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Detecting and tracking moving objects (DATMO) is an essential component for autonomous driving and transportation. In this paper, we present a computationally low-cost and robust DATMO system which uses as input only 2D laser rangefinder (LRF) information. Due to its low requirements both in sensor needs and computation, our DATMO algorithm is meant to be used in current Autonomous Guided Vehicles (AGVs) to improve their reliability for the cargo transportation tasks at port terminals, advancing towards the next generation of fully autonomous transportation vehicles. Our method follows a Detection plus Tracking paradigm. In the detection step we exploit the minimum information of 2D-LRFs by segmenting the elements of the scene in a model-free way and performing a fast object matching to pair segmented elements from two different scans. In this way, we easily recognize dynamic objects and thus reduce consistently by between two and five times the computational burden of the adjacent tracking method. We track the final dynamic objects with an improved Multiple-Hypothesis Tracking (MHT), to which special functions for filtering, confirming, holding, and deleting targets have been included. The full system is evaluated in simulated and real scenarios producing solid results. Specifically, a simulated port environment has been developed to gather realistic data of common autonomous transportation situations such as observing an intersection, joining vehicle platoons, and perceiving overtaking maneuvers. We use different sensor configurations to demonstrate the robustness and adaptability of our approach. We additionally evaluate our system with real data collected in a port terminal the Netherlands. We show that it is able to accomplish the vehicle following task successfully, obtaining a total system recall of more than 98% while running faster than 30 Hz.