This paper describes a simple pushbroom camera model for Earth observation satellites and proposes a new algorithm to refine the orientation parameters of a camera from a set of ground control points. The relative importance of the various orientation parameters are analyzed. On the last generation of very high resolution satellites such as Pléiades and WorldView, the attitude angles are shown to be the main contributors to localization errors. Thus the proposed algorithm focuses on refining the attitude angles. It is based on a simple polynomial fitting method. Numerous experiments, which can be reproduced through the online demo associated to this paper, show that the proposed algorithm is able to reduce the localization error by one order of magnitude with only a few ground control points. A geometric simulator for the proposed model is implemented, as well as the attitude refinement algorithm.