The modelling of non-gravitational forces acting on a satellite (especially a GNSS satellite) started half a century ago. Their modelling to low Earth orbiters (LEOs), however, are more recent because of the dominating atmospheric drag, the modelling of which requires the precision of recent atmospheric models. However, this is not an issue for precise orbit determination (POD), as of the method used to compute the reduced-dynamic orbit. The method is using piecewise constant accelerations (PCA), which are absorbing the non-conservative forces that are not modelled. One expects the implementation of non-gravitational forces to reduce the amplitude and mean values of the PCA of the satellite's reduced-dynamic orbit. In this thesis assignment, four non-gravitational forces has been considered large enough for improving the POD of GPS-based LEO using the Bernese GNSS Software: the aerodynamic forces, the solar radiation pressure and the reflected and emitted Earth radiation pressure. For each force, a modelling method has been chosen and implemented in the Bernese GNSS Software. The impact of the modelled non-gravitational forces has been evaluated with Swarm and GRACE LEOs with all the available validation and comparison methods: PCA, accelerometer data, GPS observation fit, satellite laser ranging observations and K/Ka-band ranging measurements. As expected, the implementation of all the forces reduces the standard deviation of the PCA in each direction, for both Swarm C (-8% in radial, -56% in along-track and -22% in cross-track) and GRACE A (-73% in radial, -75% in along-track and -20% in cross-track). Regarding the mean values for Swarm C a large reduction is observed in: along-track (-129%) and cross-track (-97%) direction, but the mean acceleration in radial direction increase by a few percent (7%). For GRACE A, the mean values of the PCA are reduced along each orbital axis (-88% in radial, -112% in along-track and -23% in cross-track). In addition to the PCA reduction, the precision of the reduced-dynamic orbit has also been improved by the modelling of the non-gravitational forces. In terms of values the a posteriori standard deviation of unit weight of 1.96 mm has been reduced to 1.93 mm for Swarm and from 2.3 mm to 1.45 mm for GRACE. Finally, different parameterizations of the aerodynamic forces have been carried out in order to determine the best atmospheric model and gas-surface interaction algorithm for LEO POD improvement. The impact of a horizontal wind model has been tested. More specifically: modelling the gas-surface interaction with Goodman's model using the DTM2013 atmospheric model with the horizontal wind correction HWM14 have shown the best results in LEO POD.