We implement an algorithm which estimates parameters of an internal combustion engine model using a Bayesian approach and employs an experimental design technique to iteratively suggest new experiments with the aim of decreasing the uncertainty in the parameter estimates. The primary focus here is the application of the methodology to a complex model whose computational expense limits the number of model evaluations to an extent which necessitates the use of surrogate models. In this work, we choose quadratic response surfaces as surrogates. The main goal of the considered engine model is to predict emissions formed by in-cylinder combustion during the closed-volume part of the engine cycle, employing detailed sub-models for the chemical kinetics of the fuel, turbulent mixing, and convective heat transfer. The model is applied here to an ultra-low emission Homogeneous Charge Compression Ignition (HCCI) engine fuelled with iso-octane. We find rapid convergence of the iterative algorithm in the considered case, as shown by a substantial reduction in parametric uncertainty in each iteration, using informative as well as non-informative priors.