In 3D pedestrian indoor navigation applications, position estimation based on inertial measurement units (IMUss) fails when moving platforms (MPs), such as escalators and elevators, are not properly implemented. In this work, we integrate the MPs in an upper 3D-simultaneous localization and mapping (SLAM) algorithm which is cascaded to the pedestrian dead-reckoning (PDR) technique. The step and heading measurements resulting from the PDR are fed to the SLAM that additionally estimates a map of the environment during the walk in order to reduce the remaining drift. For integrating MPs, we present a new proposal function for the particle filter implementation of the SLAM to account for the presence of MPs. In addition, a new weighting function for features such as escalators and elevators is developed and the features are learned and stored in the learned map. With this, locations of MPs are favored when revisiting the MPs again. The results show that the mean height error is about 0.1 m and the mean position error is less than 1 m for walks with long distances along the floors, even when using multiple floor level changes with different numbers of floors in a multistory environment. For walks with short walking distances and many floor level changes, the mean height error can be higher (about 0.5 m). The final floor number is in all cases except one correctly estimated.