We present a novel online capable hybrid interval-probabilistic localization method using publicly available 2D building maps. Given an initially large uncertainty for the orientation and position derived from GNSS data, our novel interval-based approach first narrows down the orientation to a smaller interval and provides a set described by a minimal polygon for the position of the vehicle that encloses the feasible set of poses by taking the building geometry into account using 3D Light Detection and Ranging (LiDAR) sensor data. Second, we perform a probabilistic Maximum Likelihood Estimation (MLE) to determine the best solution within the determined feasible set. The MLE is converted into a least-squares problem that is solved by an optimization approach that takes the bounds of the solution set into account so that only a solution within the feasible set is selected as the most likely one. We experimentally show with real data that the novel interval-based localization provides sets of poses that contain the true pose for more than 99% of the frames and that the bounded optimization provides more reliable results compared to a classical unbounded optimization and a Monte Carlo Localization approach.