An essential task for Intelligent Transportation System is to obtain precise knowledge of local environments as well as the local (within structured environment) and global vehicle pose. Market entry and large-scale production of autonomous driving functions postulate two elementary constraints. First, the utilized sensor setup has to be both cost-efficient and space-saving. Second, the system has to be fail-safe according to Automotive Safety Integrity Level1D. This paper presents an approach to robustly estimate the vehicles pose both within the current lane and a digital map via pose graph optimization. Outliers and ambiguities are rejected by a suitable loss function and therefore remove the necessity of refined statistical tests. Fall-back solutions, when single sensors are permanently corrupted, are provided by solving various graphs simultaneously. Experimentally, the applicability and performance of the presented approach is demonstrated using an Opel Insignia and its 2D dynamic sensors, with an additional gray-scale camera mounted at the front and at the rear window, a low-cost GNSS receiver and a previously recorded digital map. The graph-based approach has a mean solver time of 14.48 ms and a maximal lateral error below 27.03 cm with a Standard Deviation of 10.05 cm and outperforms the previously presented Extended Kalman Filter and Particle Filter approaches [1].