This paper presents a solution to the consistency problem of SLAM algorithms. We propose here to model the drift affecting the estimation process. The divergence is seen as a bias on the vehicle localization. By using such a model , we are able to guarantee the consistency of the localization. We developed a filter taking into account the divergence and allowing to easily integrate any information helping to characterize the current drift. Geo-referenced landmarks are used in order to provide an absolute localization and drastically reduce the impact of the divergence. The filter is designed around an Extended Kalman Filter and is totally separated from the classical SLAM algorithm. Our method can consequently be connected to any existing SLAM process without trouble. A vehicle performing monocular SLAM in real time was used to validate our approach with real data. The results show that the integrity of the filter is preserved during the whole trajectory and that geo-referenced information helps reducing the natural SLAM drift .