The uncertainty on Thermospheric Mass Density (TMD), as derived from atmospheric models, can reach extremely high values. This effect is noteworthy in Low Earth Orbit (LEO), where atmospheric drag is the main perturbing force, as well as the most uncertain. LEO harbours almost 18,000 space objects at the end of 2021, around 60% of the total space debris population, and the rate of growth is increasing every year. Increasing the accuracy of TMD models, and thus the uncertainty characterisation, is important to ensure space environment sustainability in this congested and contested region. Accurate TMD modelling is a decisive factor in all space applications below the exopause, from LEO mission design to Space Situational Awareness (SSA) service provision: from conjunction assessment to re-entry and fragmentation analysis To enhance empirical TMD models, atmospheric density observations derived from satellite measurements are assimilated. This paper presents a novel approach for assimilating thermospheric density observations into atmospheric models to improve the accuracy of orbit predictions in short- to medium- term propagations. First, Global Navigation Satellite System (GNSS) derived density data from Swarm satellites are ingested from the publicly available Level 2 data products of the European Space Agency (ESA). In a second step, density data is assimilated into the empirical model NRMLSISE-00, using Principal Component Analysis (PCA) to decompose into the main temporal and spatial modes, providing useful physical insight into the main variables driving the model. Thirdly, the model is tested on several cases, whose data was not assimilated, such as LEO satellites that are well-tracked with GNSS-derived positions: Sentinel, and GRACE. The model is also tested with objects with less accurate reference trajectories, such as catalogued space debris in LEO. Finally, the orbits are propagated, using the improved drag model that includes the neutral density from the assimilation of the GNSS-derived observations into NLRMSISE-00. The accuracy of the method is assessed and compared to non-assimilated models. During the discussion of the results, other sources of uncertainty are analysed. To name a few, geomagnetic activity, solar radiation pressure coefficient, attitude knowledge, and spacecraft parameters such as mass, area, drag coefficient, and so on. The improvement on the state accuracy and uncertainty realism after a medium-term propagation is analysed and the application to catalogue maintenance discussed. @en