Localization without prior knowledge can be a difficult task for a vehicle. An answer to this problematic lies in the Simultaneous Localization And Mapping (SLAM) approach where a map of the surroundings is built while simultaneously being used for localization purposes. However, SLAM algorithms tend to drift over time, making the localization inconsistent. In this paper, we propose to model the drift as a localization bias and to integrate it in a general architecture. The latter allows any feature-based SLAM algorithm to be used while taking advantage of the drift integration. Based on previous works, we extend the bias concept and propose a new architecture which drastically improves the performance of our method, both in terms of computational power and memory required. We validate this framework on real data with different scenarios. We show that taking into account the drift allows us to maintain consistency and improve the localization accuracy with almost no additional cost.