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Accurate and consistent vehicle localization in urban areas is challenging due to the large-scale and complicated environments. In this paper, we propose onlineFGO, a novel time-centric graph-optimization-based localization method that fuses multiple sensor measurements with the continuous-time trajectory representation for vehicle localization tasks. We generalize the graph construction independent of any spatial sensor measurements by creating the states deterministically on time. As the trajectory representation in continuous-time enables querying states at arbitrary times, incoming sensor measurements can be factorized on the graph without requiring state alignment. We integrate different GNSS observations: pseudorange, deltarange, and time-differenced carrier phase (TDCP) to ensure global reference and fuse the relative motion from a LiDAR-odometry to improve the localization consistency while GNSS observations are not available. Experiments on general performance, effects of different factors, and hyper-parameter settings are conducted in a real-world measurement campaign in Aachen city that contains different urban scenarios. Our results show an average 2D error of 0.99m and consistent state estimation in urban scenarios.