This paper presents the filter for Hypothesised and Independent Stochastic Populations (HISP), a multi-object joint detection/tracking algorithm derived from a recent estimation framework for stochastic populations, in the context of Space Situational Awareness. Designed for multi-object estimation problems where the data association between tracks and collected observations is moderately ambiguous, the HISP filter has a linear complexity with the number of objects and the number of observations. Because of its scalable complexity, the HISP filter is a promising solution for the construction of a large-scale catalogue of Resident Space Objects. We illustrate the HISP filter on a challenging surveillance scenario built from real data for 115 satellites of PlanetLabs’ Dove constellation, and simulated observations collected from two sensors with limited coverage and measurement noise, in the presence of false positives and missed detection.