Surveillance activities with ground-based assets in the context of space situational awareness are particularly challenging. The observation process is indeed hindered by short observation arcs, limited observability, missed detections, measurement noise, and contamination by clutter. This paper exploits a recent estimation framework for stochastic populations for space situational awareness surveillance scenarios. This framework shares the flexibility of the finite set statistics framework in the modeling of a dynamic population of objects and the representation of all the sources of uncertainty in a single coherent probabilistic framework and the intuitive approach of traditional track-based techniques to describe individual objects and maintain track continuity. We present a recent multi-object filtering solution derived from this framework, the filter for distinguishable and independent stochastic populations, and propose a bespoke implementation of the multitarget tracking algorithm for a space situational awareness surveillance activity. The distinguishable and independent stochastic populations filter is tested on a surveillance scenario involving two ground-based Doppler radars in a challenging environment with significant measurement noise, limited observability, missed detections, false alarms, and no a priori knowledge about the number and the initial states of the objects in the scene. The tracking algorithm shows good performance in initiating tracks from object-generated observations and in maintaining track custody throughout the scenario, even when the objects are outside of the sensors’ fields of view, despite the challenging conditions of the surveillance scenario.