In the context of railway safety, it is crucial to know the positions of all trains moving along the infrastructure. In this contribution, we present an algorithm that extracts the positions of moving trains for a given point in time from Distributed Acoustic Sensing (DAS) signals. These signals are obtained by injecting light pulses into an optical fiber close to the railway tracks and measuring the Rayleigh backscatter. We show that the vibrations of moving objects can be identified and tracked in real-time yielding train positions every second. To speed up the algorithm, we describe how the calculations can partly be based on graphical processing units. The tracking quality is assessed by counting the inaccurate and lost train tracks for two different types of cable installations.