurity transport coefficients by using charge exchange recombination spectroscopy measurements of Ne X, Ne VIII, O VIII, and C VI lines. Due to their close atomic numbers, neon, oxygen and carbon impurity ions are assumed to have the same diffusion coefficient D and convection velocity v. In order to reduce a large computational cost, which a non- parametric approach typically entails, we have derived an analytical steady state solution for impurity profiles for given background plasma parameters and transport coefficients. Since the ratio of v to D only describes the equilibrated profile of the sum of all impurity charge states, steady-state measurements can still decouple D and v if different charge states are simultaneously observed. We have formulated a non-parametric analysis framework based on the Bayesian probability theory and conducted transport coefficient measurements for a Type III ELMy H-mode plasma at ASDEX Upgrade. The charge exchange reactions with the background neutrals, which are known to affect the impurity charge state balance, are taken into account by introducing additional free parameters. While D at the pedestal is close to the neoclassical level (<1 m/s2), a large diffusion coefficient and a strong outward pinch are inferred right inside the pedestal top.