Location data generated from GPS equipped moving objects are typically collected as streams of spatio-temporal (x,y,t) points that when put together form corresponding {\em trajectories}. Most existing studies focus on building ad-hoc querying, analysis, as well as data mining techniques on formed trajectories. As a prior step, trajectory construction is evidently necessary for mobility data processing and understanding -- including tasks like trajectory data cleaning, compression, and segmentation to identify semantic trajectory episodes like stops (e.g. while sitting and standing) and moves (while jogging, walking, driving etc). However, such methods in the current literature, are typically based on offline procedures, which is not sufficient for real life trajectory applications that rely on timely delivery of computed trajectories to serve real time query answers. Filling this gap, our paper proposes a platform, namely SeTraStream, for real-time semantic trajectory construction. Our online framework is capable of providing real-life trajectory data {\em cleaning}, {\em compression}, {\em segmentation} over streaming movement data.