Surgical tool tracking is an essential building block for computer assisted interventions (CAI) and applications like video summarization, workflow analysis and surgical navigation. Vision-based instrument tracking in laparoscopic surgical data faces significant challenges such as fast instrument motion, multiple simultaneous instruments, and re-initialization due to out-of-view conditions or instrument occlusions. In this paper, we propose a real-time multiple object tracking framework for whole laparoscopic tools, which extends an existing single object tracker. We introduce a geometric object descriptor, which helps with overlapping bounding box disambiguation, fast motion and optimal assignment between existing trajectories and new hypotheses. We achieve 99.51% and 75.64% average accuracy on ex-vivo robotic data and in-vivo laparoscopic sequences respectively from the Endovis'15 Instrument Tracking Dataset. The proposed geometric descriptor increased the performance on laparoscopic data by 32%, significantly reducing identity switches, false negatives and false positives. Overall, the proposed pipeline can successfully recover trajectories over long-sequences and it runs in real-time at approximately 25-29 fps.